Isolated power systems, even in renewable-rich areas, remain heavily dependent on imported fossil fuels. Regulatory reforms largely target national interconnected grids, leaving these systems overlooked, and few regulatory frameworks extend beyond techno-economic analysis. This paper introduces a novel and comprehensive methodological framework to update the regulation of isolated power systems and enable their energy transition. It delivers a step-by-step, interdisciplinary, multi-actor process for diagnosing regulatory and market barriers, designing reforms, and producing legislation-ready recommendations. The framework comprises five main stages: (1) Principles definition and team formation, (2) Interdisciplinary and multi-actor diagnosis, (3) Interdisciplinary analysis and proposals development, (4) Synthesis and verification, and (5) Final proposal. Its objectives aim to accelerate the adoption of renewable and emerging technologies, reduce investor uncertainty, and involve local participation. We demonstrate the framework's application by analyzing Chile's isolated power systems and aligning regulatory proposals with local needs, regional and national energy-environmental goals. Resulting reform proposals include: expansion of regulatory principles; a new taxonomy for classifying power systems, plus a transition pathway between categories; an auction-based co-planning process; a revised tariff structure; and mechanisms for early citizen participation and transparency. Beyond offering Chilean policymakers concrete regulatory reforms for isolated power systems and their energy transition, the framework is readily adaptable to other countries facing similar challenges.

This paper studies the feasible region of the ramping operations of a generator in a virtual power plant (VPP) environment, through a network–flow (NF) based formulation. The network structure embeds many of the technical characteristics of the power unit into a tight and compact formulation. However, power limits across consecutive periods, i.e., ramp–up/down operations, are included as side constraints into the problem, affecting the convex–hull of the network. To improve the NF formulation with ramping constraints, we introduce a set of valid inequalities that tighten the overall feasible region of the generators represented via network. Computational experiments were carried out within a VPP environment to compare the proposed formulation with other unit commitment (UC) formulations, showing that the proposed inequalities effectively tighten the feasible region. The experiments were conducted using different combinations of sets of five generating units in a self– UC context over different time spans. We solved the problems with different state–of–the–art mixed integer linear programming (MILP) solvers to demonstrate the performance of the proposed inequalities in different contexts. Results indicate reductions of approximately 90% in the best cases and 75% in the worst cases in the integrality gap compared to the other formulations.

This article presents an electrothermal model of modular photovoltaic (PV) panels with protective bypass diodes (BD) capable of receiving unique irradiance inputs to accurately represent partial shading (PS) of building-integrated PV (BIPV) systems. The electrical modeling of the electrothermal model uses an eleven-parameter functional form (11PFF) of the single diode model (SDM) and incorporates an electrical representation of the BDs. The thermal modeling of the electrothermal model determines PV panel and BD junction box temperatures from measurable environmental variables, which directly influence the model's electrical behavior. A parameter identification method for the electrothermal model, based on experimental current-voltage curves, is developed: it is validated with experimental data from Valparaiso, Chile, achieving an out-of-sample mean absolute percentage error of 6.26% in power prediction. The calibrated electrothermal model is built in an electromagnetic transient program to benchmark its computational efficiency against a competitive model and it is also implemented in a Python-SketchUp framework to estimate BIPV energy production based on the dynamic BIPV system shading and the environmental data. A case study in Perugia, Italy, shows that the simulation framework, which integrates the validated electrothermal model with CAD-based PS analysis and environmental condition data, yields more realistic energy estimates than a similar framework using a competitive electrothermal model, (deviations of up to 13.21% ) and no significant increase in computational burden.

