AC Optimal Power Flow Research Articles

Optimal operation of multi-energy carriers considering energy hubs in unbalanced distribution networks under uncertainty

This article presents a two-stage stochastic programming model to address the dispatching scheduling problem in an energy hub, considering an unbalanced active low-voltage (LV) network. A three-phase version of the second-order cone relaxation of DistFlow AC optimal power flow (AC-OPF) is employed to incorporate unbalanced network constraints, while the objective minimizes the Local Energy Community (LEC) operational cost. The model results have been validated using OpenDSS, encompassing energy losses, voltage levels, and active/reactive power. Likewise, a comparative analysis between the three-phase model and the traditional single-phase model, using a modified version of the IEEE European LV Test Feeder as a case study, reveals interesting differences, such that the single-phase model underestimates voltage limits during photovoltaic (PV) system operation and overestimates energy purchased from the main grid, compared with the three-phase model. Similarly, the comparison results reveal that discrepancies between the single and three-phase models intensify as the power injected from PV systems rises. This notably impacts the total energy purchased from the grid, battery operation, and the satisfaction of thermal consumption through electricity. Finally, while the three-phase model offers valuable insights into security levels for voltage and grid energy purchase, its longer computational time makes it more suitable for strategic use rather than daily operational frameworks.

Optimal operation of a residential energy hub participating in electricity and heat markets

The integration of electricity and heat networks provides significant benefits by enhancing system flexibility and improving overall energy efficiency. Energy hubs play an important role in these interconnected systems, facilitating the production, conversion, and storage of energy across different forms. Potential flexible loads that may exist in an energy hub can further optimize its resource utilization and operational stability. In this respect, this paper addresses the day-ahead energy management of a residential complex modeled as an energy hub, incorporating medium-scale generation and storage units, as well as must-run and flexible loads. We also consider energy hub operator’s energy transactions in power distribution system and district heating and aim to obtain the optimal bidding strategy of this profit-driven agent. The negotiations among the energy hub operator, distribution system operator, and district heat network operator are modeled as a single-leader multi-follower Stackelberg game. A Nash Equilibrium of this game can be obtained by modeling the interactions among players as a bi-level optimization problem. The lower-level problems account for multi-period optimal power flow, modeled as an exact AC optimal power flow, and multi-period optimal thermal flow. The upper-level problem models the energy management of the energy hub. Replacing the lower-level problems with their optimality conditions, the optimal bidding of the energy hub operator can be obtained by solving the resulted mixed-integer linear programming problem as a mathematical program with equilibrium constraints. Finally, we numerically evaluate the proposed framework in a case study for a large residential complex participating in a power distribution and a heat network.

Bi-level expansion planning of power system considering wind farms based on economic and technical objectives of transmission system operator

Planning for the expansion of generation and transmission infrastructure, with a focus on integrating wind farms is presented in this study according to the goals of economic efficiency, operational performance, security, and reliability of the transmission system operator. The approach incorporates a bi-level optimization framework, with the upper level outlining the formulation of power system expansion planning to reduce construction and operational costs while adhering to the investment budget limits. In the lower-level model, which economic reliable-secure functioning is formulated for the transmission network. The objective function of the problem aims to minimize operational costs, energy losses, and anticipated energy not supplied, and the voltage security index. The constraints of this problem include AC optimal power flow model, security, and reliability limits. Scheme extracts a convex-linear model for the formulation using the conventional linearization technique. Pareto optimization driven by the aggregation of weighted functions results in a single-objective framework for the lower-level problem, and the Karush-Kuhn-Tucker technique presents a single-level model for the scheme. The approach utilizes stochastic optimization has been adopted to model load, wind farms, and network equipment availability uncertainties. Finally, the study cases yielded numerical findings that showcase the efficacy of the proposed scheme in achieving the desired economic, operational, security, and reliability status within the transmission network. This is particularly true in situations where there is appropriate generation and transmission expansion.

A Neural Network Approach to Physical Information Embedding for Optimal Power Flow

With the increasing share of renewable energy in the power system, traditional power flow calculation methods are facing challenges of complexity and efficiency. To address these issues, this paper proposes a new framework for AC optimal power flow analysis based on a physics-informed convolutional neural network (PICNN) approach, which enables the neural network to learn solutions that follow physical laws by embedding the power flow equations and other physical constraints into the loss function of the network. Compared with the traditional power flow calculation method, the calculation speed of this method is improved by 10–30 times. Compared to traditional neural network models, the method provides higher accuracy, with an average increase in accuracy of up to 2.5–10 times. In addition, this paper introduces a methodology to extract worst-case guarantees for violations of the neural network’s predicted power generation constraints, determining the worst possible violation that could result from any neural network output across the entire input domain, and taking appropriate measures to reduce the violation. The method is experimentally shown to be highly accurate and reliable for the AC optimal power flow (AC-OPF) analysis problem, while reducing the dependence on a large amount of labelled data.

