DC Optimal Power Flow Research Articles

Surrogate Formulation for Chance-Constrained DC Optimal Power Flow With Affine Control Policy

Surrogate Formulation for Chance-Constrained DC Optimal Power Flow With Affine Control Policy

Research on distributed optimal scheduling method based on consensus

Abstract With access to large-scale distributed power sources, the physical structure of the power grid system tends to be distributed. The application of traditional centralized optimal scheduling methods will lead to a surge in communication overhead and computational complexity, which will affect the performance and efficiency of the solution. In this paper, the minimum operating cost of the system is taken as the goal, and the distributed direct current optimal power flow (DC-OPF) optimization calculation of the photovoltaic-storage power generation system is considered to approximately solve the economic dispatch problem. The DC optimal power flow model with energy storage charging penalty is constructed. Then, the distributed optimization method based on the consensus alternating direction multiplier method (ADMM) is adopted. By decoupling the objective function and constraints of the whole system problem, the fully distributed DC-OPF calculation is realized by introducing the global consensus variable to deal with the boundary buses. Finally, the improved IEEE 30-bus example is used to test the method, and the simulation results verify the convergence and accuracy of the method.

Equality‐embedded augmented Lagrangian neural network for DC optimal power flow

AbstractDirect current optimal power flow (DC‐OPF) problems need to be solved more frequently to maintain safety and economic power system operation. Traditional solvers take too much time to get optimal results. To overcome it, a new self‐supervised augmented Lagrangian neural network (ALNN) is proposed to solve DC‐OPF problem. The proposed ALNN consists of two neural networks: the control net and the penalty net. The control net predicts active power of generators; the penalty net updates the Lagrangian multipliers. The equality constraints are embedded into the control net to guarantee no equality violations. The generalized reduced gradient method is used to reduce theviolations of inequality constraint. The effectiveness of the proposed model is demonstrated on IEEE 118‐bus. The results show that with the help of equality embedding, the equality constraints are always satisfied, which in turn improves the feasibility of ALNN. Compared to the state‐of‐art models, the proposed model has higher feasibility and less constraint violations without comprising optimality. What is more, most of the inactive constraints can be found during the training process and then they are used to speed up the post‐processing part.

A hybrid quantum–classical algorithm for mixed-integer optimization in power systems

Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs’ sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid “quantum–classical” approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum–classical algorithms for power system mixed integer optimization problems.

Importance Sampling Approach to Chance-Constrained DC Optimal Power Flow

Importance Sampling Approach to Chance-Constrained DC Optimal Power Flow

A four-stage fast reliability assessment framework for renewables-dominated strong power systems with large-scale energy storage by temporal decoupling and contingencies filtering

Reliability assessment for renewables-dominated strong power systems presents significant challenges, primarily due to the overwhelming computational demands posed by large-scale renewable generation and energy storage. In response to the limitations and lack of scalability in traditional methods, this study introduces a novel four-stage fast reliability assessment framework tailored for renewables-dominated strong power systems. First and foremost, the pre-dispatch and temporal decoupling of energy storage serve as vital foundations for the fast assessment framework. Following the pre-dispatch model, an adaptive scenario clustering technique is proposed to eliminate redundant scenarios while retaining extreme ones. Consequently, a quick verification process for contingencies is established, employing DC optimal power flow in the worst-case scenario to identify potential load shedding. Then, all contingencies are filtered to only effective ones for reliability indices computation. Finally, a modified reliability calculation model with linear AC power flow is built using the filtered contingency set and reduced scenarios. The efficacy of this approach is validated through four numerical experiments, demonstrating impressive efficiency and computation feasibility. For accuracy, the proposed method shows a 3.7% average error in a modified IEEE RTS system, and for efficiency, the proposed method finishes N-2 analysis in 424 s for a 62-bus-212-line case as well as 4924 s for a 200-bus-490-line case.

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.

