Enhancing Renewable Energy Integration:A Gaussian-Bare-Bones Levy Cheetah Optimization Approach to Optimal Power Flow in Electrical Networks

In the contemporary era,the global expansion of electrical grids is propelled by various renewable energy sources(RESs).Efficient integration of stochastic RESs and optimal power flow(OPF)management are critical for network optimization.This study introduces an innovative solution,the Gaussian Bare-Bones Levy Cheetah Optimizer(GBBLCO),addressing OPF challenges in power generation systems with stochastic RESs.The primary objective is to minimize the total operating costs of RESs,considering four functions:overall operating costs,voltage deviation management,emissions reduction,voltage stability index(VSI)and power loss mitigation.Additionally,a carbon tax is included in the objective function to reduce carbon emissions.Thorough scrutiny,using modified IEEE 30-bus and IEEE 118-bus systems,validates GBBLCO’s superior performance in achieving optimal solutions.Simulation results demonstrate GBBLCO’s efficacy in six optimization scenarios:total cost with valve point effects,total cost with emission and carbon tax,total cost with prohibited operating zones,active power loss optimization,voltage deviation optimization and enhancing voltage stability index(VSI).GBBLCO outperforms conventional techniques in each scenario,showcasing rapid convergence and superior solution quality.Notably,GBBLCO navigates complexities introduced by valve point effects,adapts to environmental constraints,optimizes costs while considering prohibited operating zones,minimizes active power losses,and optimizes voltage deviation by enhancing the voltage stability index(VSI)effectively.This research significantly contributes to advancing OPF,emphasizing GBBLCO’s improved global search capabilities and ability to address challenges related to local minima.GBBLCO emerges as a versatile and robust optimization tool for diverse challenges in power systems,offering a promising solution for the evolving needs of renewable energy-integrated power grids.

A multi-objective power flow optimization control strategy for a power split plug-in hybrid electric vehicle using game theory

Power flow optimization control,which governs the energy flow among engine,battery,and motor,plays a very important role in plug-in hybrid electric vehicles(PHEVs).Its performance directly affects the fuel economy of PHEVs.For the purpose of improving fuel economy,the electric system including battery and motor will be frequently scheduled,which would affect battery life.Therefore,a multi-objective optimization mechanism taking fuel economy and battery life into account is necessary,which is also a research focus in field of hybrid vehicles.Motivated by this issue,this paper proposes a multi-objective power flow optimization control strategy for a power split PHEV using game theory.Firstly,since the demand power of driver which is necessary for the power flow optimization control,cannot be known in advance,the demand power of driver can be modelled using a Markov chain to obtain predicted demand power.Secondly,based on the predicted demand power,the multi-objective optimization control problem is transformed into a game problem.A novel non-cooperative game model between engine and battery is established,and the benefit function with fuel economy and battery life as the optimization objective is proposed.Thirdly,under the premise of satisfying various constraints,the participants of the above game maximize their own benefit function to obtain the Nash equilibrium,which comprises of optimal power split scheme.Finally,the proposed strategy is verified compared with two baseline strategies,and results show that the proposed strategy can reduce equivalent fuel consumption by about 15%compared with baseline strategy 1,and achieve similar fuel economy while greatly extend battery life simultaneously compared with baseline strategy 2.

Optimal Power Flow Solution Using Particle Swarm Optimization Technique with Global-Local Best Parameters

This paper proposes an efficient method for optimal power flow solution （OPF） using particle swarm optimization （PSO） technique. The objective of the proposed method is to find the steady state operation point in a power system which minimizes the fuel cost, while maintaining an acceptable system performance in terms of limits on generator power, line flow limits and voltage limits. In order to improvise the performance of the conventional PSO （cPSO）, the fine tuning parameters- the inertia weight and acceleration coefficients are formulated in terms of global-local best values of the objective function. These global-local best inertia weight （GLBestlW） and global-local best acceleration coefficient （GLBestAC） are incorporated into PSO in order to compute the optimal power flow solution. The proposed method has been tested on the standard IEEE 30 bus test system to prove its efficacy. The results are compared with those obtained through cPSO. It is observed that the proposed algorithm is computationally faster, in terms of the number of load flows executed and provides better results than the conventional heuristic techniques.

