Optimal Power Flow Problem Research Articles

Improved Mayfly Algorithm for Optimizing Power Flow with Integrated Solar and Wind Energy

Across the globe, the transition towards sustainable energy systems necessitates seamless implementation of Renewable Energy Sources (RES) into traditional power grids. Such RESs include solar and wind power. The current research work intends to overcome the challenges associated with Optimal Power Flow (OPF) problem in power systems in which the traditional operation parameters ought to be optimized for effective and trustworthy integration of the RESs. The current study proposes an innovative nature-inspired approach by enhancing the Mayfly algorithm on the basis of mating behaviour of mayflies. The aim of this approach is to tackle the complexities introduced by dynamic and discontinuous nature of solar and wind power. The improved Mayfly algorithm aims at minimizing power losses, emission, optimize voltage profiles, and ensure reliable integration of solar and wind power. The current study outcomes provide knowledgeable insights towards power flow optimization in power systems with high penetration of renewable energy. The application results reveal that the improved mayfly algorithm achieved better efficacy compared to the classical mayfly algorithm and the rest of the optimization algorithms.

An Enhanced Sparrow Search Algorithm for Solving Optimal Power Flow Problem Considering Renewable Energy Systems

An Enhanced Sparrow Search Algorithm for Solving Optimal Power Flow Problem Considering Renewable Energy Systems

A novel honey badger algorithm with golden sinusoidal survival rate selection for solving optimal power flow problem

A novel honey badger algorithm with golden sinusoidal survival rate selection for solving optimal power flow problem

Integration of optimal power flow with combined heat and power dispatch of renewable wind energy based power system using chaotic driving training based optimization

Combined heat and power economic dispatch (CHPED) based optimal power flow (OPF) problem has been studied in this article using a new, practical approach based on chaotic driving training optimization (DTBO) (CDTBO). In the proposed technique (CDTBO), the chaotic based learning is integrated with DTBO to overcome the local optimal problem and inferior convergence speed of the existing algorithms. OPF is an important concern to retain the power system running effectively. In order to meet the demand for reasonably priced power generation with optimal power flow in transmission lines, the authors combined CHPED and OPF. Since fuel is changing daily in the current environment, using renewable energy sources to generate electricity economically is crucial. The renewable energy source like wind energy is integrated with thermal units for economic power generation with reducing the thermal fuel consumption of CHPED-based OPF system. The proposed technique implemented on CHPED based IEEE-30 bus system for renewable and without renewable energy sources with considering different cases. The suggested problem considering with valve point loading of thermal units, transmission losses and uncertainties of wind speed to address the non-linearity of the renewable-based CHPED-OPF system. Cost minimization, voltage deviation control, transmission losses minimization and stability index are the single objectives of the prospective system. Furthermore tested on multi-objective functions for simultaneously minimization of cost with emission and simultaneously minimization of active power loss with voltage profile. It is observed that the proposed CDTBO technique helps to reduce the cost by 2% and 12.8% for renewable based system as compared to non-renewable system for multi-objective function. The robustness of the proposed solution has been verified by implementing the statistical analysis on two systems with least variation of mean and optimal values of cost with the tolerance of less than 0.0035%. A comparison has been made with recent well known optimization techniques to address the superiority of the suggested CDTBO algorithm.

Towards low-carbon power networks: Optimal location and sizing of renewable energy sources and hydrogen storage

This paper proposes a systematic optimization framework to jointly determine the optimal location and sizing decisions of renewables and hydrogen storage in a power network to achieve the transition to low-carbon networks efficiently. We obtain these strategic decisions based on the multi-period alternating current optimal power flow (AC MOPF) problem that jointly analyzes power network, renewable, and hydrogen storage interactions at the operational level by considering the uncertainty of renewable output, seasonality of electricity demand, and electricity prices. We develop a tailored solution approach based on second-order cone programming within a Benders decomposition framework to provide globally optimal solutions. In a test case, we show that the joint integration of renewable sources and hydrogen storage and consideration of the AC MOPF model significantly reduces the operational cost of the power network. In turn, our findings can provide quantitative insights to decision-makers on how to integrate renewable sources and hydrogen storage under different settings of the hydrogen selling price, renewable curtailment cost, emission tax price, and conversion efficiency.

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.

