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

Optimal Power Flow Solution Integrated with TCSC to Improved Voltage Profile and Losses Reduction in Power System Using Effective Intelligent Technique

Optimal Power Flow Solution Integrated with TCSC to Improved Voltage Profile and Losses Reduction in Power System Using Effective Intelligent Technique

Snake Optimization Based Optimal Power Flow

Snake Optimization Based Optimal Power Flow

Electricity arbitrage for mobile energy storage in marginal pricing mechanism via bi-level programming

The rapid growth of renewable energy is integrated into the distribution system. The creation of both new market mechanisms and investment models has critical effects on the economics and security of the distribution market. Mobile energy storage has been used to increase the resilience of distribution grids due to their advantages in mobility and flexibility, which offer electricity arbitrage options for merchant investments. This paper presents a bi-level optimization framework based on location marginal pricing settlement of mobile energy storage financial rights revenue in active distribution systems. In the developed framework, the upper-level problem determines the optimal capacity, routing, and dispatching of mobile energy storage to maximize revenue in the liberalized electricity market. The lower-level problem performs the joint optimization of energy and reserve market clearing as well as renewable energy capacity optimization based on the alternating current optimal power flow model. The non-convexity of the line flow and location marginal pricing is linearized via second-order cone relaxation and Karush-Kuhn-Tucker. The bi-level programming is reformatted as mathematical programming with equilibrium constraints. Further, the revenue risk due to renewable energy uncertainty is measured via conditional value-at-risk. Finally, the effectiveness of the optimization framework and solution method is verified using the modified IEEE-33 test system. The results show that mobile energy storage promotes renewable energy and reduces distribution network costs by 2.3%.

Collaborative Optimization Framework for Coupled Power and Transportation Energy Systems Incorporating Integrated Demand Responses and Electric Vehicle Battery State-of-Charge

The growing adoption of electric vehicles (EVs) and advancements in dynamic wireless charging (DWC) technology have strengthened the interdependence between power distribution networks (PDNs) and electrified transportation networks (ETNs), leading to the emergence of coupled power and transportation energy systems (CPTESs). This development introduces new challenges, particularly as DWC technology shifts EV charging demand from residential plug-in charging to charging-while-driving during commuting hours, causing simultaneous congestion in both ETNs and PDNs during peak times. The present work addresses this issue by developing a collaborative optimization framework for CPTESs that incorporates integrated demand responses (IDRs) and EVs battery state-of-charge (SOC). In the ETN, a multiperiod traffic assignment model with time-shiftable traffic demands (MTA-TSTD) is established to optimize travelers’ routes and departure times while capturing traffic flow distribution. Meanwhile, effective path generation models with EVs battery SOC are proposed to optimize charging energy during driving and construct the effective path sets for MTA-TSTD. In the PDN, a multiperiod optimal power flow model with time-shiftable power demands (MOPF-TSPD) is formulated to schedule local generators and flexible power demands while calculating the power flow distribution. To enhance temporal and spatial coordination in CPTESs, a distributed coordinated operation model considering IDRs is proposed, aiming to optimize energy consumption, alleviate congestion, and ensure system safety. Finally, an adaptive effective path generation algorithm and an ETN–PDN interaction algorithm are devised to efficiently solve these models. Numerical results on two test systems validate the effectiveness of the proposed models and algorithms.

An integrated approach for multi-objective differential algorithm based event constrained optimal power flow for power system resiliency enhancement

ABSTRACT Due to climatic changes, the probability of occurrence and the intensity of extreme weather events increase day by day which leads to power outages. The probability of failure events is calculated using Monte Carlo simulation technique which is used to identify the most frequent failure events. The least eigenvalues of the inverse reduced Jacobian matrix decide the sensitive buses for load shedding using V-Q sensitivity analysis. This work presents the multi-objective differential evolution (MODE) algorithm for solving resilient constrained optimal power flow (RCOPF) in a deregulated power system. The control variables namely the real power of generators in a base case and under event, generator bus voltage magnitude, the real and reactive power demand of the selected load buses, tap settings and capacitor bank ratings. This algorithm is validated in IEEE 30 bus test system and the Indian 62 bus utility test system to show the effectiveness in four different cases including tie lines and distributed generation.