Dynamic security constrained AC optimal power flow for microgrids

To ensure the continuous operation of a microgrid, proactive planning is essential, especially when contemplating possible dynamic events that alter the scheduled scenarios for the islanded operation or during its transition from connected to islanded mode. This paper introduces an innovative mathematical programming model for the AC optimal power flow (AC-OPF) with dynamic security constraints (DSCs), considering two scenarios: the islanded operation and the transition. This model uses positive-sequence equations to represent the inverter-based resources (IBRs) for grid-forming and grid-following roles, along with a fourth-order synchronous generator model equipped with excitation and frequency control systems. They assess the dynamic response to specific events such as short-circuits, decreases in PV generation, increases in load demand during the islanded operation, and the transition itself. The DSCs are applied to dispatchable distributed energy resources (DERs), which react to variations in the microgrid, considering generation and opportunity costs to minimize the discrepancy between planned and secure operating points. The mathematical programming model is implemented using AMPL, and solutions are obtained through the nonlinear optimization solver IPOPT. The tests are conducted in an adapted version of the microgrid being developed at the University of Campinas that includes a synchronous generator, photovoltaic (PV) generation, and a battery energy storage system (BESS). Results demonstrate the model’s effectiveness in adjusting generation dispatch to withstand defined events and optimizing generation resources, even when limits are not reached.

Ensuring data privacy in AC Optimal Power Flow with a distributed co-simulation framework

During the energy transition, the significance of collaborative management among institutions is rising, confronting challenges posed by data privacy concerns. Prevailing research on distributed approaches, as an alternative to centralized management, often lacks numerical convergence guarantees or is limited to single-machine numerical simulation. To address this, we present a distributed approach for solving AC Optimal Power Flow (OPF) problems within a geographically distributed environment. This involves integrating the energy system Co-Simulation (eCoSim) module in the eASiMOV framework with the convergence-guaranteed distributed optimization algorithm, i.e., the Augmented Lagrangian based Alternating Direction Inexact Newton method (aladin). Comprehensive evaluations across multiple system scenarios reveal a marginal performance slowdown compared to the centralized approach and the distributed approach executed on single machines—a justified trade-off for enhanced data privacy. This investigation serves as empirical validation of the successful execution of distributed AC OPF within a geographically distributed environment, highlighting potential directions for future research.

Initial estimate of AC optimal power flow with graph neural networks

Optimal power flow (OPF) is a crucial task in power system management and control; accurate and time-efficient solutions for OPF are necessary to ensure cost-efficient and reliable power system operation. We introduce a novel solution to solving alternating current OPF (ACOPF), a nonlinear and nonconvex optimization problem, by combining the speed of a trained deep learning model with the accuracy of iterative solvers. The proposed framework uses a graph neural network (GNN) to exploit the graph structure of a power system in conjunction with proximal policy optimization, a deep reinforcement learning algorithm, to compute initial guesses for an interior point solver (IPS), providing a warm start, allowing the solver to converge in fewer iterations. Existing literature that explores warm start ACOPF solutions using machine learning choose to compute initial guesses that are trained to be feasible and cost-minimizing. Our approach trains the GNN-based reinforcement learning agent to produce an output that minimizes IPS convergence time by designing a reward function that is a function of the IPS convergence time. We evaluate the proposed framework using IEEE test case environments, using PyPower’s IPS-based ACOPF solver and a GNN-based framework that computes ACOPF solutions directly as baselines, demonstrating significantly improved convergence times.

