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R.A. Verzijlbergh
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1
The large-scale development of offshore wind is a complex socio-technical challenge in which technological performance, economic viability, government policy, energy markets, and the decisions of multiple actors are strongly interconnected. Governments use policy and tender procedures to shape offshore wind development, while developers and investors must make long-term design, bidding, and investment decisions under considerable uncertainty. These decisions depend on expectations of future energy production and project revenues. Technical modelling uncertainty can therefore propagate beyond engineering calculations into financial assessments, tender strategies, and ultimately the viability and deployment of offshore wind projects. Improving the information available to decision-makers is consequently important for both individual projects and the wider transition towards a low-carbon electricity system.
Wake prediction represents one important source of uncertainty within this decision-making system. Wind turbines reduce downstream wind speeds, affecting the production of neighbouring turbines and therefore the expected energy yield of a wind farm. Engineering wake models such as Jensen are computationally efficient but rely on simplifying assumptions, while high-fidelity Large Eddy Simulations (LES) provide substantially more detailed representations of wake behaviour at much greater computational cost. This creates a trade-off between the accuracy of information available for decision-making and the computational effort required to generate it, particularly when many layouts or scenarios must be evaluated.
This thesis investigates whether recent advances in artificial intelligence can reduce this trade-off by using a Graph Neural Network (GNN) trained directly on high-fidelity LES data. The central research question is: To what extent can a Graph Neural Network, trained on LES data, improve the accuracy of offshore wind-farm wake predictions while maintaining computational efficiency compared to traditional engineering wake models?
A turbine-interaction GNN was developed in which turbines are represented as nodes and potential wake interactions as directed edges. Through message passing, the model learns how upstream turbines influence downstream wind-speed deficits. The architecture was first verified using synthetic Jensen data and subsequently evaluated using the WINS50 LES dataset. The experiments investigated heterogeneous inflow information, turbulence intensity and atmospheric-stability indicators, graph construction, and alternative message-passing architectures. Finally, a multi-farm GNN was trained on 25 wind farms and evaluated on the unseen future_052 layout, with Jensen/NOJ as the principal engineering-model baseline.
The experiments demonstrate that the GNN can successfully learn turbine–turbine wake relationships. The LES experiments further showed that additional model information and complexity do not automatically improve prediction accuracy. Local wind speed provided useful information about heterogeneous conditions, while local wind direction offered limited additional benefit. Turbulence intensity generally improved performance, and exploratory experiments indicated that atmospheric-stability information may provide further predictive value. Graph construction also revealed a trade-off between accuracy and computational cost: wider interaction corridors improved predictions, whereas full connectivity provided only a small additional improvement at substantially greater computational cost. Similarly, an attention-based architecture did not outperform the edge-conditioned NNConv model. These findings indicate that a relatively simple, physically informed graph representation can efficiently capture relevant wake interactions.
The strongest result was obtained in the final cross-farm experiment. When trained on 25 wind farms and evaluated on the excluded future_052 layout, the GNN achieved a mean absolute error of 0.7888 m/s compared with 1.0859 m/s for Jensen, representing an approximately 27% reduction in prediction error. The GNN also exhibited virtually no mean prediction bias. At the same time, including graph construction, evaluation of the complete test set was approximately 4.5 times faster than the Jensen implementation. The results therefore demonstrate that wake relationships learned from computationally expensive LES simulations can be transferred to an unseen wind-farm layout while retaining computationally efficient evaluation.
Importantly, these improvements can affect the information on which offshore wind decisions are based. An illustrative valuation case translated predicted wind speeds into annual energy production (AEP) and discounted lifetime revenues. For the considered wind farm, the LES reference resulted in an AEP of approximately 5318 GWh. The GNN overestimated AEP by only approximately 0.6%, corresponding to a discounted lifetime revenue error of approximately EUR 22.8 million under the case-study assumptions. The Jensen model produced a substantially larger energy-production and revenue error. Although this does not constitute a complete financial valuation, it demonstrates how technical modelling errors can propagate into economically significant differences in project assessment.
The contribution of this thesis therefore extends beyond improving a technical wake-prediction metric. More accurate and computationally efficient wake predictions can improve one important source of information within a wider system of interconnected technical, economic, and policy decisions. For developers and investors, this can support more reliable comparisons of layouts, expected revenues, investment alternatives, and tender strategies, while efficient evaluation enables a larger number of scenarios to be considered under uncertainty. For governments, better-inf
...
Wake prediction represents one important source of uncertainty within this decision-making system. Wind turbines reduce downstream wind speeds, affecting the production of neighbouring turbines and therefore the expected energy yield of a wind farm. Engineering wake models such as Jensen are computationally efficient but rely on simplifying assumptions, while high-fidelity Large Eddy Simulations (LES) provide substantially more detailed representations of wake behaviour at much greater computational cost. This creates a trade-off between the accuracy of information available for decision-making and the computational effort required to generate it, particularly when many layouts or scenarios must be evaluated.
This thesis investigates whether recent advances in artificial intelligence can reduce this trade-off by using a Graph Neural Network (GNN) trained directly on high-fidelity LES data. The central research question is: To what extent can a Graph Neural Network, trained on LES data, improve the accuracy of offshore wind-farm wake predictions while maintaining computational efficiency compared to traditional engineering wake models?
A turbine-interaction GNN was developed in which turbines are represented as nodes and potential wake interactions as directed edges. Through message passing, the model learns how upstream turbines influence downstream wind-speed deficits. The architecture was first verified using synthetic Jensen data and subsequently evaluated using the WINS50 LES dataset. The experiments investigated heterogeneous inflow information, turbulence intensity and atmospheric-stability indicators, graph construction, and alternative message-passing architectures. Finally, a multi-farm GNN was trained on 25 wind farms and evaluated on the unseen future_052 layout, with Jensen/NOJ as the principal engineering-model baseline.
The experiments demonstrate that the GNN can successfully learn turbine–turbine wake relationships. The LES experiments further showed that additional model information and complexity do not automatically improve prediction accuracy. Local wind speed provided useful information about heterogeneous conditions, while local wind direction offered limited additional benefit. Turbulence intensity generally improved performance, and exploratory experiments indicated that atmospheric-stability information may provide further predictive value. Graph construction also revealed a trade-off between accuracy and computational cost: wider interaction corridors improved predictions, whereas full connectivity provided only a small additional improvement at substantially greater computational cost. Similarly, an attention-based architecture did not outperform the edge-conditioned NNConv model. These findings indicate that a relatively simple, physically informed graph representation can efficiently capture relevant wake interactions.
The strongest result was obtained in the final cross-farm experiment. When trained on 25 wind farms and evaluated on the excluded future_052 layout, the GNN achieved a mean absolute error of 0.7888 m/s compared with 1.0859 m/s for Jensen, representing an approximately 27% reduction in prediction error. The GNN also exhibited virtually no mean prediction bias. At the same time, including graph construction, evaluation of the complete test set was approximately 4.5 times faster than the Jensen implementation. The results therefore demonstrate that wake relationships learned from computationally expensive LES simulations can be transferred to an unseen wind-farm layout while retaining computationally efficient evaluation.
Importantly, these improvements can affect the information on which offshore wind decisions are based. An illustrative valuation case translated predicted wind speeds into annual energy production (AEP) and discounted lifetime revenues. For the considered wind farm, the LES reference resulted in an AEP of approximately 5318 GWh. The GNN overestimated AEP by only approximately 0.6%, corresponding to a discounted lifetime revenue error of approximately EUR 22.8 million under the case-study assumptions. The Jensen model produced a substantially larger energy-production and revenue error. Although this does not constitute a complete financial valuation, it demonstrates how technical modelling errors can propagate into economically significant differences in project assessment.
The contribution of this thesis therefore extends beyond improving a technical wake-prediction metric. More accurate and computationally efficient wake predictions can improve one important source of information within a wider system of interconnected technical, economic, and policy decisions. For developers and investors, this can support more reliable comparisons of layouts, expected revenues, investment alternatives, and tender strategies, while efficient evaluation enables a larger number of scenarios to be considered under uncertainty. For governments, better-inf
...
The large-scale development of offshore wind is a complex socio-technical challenge in which technological performance, economic viability, government policy, energy markets, and the decisions of multiple actors are strongly interconnected. Governments use policy and tender procedures to shape offshore wind development, while developers and investors must make long-term design, bidding, and investment decisions under considerable uncertainty. These decisions depend on expectations of future energy production and project revenues. Technical modelling uncertainty can therefore propagate beyond engineering calculations into financial assessments, tender strategies, and ultimately the viability and deployment of offshore wind projects. Improving the information available to decision-makers is consequently important for both individual projects and the wider transition towards a low-carbon electricity system.
Wake prediction represents one important source of uncertainty within this decision-making system. Wind turbines reduce downstream wind speeds, affecting the production of neighbouring turbines and therefore the expected energy yield of a wind farm. Engineering wake models such as Jensen are computationally efficient but rely on simplifying assumptions, while high-fidelity Large Eddy Simulations (LES) provide substantially more detailed representations of wake behaviour at much greater computational cost. This creates a trade-off between the accuracy of information available for decision-making and the computational effort required to generate it, particularly when many layouts or scenarios must be evaluated.
This thesis investigates whether recent advances in artificial intelligence can reduce this trade-off by using a Graph Neural Network (GNN) trained directly on high-fidelity LES data. The central research question is: To what extent can a Graph Neural Network, trained on LES data, improve the accuracy of offshore wind-farm wake predictions while maintaining computational efficiency compared to traditional engineering wake models?
A turbine-interaction GNN was developed in which turbines are represented as nodes and potential wake interactions as directed edges. Through message passing, the model learns how upstream turbines influence downstream wind-speed deficits. The architecture was first verified using synthetic Jensen data and subsequently evaluated using the WINS50 LES dataset. The experiments investigated heterogeneous inflow information, turbulence intensity and atmospheric-stability indicators, graph construction, and alternative message-passing architectures. Finally, a multi-farm GNN was trained on 25 wind farms and evaluated on the unseen future_052 layout, with Jensen/NOJ as the principal engineering-model baseline.
The experiments demonstrate that the GNN can successfully learn turbine–turbine wake relationships. The LES experiments further showed that additional model information and complexity do not automatically improve prediction accuracy. Local wind speed provided useful information about heterogeneous conditions, while local wind direction offered limited additional benefit. Turbulence intensity generally improved performance, and exploratory experiments indicated that atmospheric-stability information may provide further predictive value. Graph construction also revealed a trade-off between accuracy and computational cost: wider interaction corridors improved predictions, whereas full connectivity provided only a small additional improvement at substantially greater computational cost. Similarly, an attention-based architecture did not outperform the edge-conditioned NNConv model. These findings indicate that a relatively simple, physically informed graph representation can efficiently capture relevant wake interactions.
The strongest result was obtained in the final cross-farm experiment. When trained on 25 wind farms and evaluated on the excluded future_052 layout, the GNN achieved a mean absolute error of 0.7888 m/s compared with 1.0859 m/s for Jensen, representing an approximately 27% reduction in prediction error. The GNN also exhibited virtually no mean prediction bias. At the same time, including graph construction, evaluation of the complete test set was approximately 4.5 times faster than the Jensen implementation. The results therefore demonstrate that wake relationships learned from computationally expensive LES simulations can be transferred to an unseen wind-farm layout while retaining computationally efficient evaluation.
Importantly, these improvements can affect the information on which offshore wind decisions are based. An illustrative valuation case translated predicted wind speeds into annual energy production (AEP) and discounted lifetime revenues. For the considered wind farm, the LES reference resulted in an AEP of approximately 5318 GWh. The GNN overestimated AEP by only approximately 0.6%, corresponding to a discounted lifetime revenue error of approximately EUR 22.8 million under the case-study assumptions. The Jensen model produced a substantially larger energy-production and revenue error. Although this does not constitute a complete financial valuation, it demonstrates how technical modelling errors can propagate into economically significant differences in project assessment.
The contribution of this thesis therefore extends beyond improving a technical wake-prediction metric. More accurate and computationally efficient wake predictions can improve one important source of information within a wider system of interconnected technical, economic, and policy decisions. For developers and investors, this can support more reliable comparisons of layouts, expected revenues, investment alternatives, and tender strategies, while efficient evaluation enables a larger number of scenarios to be considered under uncertainty. For governments, better-inf
Wake prediction represents one important source of uncertainty within this decision-making system. Wind turbines reduce downstream wind speeds, affecting the production of neighbouring turbines and therefore the expected energy yield of a wind farm. Engineering wake models such as Jensen are computationally efficient but rely on simplifying assumptions, while high-fidelity Large Eddy Simulations (LES) provide substantially more detailed representations of wake behaviour at much greater computational cost. This creates a trade-off between the accuracy of information available for decision-making and the computational effort required to generate it, particularly when many layouts or scenarios must be evaluated.