The Calibrated Safety Constraints Optimal Power Flow for the Operation of Wind-Integrated Power Systems

As the penetration of renewable energy sources (RESs), particularly wind power, continues to rise, the uncertainty in power systems increases. This challenges traditional optimal power flow (OPF) methods. This paper proposes a Calibrated Safety Constraints Optimal Power Flow (CSCOPF) model that uses the Improved Acceleration Coefficient-Based Bee Swarm algorithm (IACBS) in combination with the equivalent current injection (ECI) model. The proposed method addresses key challenges in wind-integrated power systems by ensuring preventive safety scheduling and enabling effective power incident safety analysis (PISA). This improves system reliability and stability. This method incorporates mixed-integer programming, with continuous and discrete variables representing power outputs and control mechanisms. Detailed numerical simulations were conducted on the IEEE 30-bus test system, and the feasibility of the proposed method was further validated on the IEEE 118-bus test system. The results show that the IACBS algorithm outperforms the existing methods in both computational efficiency and robustness. It achieves lower generation costs and faster convergence times. Additionally, the CSCOPF model effectively prevents power grid disruptions during critical incidents, ensuring that wind farms remain operational within predefined safety limits, even in fault scenarios. These findings suggest that the CSCOPF model provides a reliable solution for optimizing power flow in renewable energy-integrated systems, significantly contributing to grid stability and operational safety.

Stochastic optimal power flow framework with incorporation of wind turbines and solar PVs using improved liver cancer algorithm

AbstractThe present study introduces a nature inspired improved liver cancer algorithm (ILCA) for solving the non‐convex engineering optimization issues. The traditional LCA (t‐LCA) inspires from the conduct of liver tumours and integrates biological ethics during the optimization procedure. However, t‐LCA facing stagnation issues and may trap into local optima. To avoid such issues and provide the optimal solution, there are some modifications are implemented into the internal structure of t‐LCA based on Weibull flight operator, mutation‐based approach, quasi‐opposite‐based learning and gorilla troops exploitation‐based mechanisms to enhance the overall strength of the algorithm to obtain the global solution. For validation of ILCA, the non‐parametric and the statistical analysis are performed using benchmark standard functions. Moreover, ILCA is applied to resolve the stochastic renewable‐based (wind turbines + PVs) optimal power flow problem using a modified RER‐based IEEE 57‐bus. The objective of this work is to obtain the minimum predicted power losses and enhance the predicted voltage stability. By incorporation of renewable resources into the modified IEEE57‐bus network can help the system to reduce the power losses from 5.6622 to 3.8142 MW, while the voltage stability is enhanced from 0.1700 to 0.1164 p.u.

Data-driven adaptive Lyapunov function based graphical deep convolutional neural network for smart grid congestion management

Optimal power flow by leveraging network grid topology will ensure stable operation of the smart grid. Energy management in grid-connected systems aimed to reduce computational non-linearities and ensure reliable operation of the smart grid. The conventional method manages congestion with optimal scheduling for every 10–15 min. Hence congestion in the smart grid occurs during secured energy distribution. In smart grid, instant congestion and energy management are needed. This research, work is devoted to a novel data-driven adaptive Lyapunov function with a Graphical Deep Convolutional Neural Network (GDCNN) regulated optimal flow by accurate energy management. By employing novel Graph theory-based network, the congestion data are obtained to train the proposed GDCNN. A Comparison of obtained results with existing baseline methods has been carried for claiming the novelties of proposed GDCNN. It is observed, that compared to existing machine learning-based extended subspace identification techniques. Our method has better optimal power regulation within 1.8 s by controlling power sources. Also, numerical simulation on IEEE 68 bus system shows the proposed GDCNN have superior performance, reliability, and optimal energy management. This by integrating the benefits of adaptive Lyapunov function and graphical convolutional network.

