Optimal Power Flow Approach Research Articles

A data-driven mixed integer programming approach for joint chance-constrained optimal power flow under uncertainty

A data-driven mixed integer programming approach for joint chance-constrained optimal power flow under uncertainty

A New-Fangled Approach for Optimal Placement of Facts Controllers in a Hybridized System

This paper proposes a novel approach for Optimal Power Flow (OPF) problems in power systems by integrating the optimal placement of Flexible Alternating Current Transmission System (FACTS) devices with a hybrid renewable energy system comprising wind and photovoltaic (PV). The objective is to optimize the placement of FACTS devices to simultaneously minimize power loss, voltage deviation and reduce gross cost. To achieve this goal, the Enhanced Multi – Strategies Sparrow Search Algorithm (EMSSA) is employed, which combines multiple optimization strategies inspired by the collaborative foraging behavior of sparrows. By considering multiple objectives, including power loss reduction, voltage deviation reduction, and gross cost minimization, the proposed methodoloty aims to identify optimal locations for installing FACTS devices such as SVC (Static Var Compensator), TCSC (Thyristor Controlled Seris Compensator), TCPS (Thyristor Controlled Phase Shifter). The results showcase the capability of the proposed methodology to achieve significant improvements in power system performance, thereby contributing to the efficient and sustainable operation of modern power grids. This research also provides valuable insights for power system operators and planners to make decisions regarding the deployment of FACTS devices and the integration of renewable energy sources.

Deep Q-Learning-Based Mud Ring Optimization Approach for Optimal Power Flow in Islanded DC Microgrid

Microgrid (MG) is the basic element that recreates a significant role in integrating renewable energy sources (RES). Direct current (DC) MG has advantages over alternating current (AC) for many applications. A DC-MG is connected to the islanded mode through power electronic converters, which are also an important component for RES integration. Due to environmental factors, RES will struggle to load the conditions. Branches of DC-MG have battery energy storage systems (BESSs) installed for compensating the supply–load imbalance. Even though BESS are installed, accurate maintenance is still required to maintain a balanced power flow. This work proposes an adaptive deep Q-learning (DQL) based mud ring optimization technique (DQMR) for optimal power flow in islanded DC-MG. DQL is effective for the task with discrete and low-dimensional action spaces, and mud ring algorithm (MRA) is to clear up large-scale optimization problems and power flow problems. The implementation is done through MATLAB/Simulink model. The error is minimized to 6% by this method, and the losses are also reduced. IEEE-9 bus system and IEEE-30 bus system are used in the proposed work to validate the performance.

Giant Trevally Optimization Approach for Probabilistic Optimal Power Flow of Power Systems Including Renewable Energy Systems Uncertainty

In this study, the Giant Trevally Optimizer (GTO) is employed to solve the probabilistic optimum power flow (P-OPF) issue, considering Renewable Energy Source (RES) uncertainties, achieving notable cost reduction. The objective function is established to minimize the overall generation cost, including the RES cost, which significantly surpassing existing solutions. The uncertain nature of the RES is represented through the employment of a Monte Carlo Simulation (MCS), strengthened by the K-means Clustering approach and the Elbow technique. Various cases are investigated, including various combinations of PV systems, WE systems, and both fixed and fluctuating loads. The study demonstrates that while considering the costs of solar, wind, or both might slightly increase the total generation cost, the cumulative generation cost remains significantly less than the scenario that does not consider the cost of RESs. The superior outcomes presented in this research underline the importance of considering RES costs, providing a more accurate representation of real-world system dynamics and enabling more effective decision making.

