AC Optimal Power Flow Research Articles

A SOCP-Based ACOPF for Operational Scheduling of Three-Phase Unbalanced Distribution Systems and Coordination of PV Smart Inverters

The proliferation of distributed energy resources (DERs) imposes new challenges to distribution system operation, e.g., power quality issues. To overcome these challenges and enhance system operation, it is critical to effectively utilize all available resources and accurately characterize unbalanced distribution networks in operational tools. This paper proposes a convex second-order-cone programming (SOCP)-based AC optimal power flow (ACOPF) model for three-phase unbalanced distribution networks, including smart inverters and Volt-VAr controller (VVC) devices. Reactive power-voltage (Q-V) characteristics of smart inverters of solar photovoltaic (PV) units are also modeled. Moreover, the settings of Q-V characteristics of VVC are co-optimized within the proposed ACOPF, considering the allowable range of the IEEE 1547-2018 standard. Furthermore, dynamic analyses are conducted to verify the stability of optimal settings of VVC. The proposed models are tested on an actual 1747-node primary distribution feeder in Arizona. The results illustrate the effectiveness of the proposed ACOPF for unbalanced systems in providing an optimal solution while capturing the non-linearity and non-convexity of ACOPF. By co-optimizing settings, system operation is improved due to the flexibility of adjusting reactive power output from PV units with VVC. The time-domain simulations show that the optimal settings cause no stability issue for the distribution system.

Regional Sensitivity Analysis for Maximum Static Transfer Capability of Power Systems by Dimension-Adaptive Sparse Grid Interpolation

The maximum static transfer capability (MSTC) can be regarded as a measure of the power transmission ability of power systems in steady-state operation. These emerging uncertainty sources pose a difficult challenge for the efficient analysis and effective control of MSTC. To address this challenge, the dimension-adaptive sparse grid interpolation (DASGI) method is applied with modified boundaries of the collocation points to establish a surrogate model for the faster calculation of the MSTC based on AC optimal power flow (AC-OPF), thus accelerating its probabilistic analysis as well. Subsequently, the regional sensitivity analysis (RSA) is introduced in terms of contribution to the sample mean (CSM) and to the sample variance (CSV) to identify the critical regions of the uncertainty sources. Hence, an adjustment strategy is developed to increase the mean or decrease the variance of MSTC for secure and stable power transmission. Furthermore, the total CSM (TCSM) and total CSV (TCSV) are proposed as indicators to select the most influential random inputs as the preliminary step of RSA, which reduces the analytical burden. The effectiveness of this proposition is illustrated on the modified IEEE 118-bus system and the Polish 2383-bus power system, where the Monte Carlo simulation method, in combination with the AC-OPF-based MSTC model, provides an accuracy reference and a traditional sensitivity index provides the term for comparison.

Tightening QC Relaxations of AC Optimal Power Flow through Improved Linear Convex Envelopes

Tightening QC Relaxations of AC Optimal Power Flow through Improved Linear Convex Envelopes

FRMNet: A Feasibility Restoration Mapping Deep Neural Network for AC Optimal Power Flow

FRMNet: A Feasibility Restoration Mapping Deep Neural Network for AC Optimal Power Flow

Collaborative operation optimization of distribution system and virtual power plants using multi‐agent deep reinforcement learning with parameter‐sharing mechanism

AbstractWith the increasing integration of distributed energy resources (DERs) into distribution systems, the optimization of system operation has become complex, facing challenges such as inadequate consideration of market participants’ benefits, poor computational efficiency, and data privacy concerns. This paper introduces the concept of a virtual power plant (VPP) as a solution for energy integration and management. To strike a balance between operational safety and the interests of market participants, a dual‐layer model is proposed. This model considers the benefits of both Distribution System Operators (DSO) and VPP, while also enhancing the consideration of distribution network constraints. The DSO considers AC optimal power flow and utilizes penalty functions to ensure network security in case of violations. To enhance computational efficiency and privacy, the paper presents the parameter‐sharing twin delayed deep deterministic policy gradient approach. This approach allows multiple intelligent agents to share a neural network model, effectively reducing the computational load. During the training process, only essential data is exchanged among the agents, ensuring the privacy of sensitive information. The effectiveness of the proposed model and the algorithm is validated through a case study on an IEEE 33‐node system.