Improved multi-objective artificial bee colony algorithm for optimal power flow problem

The artificial bee colony(ABC) algorithm is improved to construct a hybrid multi-objective ABC algorithm, called HMOABC, for resolving optimal power flow(OPF) problem by simultaneously optimizing three conflicting objectives of OPF, instead of transforming multi-objective functions into a single objective function. The main idea of HMOABC is to extend original ABC algorithm to multi-objective and cooperative mode by combining the Pareto dominance and divide-and-conquer approach. HMOABC is then used in the 30-bus IEEE test system for solving the OPF problem considering the cost, loss, and emission impacts. The simulation results show that the HMOABC is superior to other algorithms in terms of optimization accuracy and computation robustness.

Security Constrained Distributed Optimal Power Flow of Interconnected Power Systems

The security constrained distributed optimal power flow （DOPF） of interconnected power systems is presented. The centralized OPF problem of the multi-area power systems is decomposed into independent DOPF subproblems, one for each area. The dynamic security region （DSR） to guarantee the transient stability constraints and static voltage stability region （SVSR） constraints, and line current limits are included as constraints. The solutions to the DOPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the centralized OPF solution. The nonlinear DOPF subproblem is solved by predictor-corrector interior point method （PClPM）. The IEEE three-area RTS-96 system is worked out in order to demonstrate the effectiveness of the proposed method.

Three-Phase Optimal Power Flow for Study of PV Plant Distributed Impact on Distribution Systems

This paper presents a TOPF （three-phase optimal power flow） model that represents photovoltaic systems. The PV plant is modeled in the TOPF as active and reactive power source. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. The reduction of unbalance voltage and losses in the distribution systems is obtained by actions of reactive power control of the inverter. The TOPF is formulated by current balance equations and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems for different scenarios of solar irradiance and temperature, thus providing a detailed view of the impact of photovoltaic distributed generation.

Applying Convex Optimal Power Flow to Combined Economic and Emission Dispatch

This paper addresses the problem of reducing CO2 emissions by applying convex optimal power flow model to the combined economic and emission dispatch problem. The large amount of CO2 emissions in the power industry is a major source of global warming effect. An efficient and economic approach to reduce CO2 emissions is to formulate the emission reduction problem as emission dispatch problem and combined with power system economic dispatch (ED). Because the traditional optimal power flow (OPF) model used by the economic dispatch is nonlinear and nonconvex, current nonlinear solvers are not able to find the global optimal solutions. In this paper, we use the convex optimal power flow model to formulate the combined economic and emission dispatch problem. The advantage of using convex power flow model is that global optimal solutions can be obtained by using mature industrial strength nonlinear solvers such as MOSEK. Numerical results of various IEEE power network test cases confirm the feasibility and advantage of convex combined economic and emission dispatch (CCEED).

Optimal Power Flow Using Firefly Algorithm with Unified Power Flow Controller

Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, it is minimizing optimization problem and subjected to many complex objective functions and constraints. Hence, firefly algorithm is used to solve OPF in this paper. The aim of the firefly is to optimize the control variables, namely generated real power, voltage magnitude and tap setting of transformers. Flexible AC Transmission system (FACTS) devices may used in the power system to improve the quality of the power supply and to reduce the cost of the generation. FACTS devices are classified into series, shunt, shunt-series and series-series connected devices. Unified power flow controller (UPFC) is shunt-series type device that posses all capabilities to control real, reactive powers, voltage and reactance of the connected line in the power system. Hence, UPFC is included in the considered IEEE 30 bus for the OPF solution.

Improved Proximal Policy Optimization Algorithm for Sequential Security-constrained Optimal Power Flow Based on Expert Knowledge and Safety Layer

In recent years,reinforcement learning(RL)has emerged as a solution for model-free dynamic programming problem that cannot be effectively solved by traditional optimization methods.It has gradually been applied in the fields such as economic dispatch of power systems due to its strong selflearning and self-optimizing capabilities.However,existing economic scheduling methods based on RL ignore security risks that the agent may bring during exploration,which poses a risk of issuing instructions that threaten the safe operation of power system.Therefore,we propose an improved proximal policy optimization algorithm for sequential security-constrained optimal power flow(SCOPF)based on expert knowledge and safety layer to determine active power dispatch strategy,voltage optimization scheme of the units,and charging/discharging dispatch of energy storage systems.The expert experience is introduced to improve the ability to enforce constraints such as power balance in training process while guiding agent to effectively improve the utilization rate of renewable energy.Additionally,to avoid line overload,we add a safety layer at the end of the policy network by introducing transmission constraints to avoid dangerous actions and tackle sequential SCOPF problem.Simulation results on an improved IEEE 118-bus system verify the effectiveness of the proposed algorithm.