Distributed Slack-Bus Based DC Optimal Power Flow With Transmission Loss: A Second-Order Cone Programming Approach and Sufficient Conditions

Distributed Slack-Bus Based DC Optimal Power Flow With Transmission Loss: A Second-Order Cone Programming Approach and Sufficient Conditions

Interpretable Machine Learning for DC Optimal Power Flow with Feasibility Guarantees

Interpretable Machine Learning for DC Optimal Power Flow with Feasibility Guarantees

A market-based real-time algorithm for congestion alleviation incorporating EV demand response in active distribution networks

The dynamic charging behavior of electric vehicles (EVs) is causing frequent line-overloading problems and serious power security issues. Controlled and smart charging mechanisms for EVs incorporating demand response (DR) may provide significant operational flexibility to the grid operators and reduce charging costs for EV users. However, controlling EV charging may cause inconvenience to individual EV users. A market-based mechanism is proposed in this research work that allows EV users and households to participate in the network congestion alleviation DR program online while maintaining the power quality. Consumers submit their charging requirements (e.g., charging power and charging deadlines) and load curtailment tolerances to the aggregator. The aggregator is an entity assumed to have a long-term contract with the distribution system operator (DSO) and regularly receives network congestion information on behalf of retail energy users. Lyapunov optimization (LO) framework is used to reschedule the EVs, and household loads using DC optimal power flow (DCOPF) to get the dynamic congestion cost signal (CCS). The developed strategy is tested on a modified IEEE 33-bus radial active distribution network (ADN). Simulation results illustrate that the designed algorithm is promising in mitigating network congestion by ensuring significantly fewer violations of network constraints (i.e., line limits) both in terms of capacity and frequency. It also results in less energy cost as compared to other benchmark algorithms, e.g., greedy algorithm, and provides a guarantee of meeting EV charging, and flexible household loads’ (FHL) delay tolerance constraints. The average curtailment ratio of FHL and the service delay for EV-charging requests are converged to the user-defined limits, i.e., 0.25 for curtailment ratio tolerance and 10 times-lots for EV service delay. Unlike other counterparts, the developed algorithm is especially suitable for real-time applications as the per-slot average computational cost is negligible, i.e., 0.55 s.

Decentralized DC optimal power flow model based on improved Lagrangian and consensus algorithm

Renewable energy sources such as wind power and photovoltaic are integrated into the power system in a high proportion and a decentralized manner. Driven by factors such as the privacy of the interests of various power sources, the efficiency of communication and computing and the reliability of transaction security, various forms of power sources are managed and controlled in a decentralized manner. It makes the traditional centralized DC optimal power flow difficult to realize. So, based on Lagrangian algorithm and improving traditional consistency algorithms, a decentralized DC optimal power flow model is proposed. Firstly, the decentralized calculation methods of active power, phase and line active power flow at nodes based on the consensus are presented. Secondly, based on Lagrangian algorithm, an improved DC optimal power flow model considering line constraints is derived. Thirdly, the calculation principle of decentralized DC optimal power flow model is proposed. It consists of two parts: the main iteration and the sub iteration. The main iteration is an iterative process with phase angle as a variable. Sub iteration is a process with Lagrange multipliers as iteration variables and using the Kaczmarz algorithm to prevent non convergence of iterations. Finally, a real system and IEEE14 bus system are taken as an example to demonstrate the accuracy of the proposed method compared to the Matpower and Injection Shift Factors(ISF) method.

Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow

In this paper, we tackle the resolution of chance-constrained problems reformulated via sample average approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program (MIP) cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k-envelopes and can be computed off-line using polynomial-time algorithms and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically constrained version of the DC optimal power flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system’s constraints be lower than some positive threshold. In a series of numerical experiments that involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best performing convex inner approximations currently available in the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported in part by the European Research Council under the EU Horizon 2020 research and innovation program [Grant 755705], in part by the Spanish Ministry of Science and Innovation [Grant AEI/10.13039/501100011033] through project PID2020-115460GB-I00, and in part by the Junta de Andalucía and the European Regional Development Fund through the research project P20_00153. Á. Porras is also financially supported by the Spanish Ministry of Science, Innovation and Universities through the University Teacher Training Program with fellowship number FPU19/03053. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0302 .