A novel state estimation method for distribution networks with low observability based on linear AC optimal power flow model

The state estimation (SE) problem is one of the key functions in real-time control and management of modern electrical distribution networks. However, due to the complex network configuration and the limited number of measuring devices in these networks, the SE problem faces many challenges. In this manuscript, a new state estimation methodology is proposed based on the AC optimal power flow (ACOPF) model for distribution networks with a small number of real-time measurements. The proposed method is formulated in the form of a mixed integer linear programming problem (MILP), where the estimated states are regarded as the decision variables in the optimization problem. The load consumption values are also assumed as the decision variables where the estimation limits of these variables are determined by pseudo-measurements taken from the historical data. The main objective function is to maximize the state estimation accuracy, while the power flow equations are defined as the problem constraints. The efficiency of the proposed methodology is evaluated by implementing on the test networks and comparing the estimation results accuracy with the conventional weighted least squares (WLS) method. The obtained numerical results show the superior performance of OPF-based SE model to WLS method. Moreover, linearizing the formulation demonstrates an acceptable precision while ensuring convergence and optimum solution in low observability conditions.

Energy management of distribution network with inverter‐based renewable virtual power plant considering voltage security index

AbstractVirtual power plants (VPP) with resources and storages are able to control the active power of the network. They are also connected to the network through an inverter, which is capable of controlling reactive power. Therefore, it is expected that the optimal use of inverter‐based VPP can play an effective role in improving the economic and technical status of the distribution network. So, the operation of a smart distribution system is presented in this paper by considering inverter‐based VPPs constrained to the operator's measures. The weighted sum of expected energy loss (EEL) and voltage security index (VSI) is minimized while considering AC optimal power flow equations, restrictions of network's security, and operating model of the inverter‐based VPPs. Uncertainties with an origin of the amount of demand, renewable energy, and parameters of mobile energy storage are also discussed. The uncertainties are modelled using a stochastic optimization approach relying on the unscented transformation (UT). Evaluating inverter‐based VPP performance, providing models of flexible resources such as responsive loads and mobile storages, checking network voltage security status, and modelling uncertainties using the UT method are among the innovations of this study. According to the results, it is demonstrated that the technical situation of the distribution system is improved with the help of optimal management of the VPP. With energy management of the inverter‐based VPP, the suggested design has succeeded to enhance the operating status (voltage security) of the system by approximately 33–73% (12%) in comparison to power flow studies.

A Fully-Decentralized Transactive Energy Management Under Distribution Network Constraints via Peer-to-Peer Energy Trading

Peer-to-peer (P2P) energy trading is seen as a promising method for distributed transactive energy (TE) management. Since distribution network is used for electricity transfer, physical constraints should be imposed during the P2P trading. In this paper, we propose a P2P-based distributed TE management approach considering distribution network constraints and product differentiation for P2P energy trading between different buses. A multi-period AC optimal power flow (OPF) model is used to monitor power flow in distribution system, and the exactness of second-order cone relaxation is recovered by the convex-concave procedure, making sure that P2P transactions do not violate network constraints. Moreover, we propose a fully-decentralized variant of alternating direction method of multipliers for clearing P2P transactions in a fully-decentralized manner under AC power flow constraints. Our proposed variant does not need any interactions with the central supervisor in comparison with the traditional one. Finally, numerical results on IEEE 33-bus and 141-bus distribution systems verify the effectiveness of our proposed method in ensuring physical feasibility, lowering data communication and protecting data privacy during P2P energy trading.