This thesis investigates whether recent advances in artificial intelligence can reduce this trade-off by using a Graph Neural Network (GNN) trained directly on high-fidelity LES data. The central research question is: To what extent can a Graph Neural Network, trained on LES data, improve the accuracy of offshore wind-farm wake predictions while maintaining computational efficiency compared to traditional engineering wake models?
A turbine-interaction GNN was developed in which turbines are represented as nodes and potential wake interactions as directed edges. Through message passing, the model learns how upstream turbines influence downstream wind-speed deficits. The architecture was first verified using synthetic Jensen data and subsequently evaluated using the WINS50 LES dataset. The experiments investigated heterogeneous inflow information, turbulence intensity and atmospheric-stability indicators, graph construction, and alternative message-passing architectures. Finally, a multi-farm GNN was trained on 25 wind farms and evaluated on the unseen future_052 layout, with Jensen/NOJ as the principal engineering-model baseline.
The experiments demonstrate that the GNN can successfully learn turbine–turbine wake relationships. The LES experiments further showed that additional model information and complexity do not automatically improve prediction accuracy. Local wind speed provided useful information about heterogeneous conditions, while local wind direction offered limited additional benefit. Turbulence intensity generally improved performance, and exploratory experiments indicated that atmospheric-stability information may provide further predictive value. Graph construction also revealed a trade-off between accuracy and computational cost: wider interaction corridors improved predictions, whereas full connectivity provided only a small additional improvement at substantially greater computational cost. Similarly, an attention-based architecture did not outperform the edge-conditioned NNConv model. These findings indicate that a relatively simple, physically informed graph representation can efficiently capture relevant wake interactions.
The strongest result was obtained in the final cross-farm experiment. When trained on 25 wind farms and evaluated on the excluded future_052 layout, the GNN achieved a mean absolute error of 0.7888 m/s compared with 1.0859 m/s for Jensen, representing an approximately 27% reduction in prediction error. The GNN also exhibited virtually no mean prediction bias. At the same time, including graph construction, evaluation of the complete test set was approximately 4.5 times faster than the Jensen implementation. The results therefore demonstrate that wake relationships learned from computationally expensive LES simulations can be transferred to an unseen wind-farm layout while retaining computationally efficient evaluation.
Importantly, these improvements can affect the information on which offshore wind decisions are based. An illustrative valuation case translated predicted wind speeds into annual energy production (AEP) and discounted lifetime revenues. For the considered wind farm, the LES reference resulted in an AEP of approximately 5318 GWh. The GNN overestimated AEP by only approximately 0.6%, corresponding to a discounted lifetime revenue error of approximately EUR 22.8 million under the case-study assumptions. The Jensen model produced a substantially larger energy-production and revenue error. Although this does not constitute a complete financial valuation, it demonstrates how technical modelling errors can propagate into economically significant differences in project assessment.
The contribution of this thesis therefore extends beyond improving a technical wake-prediction metric. More accurate and computationally efficient wake predictions can improve one important source of information within a wider system of interconnected technical, economic, and policy decisions. For developers and investors, this can support more reliable comparisons of layouts, expected revenues, investment alternatives, and tender strategies, while efficient evaluation enables a larger number of scenarios to be considered under uncertainty. For governments, better-inf
Fundamental Approaches to Dutch Electricity Price Formation
A Structural Approach Benchmarked Against a Hybrid Merit-Order Calibration, with Battery Storage Valuation
This thesis asks how much of the Dutch day-ahead electricity price can be explained by economic dispatch models with no fitted parameters, and what the remaining gap reveals about the market.
The Dutch market combines a gas-dominated thermal fleet, roughly 13 GW of combined heat and power (CHP) with heat-driven must-run obligations, and solar PV capacity that grew 26% over 2023–2025, most of it rooftop and largely invisible in metered generation. Against this background I build a ladder of economic dispatch variants that add structural realism step by step: CHP constraints, unit commitment, procurement-informed mark-ups, and four alternative treatments of cross-border trade. These are compared with a 44-parameter hybrid merit-order stack (MOS) calibrated on 2023 EPEX prices (RMSE 36.75 EUR/MWh), with 2024 and 2025 held out.
The cross-border treatment decides the outcome. Prescribing observed flows in a single-node LP sharply increases the error (RMSE 103 EUR/MWh), whereas letting the LP trade endogenously against the five neighbours’ observed day-ahead prices under NTC limits reaches RMSE 22.7–24.5 EUR/MWh in all three years with no fitted parameters, better than the calibrated MOS in every year. Because the neighbour prices are realised values for the same delivery hours, these two-node results are ex-post reconstructions rather than forecasts. A 5-parameter correction on the single-node model, which rescales its solar term by CBS-reported PV capacity, also outperforms the MOS on 2025 out-of-sample data (38.1 versus 40.6 EUR/MWh). Within the window tested, structural parameters proved more stable than fitted coefficients.
An exhaustive ablation of the calibrated model identifies CHP must-run as the dominant parameter group. Storage arbitrage, used as an economic test, ranks the models differently from RMSE: models that score best on price level do not necessarily preserve the spread a battery trades on. Making storage endogenous in the dispatch produces a self-cannibalisation curve: scaling a four-hour fleet from 0.5 to 20 GWh cuts arbitrage value from 17.9 to 5.4 EUR/kWh/yr, interconnection retains 1.9–3.4 times the isolated-market value, and every endogenous value falls below the annualised capital cost of roughly 34 EUR/kWh/yr. Day-ahead arbitrage alone therefore does not finance storage in this model; ancillary and imbalance revenues are out of scope.
The main limitations are the two-year out-of-sample window and the reliance on observed neighbour prices. Within those bounds, the practical conclusion is that in interconnected markets with public neighbour-price and NTC data, two node coupling should be the first structural lever attempted before any calibration. ...
The Dutch market combines a gas-dominated thermal fleet, roughly 13 GW of combined heat and power (CHP) with heat-driven must-run obligations, and solar PV capacity that grew 26% over 2023–2025, most of it rooftop and largely invisible in metered generation. Against this background I build a ladder of economic dispatch variants that add structural realism step by step: CHP constraints, unit commitment, procurement-informed mark-ups, and four alternative treatments of cross-border trade. These are compared with a 44-parameter hybrid merit-order stack (MOS) calibrated on 2023 EPEX prices (RMSE 36.75 EUR/MWh), with 2024 and 2025 held out.
The cross-border treatment decides the outcome. Prescribing observed flows in a single-node LP sharply increases the error (RMSE 103 EUR/MWh), whereas letting the LP trade endogenously against the five neighbours’ observed day-ahead prices under NTC limits reaches RMSE 22.7–24.5 EUR/MWh in all three years with no fitted parameters, better than the calibrated MOS in every year. Because the neighbour prices are realised values for the same delivery hours, these two-node results are ex-post reconstructions rather than forecasts. A 5-parameter correction on the single-node model, which rescales its solar term by CBS-reported PV capacity, also outperforms the MOS on 2025 out-of-sample data (38.1 versus 40.6 EUR/MWh). Within the window tested, structural parameters proved more stable than fitted coefficients.
An exhaustive ablation of the calibrated model identifies CHP must-run as the dominant parameter group. Storage arbitrage, used as an economic test, ranks the models differently from RMSE: models that score best on price level do not necessarily preserve the spread a battery trades on. Making storage endogenous in the dispatch produces a self-cannibalisation curve: scaling a four-hour fleet from 0.5 to 20 GWh cuts arbitrage value from 17.9 to 5.4 EUR/kWh/yr, interconnection retains 1.9–3.4 times the isolated-market value, and every endogenous value falls below the annualised capital cost of roughly 34 EUR/kWh/yr. Day-ahead arbitrage alone therefore does not finance storage in this model; ancillary and imbalance revenues are out of scope.
The main limitations are the two-year out-of-sample window and the reliance on observed neighbour prices. Within those bounds, the practical conclusion is that in interconnected markets with public neighbour-price and NTC data, two node coupling should be the first structural lever attempted before any calibration. ...
This thesis asks how much of the Dutch day-ahead electricity price can be explained by economic dispatch models with no fitted parameters, and what the remaining gap reveals about the market.
The Dutch market combines a gas-dominated thermal fleet, roughly 13 GW of combined heat and power (CHP) with heat-driven must-run obligations, and solar PV capacity that grew 26% over 2023–2025, most of it rooftop and largely invisible in metered generation. Against this background I build a ladder of economic dispatch variants that add structural realism step by step: CHP constraints, unit commitment, procurement-informed mark-ups, and four alternative treatments of cross-border trade. These are compared with a 44-parameter hybrid merit-order stack (MOS) calibrated on 2023 EPEX prices (RMSE 36.75 EUR/MWh), with 2024 and 2025 held out.
The cross-border treatment decides the outcome. Prescribing observed flows in a single-node LP sharply increases the error (RMSE 103 EUR/MWh), whereas letting the LP trade endogenously against the five neighbours’ observed day-ahead prices under NTC limits reaches RMSE 22.7–24.5 EUR/MWh in all three years with no fitted parameters, better than the calibrated MOS in every year. Because the neighbour prices are realised values for the same delivery hours, these two-node results are ex-post reconstructions rather than forecasts. A 5-parameter correction on the single-node model, which rescales its solar term by CBS-reported PV capacity, also outperforms the MOS on 2025 out-of-sample data (38.1 versus 40.6 EUR/MWh). Within the window tested, structural parameters proved more stable than fitted coefficients.
An exhaustive ablation of the calibrated model identifies CHP must-run as the dominant parameter group. Storage arbitrage, used as an economic test, ranks the models differently from RMSE: models that score best on price level do not necessarily preserve the spread a battery trades on. Making storage endogenous in the dispatch produces a self-cannibalisation curve: scaling a four-hour fleet from 0.5 to 20 GWh cuts arbitrage value from 17.9 to 5.4 EUR/kWh/yr, interconnection retains 1.9–3.4 times the isolated-market value, and every endogenous value falls below the annualised capital cost of roughly 34 EUR/kWh/yr. Day-ahead arbitrage alone therefore does not finance storage in this model; ancillary and imbalance revenues are out of scope.
The main limitations are the two-year out-of-sample window and the reliance on observed neighbour prices. Within those bounds, the practical conclusion is that in interconnected markets with public neighbour-price and NTC data, two node coupling should be the first structural lever attempted before any calibration.
The Dutch market combines a gas-dominated thermal fleet, roughly 13 GW of combined heat and power (CHP) with heat-driven must-run obligations, and solar PV capacity that grew 26% over 2023–2025, most of it rooftop and largely invisible in metered generation. Against this background I build a ladder of economic dispatch variants that add structural realism step by step: CHP constraints, unit commitment, procurement-informed mark-ups, and four alternative treatments of cross-border trade. These are compared with a 44-parameter hybrid merit-order stack (MOS) calibrated on 2023 EPEX prices (RMSE 36.75 EUR/MWh), with 2024 and 2025 held out.
The cross-border treatment decides the outcome. Prescribing observed flows in a single-node LP sharply increases the error (RMSE 103 EUR/MWh), whereas letting the LP trade endogenously against the five neighbours’ observed day-ahead prices under NTC limits reaches RMSE 22.7–24.5 EUR/MWh in all three years with no fitted parameters, better than the calibrated MOS in every year. Because the neighbour prices are realised values for the same delivery hours, these two-node results are ex-post reconstructions rather than forecasts. A 5-parameter correction on the single-node model, which rescales its solar term by CBS-reported PV capacity, also outperforms the MOS on 2025 out-of-sample data (38.1 versus 40.6 EUR/MWh). Within the window tested, structural parameters proved more stable than fitted coefficients.
An exhaustive ablation of the calibrated model identifies CHP must-run as the dominant parameter group. Storage arbitrage, used as an economic test, ranks the models differently from RMSE: models that score best on price level do not necessarily preserve the spread a battery trades on. Making storage endogenous in the dispatch produces a self-cannibalisation curve: scaling a four-hour fleet from 0.5 to 20 GWh cuts arbitrage value from 17.9 to 5.4 EUR/kWh/yr, interconnection retains 1.9–3.4 times the isolated-market value, and every endogenous value falls below the annualised capital cost of roughly 34 EUR/kWh/yr. Day-ahead arbitrage alone therefore does not finance storage in this model; ancillary and imbalance revenues are out of scope.