Risk Control of Transmission Line Overload for Wind-Integrated Power Systems

With the rapid development of the wind generation,uncertainties of random wind and load bring some inevitable impacts on the security of power system. Once the uncertainty causes line power to exceed its limit, line overload will occur. The paper presents the risk control of transmission line overload for windintegrated power systems. Firstly, a risk control model of line overload is proposed considering the uncertainties of loads,generator outputs and wind powers. The generation cost and security level of system associated with overload can be optimally controlled. Then path following interior point method is employed to carry out the optimal control. Finally the simulation is made on the modified IEEE-30 bus system. Results show that the risk of line overload is effectively reduced through the optimization of control variables.

Disturbance Evaluation in Power System Based on Machine Learning

The operation complexity of the distribution system increases as a large number of distributed generators(DG)and electric vehicles were introduced,resulting in higher demands for fast online reactive power optimization.In a power system,the characteristic selection criteria for power quality disturbance classification are not universal.The classification effect and efficiency needs to be improved,as does the generalization potential.In order to categorize the quality in the power signal disturbance,this paper proposes a multi-layer severe learning computer auto-encoder to optimize the input weights and extract the characteristics of electric power quality disturbances.Then,a multi-label classification algorithm based on rating is proposed to understand the relationship between the labels and identify the various power quality disturbances.The two algorithms are combined to construct a multi-label classification model based on a multi-level extreme learning machine,and the optimal network structure of the multi-level extreme learning machine as well as the optimal multi-label classification threshold are developed.The proposed method can be used to classify the single and compound power quality disturbances with improved classification effect,reliability,robustness,and anti-noise performance,according to the experimental results.The hamming loss obtained by the proposed algorithm is about 0.17 whereas ML-RBF,SVM and ML-KNN schemes have 0.28,0.23 and 0.22 respectively at a noise intensity of 20 dB.The average precision obtained by the proposed algorithm 0.85 whereas the ML-RBF,SVM and ML-KNN schemes indicates 0.7,0.77 and 0.78 respectively.

Comparison of Economic Dispatch, OPF and Security Constrained-OPF in Power System Studies RN

Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has also increased as more devices are being connected to the network. To understand the physical laws governing the operation of the network, techniques such as optimal power flow (OPF), Economic dispatch (ED) and Security constrained optimal power flow (SCOPF) were developed. These techniques have been used extensively in network operation, planning and so on. However, an in-depth presentation showcasing the merits and demerits of these techniques is still lacking in the literature. Hence, this paper intends to fill this gap. In this paper, Economic dispatch, optimal power flow and security-constrained optimal power flow are applied to a 3-bus test system using a linear programming approach. The results of the ED, OPF and SC-OPF are compared and presented.

Optimal Dispatch in Power Systems with Intermittent Power Sources

With the increasing integration of intermittent power sources (IPSs) into the power system, the uncertainty of IPSs requires solution and current dispatch system needs improvement. This paper aims to generate the optimal dispatch plan for day-ahead scheduling and real-time dispatch using the proposed model of characteristic optimal power flow (COPF). The integral time period represented by the median load point and the heavy and light load point with simplicity and accuracy. Simulation case studies on a 30-bus system are presented, which shows that COPF is an effective model to generate the optimal dispatch plan for power systems with high penetration of IPSs.

LMP Congestion Management Using Enhanced STF-LODF in Deregulated Power System

Nowadays electricity market industry is become a major impact on power system for privatization and deregulation of power in global wise. As per the limitation of the transmission system, the complexity arises and the supply fact will be with demand at the time of balancing. The congestion of the power system is occurring based on the transmission limits of the power desire and amount for operating the system. In order to avoid transmission line congestion, enhanced STF-LODF method is proposed. It shows the regulated line transmission flow with generating units by implementing renewable energy resources (RER) based on enhanced STF-LODF in power systems. It avoids the congestion of transmission line frequently in the power system and manages price based on pricing and sensitivity approach, and also manages optimal location of congestion transmission and instability issues of voltage. The congestion management of Locational Marginal Pricing (LMP) is performed with minimum line loss, less cost, line flow, better sensitivity and better performances in optimal power flow and control flow. The efficiency of the proposed power system is analyzed and verified by the simulation results of tested IEEE 14 bus system.