An AC optimal power flow framework for active–reactive power scheduling considering generator capability curve

AbstractThis paper presents a simplified optimal power flow (OPF) framework to facilitate co‐optimised active and reactive power scheduling for synchronous generators and price‐sensitive demands. The proposed framework creates an opportunity for generators and loads to simultaneously participate in a combined market for active and reactive power. The co‐optimisation of active and reactive power generation is constrained by the interdependence of the active and reactive power capacities, which is represented by the generator capability curve. Thus, a detailed mathematical derivation of the opportunity costs across various regions of the generator capability curve is presented. This study considers a detailed generator capability curve that considers the armature, field, under‐excitation, and prime mover limits. The interdependence of active and reactive power consumption for demand is modelled using the concept of power‐factor. The OPF problem for generator and load scheduling is formulated as a non‐linear optimisation task, leveraging the inherent properties of the generator capability curve, that is, piecewise smoothness, continuity, and the monotonically increasing slope magnitudes. Furthermore, to simplify the OPF formulation, the non‐linear capability curve is represented as a combination of the linear curves. To demonstrate the effectiveness of the proposed OPF methodologies, suitable case studies are conducted using different test systems.

Optimal scheduling of BESS for congestion management considering reliability and OTS

The present research explores transmission congestion control in Battery based Energy Storage Systems (BESS) integrated grids using Optimal Transmission Switching (OTS). The oversimplification of underlying assumptions in prior OTS-based congestion management strategies leads to excessive line switching which is undesirable. Hence, a novel reliability constrained alternating current optimal power flow (AC-OPF) based OTS is presented to mitigate the line congestion in the BESS integrated grids. The suggested approach is solved to acquire the OTS solution for 24 h time frame with the primary goal of minimising generating costs subjected to ac power flow equality, BESS, reliability, and transmission congestion constraints. The proposed approach makes use of the integer variable to represent the transmission switching operations and is solved by using a mixed-integer non-linear programming (MINLP) solver. The inclusion of reliability constraints ensures the system reliability by limiting the value of load failure probability to a pre-specified limit. The feasibility of this approach is validated by testing it on a standard IEEE test system for various loading scenarios. The results exhibit that coordinated charging/discharging of BESS supports reducing the number of lines switchings required for congestion management compared to the existing approaches, substantially.

Reactive power management considering Transmission System Operator and Distribution System Operator coordination

The increasing integration of Distribution Energy Resources (DER) in the distribution system has brought the necessity of a change in grid management and also for better coordination between the Transmission System Operator (TSO) and the Distribution System Operator (DSO). This work proposes a reactive power management model to be used by DSOs, in which reactive power flexibility from DER, and also from On-Load Tap Changer (OLTC) transformers and capacitor banks are used to handle voltage problems that may arise in both transmission and distribution grids due to the uncertain production of Renewable Energy Sources (RES). Besides, it is proposed that the DSO may provide a service to the TSO, in which the latter requests a reactive power setpoint from the first one, in the TSO-DSO boundary. Adaptive robust optimization on an Alternating Current Optimal Power Flow (AC-OPF) is modelled, ensuring that the DSO receives a feasible solution and is able to manage congestion and voltage problems. The proposed model is compared with its stochastic equivalent to assess its strengths and drawbacks. To test and validate the proposed models, a 37-bus Medium Voltage (MV) distribution grid with high RES penetration is used. An important conclusion is that, though the robust model presents a safer solution than the stochastic model, the operator must be aware of the trade-off between the desired level of robustness and the expected operating cost.

Learning Regionally Decentralized AC Optimal Power Flows With ADMM

One potential future for the next generation of smart grids is the use of decentralized optimization algorithms and secured communications for coordinating renewable generation (e.g., wind/solar), dispatchable devices (e.g., coal/gas/nuclear generations), demand response, battery & storage facilities, and topology optimization. The Alternating Direction Method of Multipliers (ADMM) has been widely used in the community to address such decentralized optimization problems and, in particular, the AC Optimal Power Flow (AC-OPF). This paper studies how machine learning may help in speeding up the convergence of ADMM for solving AC-OPF. It proposes a novel decentralized machine-learning approach, namely ML-ADMM, where each agent uses deep learning to learn the consensus parameters on the coupling branches. The paper also explores the idea of learning only from ADMM runs that exhibit high-quality convergence properties, and proposes filtering mechanisms to select these runs. Experimental results on test cases based on the French system demonstrate the potential of the approach in speeding up the convergence of ADMM significantly.