The main limitations are the two-year out-of-sample window and the reliance on observed neighbour prices. Within those bounds, the practical conclusion is that in interconnected markets with public neighbour-price and NTC data, two node coupling should be the first structural lever attempted before any calibration.
Study into the role that measurement uncertainty of solar irradiance data plays in industrial applications in the utility-scale solar PV industry. Study was performed in collaboration with Hukx Sensor Technology.
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Study into the role that measurement uncertainty of solar irradiance data plays in industrial applications in the utility-scale solar PV industry. Study was performed in collaboration with Hukx Sensor Technology.
Master thesis
(2025)
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M.F. Triezenberg, J.W. van Wingerden, R.A. Verzijlbergh, J. Sun, M. Becker, J. Maljaars
As the energy transition accelerates, improving wind energy efficiency and forecasting becomes increasingly critical. One key challenge lies in reconstructing high-fidelity atmospheric boundary layer (ABL) flow fields from sparse measurements, especially in regions influenced by wind turbines. This thesis explores the use of Latent Diffusion Models (LDMs) to reconstruct physically plausible ABL flow fields from limited spatial data. Where previous work focused on homogeneous, neutral ABL states, this research extends the methodology to more diverse and realistic conditions by including both stable and neutral boundary layers with embedded wind farms. A conditional diffusion model is trained in the latent space of an autoencoder (AE), using both local measurements and global atmospheric labels. The model is evaluated using statistical, physical, and spectral metrics, and its ability to generalize across multiple ABL regimes is analyzed. Results show that the model can generate realistic reconstructions from extremely sparse inputs, including turbine wake structures, and can potentially serve as a tool for initializing Large Eddy Simulations (LES). These findings mark an important step toward integrating generative models into operational wind forecasting and control systems.
...
As the energy transition accelerates, improving wind energy efficiency and forecasting becomes increasingly critical. One key challenge lies in reconstructing high-fidelity atmospheric boundary layer (ABL) flow fields from sparse measurements, especially in regions influenced by wind turbines. This thesis explores the use of Latent Diffusion Models (LDMs) to reconstruct physically plausible ABL flow fields from limited spatial data. Where previous work focused on homogeneous, neutral ABL states, this research extends the methodology to more diverse and realistic conditions by including both stable and neutral boundary layers with embedded wind farms. A conditional diffusion model is trained in the latent space of an autoencoder (AE), using both local measurements and global atmospheric labels. The model is evaluated using statistical, physical, and spectral metrics, and its ability to generalize across multiple ABL regimes is analyzed. Results show that the model can generate realistic reconstructions from extremely sparse inputs, including turbine wake structures, and can potentially serve as a tool for initializing Large Eddy Simulations (LES). These findings mark an important step toward integrating generative models into operational wind forecasting and control systems.
To Spin or Not to Spin? The Hidden Costs of Curtailment
Optimising Dispatch Strategies for Offshore Wind Turbines in the Volatile Electricity Market
Master thesis
(2025)
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J.L. van der Schans, R.A. Verzijlbergh, E. Schröder, Stefan Pfenninger, R. Bos
The increasing integration of offshore wind energy into volatile electricity markets necessitates more frequent curtailment as a response to negative pricing conditions. Although curtailment can mitigate short-term financial losses, its long-term impacts on offshore wind turbine (OWT) degradation remain largely unaddressed. This thesis investigates the hidden costs associated with curtailment, focusing specifically on the degradation of critical turbine components, including the gearbox, blades, and support structures. By developing and comparing optimisation models, this research evaluates the effectiveness of coordinated curtailment strategies that integrate asset health considerations with market-driven objectives.
Three distinct optimisation frameworks are proposed: a baseline reflecting current market-driven curtailment practices, a centralised strategy optimising asset health and financial performance collectively, and a decentralised approach applying the Alternating Direction Method of Multipliers (ADMM) to address fragmented stakeholder interests. Results indicate significant benefits from centralised coordination, showing a notable reduction in investment costs and a substantial increase in overall profit, as well as improved return on investment. However, contractual complexities and data-sharing constraints can hinder centralised implementation, highlighting the potential advantages of a decentralised strategy.
The findings underscore the value of internalising asset health into curtailment decisions, demonstrating clear financial and operational improvements. Looking ahead, the value of centralised coordination is expected to grow as electricity markets experience increasing negative price events and greater volatility, driven by a higher share of variable renewable energy sources. Consequently, internalising asset health in curtailment strategies will become increasingly essential for future energy systems.
...
Three distinct optimisation frameworks are proposed: a baseline reflecting current market-driven curtailment practices, a centralised strategy optimising asset health and financial performance collectively, and a decentralised approach applying the Alternating Direction Method of Multipliers (ADMM) to address fragmented stakeholder interests. Results indicate significant benefits from centralised coordination, showing a notable reduction in investment costs and a substantial increase in overall profit, as well as improved return on investment. However, contractual complexities and data-sharing constraints can hinder centralised implementation, highlighting the potential advantages of a decentralised strategy.
The findings underscore the value of internalising asset health into curtailment decisions, demonstrating clear financial and operational improvements. Looking ahead, the value of centralised coordination is expected to grow as electricity markets experience increasing negative price events and greater volatility, driven by a higher share of variable renewable energy sources. Consequently, internalising asset health in curtailment strategies will become increasingly essential for future energy systems.
...
The increasing integration of offshore wind energy into volatile electricity markets necessitates more frequent curtailment as a response to negative pricing conditions. Although curtailment can mitigate short-term financial losses, its long-term impacts on offshore wind turbine (OWT) degradation remain largely unaddressed. This thesis investigates the hidden costs associated with curtailment, focusing specifically on the degradation of critical turbine components, including the gearbox, blades, and support structures. By developing and comparing optimisation models, this research evaluates the effectiveness of coordinated curtailment strategies that integrate asset health considerations with market-driven objectives.
Three distinct optimisation frameworks are proposed: a baseline reflecting current market-driven curtailment practices, a centralised strategy optimising asset health and financial performance collectively, and a decentralised approach applying the Alternating Direction Method of Multipliers (ADMM) to address fragmented stakeholder interests. Results indicate significant benefits from centralised coordination, showing a notable reduction in investment costs and a substantial increase in overall profit, as well as improved return on investment. However, contractual complexities and data-sharing constraints can hinder centralised implementation, highlighting the potential advantages of a decentralised strategy.
The findings underscore the value of internalising asset health into curtailment decisions, demonstrating clear financial and operational improvements. Looking ahead, the value of centralised coordination is expected to grow as electricity markets experience increasing negative price events and greater volatility, driven by a higher share of variable renewable energy sources. Consequently, internalising asset health in curtailment strategies will become increasingly essential for future energy systems.
Three distinct optimisation frameworks are proposed: a baseline reflecting current market-driven curtailment practices, a centralised strategy optimising asset health and financial performance collectively, and a decentralised approach applying the Alternating Direction Method of Multipliers (ADMM) to address fragmented stakeholder interests. Results indicate significant benefits from centralised coordination, showing a notable reduction in investment costs and a substantial increase in overall profit, as well as improved return on investment. However, contractual complexities and data-sharing constraints can hinder centralised implementation, highlighting the potential advantages of a decentralised strategy.
The findings underscore the value of internalising asset health into curtailment decisions, demonstrating clear financial and operational improvements. Looking ahead, the value of centralised coordination is expected to grow as electricity markets experience increasing negative price events and greater volatility, driven by a higher share of variable renewable energy sources. Consequently, internalising asset health in curtailment strategies will become increasingly essential for future energy systems.
Large-Eddy Simulations of Helix Active Wake Control
Sensitivity, Robustness and Advanced Actuator Line Modelling
The current change of the Earth's climate necessitates actions to strongly reduce the human carbon footprint. For the energy sector, this implies moving to renewable energy sources like wind. The wind resource is spatially heterogeneous, where wind speeds and power densities are particularly favourable offshore. The favourable offshore wind resource, together with the limited availability of onshore land area for wind energy, motivates the move to offshore wind energy generation. Economic, spatial and environmental considerations suggest clustering wind turbines offshore into wind farms.
Wind turbines clustered in a wind farm operate on average at a lower efficiency than they would achieve in isolation. One major source of this efficiency loss is wake interaction. As wind turbines extract kinetic energy from the wind, they leave behind a region of low wind speed, the so-called wake. When wakes generated by upstream turbines impinge on downstream turbines in the farm, they reduce their power output and thus the overall farm efficiency. In the design phase, the wind farm layout is optimised to minimise wake losses; however, even in an optimal layout wake losses are significant. From the desire to further mitigate the remaining wake losses, the field of wind farm flow control (WFFC) arose, which aims to reduce wake losses by farm-wide coordinated control of the wind turbines.
Wind farm flow control strategies differ based on their working mechanism, e.g. control strategies aim to either reduce the initial wake deficit of upstream turbines by reducing the turbine thrust or redirecting wakes past downstream turbines by intentionally misaligning upstream turbines with the incoming wind direction. A newer category of strategies for WFFC is active wake control (AWC). Compared to the former quasi-steady strategies, AWC strategies are inherently dynamic as their working mechanism relies on unsteady actuation, which aims to trigger underlying instability modes of the wake flow. One of the most recently developed AWC strategies is helix active wake control. It makes use of the individual pitch control capabilities (IPC) of modern wind turbines in order to intentionally force the first instability mode of the wake.
This thesis is concerned with high-fidelity modelling of helix active wake control using large-eddy simulation (LES) of the atmospheric flow, where the effect of IPC is captured by representing the turbine in the LES by means of the actuator line model (ALM). Judging the potential of helix active wake control requires (i) quantifying the arising power-load trade-off, (ii) comparing it to established WFFC strategies like wake steering, and (iii) ultimately testing it in realistic transient atmospheric boundary layers. To this end, the overall objective of this thesis is to
"Assess the performance of helix active wake control in quasi-steady atmospheric boundary layers and develop actuator line model capabilities for its study in coarse grid real weather large-eddy simulations."
In a first step, the sensitivity of helix active wake control to the amplitude of the pitch actuation is quantified for a full wake overlap scenario. It is found that the activation of the control leads to a trade-off between power gain and additional turbine loading in terms of the incurred damage equivalent loads (DEL). While the power gain monotonically increases for pitch amplitudes between one and six degrees, the same trend is observed for the DELs of the actuated turbine. Hence, the value of activating the control and selecting its pitch amplitude setpoint will need to be determined based on a higher-level metric like the current electricity price.
In a second step, the sensitivity of the power gain achieved with helix active wake control to varying degrees of wake overlap and turbine spacing is compared to wake steering. It is found that wake steering outperforms the helix except for dense spacing combined with full wake overlap. However, when considering a varying wind direction around full wake overlap without an immediate control response, the results suggest that the power gain achieved by the helix control setpoint is more robust.
The previous finding suggests that time-varying wind directions are important for selecting the best control strategy. Hence, in a third step, an actuator line model is implemented into an atmospheric LES code, which allows for driving microscale LES with mesoscale forcing derived from numerical weather prediction models in order to include additional time scales in the problem. The correctness of the ALM implementation is verified with reference to results from four other research LES codes. Additionally, the emphasis is on ensuring accurate thrust and power predictions on coarser LES grids. To this end, the filtered lifting line correction is included in the ALM implementation.
Current corrections for coarse grid ALM-LES, e.g. the filtered lifting line correction, do not consider the complete unsteady problem. Thus, as a last step, we take the IPC actuation underlying helix active wake control as an opportunity to formally investigate unsteadiness in the ALM for scenarios corresponding to unsteady attached flow below stall. By deriving a semi-analytical solution for the two-dimensional "ALM'' its connection to Theodorsen theory is established. Further, this solution allows for determining the optimal kernel width for the unsteady ALM, which is approximately 40% of the chord length and determining bounds of its validity. Importantly, we find that even when using the optimal kernel width, the magnitude of the unsteady force cannot be accurately captured anymore by the ALM if the reduced frequency exceeds k>0.2.
In summary, this thesis contributed to the understanding of under which circumstances the application of helix active wake control for the mitigation of wake effects might be a viable option. Given that the benefits and drawbacks of the helix are at least partially complementary with wake steering control, both control strategies could be seen as pieces of a more comprehensive toolbox of wind farm flow control strategies. The activation of a respective control strategy would then happen only during periods corresponding to its identified favourable conditions. Hence, the model development conducted in the second part of this thesis aims towards building a simulation environment - spanning from mesoscale effects down to airfoil aerodynamics - within which such a selection process of WFFC strategies can be studied in realistic weather conditions. ...
