This article presents the theoretical and practical foundation of a spherical lower dimensional representation for daily medium voltage load profiles, based on principal component analysis. The objective is to unify and simplify the tasks for (i) clustering visualisation, (ii) outlier detection and (iii) generative profile modelling under one concept. The lower dimensional projection of standardised MV load profiles unveils a latent distribution in a three-dimensional sphere. This spherical structure allows us to detect outliers by fitting probability distribution models in the spherical coordinate system, identifying measurements that deviate from the spherical shape. The same latent distribution exhibits an arc shape, suggesting an underlying order among load profiles. We develop a principal curve technique to uncover this order based on similarity, offering new advantages over conventional clustering techniques. This finding reveals that energy consumption in a wide region can be seen as a continuously changing process. Furthermore, we combined the principal curve with a von Mises-Fisher distribution to create a model capable of generating profiles with continuous mixtures between clusters. The presence of the spherical distribution is validated with data from four municipalities in the Netherlands. The uncovered spherical structure implies the possibility of employing new mathematical tools from directional statistics and differential geometry for load profile modelling.

In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of Power flows (PFs) in distribution systems. The presented algorithms are the base for a new TensorPowerFlow (TPF) tool and shine for their simplicity, benefiting from multicore Central processing unit (CPU) and Graphics processing unit (GPU) parallelization. We also focus on the mathematical convergence properties of the algorithm, showing that its unique solution is at the practical operational point. The proof is validated using numerical simulations showing the robustness of the FPI algorithm compared to the classical Newton–Raphson (NR) approach. In the case study, a benchmark with different PF solution methods is performed, showing that for applications requiring a yearly simulation at 1-minute resolution, the computation time is decreased by a factor of 164, compared to the NR in its sparse formulation. Finally, a set of applications is described, highlighting the potential of the proposed formulations over a wide range of analyses in distribution systems.

This article proposes a framework to identify, visualize, and quantify risk of potential over/under voltage due to annual energy consumption and PV generation growth. The stochastic modeling considers the following: (i) Active and reactive power profiles for distribution transformers, dependent on annual energy consumption and activity in the serviced areas. (ii) Variable solar irradiance profiles that allow a broader range of PV generation scenarios for sunny, overcast, and cloudy days. The proposed framework uses multivariate-t copulas to model temporal correlations between random variables to generate synthetic scenarios. A probabilistic power flow is computed using the generated scenarios to define critical static operating regions. Results show that classical approaches may underestimate the maximum PV capacity of distribution networks when local irradiance conditions are not considered. Moreover, it is found that including annual energy consumption growth is critical to establishing realistic PV installation capacity limits. Finally, a sensitivity analysis shows that taking a 5% of overvoltage risk could increase up to 15% of the PV installed capacity limits.

The development of thorough probability models for highly volatile load profiles based on smart meter data is crucial to obtain accurate results when developing grid planning and operational frameworks. This paper proposes a new top-down modeling approach for residential load profiles (RLPs) based on multivariate elliptical copulas that can capture the complex correlation between time steps. This model can be used to generate individual and aggregated daily RLPs to simulate the operation of medium and low voltage distribution networks in flexible time horizons. Additionally, the proposed model can simulate RLPs conditioned to an annual energy consumption and daily weather profiles such as solar irradiance and temperature. The simulated daily profiles accurately capture the seasonal, weekends, and weekdays power consumption trends. Five databases with actual smart meter measurements at different time resolutions have been used for the model's validation. Results show that the proposed model can successfully replicate statistical properties such as autocorrelation of the time series, and load consumption probability densities for different seasons. The proposed model outperforms other multivariate state-of-the-art methods, such as Gaussian Mixture Models, by one order of magnitude in two different distance metrics for probability distributions.