Efficient bounds tightening based on SOCP relaxations for AC optimal power flow

Efficient bounds tightening based on SOCP relaxations for AC optimal power flow

An optimal expansion planning of power systems considering cycle-based AC optimal power flow

This paper presents a novel mixed-integer linear optimization formulation of the AC network-constrained, cost-based, integrated expansion planning problem. The formulation is used to determine the investment needs per technology including the location and sizing of new generation, energy storage, and transmission network assets in a future low-carbon power system. To reduce the size of the resulting problem, the AC optimal power flow (AC-OPF) model is represented in a compact way using cycle constraints. A bound tightening procedure is also considered to reduce the search space and improve the solver performance by adjusting the voltage bounds within the AC-OPF. Contrary to typically used formulations of the integrated expansion planning problem, the constraints considered here include all main aspects of system operation, namely unit commitment, energy storage system management, AC-OPF, and reactive power compensation. Thus, in this paper, we examine how both the proposed transmission expansion modeling developments and the interrelation of the integrated planning constraints affect the computation of the solution to the expansion planning problem. The performance of this formulation is assessed on the RTS-GMLC test system by computing the expansion plan and comparing it with the results of three other expansion planning formulations most frequently employed in the recent literature to address the integrated expansion planning problem for medium to large-scale systems. Expansion plans are computed and compared for different case studies and multiple scenarios. According to the comparative analysis, neglecting the AC-OPF or the unit commitment constraints can increase the total system costs by 7.10%–9.57% or 6.29%–8.39%, respectively. Unlike other modeling approaches, the proposed approach does not rely on simplifications that impact the quality of the solution. Thanks to the incorporated cycle-based AC-OPF constraints and the consideration of a bound tightening procedure, the computation time is reduced by 17.67%–27.21%.

Learning model combining convolutional deep neural network with a self-attention mechanism for AC optimal power flow

Alternating current optimal power flow (OPF) analysis is critical for efficient and reliable operation of power systems. For large systems or repetitive computations, the traditional methods such as the direct and gradient methods, or non-traditional methods, such as the genetic algorithm and simulating annealing, are time-consuming and unsuitable for real-time computing. The work in this paper proposes a novel framework to obtain the optimal solution of power flow in real-time using a combination of convolutional neural networks and a self-attention mechanism. All parameters of the power networks are rearranged in an image-like shape of a multi-channel image where each channel is a two-dimensional matrix. The proposed approach is adaptive with every input size of power systems as well as frequent variations of network topologies without intervention to the framework core. The encompassment of all power system contexts in which all parameters of internal elements, generation costs, and topology information are included, contributes to the higher accuracy of inference compared to other current machine-learning-based OPF-solving methods. Besides, the proposed framework established on ubiquitous platforms is effortlessly integrated into current infrastructures of power systems, and the great efficiency along with the computation speed may serve as a critical point for practical implications, such as enabling faster decision-making during real-time operations, predicting system contingencies, and remedial actions based on an offline pre-trained model. This supervised learning process is applied to the dataset of four case studies of meshed power systems: the IEEE 5-bus system (IEEE-5), the IEEE 30-bus system (IEEE-30), the IEEE 39-bus system (IEEE-39), and the IEEE 57-bus system (IEEE-57) to prove the efficacy of the proposed method.

Advancements and Future Directions in the Application of Machine Learning to AC Optimal Power Flow: A Critical Review

Optimal power flow (OPF) is a crucial tool in the operation and planning of modern power systems. However, as power system optimization shifts towards larger-scale frameworks, and with the growing integration of distributed generations, the computational time and memory requirements of solving the alternating current (AC) OPF problems can increase exponentially with system size, posing computational challenges. In recent years, machine learning (ML) has demonstrated notable advantages in efficient computation and has been extensively applied to tackle OPF challenges. This paper presents five commonly employed OPF transformation techniques that leverage ML, offering a critical overview of the latest applications of advanced ML in solving OPF problems. The future directions in the application of machine learning to AC OPF are also discussed.

Optimal transformer loss of life management in day-ahead scheduling of wind-rich power systems at the presence of dynamic ratings

Integration of wind power generations within today's power has faced power grid operators with challenges such as variable power generation and congestion issues. To settle these problems, the power system operators can make use of smart-grid technologies, one of which is dynamic rating of power equipment. In this paper, optimal day-ahead scheduling of wind-rich power systems is implemented at the presence of dynamic line rating (DLR) and dynamic transformer rating (DTR). Employing DTR brings about higher loading of transformer endangering its lifetime as costly instrument; hence, the thermal modeling of the transformer has been incorporated into the proposed model of this paper to avoid transformer's loss of life (LOL). All the constraints of the day-ahead AC optimal power flow have been considered to compose an optimization model which is programmed in the GAMS and optimized by appropriate solvers. Several experiments have been accomplished on the IEEE 24-bus system where the simulation results clearly demonstrate efficacy of the conducted approach.