Wind turbines clustered in a wind farm operate on average at a lower efficiency than they would achieve in isolation. One major source of this efficiency loss is wake interaction. As wind turbines extract kinetic energy from the wind, they leave behind a region of low wind speed, the so-called wake. When wakes generated by upstream turbines impinge on downstream turbines in the farm, they reduce their power output and thus the overall farm efficiency. In the design phase, the wind farm layout is optimised to minimise wake losses; however, even in an optimal layout wake losses are significant. From the desire to further mitigate the remaining wake losses, the field of wind farm flow control (WFFC) arose, which aims to reduce wake losses by farm-wide coordinated control of the wind turbines.
Wind farm flow control strategies differ based on their working mechanism, e.g. control strategies aim to either reduce the initial wake deficit of upstream turbines by reducing the turbine thrust or redirecting wakes past downstream turbines by intentionally misaligning upstream turbines with the incoming wind direction. A newer category of strategies for WFFC is active wake control (AWC). Compared to the former quasi-steady strategies, AWC strategies are inherently dynamic as their working mechanism relies on unsteady actuation, which aims to trigger underlying instability modes of the wake flow. One of the most recently developed AWC strategies is helix active wake control. It makes use of the individual pitch control capabilities (IPC) of modern wind turbines in order to intentionally force the first instability mode of the wake.
This thesis is concerned with high-fidelity modelling of helix active wake control using large-eddy simulation (LES) of the atmospheric flow, where the effect of IPC is captured by representing the turbine in the LES by means of the actuator line model (ALM). Judging the potential of helix active wake control requires (i) quantifying the arising power-load trade-off, (ii) comparing it to established WFFC strategies like wake steering, and (iii) ultimately testing it in realistic transient atmospheric boundary layers. To this end, the overall objective of this thesis is to
"Assess the performance of helix active wake control in quasi-steady atmospheric boundary layers and develop actuator line model capabilities for its study in coarse grid real weather large-eddy simulations."
In a first step, the sensitivity of helix active wake control to the amplitude of the pitch actuation is quantified for a full wake overlap scenario. It is found that the activation of the control leads to a trade-off between power gain and additional turbine loading in terms of the incurred damage equivalent loads (DEL). While the power gain monotonically increases for pitch amplitudes between one and six degrees, the same trend is observed for the DELs of the actuated turbine. Hence, the value of activating the control and selecting its pitch amplitude setpoint will need to be determined based on a higher-level metric like the current electricity price.
In a second step, the sensitivity of the power gain achieved with helix active wake control to varying degrees of wake overlap and turbine spacing is compared to wake steering. It is found that wake steering outperforms the helix except for dense spacing combined with full wake overlap. However, when considering a varying wind direction around full wake overlap without an immediate control response, the results suggest that the power gain achieved by the helix control setpoint is more robust.
The previous finding suggests that time-varying wind directions are important for selecting the best control strategy. Hence, in a third step, an actuator line model is implemented into an atmospheric LES code, which allows for driving microscale LES with mesoscale forcing derived from numerical weather prediction models in order to include additional time scales in the problem. The correctness of the ALM implementation is verified with reference to results from four other research LES codes. Additionally, the emphasis is on ensuring accurate thrust and power predictions on coarser LES grids. To this end, the filtered lifting line correction is included in the ALM implementation.
Current corrections for coarse grid ALM-LES, e.g. the filtered lifting line correction, do not consider the complete unsteady problem. Thus, as a last step, we take the IPC actuation underlying helix active wake control as an opportunity to formally investigate unsteadiness in the ALM for scenarios corresponding to unsteady attached flow below stall. By deriving a semi-analytical solution for the two-dimensional "ALM'' its connection to Theodorsen theory is established. Further, this solution allows for determining the optimal kernel width for the unsteady ALM, which is approximately 40% of the chord length and determining bounds of its validity. Importantly, we find that even when using the optimal kernel width, the magnitude of the unsteady force cannot be accurately captured anymore by the ALM if the reduced frequency exceeds k>0.2.
In summary, this thesis contributed to the understanding of under which circumstances the application of helix active wake control for the mitigation of wake effects might be a viable option. Given that the benefits and drawbacks of the helix are at least partially complementary with wake steering control, both control strategies could be seen as pieces of a more comprehensive toolbox of wind farm flow control strategies. The activation of a respective control strategy would then happen only during periods corresponding to its identified favourable conditions. Hence, the model development conducted in the second part of this thesis aims towards building a simulation environment - spanning from mesoscale effects down to airfoil aerodynamics - within which such a selection process of WFFC strategies can be studied in realistic weather conditions. ...
The current change of the Earth's climate necessitates actions to strongly reduce the human carbon footprint. For the energy sector, this implies moving to renewable energy sources like wind. The wind resource is spatially heterogeneous, where wind speeds and power densities are particularly favourable offshore. The favourable offshore wind resource, together with the limited availability of onshore land area for wind energy, motivates the move to offshore wind energy generation. Economic, spatial and environmental considerations suggest clustering wind turbines offshore into wind farms.
Wind turbines clustered in a wind farm operate on average at a lower efficiency than they would achieve in isolation. One major source of this efficiency loss is wake interaction. As wind turbines extract kinetic energy from the wind, they leave behind a region of low wind speed, the so-called wake. When wakes generated by upstream turbines impinge on downstream turbines in the farm, they reduce their power output and thus the overall farm efficiency. In the design phase, the wind farm layout is optimised to minimise wake losses; however, even in an optimal layout wake losses are significant. From the desire to further mitigate the remaining wake losses, the field of wind farm flow control (WFFC) arose, which aims to reduce wake losses by farm-wide coordinated control of the wind turbines.
Wind farm flow control strategies differ based on their working mechanism, e.g. control strategies aim to either reduce the initial wake deficit of upstream turbines by reducing the turbine thrust or redirecting wakes past downstream turbines by intentionally misaligning upstream turbines with the incoming wind direction. A newer category of strategies for WFFC is active wake control (AWC). Compared to the former quasi-steady strategies, AWC strategies are inherently dynamic as their working mechanism relies on unsteady actuation, which aims to trigger underlying instability modes of the wake flow. One of the most recently developed AWC strategies is helix active wake control. It makes use of the individual pitch control capabilities (IPC) of modern wind turbines in order to intentionally force the first instability mode of the wake.
This thesis is concerned with high-fidelity modelling of helix active wake control using large-eddy simulation (LES) of the atmospheric flow, where the effect of IPC is captured by representing the turbine in the LES by means of the actuator line model (ALM). Judging the potential of helix active wake control requires (i) quantifying the arising power-load trade-off, (ii) comparing it to established WFFC strategies like wake steering, and (iii) ultimately testing it in realistic transient atmospheric boundary layers. To this end, the overall objective of this thesis is to
"Assess the performance of helix active wake control in quasi-steady atmospheric boundary layers and develop actuator line model capabilities for its study in coarse grid real weather large-eddy simulations."
In a first step, the sensitivity of helix active wake control to the amplitude of the pitch actuation is quantified for a full wake overlap scenario. It is found that the activation of the control leads to a trade-off between power gain and additional turbine loading in terms of the incurred damage equivalent loads (DEL). While the power gain monotonically increases for pitch amplitudes between one and six degrees, the same trend is observed for the DELs of the actuated turbine. Hence, the value of activating the control and selecting its pitch amplitude setpoint will need to be determined based on a higher-level metric like the current electricity price.
In a second step, the sensitivity of the power gain achieved with helix active wake control to varying degrees of wake overlap and turbine spacing is compared to wake steering. It is found that wake steering outperforms the helix except for dense spacing combined with full wake overlap. However, when considering a varying wind direction around full wake overlap without an immediate control response, the results suggest that the power gain achieved by the helix control setpoint is more robust.
The previous finding suggests that time-varying wind directions are important for selecting the best control strategy. Hence, in a third step, an actuator line model is implemented into an atmospheric LES code, which allows for driving microscale LES with mesoscale forcing derived from numerical weather prediction models in order to include additional time scales in the problem. The correctness of the ALM implementation is verified with reference to results from four other research LES codes. Additionally, the emphasis is on ensuring accurate thrust and power predictions on coarser LES grids. To this end, the filtered lifting line correction is included in the ALM implementation.
Current corrections for coarse grid ALM-LES, e.g. the filtered lifting line correction, do not consider the complete unsteady problem. Thus, as a last step, we take the IPC actuation underlying helix active wake control as an opportunity to formally investigate unsteadiness in the ALM for scenarios corresponding to unsteady attached flow below stall. By deriving a semi-analytical solution for the two-dimensional "ALM'' its connection to Theodorsen theory is established. Further, this solution allows for determining the optimal kernel width for the unsteady ALM, which is approximately 40% of the chord length and determining bounds of its validity. Importantly, we find that even when using the optimal kernel width, the magnitude of the unsteady force cannot be accurately captured anymore by the ALM if the reduced frequency exceeds k>0.2.
In summary, this thesis contributed to the understanding of under which circumstances the application of helix active wake control for the mitigation of wake effects might be a viable option. Given that the benefits and drawbacks of the helix are at least partially complementary with wake steering control, both control strategies could be seen as pieces of a more comprehensive toolbox of wind farm flow control strategies. The activation of a respective control strategy would then happen only during periods corresponding to its identified favourable conditions. Hence, the model development conducted in the second part of this thesis aims towards building a simulation environment - spanning from mesoscale effects down to airfoil aerodynamics - within which such a selection process of WFFC strategies can be studied in realistic weather conditions.
Wind turbines clustered in a wind farm operate on average at a lower efficiency than they would achieve in isolation. One major source of this efficiency loss is wake interaction. As wind turbines extract kinetic energy from the wind, they leave behind a region of low wind speed, the so-called wake. When wakes generated by upstream turbines impinge on downstream turbines in the farm, they reduce their power output and thus the overall farm efficiency. In the design phase, the wind farm layout is optimised to minimise wake losses; however, even in an optimal layout wake losses are significant. From the desire to further mitigate the remaining wake losses, the field of wind farm flow control (WFFC) arose, which aims to reduce wake losses by farm-wide coordinated control of the wind turbines.
Wind farm flow control strategies differ based on their working mechanism, e.g. control strategies aim to either reduce the initial wake deficit of upstream turbines by reducing the turbine thrust or redirecting wakes past downstream turbines by intentionally misaligning upstream turbines with the incoming wind direction. A newer category of strategies for WFFC is active wake control (AWC). Compared to the former quasi-steady strategies, AWC strategies are inherently dynamic as their working mechanism relies on unsteady actuation, which aims to trigger underlying instability modes of the wake flow. One of the most recently developed AWC strategies is helix active wake control. It makes use of the individual pitch control capabilities (IPC) of modern wind turbines in order to intentionally force the first instability mode of the wake.
This thesis is concerned with high-fidelity modelling of helix active wake control using large-eddy simulation (LES) of the atmospheric flow, where the effect of IPC is captured by representing the turbine in the LES by means of the actuator line model (ALM). Judging the potential of helix active wake control requires (i) quantifying the arising power-load trade-off, (ii) comparing it to established WFFC strategies like wake steering, and (iii) ultimately testing it in realistic transient atmospheric boundary layers. To this end, the overall objective of this thesis is to
"Assess the performance of helix active wake control in quasi-steady atmospheric boundary layers and develop actuator line model capabilities for its study in coarse grid real weather large-eddy simulations."
In a first step, the sensitivity of helix active wake control to the amplitude of the pitch actuation is quantified for a full wake overlap scenario. It is found that the activation of the control leads to a trade-off between power gain and additional turbine loading in terms of the incurred damage equivalent loads (DEL). While the power gain monotonically increases for pitch amplitudes between one and six degrees, the same trend is observed for the DELs of the actuated turbine. Hence, the value of activating the control and selecting its pitch amplitude setpoint will need to be determined based on a higher-level metric like the current electricity price.
In a second step, the sensitivity of the power gain achieved with helix active wake control to varying degrees of wake overlap and turbine spacing is compared to wake steering. It is found that wake steering outperforms the helix except for dense spacing combined with full wake overlap. However, when considering a varying wind direction around full wake overlap without an immediate control response, the results suggest that the power gain achieved by the helix control setpoint is more robust.
The previous finding suggests that time-varying wind directions are important for selecting the best control strategy. Hence, in a third step, an actuator line model is implemented into an atmospheric LES code, which allows for driving microscale LES with mesoscale forcing derived from numerical weather prediction models in order to include additional time scales in the problem. The correctness of the ALM implementation is verified with reference to results from four other research LES codes. Additionally, the emphasis is on ensuring accurate thrust and power predictions on coarser LES grids. To this end, the filtered lifting line correction is included in the ALM implementation.