This paper addresses the uncapacitated joint location-inventory problem (JLIP) to design an optimal distribution network for fast-moving consumer goods where distribution centers (DCs), operating under a continuous review inventory policy, observe uncertain demand from a set of retailers, and shortages are penalized by a cost per unit and time unit. The JLIP is considered intractable, depriving a relevant network design approach when large retail chains charge a fee or issue invoice deductions for backorders. Considering the exact formulation of the inventory on-hand and backorders at each DC, and using conic programming, we show how to reformulate the JLIP with shortage costs as a convex mixed integer nonlinear problem with second-order cone constraints. Using convexity-preserving operations, we develop an extended cutting plane algorithm that takes advantage of a predefined set of linear functions representing the outer linear approximation of the backorders. The computational results highlight the efficiency of the approach in solving small-, medium-, and large-scale instances to optimality compared to the state-of-the-art algorithms available in commercial and open-source solvers.

In light of the ongoing decline in photovoltaic (PV) generation costs and its growing competitiveness with retail electricity prices, accurately predicting PV performance is increasingly important. While manufacturers have typically rated PV modules at standard test conditions (STCs), their ratings are now being enhanced by reporting module data at low irradiance conditions (LICs) and nominal operating cell temperature (NOCT). Recently, an enhanced PV model was proposed Angulo et al., 2024, capable of reproducing the behavior of a PV module across a wide range of atmospheric conditions. Although the superiority of this model is thoroughly discussed in Angulo et al., 2024, the identification of its characterizing parameters from ratings provided by manufacturers is not addressed. This paper proposes a parameter identification methodology relying on STC, LIC, and NOCT ratings. The problem at hand involves solving a complex system of eleven nonlinear equations, and is approached by progressively reducing the search space and generating adjustment functions. The methodology is tested in an automated fashion over the entire California Energy Commission PV database, which currently contains 17 710 modules, achieving a convergence rate of 99.8%. The quality of the identified model is assessed by comparing energy predictions against experimental measurements, including state-of-the-art models available in the literature. Results indicate that the identified model reduces prediction errors by about 9% compared to the best competitive model.

An accurate prediction of the performance of photovoltaic (PV) power generation systems is becoming increasingly important as this technology continues to penetrate the market. The performance of a PV system depends on a number of factors, including the type of solar PV technology employed, solar irradiance, module temperature, wind speed, ambient temperature, and other outdoor environmental conditions. Manufacturers have traditionally provided PV module ratings at standard test conditions, but they are now offering extended ratings, including operation at low irradiance conditions and nominal operating cell temperature, allowing for the development of more refined models. Recently, an 11-parameter model capable of reproducing the performance of a PV module across a wide range of atmospheric conditions was proposed by some of the authors [1], [2]. While the proposed model outperforms all existing models, it was also shown in [2] that it exhibits slightly larger errors in the case of PV thin-film technologies. A related publication proposed improvements in PV thin-film technology performance prediction by modeling the shunt admittance in the electrical circuit as a power function of the voltage, characterized by a γ exponent [3]. Taking advantage of this improvement, we propose to incorporate such a modification into the 11-parameter model and, via a trial-and-error approach, determine its optimal value. Results indicate that, by incorporating this enhancement, the error for maximum power point prediction for a wide range of atmospheric conditions is reduced by up to 7% compared to the results presented in [2].

This article addresses the main performance issues of multistep-finite-control-set model predictive control (MFCS-MPC) that make it impractical in medium-voltage high-power grid-connected converters. Current MFCS-MPC techniques synthesize nonperiodic steady-state voltages that produce harmonic-rich continuous and unpredictable Fourier spectra with variable switching frequency. This article leverages advances in optimized pulse patterns and MFCS-MPC to meet grid codes while operating at a low, fixed switching frequency and rendering a fast dynamic response. To keep the strategy viable in real time, enhancements to the sphere decoder algorithm that solves the optimization problem were made, and the computationally efficient Frank-Wolfe algorithm was used to find a new center for the sphere during transients. The control scheme is assessed through simulation and hardware-in-the-loop experiments, demonstrating its real-time viability.