Correlated Equilibrium Power Flow in Distribution Networks Using Graphical Game Theory

Modern power systems necessitate active management of distribution networks by Distribution System Operators (DSOs). A DSO can harness the flexibility capabilities of the nodes towards ensuring the safe operation of the distribution system, while optimizing a certain system objective. The objective-optimizing dispatch can be obtained by solving the Optimal Power Flow (OPF) problem. However, selfish nodes may deviate from the dispatch instruction by calculating a profitable deviation. Thus, an implementable solution needs to be not only optimal, but also an equilibrium, i.e., a point from which no node is willing to deviate. In this paper, we propose the adoption of correlated equilibrium as a solution concept that is generally more efficient than Nash and more relevant to this setting where the DSO acts as a coordinating entity. We formulate the problem of finding an efficient correlated equilibrium for distribution networks with discrete resources. The problem’s complexity is managed by exploiting the graphical structure and sparse connectivity of distribution networks, drawing on the methodology of graphical games. Simulations showcase that the proposed approach achieves an equilibrium with near-optimal efficiency, in contrast to the standard OPF approach which is shown to be unstable when each node selfishly optimizes its own objective.

Predictive control and coordination for energy community flexibility with electric vehicles, heat pumps and thermal energy storage

Electrification of private transportation and residential heating is a potential action to decrease significantly carbon emissions. However, the lack of coordination of such emerging loads can increase stress on the power distribution grid. To this end, this paper proposes a two-stage energy management strategy, to enhance the flexibility of energy communities. First, an optimization algorithm-based model predictive control (MPC) is developed for home energy management systems (HEMS) to schedule electric vehicles (EVs) for charging and discharging in cooperation with heat pump and thermal energy storages. The objective is to reduce electricity bills and EV battery degradation costs while maintaining thermal demand. Second, the predictive coordination based on the nonlinear AC optimal power flow approach is applied to enhance the grid flexibility under a community energy management system scheme. To validate the performance of the proposed method, we develop a co-simulation framework by implementing the optimization algorithm and simulation scenarios in a Python Environment and modelling the electricity grid in the PowerFactory-DIgSILENT, which are linked together. Extensive numerical simulations are carried out under the active demand response program-based hourly electricity pricing and different weather data in Sweden. The results show that the proposed method can reduce operating costs and enhance the energy flexibility of the energy community. Moreover, it can decrease the stress on the community power grid and prevent load-shedding events compared to the non-predictive coordinated method.

Simultaneous Robust State Estimation, Topology Error Processing, and Outage Detection for Unbalanced Distribution Systems

This paper proposes an efficient algorithmic approach that overcomes the critical challenges in real-time unbalanced distribution system state estimation, topology error processing, and outage identification simultaneously. These challenges include (1) limited locations of measurement devices and unsynchronized measurement data as well as missing and bad data, (2) complicated mixed-phase switch actions and mutual impedances and shunt admittances, and (3) the nonlinear nature of unbalanced distribution system power flow with distributed energy resources (DERs). A single snap-shot mixed-integer quadratic programming (MIQP) optimization framework is proposed to cope with these challenges, which simultaneously identifies real-time network topology, estimates system state, and detects the outages via analytical constraints. An AC optimal power flow (ACOPF) approach is proposed to accurately model unbalanced distribution systems. In the proposed MIQP formulation, nonlinearities due to the complicated mixed-phase switch operations and the ACOPF approach are linearized. The effectiveness of the proposed approach is verified on an actual distribution feeder in Arizona. The results illustrate that the proposed model is robust, accurate, and computationally efficient for implementation in a distribution management system (DMS).

Dynamic Optimal Power Flow of Active Distribution Network Based on LSOCR and Its Application Scenarios

Optimal power flow (OPF) is a crucial aspect of distribution network planning and operation. Conventional heuristic algorithms fail to meet the system requirements for speed and accuracy, while linearized OPF approaches are inadequate for distribution networks with high R/X ratios. To address these issues and cater to multi-period scenarios, this study proposes a dynamic linearized second-order cone programming-based (SOCP) OPF model. The model is built by first establishing a dynamic OPF model based on linearized second-order conic relaxation (LSOCR-DOPF). The components of the active distribution network, such as renewable energy power generation units, energy storage units, on-load-tap-changers, static var compensators, and capacitor banks, are then separately modeled. The model is implemented in MATLAB and solved by YALMIP and GUROBI. Finally, three representative scenarios are used to evaluate the model accuracy and effectiveness. The results show that the proposed LSOCR-DOPF model can ensure calculation time within 3 min, voltage stability, and error control within 10−6 for all three applications. This method has strong practical value in the fields of active distribution network day-ahead dispatch, accurate modeling of ZIP load, and real-time operation.