Real-Time Testing Optimal Power Flow in Smart-Transformer-Based Meshed Hybrid Microgrids: Design and Validation

The smart transformer (ST) is a multiport and multi-stage converter that allows for the formation of meshed hybrid microgrids (MHMs) by enabling AC-DC ports in medium and low voltage. This type of microgrid has advantages over the performance of conventional hybrid AC-DC microgrids (HMGs); however, the number of degrees of freedom of the ST increases the complexity of the energy management systems (EMSs), which require adequate and accurate modeling of the power flow of the converters and the MG to find the feasible solution of optimal power flow (OPF) problems in the MHM. An ST’s equivalent power flow model is proposed for formulating the MHM OPF problem and developing low-frequency equivalent models integrated with a decoupled hierarchical control architecture under a real-time simulation approach to the ST-based MHM. A simulation model of the MHM in the Simulink® environment of Matlab® 9.12 is developed and implemented under a digital real-time simulation (DRTS) approach on the OPAL-RT® platform. This model allows for determining the accuracy of the developed equivalent models, both low-frequency and power flow, and determining the MHM performance based on optimal day-ahead scheduling. Simulation test results demonstrated the ST equivalent model’s accuracy and the MHM’s accuracy for OPF problems with an optimal day-ahead scheduling horizon based on the model-in-the-loop (MIL) and DRTS approach.

Multi-objective RIME algorithm-based techno economic analysis for security constraints load dispatch and power flow including uncertainties model of hybrid power systems

In recent times, the landscape of power systems has undergone significant evolution, particularly with the integration of diverse renewable energy sources (RESs). This advancement presents an invaluable opportunity to enhance energy efficiency in the modern power grid, primarily by bolstering the role of stochastic RESs. The challenge lies in the optimal power flow (OPF), a multifaceted and non-linear optimization challenge that grows more complex with the inclusion of stochastic RESs that aims to optimize the allocation of power system resources to minimize the operational cost while maintaining the stability and security of the system. Addressing this, the current study introduces an innovative optimization approach, the Multi-Objective RIME (MORIME) algorithm. Drawing inspiration from the physical phenomenon of rime-ice, called the RIME, the MORIME seeks to effectively tackle OPF issues. This algorithm enhances solution accuracy by smartly dividing with non-dominated sorting and crowding distance mechanism. The proposed OPF model incorporates three types of RESs: solar photovoltaic, wind and small-scale hydropower units. While uncertainties in wind speed and solar irradiation are managed through Monte Carlo simulations, the small hydro unit is considered a constant power source. The efficacy of the MORIME algorithm is tested on IEEE 30 bus systems and results indicate that the MORIME method identifies the optimal solution for the multi-objective OPF problem while satisfying the power system constraints, thereby proving its effectiveness and superiority over MOWOA, MOGWO, MOALO, MOMRFO and MOAGDE in terms of Hyper Volume (HV) and reciprocal of Pareto Sets Proximity (1/PSP) metrices. The MORIME source code is available at: https://github.com/kanak02/MORIME

Multi-objective coyote optimization algorithm based on hybrid elite framework and Meta-Lamarckian learning strategy for optimal power flow problem

A multi-objective coyote optimization algorithm based on hybrid elite framework and Meta-Lamarckian learning strategy (MOCOA-ML) was proposed to solve the optimal power flow (OPF) problem. MOCOA-ML adds external archives with grid mechanism on the basis of elite non-dominated sorting. It can guarantee the diversity of the population while obtaining the Pareto solution set. When selecting elite coyotes, there is a greater probability to select the elite in sparse areas, which is conducive to the development of sparse areas. In addition, combined with Meta-Lamarckian learning strategy, based on four crossover operators (horizontal crossover operator, longitudinal crossover operator, elite crossover operator and direct crossover operator), the local search method is adaptively selected for optimization, and its convergence performance is improved. First, the simulation is carried out in 20 test functions, and compared with MODA, MOPSO, MOJAYA, NSGA-II, MOEA/D, MOAOS and MOTEO. The experimental results showed that MOCOA-ML achieved the best inverted generational distance value and the best hypervolume value in 11 and 13 test functions, respectively. Then, MOCOA-ML is used to solve the optimal power flow problem. Taking the fuel cost, power loss and total emissions as objective functions, the tests of two-objective and three-objective bechmark problems are carried out on IEEE 30-bus system and IEEE 57-bus system. The results are compared with MOPSO, MOGWO and MSSA algorithms. The experimental results of OPF demonstrate that MOCOA-ML can find competitive solutions and ranks first in six cases. It also shows that the proposed method has obtained a satisfactory uniform Pareto front.