Optimal operation of three-phase unbalanced active distribution system based on semidefinite relaxation and convex-concave procedure

The three-phase distribution optimal power flow (D-OPF) problem has attracted much attention in recent years due to practical requirements for managing distributed energy resources and multi-energy customers in unbalanced active distribution systems. To deal with the strong nonconvexity of the three-phase OPF problem, this paper develops the semidefinite programming (SDP) formulation of three-phase OPF problems considering the mutual coupling in multi-phase networks. Instead of directly dropping the rank-one constraints, a sequential convex optimization algorithm based on the convex-concave procedure (CCP) is proposed for recovering a feasible and optimal solution of three-phase power flow. The proposed iterative algorithm not only has high computational efficiency but also guarantees the optimality when the semidefinite relaxation or second-order cone relaxation method is inexact. Case studies on various IEEE testing distribution systems verify that the proposed algorithm recovers the feasible and optimal power flow solution. It also exhibits a relatively low number of iterations and short solving time in large-scale IEEE testing systems.

FACTS: Present and Future

Flexible AC Transmission Systems (FACTS) are pivotal in modernizing power systems, enhancing their stability, controllability, and efficiency. Currently, FACTS devices such as Static VAR Compensators (SVCs), Static Synchronous Compensators (STATCOMs), and Unified Power Flow Controllers (UPFCs) are employed to manage power flow, mitigate system instabilities, and improve voltage regulation across transmission networks. These technologies address present challenges, including the integration of renewable energy sources, reduction of transmission losses, and enhancement of system reliability in the face of fluctuating power demands. However, the growing complexity of power grids, driven by the increasing penetration of intermittent renewable energy, electric vehicles, and distributed generation, necessitates advanced and scalable solutions. The future of FACTS lies in the development of more sophisticated, adaptive, and intelligent devices that leverage real-time data analytics, artificial intelligence, and machine learning to optimize power flow dynamically. Future advancements are expected to focus on enhancing the interoperability of FACTS with smart grid technologies, improving the resilience of power systems against cyber-physical threats, and facilitating the transition towards more decentralized and sustainable energy systems. Moreover, the integration of energy storage with FACTS devices could revolutionize their functionality, offering not only reactive power compensation but also energy balancing capabilities. This paper explores the current applications of FACTS and envisions their future role in addressing the evolving challenges of global power systems, emphasizing the importance of innovation and strategic investment in the ongoing transformation of electrical networks.

Data-model driven probability model of branch power flow for distribution networks and its application to analysis of overload and line loss

The fluctuation of highly penetrated distributed generations (DGs) in distribution networks (DNs) increases branch overload risks, which makes the analysis uncertainty of branch power flow more complex. The probability analysis of branch power can grasp the power flow operation characteristics under uncertain conditions, which supports the power flow optimization management and ensures the safe and economic operation of DNs. Therefore, this paper proposes a data-model driven probability analysis method for branch power flow in DNs. An approximate branch power model is first derived to reveal the analytical relationship between branch power and node power. Then, based on the branch power approximation model and the forecasting error, the datasets of branch apparent power are constructed to capture the complex nonlinear characteristics of the power flow. The non-Gaussian distribution characteristics of branch apparent power and line loss are described by the optimal probability fitting method. Finally, the probability level of branch overload is evaluated and the probability distribution of line loss is analyzed. The case studies demonstrate that the branch power approximation model is highly accurate, and the probability distribution of the branch apparent power presents different characteristics. The proposed method can quickly and accurately calculate the branch overload probability level.

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.

Stochastic dual dynamic programming for optimal power flow problems under uncertainty

Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

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.

Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms

This paper presents a new optimization technique based on the hybridization of two meta-heuristic methods, Jellyfish Search (JS) and Moth Flame Optimizer (MFO), to solve the Optimal Power Flow (OPF) problem. The JS algorithm offers good exploration capacity but lacks performance in its exploitation mechanism. To improve its efficiency, we combined it with the Moth Flame Optimizer, which has proven its ability to exploit good solutions in the search area. This hybrid algorithm combines the advantages of both algorithms. The performance and precision of the hybrid optimization approach (JS-MFO) were investigated by minimizing well-known mathematical benchmark functions and by solving the complex OPF problem. The OPF problem was solved by optimizing non-convex objective functions such as total fuel cost, total active transmission losses, total gas emission, total voltage deviation, and the voltage stability index. Two test systems, the IEEE 30-bus network and the Mauritanian RIM 27-bus transmission network, were considered for implementing the JS-MFO approach. Experimental tests of the JS, MFO, and JS-MFO algorithms on eight well-known benchmark functions, the IEEE 30-bus, and the Mauritanian RIM 27-bus system were conducted. For the IEEE 30-bus test system, the proposed hybrid approach provides a percent cost saving of 11.4028%, a percent gas emission reduction of 14.38%, and a percent loss saving of 50.60% with respect to the base case. For the RIM 27-bus system, JS-MFO achieved a loss percent saving of 50.67% and percent voltage reduction of 62.44% with reference to the base case. The simulation results using JS-MFO and obtained with the MATLAB 2009b software were compared with those of JS, MFO, and other well-known meta-heuristics cited in the literature. The comparison report proves the superiority of the JS-MFO method over JS, MFO, and other competing meta-heuristics in solving difficult OPF problems.