This paper introduces an adaptive sequential droop control strategy for PV inverters to mitigate voltage rise problems in PV-rich LV distribution networks. To facilitate the effective coordination of sequential (Q−V and P−V) droop control of PV inverters, multiple control areas with the strong coupling nature of PV systems are identified based on the ε-decomposition technique. The droop control parameters are tuned and adapted, based on a consensus among PV inverters within each control area. This proposed control strategy inherits the autonomous feature of the droop control for coping with voltage rise issues while being able to avoid curtailing a significant amount of PV production. To evaluate the effectiveness of the proposed control strategy, simulations using MATLAB/Simulink are performed on a real European LV distribution network, considering a PV penetration level of about 150%. The obtained results highlight that the proposed control strategy successfully mitigates voltage rise problems while significantly reducing the amount of curtailed PV generation by approximately 35.6% and 76.2% when compared with the static sequential droop control and the static Q−V droop control and adaptive P−V droop control, respectively. Simultaneously, the effective contribution among all the PV systems towards voltage rise mitigation is obtained.

Linear optimal power flow (OPF) formulations are powerful tools applied to a large number of problems in power systems, e.g., economic dispatch, expansion planning, state estimation, congestion management, electricity markets, among others. This article proposes a novel mixed-integer linear programming formulation for the ac-OPF of three-phase unbalanced distribution networks. The model aims to minimize the total energy production cost while guaranteeing the network's voltage and current magnitude operational limits. New approximations of the Euclidean norm, which is present in the calculation of nodal voltage and branch current magnitudes, are introduced by applying a linear transformation of weighted norms and a set of intersecting planes. The accuracy, optimality, feasibility, and scalability of the proposed linearizations are compared with common linear approximations in the literature using two unbalanced distribution test systems. The obtained results show that the proposed formulation is computationally more efficient (almost twice) while being as accurate and more conservative than the benchmarked approaches with maximum errors lower than 0.1%. Thus, its potential application in a variety of distribution systems operation and planning optimization problems is endorsed.

The rapid increase in the number of PV installations in current low voltage (LV) distribution networks brings many technical operational challenges. This claims for the deployment of control strategies to deal with these concerns, especially those related to overvoltage issues. Based on this, this paper presents a comprehensive assessment of the performance of PV inverters operating with droop control for overvoltage mitigation using a stochastic methodology based on a Monte Carlo approach. The uncertainty related to the PV generation and the users’ consumption behavior is fully considered through advanced statistical modeling techniques. Voltage magnitude and loading indexes are used as key metrics to assess the technical performance of the distribution network, simulated using OpenDSS, under two droop-based control strategies: Active Power Control (APC) and coordinated Reactive and Active Power Control (RPC-APC). The effects of curtailed energy on the PV users’ revenue is also analyzed. A case of study based on real smart meter data from The Netherlands is used. According to the obtained results, both control strategies are effective to mitigate voltage violations. Nevertheless, for the case of 100% PV penetration, the droop-based coordinated RPC-APC allowed an 18% more of exported energy than the droop-based APC control strategy.

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes, while the bus voltage magnitude approximation uses a linear combination of the L1 and the L norm. The proposed approach is compared to a nonlinear power flow for an unbalanced distribution system with fixed power injections. The obtained results showed errors of less than 4% for currents and 0.005% for voltages, demonstrating that satisfactory accuracy may be obtained using the proposed linearizations.

The proliferation of PV generation systems connected to electrical distribution systems (EDSs) brings many operational challenges, and within them, over-voltage issues are regarded as the most critical. Among all the strategies available to handle these over-voltage issues, those implemented locally at the PV inverters seem to be the more promising, considering their distributed and easy-to-implement features. In this paper, the feasibility and performance assessment of a commercial PV inverter for mitigating over-voltage events in an EDS is presented. To do this, an active and reactive droop-based voltage control strategy is implemented in a commercial inverter. Realtime power hardware-in-the-loop (PHIL) laboratory tests were performed to assess the PV inverter's efficiency when absorbing reactive power, as well as its interaction with the distribution grid. According to the obtained results, the PV inverter's efficiency was not noticeably affected by the changes in reactive power. Additionally, the PV inverter responded accordingly, following the voltage control strategy implemented, providing successfully the expected voltage support services.