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

ABSTRACT We investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

Economic scheduling method for voltage‐dependent loads in a power system based on a multitime scale framework

AbstractThere are many voltage‐dependent loads (VDLs) in power systems. When the unit reserve supply is low, the transmission network adjusts the voltage of grid‐connected nodes to provide additional resources. Many reactive power devices with different regulatory performance levels and timescales must be coordinated to employ flexible VDLs to the maximum extent, and consequently, a transient stability‐constrained optimal power flow (TSCOPF) problem with mixed integers and multiperiod coupling must be solved. A multitimescale scheduling ‘day‐ahead‐intraday‐real‐time’ framework is designed for the optimal economic scheduling of VDLs. In the day‐ahead stage, the optimal scheduling period of the discrete reactive power control devices is determined. In the intraday stage, a rolling optimization model based on model predictive control is established, and the specific action times of the discrete reactive power devices are determined. In the real‐time stage, the optimal regulation strategy of the continuous reactive power control device is optimized by rolling. Then, to consider the speed and accuracy of the solution at the same time, a continuous sensitivity correction method is adopted to simplify and solve the original model. Finally, with a modified IEEE‐39 system and a modified IEEE‐118 system as examples, it is verified that the multitimescale scheduling framework maximizes the exploitation of the flexible resources of VDLs to ensure voltage security and stability and improve the economy of system operation under different scenarios.

Hunting-Based Optimization Technique for Secured Optimal Power Flow with Lines Outages in Power System

This paper aims to achieve the exact resolution of an optimal power flow (OPF) problem in an electrical network. In the OPF, the goal is to plan the production and distribution of electrical power flows to cover, at minimal fuel cost, the consumption at various points in the network. Three variants of the OPF problem are studied in this manuscript. The first one, OPF corresponds to the case where power production costs in the network are modeled with a quadratic cost. In the second variant, OPF with outages of some lines, we clarify the extent to which power flow is affected by the outages and the increasing number of overloaded lines. Finally, the last variant, secured OPF corresponds to the case where the management of production units can respect the power limit of each line by rescheduling power production units. The study focuses on congestion management in the IEEE 30 bus system by applying a model for OPF, incorporating data from both transmission lines and generators. The research proposes a Hunting Optimization Technique which is named “Multi-Objective Ant Lion Optimizer (MOALO)” to solve single and multi-objective optimization problems to find a solution for management pricing, comparing results with other research methods to show the effectiveness of the applied approach and the mathematical model representing congestion management.

A solution to multi Objective Stochastic Optimal Power Flow problem using mutualism and elite strategy based Pelican Optimization Algorithm

Wind Energy is rapidly growing into one of the most popular energy options for power generation. However, the unpredictability of wind necessitates the employment of a distribution function when describing the wind environment. In the depiction of wind speeds, the two significant parameters of the Weibull distribution, such as the scale parameter and the shape parameter are often utilized. Therefore, it is essential to choose the most appropriate approach for estimating these parameters. Furthermore, the uncertainty in delegated power from variable wind speeds makes system management challenging. In this paper, the Weibull distribution parameters were determined using the Pelican Optimization Algorithm (POA). POA has gained extensive popularity among the research community and is currently used to address a wide range of optimization problems. However, the exploration and exploitation are not properly balanced in this algorithm. To overcome this problem a novel hybrid algorithm namely Mutualism phase based POA (MPOA) is proposed with the help of mutualism phase of Symbiotic Organisms Search (SOS) algorithm. To demonstrate the efficacy and robustness MPOA is applied on multi-objective Optimal Power Flow (MO-OPF) problems. For this study IEEE 30 bus standard system and modified IEEE 30 bus system consisting of two wind farms are taken. The purpose of this work is to examine the impact of changing the Weibull parameters, reverse and penalty cost coefficients on the overall generation cost while considering all the security aspects.

A tight compact quadratically constrained convex relaxation of the Optimal Power Flow problem

In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.

Hierarchical co-optimization of EV scheduling considering customer and system in distribution networks

The global surge in the adoption of electric vehicles (EV) has affected distribution networks, with uncoordinated charging increasing peak load and loss. EV scheduling has the potential to become a business that utilizes vehicle-to-grid (V2G) technology to mitigate system impacts while providing financial incentives to customers. Efficient EV scheduling is a multi-objective optimization problem that simultaneously considers network and customer perspectives for co-optimization. This study introduces a hierarchical EV charging management platform (EVMP) with day-ahead and real-time stages that satisfy customer preferences while ensuring efficient system operation. In this process, in order to solve the computational issues of the optimal power flow (OPF) problem, including integer variables, the computational burden was alleviated by removing integer variables from the OPF problem of the day-ahead stage, and EV dynamics were effectively handled using the rolling-horizon framework in the real-time stage. This study focuses on the relationships between the objective functions at each stage and utilizes the augmented ɛ-constraint method (AUGMECON) to obtain a Pareto front that assists in stakeholder decision making. The Pareto front is constructed by considering stakeholders from both two- and three-way perspectives, allowing the system operator to select a solution from the Pareto front for decision making.