Bi-level Optimization Model of PMU Fault Recovery Based on Observability

Aiming at the failure of PMU caused by cyber-attacks and extreme natural disasters, a bi-level optimization model of PMU fault recovery based on observability is proposed in this paper. By optimizing the sequential restoration of PMU, the control center can maximize the state observability of the system under the condition of limited recovery resources and adjust the power in real time according to the recovered observable nodes, so as to alleviate the power imbalance caused by a disturbance in the recovery process. The upper optimization model takes the maximum observable branch power flow as the optimization objective, and the lower optimization model is constructed as the DC optimal power flow model with the lowest power generation cost. The upper and lower models are coupled by the branch power flow and the node observation state. Then, the lower model is transformed into KKT conditions through Lagrange multiplication, and the nonlinear objectives and constraints are linearized so that the bi-level model can be transformed into a single-level mixed integer linear programming model for solving. Finally, the effectiveness of the proposed strategy is verified by simulation analysis of IEEE39 standard systems.

New cycle-based formulation, cost function, and heuristics for DC OPF based controlled islanding

This paper presents a new formulation for intentional controlled islanding (ICI) of power transmission grids based on mixed-integer linear programming (MILP) DC optimal power flow (OPF) model. We highlight several deficiencies of the most well-known formulation for this problem and propose new enhancements for their improvement. In particular, we propose a new alternative optimization objective that may be more suitable for ICI than the minimization of load shedding, a new set of island connectivity constraints, and a new set of constraints for DC OPF with switching, and a new MILP heuristic to find initial feasible solutions for ICI. It is shown that the proposed improvements help to reduce the final optimality gaps as compared to the benchmark model on several test instances. • A new cost function that minimizes the islands’ total power imbalance. • A new formulation of DC power flow constraints that is based on KVL and avoids using big-M coefficients to model switching decisions. • New connectivity constraints for islands based on the spanning forest model that avoid using big-M coefficients. • A new MIP heuristic to find initial feasible solutions for MILP-based ICI.

A Risk-Averse Energy Sharing Market Game for Renewable Energy Microgrid Aggregators

Energy sharing has the potential to decrease operation costs by exploiting the complementarity of different entities. The further increase of microgrids’ generation capacity in the distribution network could trigger the emergence of MW-level microgrids aggregator (MGA) to participate in the regional energy sharing market (ESM) and sell excess energy. However, the uncertainty of renewable energy generation will cause the failure of energy sharing and an economic loss for the energy sharing market. Therefore, a novel two-sided market with the clearing price and risk management is proposed in this paper. In order to optimize the energy sharing strategy of MGAs, a network-constrained risk-averse two-stage stochastic game model based on DC optimal power flow (OPF) is established. The objective of the MGA is to maximize the revenue in the ESM while the subtransmission network operator (SNO) aims to achieve regional energy self-sufficiency. The sample average approximation (SAA) method is employed to approximate the stochastic Cournot-Nash equilibrium. A distributed market clearing algorithm based on the alternating direction method of multipliers (ADMM) and best response seeking is developed to solve the optimal bidding problem of MGAs and the optimal dispatch problem of the SNO. Furthermore, the existence of the SAA Nash equilibrium is also investigated. Numerical simulations prove that the proposed game model can effectively control the overbidding risk and promote regional energy self-sufficiency.

Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

We present a robust approximation of joint chance constrained DC optimal power flow in combination with a model-based prediction of uncertain power supply via R-vine copulas. It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in. This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (Eur J Oper Res (2022) https://doi.org/10.1016/j.ejor.2021.10.051). The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets. The resulting robust optimization problem has a known equivalent tractable reformulation. To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes. The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model. Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts. The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas. We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.