Current corrections for coarse grid ALM-LES, e.g. the filtered lifting line correction, do not consider the complete unsteady problem. Thus, as a last step, we take the IPC actuation underlying helix active wake control as an opportunity to formally investigate unsteadiness in the ALM for scenarios corresponding to unsteady attached flow below stall. By deriving a semi-analytical solution for the two-dimensional "ALM'' its connection to Theodorsen theory is established. Further, this solution allows for determining the optimal kernel width for the unsteady ALM, which is approximately 40% of the chord length and determining bounds of its validity. Importantly, we find that even when using the optimal kernel width, the magnitude of the unsteady force cannot be accurately captured anymore by the ALM if the reduced frequency exceeds k>0.2.
In summary, this thesis contributed to the understanding of under which circumstances the application of helix active wake control for the mitigation of wake effects might be a viable option. Given that the benefits and drawbacks of the helix are at least partially complementary with wake steering control, both control strategies could be seen as pieces of a more comprehensive toolbox of wind farm flow control strategies. The activation of a respective control strategy would then happen only during periods corresponding to its identified favourable conditions. Hence, the model development conducted in the second part of this thesis aims towards building a simulation environment - spanning from mesoscale effects down to airfoil aerodynamics - within which such a selection process of WFFC strategies can be studied in realistic weather conditions.
Master thesis
(2024)
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S.I.H. Sekha, R.A. Verzijlbergh, S. Kenjeres, J.W. van Wingerden, E. Taschner
The Helix approach is a dynamic control method that mitigates wind turbine wake effects by pitching the turbine blades individually. In current literature the method is mainly researched with a high-fidelity actuator line model (ALM). Because of the computational constraints imposed by this model, the effect of the Helix has not been researched for turbine arrays longer than 3. To investigate the effects of the Helix on a farm size scale, a lower fidelity model capturing the Helix is developed in this research. This model is based on a uniform actuator disk model and is called the H-ADM. The H-ADM is validated in laminar conditions at a fine resolution by comparing wake recovery to the ALM. The H-ADM captures both the additional wake mixing and wake displacement caused by the Helix. Furthermore, the H-ADM correctly predicts differences between the counterclockwise (CCW) and clockwise (CW) Helix. Due to modelling assumptions, the H-ADM can run simulations at a coarser resolution and with a smaller time-step than the ALM. Computational gains are achieved with the H-ADM as a result. This research shows that similar simulations are executed over 640 times faster for the H-ADM compared to ALM. The model is used to gain a deeper understanding of the mechanisms causing differences between the CCW and CW Helix. It turns out these differences fade away if no rotational force is exerted by the wind turbine. Finally, the computational gains of the H-ADM are leveraged by applying the Helix on the first row of a large scale wind farm with 48 turbines. For the considered farm the CCW Helix seems to outperform the CW Helix in terms of total power gains.
...
The Helix approach is a dynamic control method that mitigates wind turbine wake effects by pitching the turbine blades individually. In current literature the method is mainly researched with a high-fidelity actuator line model (ALM). Because of the computational constraints imposed by this model, the effect of the Helix has not been researched for turbine arrays longer than 3. To investigate the effects of the Helix on a farm size scale, a lower fidelity model capturing the Helix is developed in this research. This model is based on a uniform actuator disk model and is called the H-ADM. The H-ADM is validated in laminar conditions at a fine resolution by comparing wake recovery to the ALM. The H-ADM captures both the additional wake mixing and wake displacement caused by the Helix. Furthermore, the H-ADM correctly predicts differences between the counterclockwise (CCW) and clockwise (CW) Helix. Due to modelling assumptions, the H-ADM can run simulations at a coarser resolution and with a smaller time-step than the ALM. Computational gains are achieved with the H-ADM as a result. This research shows that similar simulations are executed over 640 times faster for the H-ADM compared to ALM. The model is used to gain a deeper understanding of the mechanisms causing differences between the CCW and CW Helix. It turns out these differences fade away if no rotational force is exerted by the wind turbine. Finally, the computational gains of the H-ADM are leveraged by applying the Helix on the first row of a large scale wind farm with 48 turbines. For the considered farm the CCW Helix seems to outperform the CW Helix in terms of total power gains.
Outsmarting the Storm: Evaluating AI in Weather Forecasting
A Comparative Analysis of the AI-Driven GraphCast and Pangu-Weather Models Against HRES and Aspire in Operational Context, Evaluated with Observational Data
This thesis evaluates AI-based weather forecasting models—specifically GraphCast and Pangu-Weather—against traditional numerical weather prediction models like the ECMWF High-Resolution Model (HRES) and the Aspire Meso and LES models, focusing on the Netherlands due to its dense observational network and wind energy infrastructure. The study examines operational considerations, including computational costs and hardware requirements, highlighting that while AI models offer significant computational efficiency during inference, they require substantial resources for training and have limitations in local adaptability and variable inclusion (e.g., Pangu-Weather lacks precipitation data). Performance analysis demonstrates that GraphCast consistently outperforms HRES, Pangu-Weather, and Aspire Meso across various meteorological variables and lead times. Despite the advantages, the models exhibit baseline errors due to shared data sources like ERA5, leading to correlated errors that limit the effectiveness of ensemble forecasting. The research underscores the potential of AI models to enhance forecast accuracy and reduce imbalance costs in wind energy production but also emphasizes challenges related to the black-box nature of AI models, data bottlenecks, and limitations imposed by neural scaling laws, where larger models do not necessarily yield better performance. Recommendations for future work include incorporating more observational data, enhancing model modularity and adaptability, improving temporal resolution, expanding variable ranges, emphasizing validation against observational data, and exploring advanced ensemble techniques. The findings suggest that while AI-based models like GraphCast and Pangu-Weather hold significant promise for advancing weather forecasting, addressing limitations in data quality, model architecture, and operational flexibility is crucial for realizing their full potential in operational settings.
...
This thesis evaluates AI-based weather forecasting models—specifically GraphCast and Pangu-Weather—against traditional numerical weather prediction models like the ECMWF High-Resolution Model (HRES) and the Aspire Meso and LES models, focusing on the Netherlands due to its dense observational network and wind energy infrastructure. The study examines operational considerations, including computational costs and hardware requirements, highlighting that while AI models offer significant computational efficiency during inference, they require substantial resources for training and have limitations in local adaptability and variable inclusion (e.g., Pangu-Weather lacks precipitation data). Performance analysis demonstrates that GraphCast consistently outperforms HRES, Pangu-Weather, and Aspire Meso across various meteorological variables and lead times. Despite the advantages, the models exhibit baseline errors due to shared data sources like ERA5, leading to correlated errors that limit the effectiveness of ensemble forecasting. The research underscores the potential of AI models to enhance forecast accuracy and reduce imbalance costs in wind energy production but also emphasizes challenges related to the black-box nature of AI models, data bottlenecks, and limitations imposed by neural scaling laws, where larger models do not necessarily yield better performance. Recommendations for future work include incorporating more observational data, enhancing model modularity and adaptability, improving temporal resolution, expanding variable ranges, emphasizing validation against observational data, and exploring advanced ensemble techniques. The findings suggest that while AI-based models like GraphCast and Pangu-Weather hold significant promise for advancing weather forecasting, addressing limitations in data quality, model architecture, and operational flexibility is crucial for realizing their full potential in operational settings.
The Production and Delivery of Green Hydrogen and Recovered Waste Heat
A Techno-Economic Analysis of a Multi-MW Alkaline and PEM Electrolysis Plant
In this thesis, both a 10 MW Alkaline Electrolyser (AE) and a 10 MW Proton-Exchange Membrane (PEM) electrolyser system are evaluated through a comprehensive techno-economic feasibility study, spanning a 25-year operational lifespan. The systems are designed to serve a dual function, producing green hydrogen at 350 bar for utilisation at a hydrogen refuelling station for heavy-duty trucks, as well as recovering waste heat via a tie-in on the cooling system of the electrolyser to directly supply a medium-temperature district heating network at 70 °C. The latter is achieved by connecting the tie-in to a heat exchanger, resulting in a cost-effective heat recovery without the implementation of an expensive heat pump. Both electrolysis systems are operated at 80 °C and powered by offshore wind power, delivered to the electrolyser system through a virtual PPA.
ERA5 data on the wind speed was employed, which was converted into power data via the wind farm power curve. The wind farm power curve was produced by coupling wind farm power production data to the ERA5 wind speed. This method proved to be effective in simulating the power production of a wind farm, as it included the wind farm wake effects and the global-blockage effect.
The performance of the AE system was simulated through a semi-empirical model for both the polarization and Faraday efficiency curve, while the performance of the PEM electrolyser system was simulated by an empirical approach for the polarization curve and a semi-empirical model for the Faraday efficiency curve. A degradation efficiency method is proposed, which employs a constant degradation factor to describe the decreasing performance over the lifetime of the stack. The degradation efficiency effectively illustrated the heat-producing degradation in electrolyser cells.
The techno-economic aspect of the research involved a detailed analysis of the Levelised Costs of Hydrogen and Heat (LCoH2 and LCoHeat). The LCoH2 of green hydrogen from the AE system was 6.08 euro/kg, while the LCoHeat of the recovered waste heat was 1.57 euro/MWh. For the PEM electrolyser system, the LCoH2 was determined to be 5.59 euro/kg, while the associated LCoHeat for the recovered waste heat was 1.55 euro/MWh. The profits of selling the recovered waste can be utilised to decrease the LCoH2. When a recovered waste heat-selling price of 50 euro/MWh was assumed, the LCoH2 of the AE and PEM electrolyser system decreased by 0.64 euro/kg and 0.44 euro/kg, respectively.
The sensitivity analysis on the LCoH2 indicated that the PPA price was the most influential factor on the LCoH2, followed by the Capital Expenditures (CAPEX) of the electrolyser system, and the start-of-life stack efficiency. When assessing the LCoHeat, the sensitivity analysis revealed that the most impacting parameters on the LCoHeat were the capacity of the installed electrolysis plant, the discount rate and the CAPEX of the heat exchanger. ...
ERA5 data on the wind speed was employed, which was converted into power data via the wind farm power curve. The wind farm power curve was produced by coupling wind farm power production data to the ERA5 wind speed. This method proved to be effective in simulating the power production of a wind farm, as it included the wind farm wake effects and the global-blockage effect.
The performance of the AE system was simulated through a semi-empirical model for both the polarization and Faraday efficiency curve, while the performance of the PEM electrolyser system was simulated by an empirical approach for the polarization curve and a semi-empirical model for the Faraday efficiency curve. A degradation efficiency method is proposed, which employs a constant degradation factor to describe the decreasing performance over the lifetime of the stack. The degradation efficiency effectively illustrated the heat-producing degradation in electrolyser cells.
The techno-economic aspect of the research involved a detailed analysis of the Levelised Costs of Hydrogen and Heat (LCoH2 and LCoHeat). The LCoH2 of green hydrogen from the AE system was 6.08 euro/kg, while the LCoHeat of the recovered waste heat was 1.57 euro/MWh. For the PEM electrolyser system, the LCoH2 was determined to be 5.59 euro/kg, while the associated LCoHeat for the recovered waste heat was 1.55 euro/MWh. The profits of selling the recovered waste can be utilised to decrease the LCoH2. When a recovered waste heat-selling price of 50 euro/MWh was assumed, the LCoH2 of the AE and PEM electrolyser system decreased by 0.64 euro/kg and 0.44 euro/kg, respectively.
The sensitivity analysis on the LCoH2 indicated that the PPA price was the most influential factor on the LCoH2, followed by the Capital Expenditures (CAPEX) of the electrolyser system, and the start-of-life stack efficiency. When assessing the LCoHeat, the sensitivity analysis revealed that the most impacting parameters on the LCoHeat were the capacity of the installed electrolysis plant, the discount rate and the CAPEX of the heat exchanger. ...
In this thesis, both a 10 MW Alkaline Electrolyser (AE) and a 10 MW Proton-Exchange Membrane (PEM) electrolyser system are evaluated through a comprehensive techno-economic feasibility study, spanning a 25-year operational lifespan. The systems are designed to serve a dual function, producing green hydrogen at 350 bar for utilisation at a hydrogen refuelling station for heavy-duty trucks, as well as recovering waste heat via a tie-in on the cooling system of the electrolyser to directly supply a medium-temperature district heating network at 70 °C. The latter is achieved by connecting the tie-in to a heat exchanger, resulting in a cost-effective heat recovery without the implementation of an expensive heat pump. Both electrolysis systems are operated at 80 °C and powered by offshore wind power, delivered to the electrolyser system through a virtual PPA.