This work presents a Convex Hull Pricing framework based on a network-flow formulation of the Unit Commitment problem, incorporating generation ramp constraints directly in the model. The inclusion of ramp constraints directly impacts the feasible solution polyhedron, which no longer exhibits total unimodularity (TU). As a consequence, subproblems can no longer be solved using shortest-path algorithms for network flow problems. Instead, MIP solvers must be used which, due to their preprocessing capabilities, significantly reduce the number of variables and constraints, thereby improving computational efficiency. The solution approach relaxes the system power balance constraint and applies a primal-dual Bienstock-Zuckerberg (BZ) algorithm. Through an iterative process, the method generates partitions of the arc variables associated with generating units, effectively approximating the feasible solution space and enhancing computational performance over successive iterations. Computational experiments on instances from the California and FERC systems (without transmission network). The proposed method is benchmarked against two state-of-the-art approaches: the Dantzig-Wolfe (DW) decomposition and the Level Method (LM). The results show that the BZ algorithm outperforms the DW and LM approaches, reducing the average computational times by 40 % and 18 % for the CA system compared to LM and DW, respectively. For the FERC system, the reductions are 17 % (LM) and 9% (DW). In addition, the proposed approach exhibits a lower standard deviation across the simulated instances, which indicates more robust performance. Moreover, with a 0.5 % gap, BZ achieved the lowest normalized uplift on both instances (California and FERC), outperforming LM and DW, which indicates that, given the prescribed gap, the proposed methodology attains a solution closer to the global optimum.

The ever-increasing proliferation of Distributed Energy Resources is changing the monopolistic structure of the electrical distribution systems. This observation implies that every agent connected to the distribution grid becomes a potential active participant within a potential Local Energy Market which faces massive design challenges in terms of Distributed Energy Resources management, private information concerns and the safe operation of the distribution network guided by the Distribution System Operator. Considering that every agent aims to optimize their own cost function and that the electricity market has many coupled constraints involving the prosumer's behavior, we propose a Generalized Nash Equilibrium Problem to model an Energy Sharing Game considering all agents' preferences. The Utility acts as an extra agent that could sell energy in shortage scenarios and buy energy in excess scenarios under a framework where selling rates differ from the buying rates. We characterize the solution of this game and describe the conditions for a unique solution in terms of price. The model is used to define ahead transactions, and then we propose a framework to deal with the real-time operation. Under this scheme, each agent earns profits from the proposed operation compared to the case where there is no market. Under the conditions defined in the computational study, an overall cost reduction (generation costs plus transaction costs) of 42% was achieved in real-time concerning the maximum cost reduction achievable based on perfect demand prediction capability.

As the cost of photovoltaic (PV) power generation declines and becomes competitive in the electricity business, there is an increasing need to accurately predict the performance of this technology under a wide range of operating conditions. The performance of a PV module may be captured via its current–voltage ( I – V ) characteristic. The single-diode model is an adequate approximation of this characteristic when the parameters are determined for the atmospheric conditions at which the curve was measured. However, capturing the dependency of these parameters so that the model can reproduce I – V characteristics for a wide range of atmospheric conditions is a challenging task. The objective of this article is to develop such model. To accomplish this task, a large-scale data repository consisting of climatic and operational measurements is used to train an artificial neural network (NN) that captures the behavior of each parameter. The trained NN is then utilized to recreate I – V curves for a broad spectrum of environmental conditions. The analysis of the parameter behavior and the curves predicted by the NN model allows the identification of an improved PV model by searching through a kernel of functions. As the results show, the proposed model outperforms current functional models available in the literature, by reducing the error in power estimation by about 6% when measured for a wide operating range.

Electric treeing is a mechanism of failure in solid polymeric insulations. Under some conditions, trees grow through filamentary trees, which have a small diameter and do not cause breakdown when they reach the counter-electrode. In this case, reverse trees grow opposite to the forward-filamentary tree. Several methods are available to model electric trees and their phenomenology. Among them is the kinetic model, which proposes that electric trees grow due to microfractures present in the material. This model had previously been considered to model tree growth, but we extended it to include the widening of tree branches in a prior study. In this work, we included the phenomenology of reverse trees and their relationship with filamentary trees. The simulation showed that filamentary trees grow until they are close to the counter-electrode, and when reverse trees begin to form, their branches widen. From this point, filamentary trees do not grow, but branches widen until the current density is high enough for final dielectric breakdown.