A Fully Analytical Approach for the Real-Time Dynamic Reliability Evaluation of Composite Power Systems with Renewable Energy Sources

Renewable energy sources (RES) have strong uncertainties, which significantly increase the risks of power imbalance and load shedding in composite power systems. It is thus necessary to evaluate the operational reliability for guiding economic dispatch and reducing the risks. Current methods cannot meet the requirement for the operational timeliness of reliability evaluations due to the high computational complexity of the optimal power flow (OPF) calculations of massive contingencies. This paper proposes a fully analytical approach to construct fast-to-run analytical functions of reliability indices and avoid reassessments when the load and RES change. The approach consists of uniform design (UD)-based contingency screening and a modified stochastic response surface method (mSRSM). The contingency screening method is used to select critical contingencies while considering the uncertainties. The mSRSM is used to construct the analytical functions of the load shedding to the load and RES generation for the selected contingencies. An analytical function of a smooth virtual variable that maps to the load shedding is established in such a way that, when the load and RES vary, the reliability can be assessed within a very short time rather than using laborious OPF calculations. Case studies illustrate the excellent performance of the proposed method for real-time reliability evaluation.

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.

A multi-objective robust dispatch strategy for renewable energy microgrids considering multiple uncertainties

The demand for low-carbon transformations and the uncertainty of renewable energy sources and loads present significant challenges for the optimal dispatch of microgrid. This study proposed a multi-objective robust dispatch strategy to reduce the risks associated with the uncertainty of renewable energy source output and loads while promoting low-carbon and economical microgrid operation. The economic emission dispatch problem for a microgrid was formulated as a multi-objective robust dual-layer optimization model. Consequently, a high-dimensional adjustable linear polyhedral uncertainty set was proposed to describe the uncertainty of renewable energy sources and loads. This study transformed the original model into an easy-to-solve single-layer second-order cone programming optimal power flow optimization model by employing second-order cone relaxation and duality transformation. Thereafter, a synthetic membership function was proposed to determine the optimal compromise solution. To determine the charging and discharging statuses of the battery storage system and the electricity traded between the microgrid and the external power grid, a battery storage system control strategy based on time-of-use electricity prices and real-time power flow calculations was proposed. Simulations conducted on a modified IEEE-30 bus system demonstrated that the proposed strategy effectively reduced the economic costs and carbon emissions of the microgrid by 8.23 % and 2.43 %, respectively.

Decentralized Stochastic Recursive Gradient Method for Fully Decentralized OPF in Multi-Area Power Systems

This paper addresses the critical challenge of optimizing power flow in multi-area power systems while maintaining information privacy and decentralized control. The main objective is to develop a novel decentralized stochastic recursive gradient (DSRG) method for solving the optimal power flow (OPF) problem in a fully decentralized manner. Unlike traditional centralized approaches, which require extensive data sharing and centralized control, the DSRG method ensures that each area within the power system can make independent decisions based on local information while still achieving global optimization. Numerical simulations are conducted using MATLAB (Version 1.0.0.1) to evaluate the performance of the DSRG method on a 3-area, 9-bus test system. The results demonstrate that the DSRG method converges significantly faster than other decentralized OPF methods, reducing the overall computation time while maintaining cost efficiency and system stability. These findings highlight the DSRG method’s potential to significantly enhance the efficiency and scalability of decentralized OPF in modern power systems.