In integrated power and gas energy system optimization models (ESOMs), pipeline gas transmission with linepack is a particularly complex problem due to its non-linear and non-convex character. For ESOMs based on mixed-integer linear programming, piecewise linearization is a well-established convexification approach for this problem, which, however, requires binary variables to model feasible combinations of linear gas flow and pressure segments and thus can quickly become computationally challenging. In order to improve computational performance, this paper proposes a piecewise linearization method specifically designed to be tight, resulting in a reduced problem space a solver can explore faster. We provide numerical results comparing the proposed formulation against two piecewise linearizations from the literature, both from a theoretical point of view and in terms of practical computational performance, with results showing an average speed-up of 2.57 times for our case study. Test cases are carried out on a modified 24-bus IEEE Reliability Test System and a 12-node gas system, considering discrete unit commitment decisions.

In order to achieve a timely transition towards sustainable energy systems within a large landscape of multi-sectors and multi-technologies, decision-makers and industry practitioners can rely on time- and space-discretized energy system optimization models. However, such models are often burdened by the computational costs arising from the growing problem complexity, which is especially due to the time discretization. The common strategy to lower the computational cost is to uniformly reduce the temporal resolution, sacrificing the quality of the solution. In light of this, we propose the concept and a formulation of fully flexible temporal resolution, wherein each decision variable and constraint can have a separate temporal resolution. After introducing the formulation in detail, we demonstrate its capability by applying it to an EU-wide case study optimizing both capacity investment and operation decisions of the inter-connected energy system across the different countries. We show that the proposed flexible formulation allows us to flexibly remove variables and constraints that are not needed without losing accuracy, and to simplify the time discretization (e.g., in space) while pushing the Pareto front by simultaneously speeding up computation and limiting losses in accuracy. In conclusion, we highlight the promise of adopting fully flexible temporal resolution and encourage future research to explore further temporal resolution configurations beyond our examples.

Nowadays, most modern power systems are evolving towards a considerable capacity expansion in their energy storage and interconnection facilities. However, these great developments are not being accomplished fast enough to accommodate the high penetration of variable renewable energy sources. This situation raises demand variability, requiring more flexibility from thermal generators, especially due to their more frequent start-up and shut-down processes. Consequently, the unit commitment requires more accurate and detailed modeling while maintaining computational efficiency. This paper analyzes some of the best models to manage long-duration start-up costs according to the real fuel-consumption curves of a gas-fired generation portfolio. Moreover, we propose a tight and compact MILP piecewise formulation that enhances the resolution of start-up representations and achieves outstanding results compared to the literature benchmarks. The successful performance of this methodology is proven in several large-size case studies focusing on the medium term. Furthermore, conventional day-ahead problems are also run to demonstrate the overall competitiveness of the formulation.

To achieve climate goals by 2050, accurate energy system optimization (MIP) models are needed to help decision-makers make investment plans. To increase accuracy, a high resolution in the temporal and spatial dimensions is needed, as well as many details on the operational capabilities of energy generators. However, this results in large-scale models that do not scale well. Thus, researchers often seek the right trade-off between computational tractability and accuracy. Here, we present a tighter formulation for optimal storage operation and investment problems, including reserves, along with the methodology we used to obtain it, based on the work of [2]. Additionally, we present some preliminary work aiming to provide tight and compact unit commitment models with different levels of detail. These models can be included in large-scale energy system optimization models to increase model accuracy while keeping the models computationally tractable.

As energy sectors become increasingly interconnected, selecting appropriate representations of physical characteristics in energy system optimization models has become challenging. This study evaluates the necessity of transmission and generator models by systematically excluding each one and assessing the impact on objective values, solution time, and feasibility of the resulting system design. We apply this analysis to two contrasting case studies optimizing the design and operation of: the IEEE 118-bus test power system and a zero-emission multi-energy system of the Netherlands. Results show that modeling Kirchhoff's Voltage Law (KVL) and alternating-current (AC) transmission losses is essential for accuracy and feasibility. KVL prevents unrealistic network loops; hence improving network utilization. Additionally, we evaluate two linearization methods for the AC transmission losses. Our findings indicate that tangent-based linear approximations often lead to infeasibility with three or fewer segments, whereas a piecewise-linear approach with at least two segments ensures accurate and computationally efficient solutions.