Optimal Reactive Power Compensation via D-STATCOMs in Electrical Distribution Systems by Applying the Generalized Normal Distribution Optimizer

This research deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) via the application of a master–slave optimization technique. The master stage determines the nodes where the D-STATCOMs must be located and their nominal rates by applying the generalized normal distribution optimizer (GNDO) with a discrete–continuous codification. In the slave stage, the successive approximations power flow method is implemented in order to establish the technical feasibility of the solution provided by the master stage, i.e., voltage regulation and device capabilities, among other features. The main goal of the proposed master–slave optimizer is to minimize the expected annual operating costs of the distribution grid, which includes the energy loss and investment costs of the D-STATCOMs. With the purpose of improving the effectiveness of reactive power compensation during the daily operation of the distribution grid, an optimal reactive power flow (ORPF) approach is used that considers the nodes where D-STATCOMs are located as inputs in order to obtain their daily expected dynamical behavior with regard to reactive power injection to obtain additional net profits. The GNDO approach and the power flow method are implemented in the MATLAB programming environment, and the ORPF approach is implemented in the GAMS software using a test feeder comprising 33 nodes with both radial and meshed configurations. A complete comparative analysis with the Salp Swarm Algorithm is presented in order to demonstrate the effectiveness of the proposed two-stage optimization approach in the fixed operation scenario regarding the final objective function values. In addition, different tests considering the possibility of hourly power injection using D-STATCOMs through the ORPF solution demonstrate that additional gains can be obtained in the expected annual operative costs of the grid.

A Gradient-Based Approach for Solving the Stochastic Optimal Power Flow Problem with Wind Power Generation

Although wind power generation improves decarbonization of the electricity sector, its increasing penetration poses new challenges for power systems planning, operation and control. In this paper, we propose a solution approach for Stochastic Optimal Power Flow (SOPF) models under uncertainty in wind power generation. Two complicating issues are handled: i) difficulties imposed by probability density functions used to formulate wind power costs and their derivatives; ii) the non-differentiability of the cost function for thermal units. Due to such issues, SOPF models cannot be solved by gradient-based approaches and have been solved by meta-heuristics only. We obtain exact analytical expressions for the first and second order derivatives of wind power costs and propose a technique for handling non-differentiability in thermal costs. The equivalent SOPF model that results from such recasting is a differentiable NLP problem which can be solved by efficient gradient-based algorithms. Finally, we propose a modified log-barrier primal-dual interior/exterior-point method for solving the equivalent SOPF model which, differently from meta-heuristic approaches, is able to calculate important dual variables such as energy prices. Our approach, which is applied to the IEEE 30-, 57- 118- and 300-bus systems, strongly outperforms a meta-heuristic approach in terms of computation times and optimality.

Power circle diagrams and aggregate flexibility curves for active distribution networks

The circular geometry of nonlinear power flow equations has conventionally been exploited as circle diagrams and capability curves for the steady-state analysis of the power network. Building upon such concepts and motivated by the need to analyze the power flow pattern due to resources in the distribution network, the flexibility of an individual bus to inject or draw apparent power in an active distribution network while maintaining the network’s static security is quantified in this paper. The power injection flexibility at multiple buses is aggregated at the bulk power delivery substation, i.e., the transmission-distribution interface bus. Flexibility aggregation is further subjected to the generation and storage capabilities of resources present in the distribution network. The circle diagrams are reported for the 33 bus active distribution network, while the aggregate flexibility curves are obtained for the modified 33 bus and 85 bus test networks using a continuation optimal power flow approach. These results, along with a comparison with a previous approach, indicate the practicality of the shapes of the aggregate flexibility curves for active distribution networks.