Spatiotemporal Operational Emissions Associated With Light-, Medium-, and Heavy-Duty Transportation Electrification

The spatiotemporal distribution of pollutants plays a significant role on their impact on ecosystems and human health. This paper presents a strategy for calculating spatiotemporal operational emissions of road transportation and the electric grid to quantify the impact of transportation electrification. Emissions from internal combustion engine vehicles and offset emissions from electric vehicles (EVs) are considered using actual transportation networks and travel data. The spatiotemporal charging demand for light-duty and medium- and heavy-duty EVs are estimated in a behaviorally-informed way and mapped to electrical buses within the power grid and an ac optimal power flow with unit commitment is solved. The methodology is demonstrated with ten scenarios simulated on a grid with 7000 electrical buses geographically sited in Texas, created with actual generator data for the 2020 grid, and a future case including anticipated generator updates by 2030. Results show overall transportation emissions reductions in daily operational emissions of up to 20–30% for all pollutants studied, outweighing the increase in emissions from the electric grid. Considering emissions on an hourly basis, up to approximately 1000% reduction in CO emissions is observed.

Robust Short-Term Operation of AC Power Network With Injection Uncertainties

With uncertain injections from Renewable Energy Sources (RESs) and loads, deterministic AC Optimal Power Flow (OPF) often fails to provide optimal setpoints of conventional generators. A computationally time-efficient, economical, and robust solution is essential for ACOPF with short-term injection uncertainties. Usually, applying Robust Optimization (RO) for conventional non-linear ACOPF results in computationally intractable Robust Counterpart (RC), which is undesirable as ACOPF is an operational problem. Hence, this paper proposes a single-stage non-integer non-recursive RC of ACOPF, using a dual transformation, for short-term injection uncertainties. The proposed RC is convex, tractable, and provides base-point active power generations and terminal voltage magnitudes (setpoints) of conventional generators that satisfy all constraints for all realizations of defined injection uncertainties. The non-linear impact of uncertainties on other variables is inherently modeled without using any affine policy. The proposed approach also includes the budget of uncertainty constraints for low conservatism of the obtained setpoints. Monte-Carlo Simulation (MCS) based participation factored AC power flows validate the robustness of the obtained setpoints on NESTA and case9241pegase systems for different injection uncertainties. Comparison with previous approaches indicates the efficacy of the proposed approach in terms of low operational cost and computation time.

Compact Optimization Learning for AC Optimal Power Flow

Compact Optimization Learning for AC Optimal Power Flow

Energy management system based on economic Flexi-reliable operation for the smart distribution network including integrated energy system of hydrogen storage and renewable sources

This paper presents the energy management of smart distribution network including integrated system of hydrogen storage and renewable sources. Objective is to assess economic, operation, flexibility, and reliability goals of the distribution system operator. Objective function minimizes costs of operation, reliability, energy losses, and network flexibility. Scheme is constrained by AC optimal power flow equations, network reliability limitation, and integrated system model. Scheme utilizes scenario-based stochastic optimization to model of uncertainties, such as load, parameters of renewable resources, energy prices, and the availability of network equipment. Novelty is modeling and performance evaluation of the proposed integrated system as a type of flexibility resource in the operation of distribution systems proportional to the economic, operation, flexibility, and reliability objectives of the network operator. Numerical results demonstrate energy management capabilities of the discussed integrated energy system, which contribute to enhancing economic and technical conditions of distribution network. The inclusion of hydrogen storage in the renewable integrated energy system has been found to enhance the economic viability, operational efficiency, and reliability of the distribution network by around 46.8%, 41%–53%, and 95%, respectively, when compared to network power flow. Aforementioned integrated system demonstrates 100% flexibility through the utilization of hydrogen storage.