Assessing the impacts of nonideal communications on distributed optimal power flow algorithms

Power system operators are increasingly looking toward distributed optimization to address various challenges facing electric power systems. To assess their capabilities in environments with nonideal communications, this paper investigates the impacts of data quality on the performance of distributed optimization algorithms. Specifically, this paper compares the performance of the Alternating Direction Method of Multipliers (ADMM), Analytical Target Cascading (ATC), and Auxiliary Problem Principle (APP) algorithms in the context of DC Optimal Power Flow (DC OPF) problems. Using several test systems, this paper characterizes the performance of these algorithms in terms of their convergence rates and solution quality under three data quality nonidealities: (1) additive Gaussian noise, (2) bad data (large error), and (3) intermittent communication failure.

Operation-adversarial scenario generation

This paper proposes a modified conditional generative adversarial network (cGAN) model to generate net load scenarios for power systems that are statistically credible, conditioned by given labels (e.g., seasons), and, at the same time, “stressful” to the system operations and dispatch decisions. The measure of stress used in this paper is based on the operating cost increases due to net load changes. The proposed operation-adversarial cGAN (OA-cGAN) internalizes a DC optimal power flow model and seeks to maximize the operating cost and achieve a worst-case data generation. The training and testing stages employed in the proposed OA-cGAN use historical day-ahead net load forecast errors and has been implemented for the realistic NYISO 11-zone system. Our numerical experiments demonstrate that the generated operation-adversarial forecast errors lead to more cost-effective and reliable dispatch decisions.

Constraint-guided Deep Neural Network for solving Optimal Power Flow

Due to the nonlinear and non-convex attributes of the optimization problems in power systems such as Optimal Power Flow (OPF), traditional iterative optimization algorithms require significant amount of time to converge for large electric networks. Therefore, power system operators seek other methods such as DC Optimal Power Flow (DC-OPF) to obtain faster results, to obtain the state of the system. However, DC-OPF provides approximated results, neglecting important features of the system such as voltages and reactive power. Fortunately, recent developments in machine learning have led to new approaches for solving such problems faster, more flexible, and more accurate. In this paper, a Deep Neural Network-based Optimal Power Flow (DNN-OPF) algorithm is implemented on small to large case studies to show the accuracy and efficiency of the ML-based algorithms. The paper provides a novel approach to classify the feasible and infeasible AC-OPF problems, and suggests a constraint-guided method, based on normalizing outputs and using particular activation functions to respect the limits of generators. Furthermore, the proposed post-processing approach guarantees the feasibility of the solutions. The suggested method is applied on IEEE24-bus, IEEE 300 bus, and PEGASE 1354 bus systems and the results show significant improvement on accuracy of the results and execution time, comparing to traditional gradient-based methods, such as Newton–Raphson and Gauss–Seidel methods.

DC Optimal Power Flow Model to Assess the Irradiance Effect on the Sizing and Profitability of the PV-Battery System

The decreasing cost of renewable energy resources and the developments in storage system technologies over recent years have increased the penetration of photovoltaic systems to face the high rise in the electricity load. Likewise, there has also been an increase in the demand for tools that make this integration process in the current power systems profitable. This paper proposes a mathematical model based on the DC optimal power flow equations to find the optimal capacity of the PV panels and batteries for a standalone system or a system supported by the grid, while the investment and the energy required by the grid are minimized. In this regard, five different locations have been used as case studies to measure the influence of the irradiance level on the PV-Battery capacity installed and on the economic indicators such as CAPEX, OPEX, NPV, IRR, and the payback period. Thus, a modified 14-bus system has been used to replicate the grid technical limitations and show that a PV-Battery system connected to the grid could produce 26.9% more savings than a standalone PV-Battery and that a location with irradiance levels over 6.08 (kWh/m2/yr) could reduce the payback period for two years.