ERA5 data on the wind speed was employed, which was converted into power data via the wind farm power curve. The wind farm power curve was produced by coupling wind farm power production data to the ERA5 wind speed. This method proved to be effective in simulating the power production of a wind farm, as it included the wind farm wake effects and the global-blockage effect.
The performance of the AE system was simulated through a semi-empirical model for both the polarization and Faraday efficiency curve, while the performance of the PEM electrolyser system was simulated by an empirical approach for the polarization curve and a semi-empirical model for the Faraday efficiency curve. A degradation efficiency method is proposed, which employs a constant degradation factor to describe the decreasing performance over the lifetime of the stack. The degradation efficiency effectively illustrated the heat-producing degradation in electrolyser cells.
The techno-economic aspect of the research involved a detailed analysis of the Levelised Costs of Hydrogen and Heat (LCoH2 and LCoHeat). The LCoH2 of green hydrogen from the AE system was 6.08 euro/kg, while the LCoHeat of the recovered waste heat was 1.57 euro/MWh. For the PEM electrolyser system, the LCoH2 was determined to be 5.59 euro/kg, while the associated LCoHeat for the recovered waste heat was 1.55 euro/MWh. The profits of selling the recovered waste can be utilised to decrease the LCoH2. When a recovered waste heat-selling price of 50 euro/MWh was assumed, the LCoH2 of the AE and PEM electrolyser system decreased by 0.64 euro/kg and 0.44 euro/kg, respectively.
The sensitivity analysis on the LCoH2 indicated that the PPA price was the most influential factor on the LCoH2, followed by the Capital Expenditures (CAPEX) of the electrolyser system, and the start-of-life stack efficiency. When assessing the LCoHeat, the sensitivity analysis revealed that the most impacting parameters on the LCoHeat were the capacity of the installed electrolysis plant, the discount rate and the CAPEX of the heat exchanger.
ERA5 data on the wind speed was employed, which was converted into power data via the wind farm power curve. The wind farm power curve was produced by coupling wind farm power production data to the ERA5 wind speed. This method proved to be effective in simulating the power production of a wind farm, as it included the wind farm wake effects and the global-blockage effect.
The performance of the AE system was simulated through a semi-empirical model for both the polarization and Faraday efficiency curve, while the performance of the PEM electrolyser system was simulated by an empirical approach for the polarization curve and a semi-empirical model for the Faraday efficiency curve. A degradation efficiency method is proposed, which employs a constant degradation factor to describe the decreasing performance over the lifetime of the stack. The degradation efficiency effectively illustrated the heat-producing degradation in electrolyser cells.
The techno-economic aspect of the research involved a detailed analysis of the Levelised Costs of Hydrogen and Heat (LCoH2 and LCoHeat). The LCoH2 of green hydrogen from the AE system was 6.08 euro/kg, while the LCoHeat of the recovered waste heat was 1.57 euro/MWh. For the PEM electrolyser system, the LCoH2 was determined to be 5.59 euro/kg, while the associated LCoHeat for the recovered waste heat was 1.55 euro/MWh. The profits of selling the recovered waste can be utilised to decrease the LCoH2. When a recovered waste heat-selling price of 50 euro/MWh was assumed, the LCoH2 of the AE and PEM electrolyser system decreased by 0.64 euro/kg and 0.44 euro/kg, respectively.
The sensitivity analysis on the LCoH2 indicated that the PPA price was the most influential factor on the LCoH2, followed by the Capital Expenditures (CAPEX) of the electrolyser system, and the start-of-life stack efficiency. When assessing the LCoHeat, the sensitivity analysis revealed that the most impacting parameters on the LCoHeat were the capacity of the installed electrolysis plant, the discount rate and the CAPEX of the heat exchanger.
Solar power forecasts
Spatio-temporal solar power forecasts via regression
We aim to make solar power forecasts using regression for grid optimization. We forecast from 1 to 6 hours ahead. The forecasts prove to be accurate with a skill score of 20% compared to persistence for a lead time of one hour.
...
We aim to make solar power forecasts using regression for grid optimization. We forecast from 1 to 6 hours ahead. The forecasts prove to be accurate with a skill score of 20% compared to persistence for a lead time of one hour.
Sequential decision-making under uncertainty is an important branch of artificial intelligence research with a plethora of real-life applications. In this thesis, we generalize two fundamental properties of the decision-making process. First, we show that the theory on planning methods for finite spaces can be extended to infinite but countable spaces. Second, we propose a unified model of reinforcement learning algorithms that employ the principle of optimism in the face of uncertainty. This model is used to explain why these methods are efficient. We use the developed theory to design novel algorithms. Depending on the user's needs, these algorithms can either automate the decision-making process completely, or provide advice in decision-support systems.
We start with presenting the basic concepts from the theory of decision-making and discuss the two approaches to it: planning and reinforcement learning. We look at a few typical sequential decision-making problems of increasing difficulty. In particular, we present a game that involves grid navigation and the problems of warehouse management and wind farm operation. Next, we survey the state-of-the-art methods for solving such problems.
Based on this analysis, we identify the following research opportunities. In planning, models with non-stationary and countably-infinite data remain relatively untreated because they are equivalent to infinitely-dimensional optimization problems, which are notoriously difficult to solve even approximately. In reinforcement learning, optimistic approaches lead to computational efficiency, yet the theory of optimism remains undeveloped. Moreover, while reinforcement learning shines at playing games, such as chess, shōgi, Go, and StarCraft II, its practical applications remain few.
Next, we overview a mathematical framework of sequential decision-making under uncertainty known as the Markov decision process. We explain how the goal of the decision-maker can be expressed as an optimization problem and present two approaches to achieving this goal. The first—more common—approach assigns so-called values to different actions. The other approach uses so-called occupancies that tell how often the agent should choose the actions instead of evaluating how good these actions are. In fact, the two approaches are known to be dual to each other. While this duality is well studied in the finite case, the infinite case is less explored. To address this knowledge gap, we present a new dual formulation for countable problems, both finite and infinite.
Afterwards, we use the dual formulation to design a new planning algorithm for infinite-horizon problems with non-stationary data. These problems are essentially infinite-dimensional optimization problems and as such are impossible to solve exactly using the standard approaches. We show that they can be solved by changing what is defined as optimal behavior: instead of seeking universally optimal policies, we consider initial-decision-optimal ones. Instead of planning all of the actions beforehand, these policies can be used to plan given the currently observed data. When the next decision is required, the process can be repeated in the same manner, leading to an optimal decision-making strategy. Our approach uses the occupancy-value duality to rule out suboptimal actions based on so-called truncations: finite-time approximations of the infinite-horizon decision-making problem.
We extend the truncation approach to a more general setting of decision-making problems with countably-infinite state spaces. Instead of time-based truncations, we consider state-based ones. This allows us to limit the amount of data required to make the decisions and to design an algorithm for a class of problems that are otherwise unsolvable to optimality. This approach belongs to a family of methods called policy iteration: starting from an initial policy, it constructs a series of improvements in the decisions while ruling out choices that are provably suboptimal.
After that, we turn to reinforcement learning. For a long time, the only provably efficient reinforcement-learning methods were model-based ones; recently, a family of model-free optimistic methods emerged, each of them accompanied by an analysis of how sample-efficient the method is. We, too, study optimistic reinforcement learning, but in contrast to the existing research, we seek to understand not how efficient it is, but why it is efficient. Our analysis results in a formula that explains the three factors that cause regret—the efficiency loss—in optimistic reinforcement learning: the problem size, the measure of exploration, and the estimation error caused by the mismatch between the realized transitions and their true distribution. It can be applied to all of the existing algorithms as well as new ones. We design one such new algorithm and show how our theoretical framework can facilitate the proof of its efficiency.
Finally, we consider a high-impact real-world sequential decision-making problem known as active wake control. Wind turbines can negatively impact each other with their wakes. These wake-induced losses can be reduced by changing the turbine orientations. Unfortunately, the optimal control strategy is non-trivial. To address this, existing approaches use simplified wake models in combination with numerical optimization methods; instead we propose to use model-free reinforcement learning. As a first step towards this goal, we present a wind farm simulator that is suitable for reinforcement learning and better reflects the realities of wind farm operation than other existing tools. Using this simulator, we show that previous research used a suboptimal action representation in this problem; we identify two alternatives, both of which improve the learning efficiency. Additionally, we demonstrate that reinforcement learning is robust to errors in the observations, providing further evidence that it is a fitting approach to active wake control.
Our contributions advance the state of the art in the theory of sequential decision-making under uncertainty and its applications. These advances hint at unexplored connections between countably-infinite planning and optimistic learning, which may lead to even more efficient algorithms for sequential decision-making under uncertainty in the future. ...
We start with presenting the basic concepts from the theory of decision-making and discuss the two approaches to it: planning and reinforcement learning. We look at a few typical sequential decision-making problems of increasing difficulty. In particular, we present a game that involves grid navigation and the problems of warehouse management and wind farm operation. Next, we survey the state-of-the-art methods for solving such problems.
Based on this analysis, we identify the following research opportunities. In planning, models with non-stationary and countably-infinite data remain relatively untreated because they are equivalent to infinitely-dimensional optimization problems, which are notoriously difficult to solve even approximately. In reinforcement learning, optimistic approaches lead to computational efficiency, yet the theory of optimism remains undeveloped. Moreover, while reinforcement learning shines at playing games, such as chess, shōgi, Go, and StarCraft II, its practical applications remain few.
Next, we overview a mathematical framework of sequential decision-making under uncertainty known as the Markov decision process. We explain how the goal of the decision-maker can be expressed as an optimization problem and present two approaches to achieving this goal. The first—more common—approach assigns so-called values to different actions. The other approach uses so-called occupancies that tell how often the agent should choose the actions instead of evaluating how good these actions are. In fact, the two approaches are known to be dual to each other. While this duality is well studied in the finite case, the infinite case is less explored. To address this knowledge gap, we present a new dual formulation for countable problems, both finite and infinite.
Afterwards, we use the dual formulation to design a new planning algorithm for infinite-horizon problems with non-stationary data. These problems are essentially infinite-dimensional optimization problems and as such are impossible to solve exactly using the standard approaches. We show that they can be solved by changing what is defined as optimal behavior: instead of seeking universally optimal policies, we consider initial-decision-optimal ones. Instead of planning all of the actions beforehand, these policies can be used to plan given the currently observed data. When the next decision is required, the process can be repeated in the same manner, leading to an optimal decision-making strategy. Our approach uses the occupancy-value duality to rule out suboptimal actions based on so-called truncations: finite-time approximations of the infinite-horizon decision-making problem.
We extend the truncation approach to a more general setting of decision-making problems with countably-infinite state spaces. Instead of time-based truncations, we consider state-based ones. This allows us to limit the amount of data required to make the decisions and to design an algorithm for a class of problems that are otherwise unsolvable to optimality. This approach belongs to a family of methods called policy iteration: starting from an initial policy, it constructs a series of improvements in the decisions while ruling out choices that are provably suboptimal.
After that, we turn to reinforcement learning. For a long time, the only provably efficient reinforcement-learning methods were model-based ones; recently, a family of model-free optimistic methods emerged, each of them accompanied by an analysis of how sample-efficient the method is. We, too, study optimistic reinforcement learning, but in contrast to the existing research, we seek to understand not how efficient it is, but why it is efficient. Our analysis results in a formula that explains the three factors that cause regret—the efficiency loss—in optimistic reinforcement learning: the problem size, the measure of exploration, and the estimation error caused by the mismatch between the realized transitions and their true distribution. It can be applied to all of the existing algorithms as well as new ones. We design one such new algorithm and show how our theoretical framework can facilitate the proof of its efficiency.
Finally, we consider a high-impact real-world sequential decision-making problem known as active wake control. Wind turbines can negatively impact each other with their wakes. These wake-induced losses can be reduced by changing the turbine orientations. Unfortunately, the optimal control strategy is non-trivial. To address this, existing approaches use simplified wake models in combination with numerical optimization methods; instead we propose to use model-free reinforcement learning. As a first step towards this goal, we present a wind farm simulator that is suitable for reinforcement learning and better reflects the realities of wind farm operation than other existing tools. Using this simulator, we show that previous research used a suboptimal action representation in this problem; we identify two alternatives, both of which improve the learning efficiency. Additionally, we demonstrate that reinforcement learning is robust to errors in the observations, providing further evidence that it is a fitting approach to active wake control.