This paper addresses the significant challenge of modeling building integrated photovoltaic (BIPV) systems under partial shading (PS). Most of the existing photovoltaic (PV) system models struggle capturing accurate system performance when environmental conditions deviate from rated conditions, such as in the case of shading. Recognizing the complexity of accurately modeling BIPV system performance under low irradiance, we introduce and validate a modular electrothermal modeling approach, capable of easily capturing partial shading behaviors. The proposed PV system model is built as modules consisting of an array of PV cells connected to bypass diodes (BPDs). The electrical model of the PV cells is based on an eleven-parameter functional form single diode model (SDM) and the thermal model portion is based around measurable environmental conditions. BPDs are modeled through the Shockley equation along with a heat transfer model based on thermal resistances. The electrothermal model is validated using real PV array data at varying environmental conditions. The proposed model is also compared against an electrothermal model based on a five parameter functional form SDM, demonstrating superior performance in simulating the complicated behavior of BIPVs under low irradiance conditions. The enhanced model enables highly detailed, time-resolved shading analysis, offering a framework for future research into BIPV modeling and control.

Nonconvex AC power flow models feature larger computation burden and lack optimality guarantees to be considered in industry expansion and operational planning activities. Additionally, the consideration of full network models, in general, leads to undesirable levels of computational burden, even under the standard DC approximations. Notwithstanding, current reduction methods fail in accurately reproducing real system responses for a wide range of operating points. In this context, we propose a novel data-driven network reduction method to generate equivalent reduced DC power flow models with nonlinear load functions. Our method aims at providing a high-quality representation of the internal system by minimizing the mismatch between the response of the equivalent DC model and the complete AC power flow (or real measurements) under multiple operating-point data. Thus, the approach can be interpreted as a physics-informed machine-learning method as it trains (or estimates) some parameters of the reduced DC power-flow model to fit pre-calculated data. The method determines: 1) a reduced external equivalent network model (topology and parameters), 2) the optimal allocation of external power injections to the boundary buses, and 3) the coefficients determining artificial nonlinear load functions of the operating-point data. Out-of-sample evaluation tests corroborate the performance of our model against modified Ward reduction benchmark models.

Legacy distribution systems need to adjust to emerging operational contexts. The rise in distributed generation will introduce efficiency challenges, and the limited communication capabilities of these systems hinder centralized control methods. Academic research has thus focused on distributed control strategies for photovoltaic generators to enhance operations and handle uncertainties. Traditional literature approaches utilize distribution system models for optimizing control parameters, which presents a computational challenge. This paper proposes a Machine Learning based agent, informed by system physics, to develop a Physics-informed neural networks environment to determine control parameters within a control structure novel from existing literature. The results suggest that the proposed methodology can define control parameters with a higher degree of flexibility, outperforming all competitive frameworks by reducing operating costs, minimizing voltage violations at 6.3%; without resorting to power spillage or increasing substation supply.

The design of distribution networks that simultaneously consider location and inventory decisions seeks to balance costs and product availability. The most commonly observed measure of product availability in practical settings is the fill-rate service level. However, the optimal design of a distribution network that considers the fill rate to control shortages of fast-moving consumer goods (FMCG) is considered intractable and has only been addressed by heuristic methods. This paper addresses the optimal design of a distribution network for FMCG able to provide high fill-rate service level under a continuous review (r,Q)$(r,Q)$ policy. Considering the exact formulation for the provided fill rate, we formulated a joint location-inventory model with fill-rate service level constraints as a convex mixed integer nonlinear problem for which a novel decomposition-based outer approximation algorithm is proposed. Numerical experiments have shown that our solution approach provides good-quality solutions that are on average 0.15% and, at worst, 2.2% from the optimal solution.