CoLinFlow: An Iterative Solution Approach for the Scenario-Based AC OPF in Active Meshed Distribution Grids With Batteries

Distribution grids are characterized by an increased installation of renewable energy sources (RESs) and of batteries. Both the uncertainty of RESs and the controllability of batteries should be considered when optimizing their operation. This leads to large-scale, non-convex Optimal Power Flow (OPF) problems. Existing solution approaches either refer to radial grids or do not work under uncertainty. However, many Distribution System Operators operate their grids in meshed topologies. In this paper, CoLinFlow, an efficient solution approach for a scenario-based AC OPF in meshed balanced three-phase distribution grids with intermittent RESs and controllable batteries is proposed. First, a particular power flow form in rectangular coordinates that is accurate for meshed grids is applied. Then, Generalized Linearized Power Flow (GLPF), a novel linearization of the power flow equations based on replacing non-linear terms with constants is developed. Based on GLPF, we design CoLinFlow, a heuristic iterative scheme that at each iteration solves a convex OPF and updates GLPF until convergence. The solution of CoLinFlow at convergence is proven to be feasible with respect to the original non-convex OPF and convergence is reached after very few iterations. Also, it is shown that CoLinFlow achieves almost the same optimal objective as Ipopt, while being faster.

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

Difference-of-Convex approach to chance-constrained Optimal Power Flow modelling the DSO power modulation lever for distribution networks

The increasing expansion of renewable energy sources leads to the growth of uncertainty in the distribution network operation. Short-term operational planning performed by distribution system operators should evolve to address those new operating conditions, in particular to allow the efficient utilization of different flexibility levers. In this work, the use of a chance-constrained Alternating Current Optimal Power Flow (AC-OPF) is proposed to model the operational planning problem, considering the activation of several levers such as power modulation and power curtailment. The correlation between the renewable generation profiles and loads is considered via a joint probability constraint approximated with scenarios. The main novelty of the present manuscript is the adoption of a Difference-of-Convex approach that allows to solve the obtained optimization problem without convexification or linearization of the core OPF equations. Furthermore, the approach yields a natural and embarrassingly parallelizable scenario decomposition. The method starts with a reformulation of the model as a Difference-of-Convex optimization problem, and then a proximal bundle method algorithm is applied to solve it. The proposed methodology is tested in a 33 bus distribution network with 11 different values for the safety level defining the probability constraint, ranging from 0.75 to 1.

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

Intro to the ARPA-E Grid Optimization Competition In “Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition,” we review the state of the art in practical algorithms for scheduling power-systems operations in the short term and the results of the recent competition organized by the U.S. Advanced Research Projects Agency–Energy. We explain the mixed-integer nonlinear formulation used in the competition for nonspecialists in electrical engineering, the context and organization of the competition, and the performance of competitors. We find that the collective approaches and results of competitors provide support for efforts to move nonlinear optimization techniques into industrial applications, as they have proven to be a robust and efficient alternative to current linear approximation techniques.