Our contributions advance the state of the art in the theory of sequential decision-making under uncertainty and its applications. These advances hint at unexplored connections between countably-infinite planning and optimistic learning, which may lead to even more efficient algorithms for sequential decision-making under uncertainty in the future. ...
Sequential decision-making under uncertainty is an important branch of artificial intelligence research with a plethora of real-life applications. In this thesis, we generalize two fundamental properties of the decision-making process. First, we show that the theory on planning methods for finite spaces can be extended to infinite but countable spaces. Second, we propose a unified model of reinforcement learning algorithms that employ the principle of optimism in the face of uncertainty. This model is used to explain why these methods are efficient. We use the developed theory to design novel algorithms. Depending on the user's needs, these algorithms can either automate the decision-making process completely, or provide advice in decision-support systems.
We start with presenting the basic concepts from the theory of decision-making and discuss the two approaches to it: planning and reinforcement learning. We look at a few typical sequential decision-making problems of increasing difficulty. In particular, we present a game that involves grid navigation and the problems of warehouse management and wind farm operation. Next, we survey the state-of-the-art methods for solving such problems.
Based on this analysis, we identify the following research opportunities. In planning, models with non-stationary and countably-infinite data remain relatively untreated because they are equivalent to infinitely-dimensional optimization problems, which are notoriously difficult to solve even approximately. In reinforcement learning, optimistic approaches lead to computational efficiency, yet the theory of optimism remains undeveloped. Moreover, while reinforcement learning shines at playing games, such as chess, shōgi, Go, and StarCraft II, its practical applications remain few.
Next, we overview a mathematical framework of sequential decision-making under uncertainty known as the Markov decision process. We explain how the goal of the decision-maker can be expressed as an optimization problem and present two approaches to achieving this goal. The first—more common—approach assigns so-called values to different actions. The other approach uses so-called occupancies that tell how often the agent should choose the actions instead of evaluating how good these actions are. In fact, the two approaches are known to be dual to each other. While this duality is well studied in the finite case, the infinite case is less explored. To address this knowledge gap, we present a new dual formulation for countable problems, both finite and infinite.
Afterwards, we use the dual formulation to design a new planning algorithm for infinite-horizon problems with non-stationary data. These problems are essentially infinite-dimensional optimization problems and as such are impossible to solve exactly using the standard approaches. We show that they can be solved by changing what is defined as optimal behavior: instead of seeking universally optimal policies, we consider initial-decision-optimal ones. Instead of planning all of the actions beforehand, these policies can be used to plan given the currently observed data. When the next decision is required, the process can be repeated in the same manner, leading to an optimal decision-making strategy. Our approach uses the occupancy-value duality to rule out suboptimal actions based on so-called truncations: finite-time approximations of the infinite-horizon decision-making problem.
We extend the truncation approach to a more general setting of decision-making problems with countably-infinite state spaces. Instead of time-based truncations, we consider state-based ones. This allows us to limit the amount of data required to make the decisions and to design an algorithm for a class of problems that are otherwise unsolvable to optimality. This approach belongs to a family of methods called policy iteration: starting from an initial policy, it constructs a series of improvements in the decisions while ruling out choices that are provably suboptimal.
After that, we turn to reinforcement learning. For a long time, the only provably efficient reinforcement-learning methods were model-based ones; recently, a family of model-free optimistic methods emerged, each of them accompanied by an analysis of how sample-efficient the method is. We, too, study optimistic reinforcement learning, but in contrast to the existing research, we seek to understand not how efficient it is, but why it is efficient. Our analysis results in a formula that explains the three factors that cause regret—the efficiency loss—in optimistic reinforcement learning: the problem size, the measure of exploration, and the estimation error caused by the mismatch between the realized transitions and their true distribution. It can be applied to all of the existing algorithms as well as new ones. We design one such new algorithm and show how our theoretical framework can facilitate the proof of its efficiency.
Finally, we consider a high-impact real-world sequential decision-making problem known as active wake control. Wind turbines can negatively impact each other with their wakes. These wake-induced losses can be reduced by changing the turbine orientations. Unfortunately, the optimal control strategy is non-trivial. To address this, existing approaches use simplified wake models in combination with numerical optimization methods; instead we propose to use model-free reinforcement learning. As a first step towards this goal, we present a wind farm simulator that is suitable for reinforcement learning and better reflects the realities of wind farm operation than other existing tools. Using this simulator, we show that previous research used a suboptimal action representation in this problem; we identify two alternatives, both of which improve the learning efficiency. Additionally, we demonstrate that reinforcement learning is robust to errors in the observations, providing further evidence that it is a fitting approach to active wake control.
Our contributions advance the state of the art in the theory of sequential decision-making under uncertainty and its applications. These advances hint at unexplored connections between countably-infinite planning and optimistic learning, which may lead to even more efficient algorithms for sequential decision-making under uncertainty in the future.
We start with presenting the basic concepts from the theory of decision-making and discuss the two approaches to it: planning and reinforcement learning. We look at a few typical sequential decision-making problems of increasing difficulty. In particular, we present a game that involves grid navigation and the problems of warehouse management and wind farm operation. Next, we survey the state-of-the-art methods for solving such problems.
Based on this analysis, we identify the following research opportunities. In planning, models with non-stationary and countably-infinite data remain relatively untreated because they are equivalent to infinitely-dimensional optimization problems, which are notoriously difficult to solve even approximately. In reinforcement learning, optimistic approaches lead to computational efficiency, yet the theory of optimism remains undeveloped. Moreover, while reinforcement learning shines at playing games, such as chess, shōgi, Go, and StarCraft II, its practical applications remain few.
Next, we overview a mathematical framework of sequential decision-making under uncertainty known as the Markov decision process. We explain how the goal of the decision-maker can be expressed as an optimization problem and present two approaches to achieving this goal. The first—more common—approach assigns so-called values to different actions. The other approach uses so-called occupancies that tell how often the agent should choose the actions instead of evaluating how good these actions are. In fact, the two approaches are known to be dual to each other. While this duality is well studied in the finite case, the infinite case is less explored. To address this knowledge gap, we present a new dual formulation for countable problems, both finite and infinite.
Afterwards, we use the dual formulation to design a new planning algorithm for infinite-horizon problems with non-stationary data. These problems are essentially infinite-dimensional optimization problems and as such are impossible to solve exactly using the standard approaches. We show that they can be solved by changing what is defined as optimal behavior: instead of seeking universally optimal policies, we consider initial-decision-optimal ones. Instead of planning all of the actions beforehand, these policies can be used to plan given the currently observed data. When the next decision is required, the process can be repeated in the same manner, leading to an optimal decision-making strategy. Our approach uses the occupancy-value duality to rule out suboptimal actions based on so-called truncations: finite-time approximations of the infinite-horizon decision-making problem.
We extend the truncation approach to a more general setting of decision-making problems with countably-infinite state spaces. Instead of time-based truncations, we consider state-based ones. This allows us to limit the amount of data required to make the decisions and to design an algorithm for a class of problems that are otherwise unsolvable to optimality. This approach belongs to a family of methods called policy iteration: starting from an initial policy, it constructs a series of improvements in the decisions while ruling out choices that are provably suboptimal.
After that, we turn to reinforcement learning. For a long time, the only provably efficient reinforcement-learning methods were model-based ones; recently, a family of model-free optimistic methods emerged, each of them accompanied by an analysis of how sample-efficient the method is. We, too, study optimistic reinforcement learning, but in contrast to the existing research, we seek to understand not how efficient it is, but why it is efficient. Our analysis results in a formula that explains the three factors that cause regret—the efficiency loss—in optimistic reinforcement learning: the problem size, the measure of exploration, and the estimation error caused by the mismatch between the realized transitions and their true distribution. It can be applied to all of the existing algorithms as well as new ones. We design one such new algorithm and show how our theoretical framework can facilitate the proof of its efficiency.
Finally, we consider a high-impact real-world sequential decision-making problem known as active wake control. Wind turbines can negatively impact each other with their wakes. These wake-induced losses can be reduced by changing the turbine orientations. Unfortunately, the optimal control strategy is non-trivial. To address this, existing approaches use simplified wake models in combination with numerical optimization methods; instead we propose to use model-free reinforcement learning. As a first step towards this goal, we present a wind farm simulator that is suitable for reinforcement learning and better reflects the realities of wind farm operation than other existing tools. Using this simulator, we show that previous research used a suboptimal action representation in this problem; we identify two alternatives, both of which improve the learning efficiency. Additionally, we demonstrate that reinforcement learning is robust to errors in the observations, providing further evidence that it is a fitting approach to active wake control.
Our contributions advance the state of the art in the theory of sequential decision-making under uncertainty and its applications. These advances hint at unexplored connections between countably-infinite planning and optimistic learning, which may lead to even more efficient algorithms for sequential decision-making under uncertainty in the future.
With increasing renewable energy and cross-sectoral electrification price volatility is increasing. Flexibility through demand-side management and electric storage has the potential for reducing price volatility. In this thesis, using duality theory the flexibility required for constraining price to a maximum limit is quantified.
Coordination Strategies for Reducing Price Volatility in Local Electricity Markets investigate three case studies varying with respect to type and degree of flexible resource aggregation for constraining price. Insights generated are relevant for regulators, aggregators, energy communities, and scholars focusing on the engineering and economics of local energy systems. ...
Coordination Strategies for Reducing Price Volatility in Local Electricity Markets investigate three case studies varying with respect to type and degree of flexible resource aggregation for constraining price. Insights generated are relevant for regulators, aggregators, energy communities, and scholars focusing on the engineering and economics of local energy systems. ...
With increasing renewable energy and cross-sectoral electrification price volatility is increasing. Flexibility through demand-side management and electric storage has the potential for reducing price volatility. In this thesis, using duality theory the flexibility required for constraining price to a maximum limit is quantified.
Coordination Strategies for Reducing Price Volatility in Local Electricity Markets investigate three case studies varying with respect to type and degree of flexible resource aggregation for constraining price. Insights generated are relevant for regulators, aggregators, energy communities, and scholars focusing on the engineering and economics of local energy systems.
Coordination Strategies for Reducing Price Volatility in Local Electricity Markets investigate three case studies varying with respect to type and degree of flexible resource aggregation for constraining price. Insights generated are relevant for regulators, aggregators, energy communities, and scholars focusing on the engineering and economics of local energy systems.
The energy transition requires significant investments in new power generation, storage, and transmission technology to achieve emission reduction targets while ensuring a stable supply of electricity. However, the increasingly complex, uncertain nature of the power system creates challenges for investors and requires advanced research and modeling. An exploratory analysis is preformed to determine if and how energy system optimization modeling can be used to explore the long-term economic feasibility of investments in the power sector in light of the energy transition. A modeling framework is developed utilizing energy system optimization modeling paired with the uncertainty analysis, modeling to generate alternatives, to explore and provide insights into the profitability of investments in the range of possible near-optimal power system configurations that meet government emission reduction targets. We apply the modeling framework in a case study of the Dutch power system, focusing on investments in the 2030 time frame. The case study is used as a proof of concept of the developed methodological. The case study finds that the developed modeling framework can provide insight into the range of near-optimal power system configurations that meet emission reduction targets and, through an economic analysis, can shed light on the economic feasibility of different technologies. In the particular case of the Netherlands, the case study finds a wide range of possible future near-optimal energy systems exist to meet emission reduction targets, but a lack of profitability of investments indicate policy mechanisms or alternative market arrangements are needed to ensure economic incentives exist for the necessary investments. Further research should include a parametric uncertainty analysis to provide a complete and comprehensive overview, including all types of uncertainty in the system and to identify the affects different types of uncertainty have on the profitability of investments.
...
The energy transition requires significant investments in new power generation, storage, and transmission technology to achieve emission reduction targets while ensuring a stable supply of electricity. However, the increasingly complex, uncertain nature of the power system creates challenges for investors and requires advanced research and modeling. An exploratory analysis is preformed to determine if and how energy system optimization modeling can be used to explore the long-term economic feasibility of investments in the power sector in light of the energy transition. A modeling framework is developed utilizing energy system optimization modeling paired with the uncertainty analysis, modeling to generate alternatives, to explore and provide insights into the profitability of investments in the range of possible near-optimal power system configurations that meet government emission reduction targets. We apply the modeling framework in a case study of the Dutch power system, focusing on investments in the 2030 time frame. The case study is used as a proof of concept of the developed methodological. The case study finds that the developed modeling framework can provide insight into the range of near-optimal power system configurations that meet emission reduction targets and, through an economic analysis, can shed light on the economic feasibility of different technologies. In the particular case of the Netherlands, the case study finds a wide range of possible future near-optimal energy systems exist to meet emission reduction targets, but a lack of profitability of investments indicate policy mechanisms or alternative market arrangements are needed to ensure economic incentives exist for the necessary investments. Further research should include a parametric uncertainty analysis to provide a complete and comprehensive overview, including all types of uncertainty in the system and to identify the affects different types of uncertainty have on the profitability of investments.