A distribution management system requires an accurate and computationally efficient model of its distribution network. This paper formulates an active distribution network (ADN) model taking into account legacy equipment and modern equip-ment. Legacy equipment includes mechanically switched capaci-tors and under load tap changer transformers. Modern equipment includes distributed generators in the form of photovoltaic array inverters, battery energy storage systems, and ZIP loads. The full ADN model features nonconvex and intractable equations that need to be relaxed or reformulated for computational efficiency. To address this, we assess a second order cone program relaxation, a convex hull formulation, and linear reformulations. This study explores the impact of equation relaxations and reformulations on ADN models and the impact of modern equipment on ADN management. Results on the IEEE 4-bus test feeder suggest that relaxations and reformulations greatly cut convergence time but optimal solution accuracy decreases by 16% when compared to the original, nonconvex ADN model. Larger IEEE feeder models with relaxations and reformulations converged faster than models with only a relaxation but arrived at the same feasible, but suboptimal, objective value. The true objective value for these larger IEEE feeders is unknown since they did not converge with hueristics within the allotted two hour period, showcasing the need for the relaxed and reformulated ADN models.

This paper presents a novel generalized framework for sequence-based Model Predictive Control (MPC) strategies applied to power converters. This work aims to generalize most of the existing strategies in the literature and consolidate them into a unified formulation. These strategies enable converters to operate at a constant switching frequency while generating a discrete grid current harmonic spectrum. Additionally, they retain the well-known advantages of MPC techniques, such as easy implementation, flexibility in control objectives, rapid dynamic response, and the ability to handle complex systems with multiple inputs and outputs (MIMO). Furthermore, the new formulation includes improvements that modify the state estimation model, obtaining more accurate predictions that lead to better control strategy performance. The proposed technique is applied to a case study involving a two-level converter connected to the grid through an LCL filter and is compared with the state-of-the-art sequence-based MPC strategies. Compared to the strategies in the literature and considering delay compensation, our proposal achieves a significant reduction in the grid current's THD in all the study cases. It reaches a value of 3.76%, corresponding to a 50% reduction concerning the best strategy in the literature. In addition, the fast dynamic response of this type of control technique is maintained.

This article deals with the control problem of injecting balanced grid currents from a grid-tied photovoltaic cascaded H-bridge (CHB) inverter under severe interphase power imbalances. Existing solutions are hindered by the additional harmonic content required at the inverter output voltages. Therefore, a mathematical formulation for which the solution has minimal harmonic content is proposed. The proposed solution, optimal common-mode voltage (OCMV), has an analytical form that allows deducing and analyzing the CHB operating area. The real-time implementation of the OCMV requires solving a nonlinear two-variables system; thus, an iterative and distributed algorithm is designed. By doing so, the proposed OCMV can be fully formulated and implemented using a real-time control platform. The experimental validation was carried out in a scale-down 3 kW grid-tied seven-level CHB inverter governed by phase-shifted model predictive control. The laboratory results show that the proposed OCMV allows obtaining symmetrical grid currents while maintaining low-distorted inverter output voltages.

A common practice in inventory systems with several customers requiring differentiated service levels is to group them into two or three classes, where a customer class is a group of customers with the same preset service level in terms of product availability. However, there is no evidence that grouping customers into two or three classes is optimal in terms of the ordering policy parameters. This paper studies the effect of the number of customer classes on the inventory level of a single-period inventory system with stochastic demand and individual service-level requirements from multiple customer classes. Using a Sample Average Approximation approach, we formulate computationally tractable multi-class service level models, under responsive and anticipative priority policies in cases of shortage, as mixed integer linear problems (MIPs). The effect of the number of classes on the inventory level is determined using a round-up aggregation scheme; i.e., given a sufficiently large initial number of classes, it is reduced by adding the lower service level classes to the next higher class. We analytically characterize the optimal inventory level under responsive and anticipative priority policies as a function of the initial number of classes and the number of classes grouped based on the round-up aggregation scheme. Under a responsive priority policy, we show that there is an optimal number of classes, while under an anticipative priority policy, the optimal number of classes is equal to the initial number of classes. The effect of free-riders resulting from the round-up aggregation scheme on the optimal inventory level is studied through numerical experiments.