Energy system models are essential for planning and supporting the energy transition. However, increasing temporal, spatial, and sectoral resolutions have led to large-scale linear programming (LP) models that are often (over)simplified to remain computationally tractable—frequently at the expense of model fidelity. This paper challenges the common belief that LP formulations cannot be improved without sacrificing their accuracy. Inspired by graph theory, we propose to model energy systems using energy assets (vertices), as a single building-block, and flows to connect between them. This reduces the need for additional components such as nodes and connections. The resulting formulation is more compact, without sacrificing accuracy, and leverages the inherent graph structure of energy systems. To evaluate performance, we implemented and compared four common modelling approaches varying in their use of building blocks and flow representations. We conducted experiments using TulipaEnergyModel.jl and applied them to a multi-sector case study with varying problem sizes. Results show that our single-building-block (1BB-1F) approach reduces variables and constraints by 26% and 35%, respectively, and achieves a 1.27x average speedup in solving time without any loss in model fidelity. The speedup increases with problem size, making this approach particularly advantageous for large-scale models. Our findings demonstrate that not all LPs are equal in quality and that better reformulations can lead to substantial computational benefits. This paper also aims to raise awareness of model quality considerations in energy system optimisation and promote more efficient formulations without compromising fidelity.

Energy storage, transmission, and sector coupling are some prominent flexibility solutions to support variable renewable energy (VRE) integration. However, investment cost uncertainties and public acceptance could hamper the deployment of these flexibility solutions. This raises questions about the development and cost-effectiveness of future energy systems, especially on how the dependence on local and cross-border solutions of flexibility would evolve if the uptake of these solutions is restricted. In this context, this paper identifies the synergies among flexibility options under restrictions on transmission expansion or increased costs of energy storage. It contributes to determining whether investments in energy storage and/or transmission expansion offer the least-cost transition and investigates the impact of sector coupling on these solutions. A long-term energy system planning and optimisation model towards 2050 is developed using the open-source energy system optimisation tool Balmorel, and a case study of the countries surrounding the Baltic Sea and the North Sea is established. Five cases with restrictions imposed on transmission expansion and higher energy storage technology costs are analysed at different levels of sector coupling. The results highlight the importance of transmission expansion at all levels of sector coupling. As the level of sector coupling increases, uncertainties around the cost of energy storage drive the least-cost pathways. Optimal investment solutions are found to have a mix of transmission and energy storage in capacity expansion at all levels of sector coupling.

This paper introduces the TulipaProfileFitting.jl package, a tool developed in Julia to generate renewable energy profiles that fit a given capacity factor of full load hours. It addresses the limitations of naive methods in adjusting existing profiles to match improved technology efficiency, particularly in scenarios lacking detailed weather data or technology specifications. By formulating the problem mathematically, the package provides a computationally efficient solution for creating realistic renewable energy profiles based on existing data. It ensures that the adjusted profiles realistically reflect the improvements in technology efficiency, making it an essential tool for energy modelers in analyzing future energy systems.

In this paper, we aim to analyse the impact of hydrogen production decarbonisation and electrification scenarios on the infrastructure development, generation mix, CO₂ emissions, and system costs of the European power system, considering the retrofit of the natural gas infrastructure. We define a reference scenario for the European power system in 2050 and use scenario variants to obtain additional insights by breaking down the effects of different assumptions. The scenarios were analysed using the European electricity market model COMPETES, including a proposed formulation to consider retrofitting existing natural gas networks to transport hydrogen instead of methane. According to the results, 60% of the EU's hydrogen demand is electrified, and approximately 30% of the total electricity demand will be to cover that hydrogen demand. The primary source of this electricity would be non-polluting technologies. Moreover, hydrogen flexibility significantly increases variable renewable energy investment and production, and reduces CO₂ emissions. In contrast, relying on only electricity transmission increases costs and CO₂ emissions, emphasising the importance of investing in an H₂ network through retrofitting or new pipelines. In conclusion, this paper shows that electrifying hydrogen is necessary and cost-effective to achieve the EU's objective of reducing long-term emissions.