A Deep Neural Network-Based Optimal Power Flow Approach for Identifying Network Congestion and Renewable Energy Generation Curtailment

Herein, we propose a novel method for identifying power congestion and renewable-energy source (RES) power curtailment in power grids by using deep neural network (DNN)-based optimal power flow (OPF) analysis. Synthetic data for load demand and RES power generation are used to obtain the OPF solutions by using an OPF solver. RES locations are selected based on an analysis of the congestion cases, and the DNN is trained by using the load demand and RES power as inputs and the OPF solution as the output. Thereafter, post-processing is performed on the DNN-OPF output by using network information. The final results show the accuracies of identified values on RES curtailment, line loading, generation dispatch schedule, and total generation operating cost. The IEEE 39-bus system was adopted as a case study to validate the proposed model. The results demonstrate that the proposed scheme is much faster and more suitable for transmission systems than conventional OPF methods. Furthermore, the normalized root-mean-squared error was less than 1%, and the computational time was more than 30 times faster than conventional OPF analysis.

Convex Reformulation for Two-sided Distributionally Robust Chance Constraints with Inexact Moment Information

Constraints on each node and line in power systems generally have upper and lower bounds, denoted as two-sided constraints. Most existing power system optimization methods with the distributionally robust (DR) chance-constrained program treat the two-sided DR chance constraint separately, which is an inexact approximation. This letter derives an equivalent reformulation for the generic two-sided DR chance constraint under the interval moment based ambiguity set, which does not require the exact moment information. The derived reformulation is a second-order cone program (SOCP) formulation and is then applied to the optimal power flow (OPF) problem under uncertainty. Numerical results on several IEEE systems demonstrate the effectiveness of the proposed SOCP formulation and show the differences with other DR chance-constrained OPF approaches.

Short-term reliability and economic evaluation of resilient microgrids under incentive-based demand response programs

In this paper, a flexibility oriented stochastic scheduling framework is presented to evaluate short-term reliability and economic of islanded microgrids (MGs) under different incentive-based DR (IBDR) programs. A multi-period islanding constraint is considered to prepare the MG for a resilient response once a disturbance occurs in the main grid. Also, a multi-segment optimal power flow (OPF) approach is used to model the IBDR actions and reserve resources. Moreover, uncertainties associated with electricity prices, loads, renewable generation, calls for reserve as well as uncertainties of islanding duration of the MG are considered. The ultimate goal of the MG operator is to maximize its expected profit under a certain level of security and reliability in conjunction with the minimization of energy procurement costs of customers. The MG's economy and reliability indices are studied considering normal operation and resilient condition based on appliances characteristics, customers’ and operator's behaviors. The proposed model can effectively manage MGs operation in both normal and resilient conditions in order to improve economic and reliability indices. Numerical results demonstrate that by implementing IBDR, in cases of normal and resilient operation, the expected profit of the MG operator increases about 4% and 2.7% and reliability indicator improved 60% and 56%, respectively.

A Convexification Approach for Small-Signal Stability Constrained Optimal Power Flow

In this article, a novel convexification approach for small-signal stability constraint optimal power flow has been presented that does not rely on eigenvalue analysis. The proposed methodology is based on the sufficient condition for the small-signal stability, developed as a bilinear matrix inequality (BMI), and uses network structure-preserving differential algebraic equation modeling of the power system. The proposed formulation is based on semidefinite programming and objective penalization that has been proposed for feasible solution recovery, making the method computationally efficient for large-scale systems. A vector-norm based objective penalty function has also been proposed for feasible solution recovery while working over large and dense BMIs with matrix variables. An effectiveness study carried out on WECC 9-bus, New England 39-bus, and IEEE 118-bus test systems shows that the proposed method is capable of achieving a stable equilibrium point without inflicting a high stability-induced additional cost.

A Hierarchical Control Approach for Power Loss Minimization and Optimal Power Flow within a Meshed DC Microgrid

This work considers the DC part of a hybrid AC/DC microgrid with a meshed topology. We address cost minimization, battery scheduling and the power loss minimization within the power distribution network through constrained optimization. The novelty comes from applying differential flatness properties to the microgrid components and formulating the cost and constraints in terms of the associated B-splines parametrization of the flat outputs (the voltages and currents of the system). This allows us to obtain optimal power profiles to minimize the power dissipation and the cost of the electricity purchase from the external grid. These profiles are tracked by a model predictive controller at the higher level, while at a a lower level a controller deals with the operation of the switches within the DC/DC converters. Extensive simulations under nominal and fault-affected scenarios using realistic data validate the proposed approach.

