The proposed PINN framework is capable of producing highly accurate OPF solutions while ensuring compliance with both physical laws and inertia-related constraints and highlights the potential of physics-informed learning to enable secure, efficient, and computationally scalable OPF for future low-inertia power systems.
Abstract
The problem of Optimal Power Flow (OPF) is central to the secure and economic operation of modern power systems. However, increasing renewable energy penetration, and decreasing system inertia pose significant challenges to conventional optimization-based OPF solvers. While machine learning approaches have demonstrated substantial computational speed-ups, purely data-driven methods often suffer from data dependency, limited generalization, and lack of guaranteed physical feasibility. This paper suggests a physics-informed neural network (PINN) framework for solving the OPF problem in renewable energy-dominated, low-inertia power systems. In contrast to conventional OPF formulations, the model explicitly incorporates a location-aware inertia constraint based on the concept of system inertia strength, which accounts for the electrical distance between generation units and disturbance locations. Simulation results on a 6 GW test system demonstrate high accuracy. The mean absolute error (MAE) for both the training and testing datasets is approximately 0.045% of the total system capacity. The findings demonstrate that the proposed PINN framework is capable of producing highly accurate OPF solutions while ensuring compliance with both physical laws and inertia-related constraints. Overall, the findings highlight the potential of physics-informed learning to enable secure, efficient, and computationally scalable OPF for future low-inertia power systems.
Optimal reactive power flow (ORPF) is a steady-state optimization problem used to determine reactive-power-related control settings in AC power systems while satisfying network operating constraints. In renewable-integrated transmission systems, explicitly representing the feasible reactive-power contribution of inverter-interfaced resources is essential, because wind, photovoltaic (PV), and battery energy storage system (BESS) units cannot operate as unlimited or overly flexible reactive-power sources. Their reactive capability depends on active-power output, apparent-power rating, voltage conditions, and equipment-level capability curves. This paper evaluates the impact of including these capability curves in the solution of the ORPF problem. A MATLAB-DIgSILENT PowerFactory co-simulation framework is implemented, in which MATLAB applies a hybrid particle swarm optimization-pattern search procedure and DIgSILENT PowerFactory performs repeated AC power-flow evaluations using detailed network models and predefined capability limits. The framework is tested on modified IEEE 39-bus and IEEE 118-bus systems with wind, PV, and BESS resources. The results show that neglecting capability curves can produce unrealistic reactive-power allocations for inverter-based units, whereas enforcing these limits shifts the ORPF solution toward operating points consistent with the modeled equipment capability. The study demonstrates the importance of capability-curve representation for obtaining physically meaningful steady-state ORPF results and supports clearer comparison of constrained and unconstrained dispatch cases.
José Oscullo Lala, Nathaly Verónica Orozco Garzón, Henry Ramiro Carvajal Mora et al.· Energies· 0 citations
Cyber-physical systems (CPS) are under increasing strain, which has created a number of problems for the power system, including voltage instability, line overloads, and rising power losses. In order to solve these problems, it is essential to strategically deploy energy resources at the right nodes to maximise real and reactive powers, hence lowering losses and enhancing the voltage profile, especially in crowded networks. Grid operators can more effectively meet the demand for electricity while preserving the stability of the power system thanks in large part to power flow optimisation. However, because they are unpredictable, integrating intermittent renewable energy sources (RESs) presents particular difficulties. The power flow model put out in this study includes four different kinds of energy sources: thermal power plants (which stand in for traditional energy sources), wind power plants, battery charging stations, and solar photovoltaic power plants (which represent renewable energy sources). The goal is to assess the efficiency of the upgraded IEEE 30-bus test system through optimisation utilising an integrated strategy integrating fuzzy logic and jellyfish search optimizer (JS). Practical factors like the thermal generators' ramp rate restrictions and the erratic generation patterns of renewable energy sources are taken into account by the suggested algorithm. The algorithm effectively solves the optimum power flow (OPF) problem by minimising overall generating costs and reaching solution convergence, as shown by simulation results. The suggested method demonstrates its effectiveness in solving the difficulties of power flow optimisation by taking into account real-world scenarios and adding the complexities associated with RESs. The algorithm's effectiveness in assuring an ideal and affordable power flow solution is demonstrated by its ability to handle the intermittent nature of renewable energy sources and the limitations of thermal generators.