Optimal operation and control of hybrid power systems with stochastic renewables and FACTS devices: An intelligent multi-objective optimization approach

This paper delves into the increasingly complex domain of Optimal Power Flow (OPF) within modern power systems, enhanced by the integration of unpredictable renewable energy sources. The research originally integrates stochastic photovoltaic and wind energy sources, along with a suite of Flexible AC Transmission System (FACTS) components – including thyristor-controlled series compensators, static VAR compensators, and thyristor-controlled phase shifters. The primary objective is to solve the OPF problem by reducing generation costs while accommodating the variable nature of renewable energy sources and load demands. This study prioritizes the examination of both constant and fluctuating load requirements. The inherent variability of PV and wind energy, along with load demand, is captured through the modelling of probability density functions. This approach enables a more detailed optimization process, incorporating not just the cost of thermal energy generation but also the scheduling costs of renewable sources and associated penalty costs. Moreover, the study examines the strategic placement and sizing of FACTS components, an aspect essential in minimizing the overall cost of power production. Employing both single- and multi-objective optimization algorithms, the research addresses the OPF problem in a modified IEEE-30 bus system through various case studies. The application of the recently developed flow direction algorithm, including its multi-objective variant with an ε-based constraint-handling mechanism to OPF problem is the primary contributions of this work. The results, benchmarked against several advanced metaheuristic algorithms, reveal the proposed algorithm's superior performance. This comprehensive study not only underscores the potential of integrating renewable energy sources into the grid but also highlights the efficacy of intelligent optimization strategies in managing the complexities of modern power systems.

A novel solution to optimal power flow problems using composite differential evolution integrating effective constrained handling techniques

Optimal power flow is a complex and highly non-linear problem in which steady-state parameters are needed to find a network’s efficient and economical operation. In addition, the difficulty of the Optimal power flow problem becomes enlarged when new constraints are added, and it is also a challenging task for the power system operator to solve the constrained Optimal power flow problems efficiently. Therefore, this paper presents a constrained composite differential evolution optimization algorithm to search for the optimum solution to Optimal power flow problems. In the last few decades, numerous evolutionary algorithm implementations have emerged due to their superiority in solving Optimal power flow problems while considering various objectives such as cost, emission, power loss, etc. evolutionary algorithms effectively explore the solution space unconstrainedly, often employing the static penalty function approach to address the constraints and find solutions for constrained Optimal power flow problems. It is a drawback that combining evolutionary algorithms and the penalty function approach requires several penalty parameters to search the feasible space and discard the infeasible solutions. The proposed a constrained composite differential evolution algorithm combines two effective constraint handling techniques, such as feasibility rule and ɛ constraint methods, to search in the feasible space. The proposed approaches are recognized on IEEE 30, 57, and 118-bus standard test systems considering 16 study events of single and multi-objective optimization functions. Ultimately, simulation results are examined and compared with the many recently published techniques of Optimal power flow solutions owing to show the usefulness and performance of the proposed a constrained composite differential evolution algorithm.

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

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

Calculating the Locational Marginal Price and Solving Optimal Power Flow Problem With Static VAR Compensator and Moth Flame Optimization

Calculating the Locational Marginal Price and Solving Optimal Power Flow Problem With Static VAR Compensator and Moth Flame Optimization

Optimal power flow of power system with Thyristor Controlled Series Compensation using moth flame optimization with locational marginal price

Consideration of transmission line capacity and the optimal power flow (OPF) determines the locational marginal price (LMP), which in turn determines the performance and profitability of a producing unit. Reducing the total cost of the generators can lead to a drop in the market price of electricity. It is recommended to use numerical and repetition-based approaches for solving power flow equations due to their nonlinear nature. In order to achieve the ideal power flow at an affordable price, this paper employs a Moth Flame Optimization (MFO) to solve the equations. We then enhance the MFO's structure to make it more effective at performing the simultaneous calculations of power passing through transmission lines. One FACTS tool that has been utilized to overcome this problem is the Thyristor Controlled Series Compensation (TCSC). Lastly, the proposed MFO algorithm would include the following parameters in its output: bus voltages, line losses, produced power, total generating expenditures, and generator profits. Testing the proposed method on the IEEE 57-BUS network also shows that it improves upon the OPF problem.