Solution approach for optimal power flow considering wind turbine and environmental emissions

The power grid is changing expeditiously with the increasing penetration of renewable energy sources (RES). Optimal utilization of RES reduces the burden on the primary grid and makes the grid more resilient. Traditional optimal power flow (OPF) is a complex problem in power management systems, and the complexity further increases with the integration of RES due to their intermittency. This paper presents the complete formulation of the OPF model incorporating wind turbines (WT) and environmental emissions for proper scheduling, planning, and efficient operation of thermal generating units (TGU) using the Ant Lion Optimization (ALO) algorithm. The formulation of the OPF problem comprises forecasted active power generation of WT, depending on the real-time measurement and probabilistic wind speed models. The results are analyzed from the perspective of operating cost, voltage profile, and transmission power losses in the system. The OPF approach and the solution methodology are tested on the IEEE 30 and IEEE 57-bus systems. The effectiveness of the proposed ALO algorithm is evaluated against well-established algorithms like Particle Swarm Optimization and Teaching-learning-based optimization. The comparison emphasizes the effectiveness of the ALO approach for solving various OPF problems with complex and non-smooth objective functions.

Coordinated Inverter Control to Increase Dynamic PV Hosting Capacity: A Real-Time Optimal Power Flow Approach

High penetrations of distributed photovoltaics (PV) could cause adverse grid impacts, such as voltage violations. The recent development in inverter technologies provides the opportunity to develop control systems to realize effective PV governance, and thus, to improve dynamic PV hosting capacity for distribution grids. In this article, a novel distributed energy resource management system (DERMS) solution is proposed by adopting the real-time optimal power flow approach for coordinated control of the distributed PV inverters. The proposed approach eliminates the dependence on load knowledge via measurement feedback correction, and it can be implemented in real time. One challenge is that the technique is sensitive to the data availability and integrity of voltage measurements. Therefore, a decentralized DERMS approach is developed by leveraging the concepts of state estimation. The framework and the effectiveness of the solution approach are numerically demonstrated on a real distribution feeder in Southern California.

A learning-augmented approach for AC optimal power flow

Due to the high nonlinearity of AC optimal power flow (OPF), numerous efforts have been made in recent decades to find efficient methods. Machine learning (ML) has proven to significantly reduce the computational costs in many real-world problems. Thus, this paper develops a learning-augmented method for solving AC OPF, which integrates both power network equations and ML to yield near-optimal solutions. More specifically, ML models are developed to first predict bus voltage magnitudes and angles. Then, physics-based network equations are employed to calculate the power injection at different buses. Three ML algorithms, i.e., random forest, multi-target decision tree, and extreme learning machine, are explored and compared. To evaluate the efficiency of the proposed learning-augmented AC OPF solver, the MATPOWER Interior Point Solver is adopted as a baseline. Case studies on both 500-bus and 4918-bus test networks show that the proposed learning-augmented method has reduced the computational time by 15–100 times depending on the network size with a minimal loss in optimality.

Optimal Operation of Grid-Connected Microgrids with Photovoltaic Generation and Storage

A key motivator for wider deployment of microgrids (small electric networks with distributed generation connected that operate either connected at low and medium voltage levels or isolated mode) is to bring about the decentralization of the generation. This goal is because microgrids use renewable power sources and storage energy systems. However, the microgrids operation represents various challenges for grid-connected microgrids about the power interchanges with the distribution network. If the operation is performed under optimal conditions, there are benefits for microgrid investment. This paper proposes a detailed formulation to operate microgrids with photovoltaic systems and storage. The model can be used with multiple microgrids interconnected considering electricity prices and tariffs. The model corresponds to an optimal power flow approach for microgrids considering some energy storage systems. The mathematical model considers explicitly electricity tariffs. Illustrative results indicate the optimal operation of microgrids considering a load curve; specifically, the microgrid is designed to operate at different operational circumstances. A case includes multiple microgrids interconnected at different electricity prices. The electricity tariffs determine the power interchanges between the distribution network and the microgrid. Such insights about the optimal operation of microgrids provide a wide range of applications, particularly in operation and feasibility of projects.