A Multi-Period Charging Service Pricing Game for Public Charging Network Operators Considering the Dynamics of Coupled Traffic-Power Systems

The proliferation of electric vehicles (EVs) couples the operations of traffic systems and power systems, necessitating the interdependent traffic-power modeling to optimize the on-road EV charging decisions. In this paper, the multi-period charging service pricing interactions between multiple charging network operators (CNOs) are discussed considering the dynamics of traffic-power systems. A multi-period user equilibrium model considering mixed vehicle types is formulated to describe the possible vehicle trip transitions between different periods in urban transportation network. For the power distribution network, a convexified multi-period AC optimal power flow model is adopted for local electricity market clearing. With the dynamics of traffic-power systems, the pricing interaction between multiple CNOs is a non-cooperative game. We analyze the existence of Nash Equilibrium with fixed-point theory, and propose an iterative method based on the best response strategy to find <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -Nash Equilibrium. Numerical studies based on an interdependent power-traffic system consisting of two 18-node power distribution networks and one revised Nguyen-Dupuis transportation network demonstrate that with the proposed CNOs’ charging pricing strategy, the CNOs’ service profits can increase by 1%-3% while the PDNs’ operation costs decrease about 1%-2% for the interdependent traffic-power system.

Distributionally Robust Optimal Power Flow via Ellipsoidal Approximation

This paper proposes a distributionally robust joint chance-constrained AC optimal power flow to manage the risk of operational limits violations which are caused by uncertain renewable generation. By determining the dispatch schedule, this approach can help to decrease the risk of renewable curtailment, load shedding, or emergency redispatch in real-time. To model the proposed approach, the renewable uncertainty is first modeled as a distributionally robust ellipsoidal bound based on the Wasserstein metric. This bound is built upon a limited historical renewable forecast errors dataset without any assumption on the probability distribution of uncertainty. Then, this uncertainty bound is adopted within a semidefinite relaxation of the optimal power flow. The system responses to the renewable generation forecast errors are modeled as linear sensitivities, where all conventional generators are responsible for compensating the impacts of renewable forecast errors. Numerical experiments on IEEE 14-bus and 118-bus systems show the validity and scalability of the proposed method. Furthermore, the effectiveness of the proposed approach in terms of meeting probabilistic guarantees, cost-effectiveness and computational time is also demonstrated in the experiments.

Quadratic Taylor Expansion-Based Approximate Dynamic Programming for Fully Decentralized AC-OPF of Multi-Area Power Systems

In this paper, a quadratic Taylor expansion-based approximate dynamic programming (QTE-ADP) algorithm is proposed for the decentralized solution of multi-area AC-optimal power flow (MA-ACOPF). Different from traditional ADP algorithms, the proposed algorithm does not need to approximate the value function via a given function structure, but directly obtains the quadratic Taylor expansion (QTE) of value function based on KKT conditions. Moreover, compared with the commonly used linearized value function approximation techniques, the information used to approximate the value function is also extended from first order to second order in the proposed algorithm, which helps to improve the accuracy and efficiency of ADP. When using QTE-ADP to solve the MA-ACOPF problem, only the boundary voltage information needs to be interchanged between adjacent areas, which facilitates preserving the information privacy and decision independence of each area. Numerical simulations on several test systems demonstrate that the proposed algorithm has good performance in terms of accuracy, efficiency, and adaptability.

Getting prices right on electricity spot markets: On the economic impact of advanced power flow models

As the share of variable renewable energy increases, adequate prices on electricity spot markets become increasingly important as they set signals for scarcity, investment, or demand response. Market prices are derived from the underlying welfare maximization problem. On electricity spot markets, this optimization problem is based on the non-convex and non-linear Alternating Current Optimal Power Flow (ACOPF) model. Since the ACOPF is intractable, electricity markets around the world use a linear approximation, the Direct Current Optimal Power Flow (DCOPF) model. Recent research has led to better non-linear relaxations of the ACOPF. We show that these non-linear relaxations increase welfare and imply significantly lower redispatch costs and side-payments. Most importantly, we show that the price signals obtained from non-linear relaxations are much improved. The DCOPF often yields high price differences between nodes when there is no line congestion in the AC-feasible solution or vice versa. Such biased price signals pose a significant problem in practice as they lead to inefficient demand response, distorted investment signals, and incorrect congestion incomes. The use of non-linear relaxations mitigates this problem and provides an important advantage of the resulting prices over prices based on the DCOPF.