False Data Injection Attack with Max-Min Optimization in Smart Grid

With the proliferation of information and communication technology (ICT), the smart grid is critically vulnerable to cyber-attacks such as false data injection (FDI), denial-of-service, and data spoofing. The cyber-attackers defunctionalize critical operations of the smart grid by compromising the ICT. The decisions for the critical operation of the smart grid are processed with a state estimator, and ICT makes the state estimator vulnerable to FDI attacks. Hence, vulnerability analysis of the state estimator needs to be investigated for potential FDI attacks to protect it from future cyber-attacks. This work proposes the FDI attack vector construction without the knowledge of bad data detection (BDD) threshold on linear and non-linear state estimators using max-min optimization considering the partial network information. The optimization problem is formulated from the attacker's perspective to target the manipulation of measurements in the attack zone so as to increase the generation cost. The equivalent power injection model is developed for the attack zone to construct the deceptive attacks using DC and AC power flow models. The effectiveness of the proposed framework has been tested on 5 bus PJM network, modified IEEE 30 bus, IEEE 57 bus, and IEEE 118 bus system. The proposed framework is compared with existing state-of-art methods (viz., linear attack policy, non-linear attack policy, load redistribution attack, and line flow attack) to assess its efficacy. It is observed that the developed FDI attack vector successfully bypasses the bad data detectors such as the chi-square test, largest normalized residue, and l2 detector that is normally used by the system operator. Moreover, the study compares and discusses the impact of FDI attacks on the estimated state variables obtained with state estimators and, thereby, the generation cost calculated with the DC & AC optimal power flow tool.

Combined MIMO Deep Learning Method for ACOPF with High Wind Power Integration

The higher penetration of renewable energy sources in current and future power grids requires effective optimization models to solve economic dispatch (ED) and optimal power flow (OPF) problems. Data-driven optimization models have shown promising results compared to classical algorithms because they can address complex and computationally demanding problems and obtain the most cost-effective solution for dispatching generators. This study compares the forecast performance of selected data-driven models using the modified IEEE 39 benchmark system with high penetration of wind power generation. The active and reactive power load data of each bus are generated using Monte Carlo simulations, and synthetic wind power data are generated by utilizing a physical wind turbine model and wind speed samples withdrawn from a Weibull distribution. The objective is to design and evaluate an enhanced deep learning approach for the nonlinear, nonconvex alternating current optimal power flow (ACOPF) problem. The study attempts to establish relationships between loads, generators, and bus outcomes, utilizing a multiple-input, multiple-output (MIMO) workflow. Specifically, the study compares the forecast error reduction of convolutional neural networks (CNNs), deep feed-forward neural networks (DFFNNs), combined/hybrid CNN-DFFNN models, and the transfer learning (TL) approach. The results indicate that the proposed combined model outperforms the CNN, hybrid CNN-DFFNN, and TL models by a small margin and the DFFNN by a large margin.

Model of integrated pool/conventional/alternative electricity market operation using pay-as-bid pricing

A pricing model considering the simultaneous interaction of pool, conventional and alternative markets in a power system is presented. This work inserts a competition for alternative power plants separating the pricing for these three markets. The model use the ‘Pay-as-Bid’ (PAB) pricing approach in opposite of classical marginal pricing (MP) approach because the inelastic demand characteristic and the necessity of reduce total operation cost. In the model pricing approach, an integration process involves an AC Optimal Power Flow (OPF) for obtaining awarded bids in the pool and market with the presence of conventional or alternative energy bilateral contracts. As a result, the obtained prices of pool, conventional and alternative energy incorporate the influences of the topology, voltage levels, losses and capacity limits of generators and transmission lines. Results show that agents can plan their portfolios based on reasonable stable prices that reflect the impact of supplying several electricity types and associated costs of resources in several operation scenarios and bid strategies. From the perspective of the system regulator, the minimization of payments by PAB ensures the supply of energy, transmission losses and alternative energy requirements as well as enforcing financial adequacy. Numerical cases are presented for evaluating the model

Discrete optimal power flow with prohibited zones, multiple-fuel options, and practical operational rules for control devices

Although the optimal power flow (OPF) problem has been extensively studied, solving realistic OPF models that accurately represent the operating behavior of power system components remains challenging. This paper proposes a novel model for the AC OPF problem, aiming to minimize the fuel costs of thermal units while taking into account valve-point loading effects (VPLE), prohibited operation zones (POZ), multiple fuel options (MFO), and operational rules associated with the discrete tap ratios of on-load tap changer (OLTC) transformers and with the discrete shunt susceptances of capacitor/reactor banks. These rules are represented using complementarity constraints. We propose a solution approach that integrates several strategies to address the non-smooth features of the objective function related to VPLE, the disjoint constraints and functions tied to POZ and MFO, the discrete characteristics of the reactive control variables, and the complementarity constraints governing operational rules linked to voltage control devices such as OLTC transformers and capacitor/reactor banks. The resulting optimization problem is designed to be compatible with commercial solver packages. Numerical tests on the IEEE 30, 118, and 300-bus systems aim to examine the cumulative impact of these operational factors on the optimal solution. The solution strategy proposed has demonstrated its effectiveness in solving the proposed OPF problem within reasonable computation times.