The Optimal Power Flow is essential for ensuring the reliable and cost-effective operation in modern power systems. However, solving the AC Optimal Power Flow problem is difficult because it is highly non-convex and computationally demanding, particularly when the power system operates under stressed conditions. Convex relaxation methods, such as Second-Order Cone Programming, have been widely used to obtain faster solutions, although their accuracy can be reduced in meshed transmission networks. This paper evaluates the performance of the strengthened SOCP-III relaxation for solving AC-OPF problems under stressed loading conditions. The study is carried out using the IEEE 30, 57 and 118 bus test systems respectively. Where the system load is gradually increased to represent different levels of operating stress. The obtained solutions are compared with the results of conventional AC-OPF to assess the effectiveness of the approach. The evaluation focuses on generation cost and computational efficiency. In addition, the approach preserves acceptable voltage profiles even at higher loading levels. These findings demonstrate that SOCP-III provides a good balance between computational speed and solution accuracy. The method is using increasing load conditions (100%–125%) especially suitable for real-time and large-scale power system optimization.
Aditi Ramteke, Kshitija A. Gaikwad, Shubh Arekar et al.· International Conference on...· 0 citations
Power Flow (PF) analysis is a fundamental tool in distribution systems since it determines the steady-state operating point for specified input conditions. Modern distribution networks face high distributed energy resource (DER) penetration and variable operating conditions, requiring repeated PF evaluations in time-series and scenario-based studies. Their unbalanced operation and high R/X ratios can challenge conventional PF solvers, thereby requiring accurate, robust, and scalable methods. Prior studies have examined nonlinear distribution PF solvers and uncertainty-based formulations, but the review literature remains limited to specific categories and lacks a unified discussion of linearized models, numerical robustness, and acceleration techniques. Therefore, this paper presents a state-of-the-art review of PF methods for modern distribution networks, covering 205 studies published between 2000 and 2026. It summarizes conventional nonlinear PF formulations, reviews linearized models with their assumptions and applicability, and surveys numerical robustness strategies for improved convergence. The methods are compared according to their applicability to radial, weakly meshed, and unbalanced networks, while practical selection criteria are provided based on accuracy, convergence reliability, and computational requirements. Probabilistic, interval, and fuzzy approaches are also reviewed under renewable and load uncertainty. Finally, acceleration strategies for repeated PF evaluation are discussed, emphasizing sparse numerical implementations, topology-based schemes, and physics-informed surrogate models.
Ayesha, G. Mosaico, Federico Silvestro· Energies· 0 citations
With the increasing proportion of renewable energy sources, the output characteristics of wind and solar power in power systems have become increasingly stochastic. This phenomenon not only affects clean energy utilization efficiency but also poses significant challenges to the safety and stability of traditional power grids. In these conditions, energy storage devices have become essential for reducing power fluctuations from renewable sources, and they are crucial for source-storage joint dispatching and dynamic control. Through literature review and comprehensive analysis, this study investigates characterization methods and quantification approaches for renewable energy uncertainty within source-storage coordination frameworks, explores optimization model design philosophies and related strategies, and evaluates current mainstream control technology trends. The uncertainty assessment system, established using parameters such as prediction deviations and fluctuation amplitudes, demonstrates greater scientific rigor than conventional coarse scenario segmentation methods. Multi-objective function-based collaborative planning approaches are gradually replacing single-objective modeling paradigms. Regarding real-time response performance improvement techniques, model predictive control (MPC) integrated with reinforcement learning algorithms has become a new research focus. This study aims to clarify academic frameworks in relevant fields and provide theoretical foundations and technical support for practical applications of source-storage coordination mechanisms in high-renewable-energy environments.
Di Hao· Applied and Computational En...· 0 citations
This paper presents a full Newton-based methodology for incorporating battery energy storage systems (BESS) into power flow analysis with explicit modeling of primary frequency regulation. The main contribution is the integration of frequency-dependent BESS behavior into the conventional power flow formulation, enabling the representation of active power adjustments in response to frequency deviations within a steady-state framework. Two operating modes are addressed: isolated (off-grid) operation and grid-connected (on-grid) operation in conjunction with conventional synchronous generators. The proposed formulation is embedded directly into the full Newton power flow algorithm, preserving its numerical characteristics while extending its capability to capture frequency regulation effects. The methodology is validated using two representative test systems: a 6-bus system for the off-grid scenario and the New England test system for the on-grid scenario. The results demonstrate the robustness and accuracy of the proposed approach and confirm its effectiveness in representing frequency-dependent behavior and the contribution of BESS units to primary frequency regulation under different operating conditions.
M. Lanini, J. A. Passos Filho· Journal of Control Automatio...· 0 citations