The goal of this thesis is to identify under which boundary conditions
there is a business opportunity for an innovative electric thermal energy storage, with regards to the future electricity and heat markets. To meet this target, a novel optimization model has been developed as the main tool for the analysis of the storage and its profitability under different situations. ...
there is a business opportunity for an innovative electric thermal energy storage, with regards to the future electricity and heat markets. To meet this target, a novel optimization model has been developed as the main tool for the analysis of the storage and its profitability under different situations. ...
The goal of this thesis is to identify under which boundary conditions
there is a business opportunity for an innovative electric thermal energy storage, with regards to the future electricity and heat markets. To meet this target, a novel optimization model has been developed as the main tool for the analysis of the storage and its profitability under different situations.
there is a business opportunity for an innovative electric thermal energy storage, with regards to the future electricity and heat markets. To meet this target, a novel optimization model has been developed as the main tool for the analysis of the storage and its profitability under different situations.
Increasing the Market Value of Wind Power Using Improved Stochastic Process Modeling and Optimization
A Case Study of a Belgian Wind Power Producer
Master thesis
(2019)
-
Gerrit Deen, Remco Verzijlbergh, Scott Cunningham, Stijn Van Langen, Taco Kuipers
Wind Power Producers (WPP) incur a negative result through mandatory participation on the balancing market. This study analyzes the performance of multiple improved offering strategies for a WPP offering both on the day-ahead market and the balancing market. It does so on revenue, as well as its impact on the grid and electricity market as a whole. It tests two different stochastic optimization models, one under the price-taker assumption, one under the price-maker assumption and one analytic model, which is a closed-form reformulation of the latter. It also introduces a framework for modeling the stochastic processes, which form the input to the stochastic optimization models. This framework contains an innovation in the form of an extended Gaussian Copula model to directly generate the entire scenario tree, which is tested against a conventionally reduced symmetric tree. It also introduces a framework for evaluating each step of the stochastic process modeling, with the aim of enabling structured improvement. The study shows that when taking the influence a WPP has on the imbalance price into account in the analysis of revenues, proper dependency modeling between the processes as well as endogenizing the impact a strategy has on the imbalance price in the stochastic optimization model are strict requirements for positive real-world performance. Furthermore, it shows that successful strategic offering may prove valuable for the grid and market as a whole.
...
Wind Power Producers (WPP) incur a negative result through mandatory participation on the balancing market. This study analyzes the performance of multiple improved offering strategies for a WPP offering both on the day-ahead market and the balancing market. It does so on revenue, as well as its impact on the grid and electricity market as a whole. It tests two different stochastic optimization models, one under the price-taker assumption, one under the price-maker assumption and one analytic model, which is a closed-form reformulation of the latter. It also introduces a framework for modeling the stochastic processes, which form the input to the stochastic optimization models. This framework contains an innovation in the form of an extended Gaussian Copula model to directly generate the entire scenario tree, which is tested against a conventionally reduced symmetric tree. It also introduces a framework for evaluating each step of the stochastic process modeling, with the aim of enabling structured improvement. The study shows that when taking the influence a WPP has on the imbalance price into account in the analysis of revenues, proper dependency modeling between the processes as well as endogenizing the impact a strategy has on the imbalance price in the stochastic optimization model are strict requirements for positive real-world performance. Furthermore, it shows that successful strategic offering may prove valuable for the grid and market as a whole.
Offshore wind energy is considered as a powerful form of renewable energy generation. It plays an important role in accelerating the world’s transition towards sustainable energy sources and reducing carbon emissions by fossil fuels. This study focuses on the advancement of service planning, related to this renewable energy source, by researching high resolution metocean modelling. The research aims to assess and advance the modelling performance of typical metocean parameters by using atmospheric large-eddy simulations coupled to a spectral wave model. The GPU-Resident Atmospheric Simulation Platform (GRASP) coupled to Simulating WAves Nearshore (SWAN) was used to simulate the atmospheric- and oceanic conditions in the Gemini wind farm, located in Dutch waters. Large-scale boundary- and initial conditions were provided by the fifth generation of ECMWF’s ReAnalysis (ERA5). Relevant metocean parameters were modelled using two different coupling configurations. The one-way coupled simulation concerns the forcing of SWAN by GRASP friction velocities, for an accurate representation of the one-way momentum exchange to the ocean surface. The two-way coupled simulation concerns the momentum exchange of the friction velocity and roughness length. To accurately represent the sea surface roughness, the parameterization of Taylor and Yelland (2001) was used in this study. Both coupled configurations were used to simulate the first two months of 2017, which were subsequently validated using the available observations.
This study revealed that both coupled simulations caused a reduced value for the roughness length in wind- and wave wake conditions. Furthermore, a spatially averaged reduction in the sea state is observed due to the wake effect, where the magnitude of this wave deficit follows the line of a typical wind turbine thrust curve. The effect is however small compared to a realistic significant wave height. Besides, the two-way coupled simulations provided higher average roughness lengths in comparison to the one-way coupled simulations. This resulted in higher friction velocities and drag coefficients for the two-way coupled simulations, which subsequently reduced the time- and slab averaged wind profiles.
Moreover, the modelling performance of SWAN improves when it is forced by GRASP friction velocities instead of ERA5 wind fields. In addition, the established two-way coupled simulation is proven to be an enhancement for the spectral wave model in comparison to the one-way coupled configuration. The performance of the atmospheric large-eddy simulation could also benefit from the two-way coupled configuration. However, it is sensitive to the implemented roughness length parameterization. ...
This study revealed that both coupled simulations caused a reduced value for the roughness length in wind- and wave wake conditions. Furthermore, a spatially averaged reduction in the sea state is observed due to the wake effect, where the magnitude of this wave deficit follows the line of a typical wind turbine thrust curve. The effect is however small compared to a realistic significant wave height. Besides, the two-way coupled simulations provided higher average roughness lengths in comparison to the one-way coupled simulations. This resulted in higher friction velocities and drag coefficients for the two-way coupled simulations, which subsequently reduced the time- and slab averaged wind profiles.
Moreover, the modelling performance of SWAN improves when it is forced by GRASP friction velocities instead of ERA5 wind fields. In addition, the established two-way coupled simulation is proven to be an enhancement for the spectral wave model in comparison to the one-way coupled configuration. The performance of the atmospheric large-eddy simulation could also benefit from the two-way coupled configuration. However, it is sensitive to the implemented roughness length parameterization. ...
Offshore wind energy is considered as a powerful form of renewable energy generation. It plays an important role in accelerating the world’s transition towards sustainable energy sources and reducing carbon emissions by fossil fuels. This study focuses on the advancement of service planning, related to this renewable energy source, by researching high resolution metocean modelling. The research aims to assess and advance the modelling performance of typical metocean parameters by using atmospheric large-eddy simulations coupled to a spectral wave model. The GPU-Resident Atmospheric Simulation Platform (GRASP) coupled to Simulating WAves Nearshore (SWAN) was used to simulate the atmospheric- and oceanic conditions in the Gemini wind farm, located in Dutch waters. Large-scale boundary- and initial conditions were provided by the fifth generation of ECMWF’s ReAnalysis (ERA5). Relevant metocean parameters were modelled using two different coupling configurations. The one-way coupled simulation concerns the forcing of SWAN by GRASP friction velocities, for an accurate representation of the one-way momentum exchange to the ocean surface. The two-way coupled simulation concerns the momentum exchange of the friction velocity and roughness length. To accurately represent the sea surface roughness, the parameterization of Taylor and Yelland (2001) was used in this study. Both coupled configurations were used to simulate the first two months of 2017, which were subsequently validated using the available observations.
This study revealed that both coupled simulations caused a reduced value for the roughness length in wind- and wave wake conditions. Furthermore, a spatially averaged reduction in the sea state is observed due to the wake effect, where the magnitude of this wave deficit follows the line of a typical wind turbine thrust curve. The effect is however small compared to a realistic significant wave height. Besides, the two-way coupled simulations provided higher average roughness lengths in comparison to the one-way coupled simulations. This resulted in higher friction velocities and drag coefficients for the two-way coupled simulations, which subsequently reduced the time- and slab averaged wind profiles.
Moreover, the modelling performance of SWAN improves when it is forced by GRASP friction velocities instead of ERA5 wind fields. In addition, the established two-way coupled simulation is proven to be an enhancement for the spectral wave model in comparison to the one-way coupled configuration. The performance of the atmospheric large-eddy simulation could also benefit from the two-way coupled configuration. However, it is sensitive to the implemented roughness length parameterization.
This study revealed that both coupled simulations caused a reduced value for the roughness length in wind- and wave wake conditions. Furthermore, a spatially averaged reduction in the sea state is observed due to the wake effect, where the magnitude of this wave deficit follows the line of a typical wind turbine thrust curve. The effect is however small compared to a realistic significant wave height. Besides, the two-way coupled simulations provided higher average roughness lengths in comparison to the one-way coupled simulations. This resulted in higher friction velocities and drag coefficients for the two-way coupled simulations, which subsequently reduced the time- and slab averaged wind profiles.
Moreover, the modelling performance of SWAN improves when it is forced by GRASP friction velocities instead of ERA5 wind fields. In addition, the established two-way coupled simulation is proven to be an enhancement for the spectral wave model in comparison to the one-way coupled configuration. The performance of the atmospheric large-eddy simulation could also benefit from the two-way coupled configuration. However, it is sensitive to the implemented roughness length parameterization.
Power To Paris
The Role of Carbon Capture and Storage in a Future European Electricity System that Abides by the COP21 Climate Agreement
To limit global warming to 2 degrees Celsius in 2100, the European power sector needs to transform. Renewable energy capacity is required to reach this ambition, together with transmission and storage capacity to maintain grid stability. Carbon capture and storage could potentially decrease the required renewable energy capacity, while simultaneously increasing grid flexibility. This research focuses on finding a cost-optimal composition of technologies, while abiding by the goals set in the Paris climate treaty. To investigate this objective, two optimisation models are compared: a linear programmed optimisation model with a high temporal and low technical resolution, and a unit commitment model with a low temporal but high technical resolution. Fixed costs and installed capacities are determined by the linear model. Subsequently, both models calculate the optimal generation mix. Three scenarios for 2050 were evaluated: a 'business as usual' reference scenario with maximum emission comparable to 2014 levels, a scenario with a maximum emission consistent with a 96% reduction in 2050 compared to 2014 and a scenario with that same target and the possibility to implement carbon capture and storage. The results show that the goals set by the Paris agreement increase system costs of the European power sector, but the increase is moderated by deployment of carbon capture and storage. Compared to the linear model, unit commitment increases variable costs, but this increase is modest, serving as confirmation that a linear modelling approach can be sufficient for answering a wide range of questions. To increase accuracy, one might integrate both models and provide a complete answer that integrates long time-spans and a wide variety of technical constraints.
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To limit global warming to 2 degrees Celsius in 2100, the European power sector needs to transform. Renewable energy capacity is required to reach this ambition, together with transmission and storage capacity to maintain grid stability. Carbon capture and storage could potentially decrease the required renewable energy capacity, while simultaneously increasing grid flexibility. This research focuses on finding a cost-optimal composition of technologies, while abiding by the goals set in the Paris climate treaty. To investigate this objective, two optimisation models are compared: a linear programmed optimisation model with a high temporal and low technical resolution, and a unit commitment model with a low temporal but high technical resolution. Fixed costs and installed capacities are determined by the linear model. Subsequently, both models calculate the optimal generation mix. Three scenarios for 2050 were evaluated: a 'business as usual' reference scenario with maximum emission comparable to 2014 levels, a scenario with a maximum emission consistent with a 96% reduction in 2050 compared to 2014 and a scenario with that same target and the possibility to implement carbon capture and storage. The results show that the goals set by the Paris agreement increase system costs of the European power sector, but the increase is moderated by deployment of carbon capture and storage. Compared to the linear model, unit commitment increases variable costs, but this increase is modest, serving as confirmation that a linear modelling approach can be sufficient for answering a wide range of questions. To increase accuracy, one might integrate both models and provide a complete answer that integrates long time-spans and a wide variety of technical constraints.