The integration of Distributed Energy Resources (DERs) in distribution networks comes with challenges, like power quality concerns, but also opens up new opportunities, e.g., DERs can offer competitive energy prices for final users by leveraging time arbitrage. A suitable method to fully exploit such opportunities is to compute the optimal DER schedule, either with a full three-phase network model or a more computationally efficient single-line equivalent. This paper presents under which conditions a single-line equivalent can and cannot be used to properly represent a modern and unbalanced power distribution network able to dispatch high levels of DER integration optimally. Results show that single-line equivalents might be helpful when the problem objective function limits counterflows, for example, when minimizing active power losses. Moreover, single-line equivalents might be helpful for low levels of DER integration. However, enabling single-line equivalents results in a lower hosting capacity for high levels of DER integration.

The increase of solar photovoltaic penetration poses several challenges for distribution network operation, mainly because such high penetration might cause reliability problems like protection malfunctioning, accelerated decay of voltage regulators and voltage violations. Existing solutions based on mathematical programming solve a 3-phase ACOPF to optimally exploit the available energy, however, this might increase all reliability problems above if done carelessly. As a solution to optimally exploit DERs (like local photovoltaic and storage systems) without compromising the network reliability, this paper presents a novel algorithm to solve the 3-phase ACOPF as a sequence of convex Quadratically Constrained Quadratic Programs. Results show that this solution has a lower voltage unbalance and computation time than its non-linear counterpart, furthermore, it converges to a primal feasible point for the non-linear formulation without major sacrifices on optimal DER active power injections.

Day-ahead electricity markets are inefficient due to their coarse discretisation of time and their representation of electricity production and consumption in energy per time interval. This leads to excessive costs and infeasible schedules in the market clearing results. Some real-world systems have increased the resolution to improve accuracy, but this comes at a high computational cost. We propose an alternative, based on using linear power trajectories in the day-ahead scheduling process, which represent the momentary electricity production. Changing from a traditional energy-based to such a power-based formulation of the scheduling method can reduce cost by several percentage points, leading to a cost reduction of millions of euros in real-world systems on a yearly basis. Attempting to do so by increasing the resolution of the schedule would be accompanied by large increases in computational demands. Furthermore, we provide market design options to implement power-based bidding and pricing in day-ahead electricity markets, showing that pricing and market rules which encompass existing markets are readily available for implementation, and illustrate these with examples.

The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the unit commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that restrict their application to real-world systems. This paper demonstrates that, by considering dispatchable wind and a box uncertainty set for wind availability, a fully adaptive two-stage robust UC formulation, which is typically a bi-level problem with outer mixed-integer program (MIP) and inner bilinear program, can be translated into an equivalent single-level MIP. Experiments on the IEEE 118-bus test system show that computation time, wind curtailment, and operational costs can be significantly reduced in the proposed unified stochastic–robust approach compared to both pure stochastic approach and pure robust approach, including budget of uncertainty.

In [1], the name of one co-author, Germán Morales-Espana, was rendered incorrectly as Germán Morales-Espana Mouli. The correct byline is shown above. We sincerely regret the error.