Identification of Critical Lines in Power System Based on Optimal Load Shedding

Based on risk theory, considering the probability of an accident and the severity of the sequence, combining N-1 and N-2 security check, this paper puts forward a new risk index, which uses the amount of optimal load shedding as the severity of an accident consequence to identify the critical lines in power system. Taking IEEE24-RTS as an example, the simulation results verify the correctness and effectiveness of the proposed index.

An Efficient Hybrid TLBO-PSO Approach for Congestion Management Employing Real Power Generation Rescheduling

In the present deregulated electricity market, power system congestion is the main complication that an independent system operator (ISO) faces on a regular basis. Transmission line congestion trigger serious problems for smooth functioning in restructured power system causing an increase in the cost of transmission hence affecting market efficiency. Thus, it is of utmost importance for the investigation of various techniques in order to relieve congestion in the transmission network. Generation rescheduling is one of the most efficacious techniques to do away with the problem of congestion. For optimizing the congestion cost, this work suggests a hybrid optimization based on two effective algorithms viz Teaching learning-based optimization (TLBO) algorithm and Particle swarm optimization (PSO) algorithm. For binding the constraints, the traditional penalty function technique is incorporated. Modified IEEE 30-bus test system and modified IEEE 57-bus test system are used to inspect the usefulness of the suggested methodology.

A review on applications of heuristic optimization algorithms for optimal power flow in modern power systems

Optimal power flow(OPF)is one of the key tools for optimal operation and planning of modern power systems.Due to the high complexity with continuous and discrete control variables,modern heuristic optimization algorithms(HOAs)have been widely employed for the solution of OPF.This paper provides an overview of the latest applications of advanced HOAs in OPF problems.The most frequently applied HOAs for solving the OPF problem in recent years are covered and briefly introduced,including genetic algorithm(GA),differential evolution(DE),particle swarm optimization(PSO),and evolutionary programming(EP),etc.

Small-signal Stability Constrained Optimal Power Flow Considering Eigenvalue Distribution

In the existing small-signal stability constrained optimal power flow(SSSC-OPF)algorithms,only the rightmost eigenvalue or eigenvalues that do not satisfy a given threshold,e.g.,damping ratio threshold and real-part threshold of eigenvalue,are considered in the small-signal stability constraints.The effect of steady-state,i.e.,operating point,changes on eigenvalues is not fully taken into account.In this paper,the small-signal stability constraint that can fully reflect the eigenvalue change and system dynamic performance requirement is formed by analyzing the eigenvalue distribution on the complex plane.The small-signal stability constraint is embedded into the standard optimal power flow model for generation reschedul-ing.The simultaneous solution formula of the SSSC-OPF is established and solved by the quasi-Newton approach,while penalty factors corresponding to the eigenvalue constraints are determined by the stabilization degree of constrained eigenvalues.To improve the computation speed,a hybrid algorithm for eigenvalue computation in the optimization process is proposed,which includes variable selection for eigenvalue estimation and strategy selection for eigenvalue computation.The effectiveness of the proposed algorithm is tested and validated on the New England 10-machine 39-bus system and a modified practical 68-machine 2395-bus system.

Convexification of Hybrid AC-DC Optimal Power Flow with Line-Commutated Converters

Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.

Learning the optimal power flow:Environment design matters

To solve the optimal power flow(OPF)problem,reinforcement learning(RL)emerges as a promising new approach.However,the RL-OPF literature is strongly divided regarding the exact formulation of the OPF problem as an RL environment.In this work,we collect and implement diverse environment design decisions from the literature regarding training data,observation space,episode definition,and reward function choice.In an experimental analysis,we show the significant impact of these environment design options on RL-OPF training performance.Further,we derive some first recommendations regarding the choice of these design decisions.The created environment framework is fully open-source and can serve as a benchmark for future research in the RL-OPF field.