This paper presents the design of an energy management system (EMS) capable of forecasting photovoltaic (PV) power production and optimizing power flows between PV system, grid, and battery electric vehicles (BEVs) at the workplace. The aim is to minimize charging cost while reducing energy demand from the grid by increasing PV self-consumption and consequently increasing sustainability of the BEV fleet. The developed EMS consists of two components: An autoregressive integrated moving average model to predict PV power production and a mixed-integer linear programming framework that optimally allocates power to minimize charging cost. The results show that the developed EMS is able to reduce charging cost significantly, while increasing PV self-consumption and reducing energy consumption from the grid. Furthermore, during a case study analogous to one repeatedly considered in the literature, i.e., dynamic purchase tariff and dynamic feed-in tariff, the EMS reduces charging cost by 118.44 % and 427.45% in case of one and two charging points, respectively, when compared to an uncontrolled charging policy.

The emergence of distributed energy resources can lead to congestion in distribution grids. DC distribution grids are becoming more relevant as more sources and loads connected to the low voltage grid use dc. Bipolar dc distribution grids with asymmetric loading can experience partial congestion resulting in a nodal price difference between the two polarities if a respective market model is applied. In order to take into account this price difference, this paper presents an optimal power flow (OPF) model formulated in terms of voltage and current. In the case of bipolar dc distribution grids, the single line approximation is no longer valid because current can flow in the neutral conductors as well. Moreover, loads and sources can be connected between any two nodes in the network. The proposed exact OPF formulation includes bilinear equations. The locational marginal prices (LMP) are derived by linearizing the problem at the optimal solution. Example cases show the various phenomena that can appear under asymmetric loading, such as pole-to-pole connections combined with pole-to-neutral connections, parallel sources, meshed grids and their effect on the LMP.

In power systems, demand and supply always have to be balanced. This is becoming more challenging due to the sustained penetration of renewable energy sources. Because of the increasing amount of electrical vehicles (EVs), and the high capacity and flexibility of their charging process, EVs are a good candidate for providing balancing services to electric systems. We propose a stochastic optimization method for an EV aggregator that models the uncertainty of the imbalance price, the reserve prices and the probability of acceptance and deployment of reserves. The model results in an optimal charging and discharging strategy considering day-ahead purchase, imbalance trading and reserve bids. Unlike previous studies, the reserve bids consists of both a quantity and an optimal price. Experimental evaluation shows that the proposed stochastic optimization method results in lower costs than deterministic and quantity-only bid solutions.

Approximations made in day-ahead markets can result in suboptimal or even infeasible schedules for generating units and inaccurate predictions of actual costs and wind curtailment. Here we compare different optimal models of day-ahead markets based on unit commitment (UC) formulations, especially energy- vs. power-based UC; excluding or including startup and shutdown trajectories; and deterministic vs. “ideal” stochastic models to face wind uncertainty. The day-ahead hourly schedules are then evaluated against actual wind and load profiles using a (5-min) real-time dispatch model. We find that each simplification usually causes expected generation costs to increase by several percentage points, and results in significant understatement of expected wind curtailment and, in some cases, load interruptions

Approximations made in traditional day-ahead unit commitment model formulations can result in suboptimal or even infeasible schedules for slow-start units and inaccurate predictions of actual costs and wind curtailment. With increasing wind penetration, these errors will become economically more significant. Here, we consider inaccuracies from three approximations: the use of hourly intervals in which energy production from each generator is modeled as being constant; the disregarding of startup and shutdown energy trajectories; and optimization based on expected wind profiles. The results of unit commitment formulations with those assumptions are compared to models that: (1) use a piecewise-linear power profiles of generation, load and wind, instead of the traditional stepwise energy profiles; (2) consider startup/shutdown trajectories; and (3) include many possible wind trajectories in a stochastic framework. The day-ahead hourly schedules of slow-start generators are then evaluated against actual wind and load profiles using a model real-time dispatch and quick-start unit commitment with a 5 minute time step. We find that each simplification usually causes expected generation costs to increase by several percentage points, and results in significant understatement of expected wind curtailment and, in some cases, load interruptions. The inclusion of startup and shutdown trajectories often yielded the largest improvements in schedule performance.