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.

Economic Analysis of Demand Response Incorporated Optimal Power Flow

Demand Response(DR)is one of the most cost-effective and unfailing techniques used by utilities for consumer load shifting.This research paper presents different DR programs in deregulated environments.The description and the classification of DR along with their potential benefits and associated cost components are presented.In addition,most DR measurement indices and their evaluation are also highlighted.Initially,the economic load model incorporated thermal,wind,and energy storage by considering the elasticity market price from its calculated locational marginal pricing(LMP).The various DR programs like direct load control,critical peak pricing,real-time pricing,time of use,and capacity market programs are considered during this study.The effect of demand response in electricity prices is highlighted using a simulated study on IEEE 30 bus system.Simulation is done by the Shuffled Frog Leap Algorithm(SFLA).Comprehensive performance comparison on voltage deviations,losses,and cost with and without considering DR is also presented in this paper.

OPTIMAL POWER ALLOCATION WITH AF AND SDF STRATEGIES IN DUAL-HOP COOPERATIVE MIMO NETWORKS

Dual-hop cooperative Multiple-Input Multiple-Output (MIMO) network with multi-relay cooperative communication is introduced. Power allocation problem with Amplify-and-Forward (AF) and Selective Decode-and-Forward (SDF) strategies in multi-node scenario are formulated and solved respectively. Optimal power allocation schemes that maximize system capacity with AF strategy are presented. In addition, optimal power allocation methods that minimize asymptotic Symbol Error Rate (SER) with SDF cooperative protocol in multi-node scenario are also proposed. Furthermore, performance comparisons are provided in terms of system capacity and approximate SER. Numerical and simulation results confirm our theoretical analysis. It is revealed that, maximum system capacity could be obtained when powers are allocated optimally with AF protocol, while minimization of system's SER could also be achieved with optimum power allocation in SDF strategy. In multi-node scenario, those optimal power allocation algorithms are superior to conventional equal power allocation schemes.

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.

Constraint Learning-based Optimal Power Dispatch for Active Distribution Networks with Extremely Imbalanced Data

Transition towards carbon-neutral power systems has necessitated optimization of power dispatch in active distribution networks(ADNs)to facilitate integration of distributed renewable generation.Due to unavailability of network topology and line impedance in many distribution networks,physical model-based methods may not be applicable to their operations.To tackle this challenge,some studies have proposed constraint learning,which replicates physical models by training a neural network to evaluate feasibility of a decision(i.e.,whether a decision satisfies all critical constraints or not).To ensure accuracy of this trained neural network,training set should contain sufficient feasible and infeasible samples.However,since ADNs are mostly operated in a normal status,only very few historical samples are infeasible.Thus,the historical dataset is highly imbalanced,which poses a significant obstacle to neural network training.To address this issue,we propose an enhanced constraint learning method.First,it leverages constraint learning to train a neural network as surrogate of ADN's model.Then,it introduces Synthetic Minority Oversampling Technique to generate infeasible samples to mitigate imbalance of historical dataset.By incorporating historical and synthetic samples into the training set,we can significantly improve accuracy of neural network.Furthermore,we establish a trust region to constrain and thereafter enhance reliability of the solution.Simulations confirm the benefits of the proposed method in achieving desirable optimality and feasibility while maintaining low computational complexity.

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.

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.

Robust N−k Security-constrained Optimal Power Flow Incorporating Preventive and Corrective Generation Dispatch to Improve Power System Reliability

As extreme weather events have become more frequent in recent years,improving the resilience and reliability of power systems has become an important area of concern.In this paper,a robust preventive-corrective security-constrained optimal power flow(RO-PCSCOPF)model is proposed to improve power system reliability under N−k outages.Both the short-term emergency limit(STL)and the long-term operating limit(LTL)of the post-contingency power flow on the branch are considered.Compared with the existing robust corrective SCOPF model that only considers STL or LTL,the proposed ROPCSCOPF model can achieve a more reliable generation dispatch solution.In addition,this paper also summarizes and compares the solution methods for solving the N−k SCOPF problem.The computational efficiency of the classical Benders decomposition(BD)method,robust optimization(RO)method,and line outage distribution factor(LODF)method are investigated on the IEEE 24-bus Reliability Test System and 118-bus system.Simulation results show that the BD method has the worst computation performance.The RO method and the LODF method have comparable performance.However,the LODF method can only be used for the preventive SCOPF and not for the corrective SCOPF.The RO method can be used for both.

Estimating Risk-aware Flexibility Areas for Electric Vehicle Charging Pools via AC Stochastic Optimal Power Flow

This paper introduces an AC stochastic optimal power flow(SOPF)for the flexibility management of electric vehicle(EV)charging pools in distribution networks under uncertainty.The AC SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks.An application of the AC SOPF is described where a distribution system operator(DSO)requires flexibility to each charging pool in a day-ahead time frame,minimizing the cost for flexibility while guaranteeing technical limits.Flexibility areas are defined for each charging pool and calculated as a function of a risk parameter involving the uncertainty of the solution.Results show that all players can benefit from this approach,i.e.,the DSO obtains a riskaware solution,while charging pools/tasks perceive a reduction in the total energy payment due to flexibility services.

Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.

Numerical study on the optimal power distribution of server racks in a data center

Data centers,as the infrastructure of all information services,cost tremendous amount of energy.Reducing the hot spot temperature in the data center room is benefit to prevent overheating of devices,and to increase cooling system efficiency.In this paper,we study the problem of optimal power distribution among racks for minimal hot spot temperature.The temperature rise matrix(TRM)model is used for the purpose of fast estimation of the thermal environment.The accuracy of the model is evaluated by conducting numerical simulations of computational fluid dynamics(CFD).Using the TRM model,optimal distributing of heating power is converted into a linear programming problem,which can be solved by highly efficient algorithms,such as Simplex.Furthermore,with realistic constraints including rack idle power and power upper limit,an iteration method is proposed to calculate the optimal power distribution along with the optimal on/off states of the racks.Obtained solutions are discussed and validated by comparing with CFD simulations.Results show that the TRM model is acceptable in evaluating temperature rises in the forced-convection-dominated scenarios,and the proposed method is able to obtain optimal power distributions under various levels of total power demand.

Multi-period integrated natural gas and electric power system probabilistic optimal power flow incorporating power-to-gas units

The increasing adoption of gas-fired power plants directly strengthens the coupling between electric power and natural gas systems. Current industrial practice in optimal power flow for electric power systems has not taken the security constraints of gas systems into consideration, resulting in an overly-optimistic solution. Meanwhile, the operation of electric power and natural gas systems is coupled over multiple periods because of the ramp rate limits of power generators and the slow dynamical characteristics of gas systems. Based on these motivations, we propose a multi-period integrated natural gas and electric power system probabilistic optimal power flow(M-GEPOPF) model, which includes dynamic gas flow models. To address the uncertainties originating from wind power and load forecasting, a probabilistic optimal power flow(POPF) calculation based on a three-point estimate method(3 PEM) is adopted. Moreover, power-togas(Pt G) units are employed to avoid wind power curtailment and enable flexible bi-directional energy flows between the coupled energy systems. An integrated IEEE RTS 24-bus electric power system and the Belgian 20-node natural gas system are employed as a test case to verify the applicability of the proposed M-GEPOPF model, and to demonstrate the potential economic benefits of Pt G units.

Hierarchical Optimal Power Flow Control for Loss Minimization in Hybrid Multi-terminal HVDC Transmission System

A hierarchical control scheme is proposed for optimal power flow control to minimize loss in a hybrid multiterminal HVDC(hybrid-MTDC)transmission system.In this scheme,the lower level is the droop control,which enables fast response to power fluctuation and ensures a stable DC voltage,and the upper level is power flow optimization control,which minimizes the losses during the operation of hybrid-MTDC and solves the contradiction between minimizing losses and preventing commutation failure.A 6-terminal hybrid-MTDC is also designed and simulated in PSCAD according to the potential demand of power transmission and wind farms integration in China to verify the proposed control strategy.First,the steady state analysis is conducted and then compared with simulation results.The analysis shows that the proposed control scheme achieves the desired minimum losses while at the same time satisfying system constraints.The proposed control scheme also guarantees that the hybrid-MTDC not only has a good dynamic response,but also remains stable during communication failure.

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.

Multi-objective Dynamic Optimal Power Flow of Wind Integrated Power Systems Considering Demand Response

This paper studies the economic environmental energy-saving day-ahead scheduling problem of power systems considering wind generation(WG)and demand response(DR)by means of multi-objective dynamic optimal power flow(MDOPF).Within the model,fuel cost,carbon emission and active power losses are taken as objectives,and an integrated dispatch modeof conventional coal-fired generation,WG and DRis utilized.The corresponding solution process to the MDOPF is based on ahybrid of a non-dominated sorting genetic algorithm-II(NSGA-II)and fuwzy satisfaction-maximizing method,where NSGA-II obtains the Pareto frontier and the fuzzy satisfaction-maximizing method is the chosen strategy.Illustrative cases of different scenarios are performed based on an IEEE 6-units\,30-nodes system,to verify the proposed model and the solution process,as well as the benefits obtained by the DR into power system.

Deep Reinforcement Learning Based Approach for Optimal Power Flow of Distribution Networks Embedded with Renewable Energy and Storage Devices

This study proposes a deep reinforcement learning(DRL)based approach to analyze the optimal power flow(OPF)of distribution networks(DNs)embedded with renewable energy and storage devices.First,the OPF of the DN is formulated as a stochastic nonlinear programming problem.Then,the multi-period nonlinear programming decision problem is formulated as a Markov decision process(MDP),which is composed of multiple single-time-step sub-problems.Subsequently,the state-of-the-art DRL algorithm,i.e.,proximal policy optimization(PPO),is used to solve the MDP sequentially considering the impact on the future.Neural networks are used to extract operation knowledge from historical data offline and provide online decisions according to the real-time state of the DN.The proposed approach fully exploits the historical data and reduces the influence of the prediction error on the optimization results.The proposed real-time control strategy can provide more flexible decisions and achieve better performance than the pre-determined ones.Comparative results demonstrate the effectiveness of the proposed approach.

A Data-driven Method for Fast AC Optimal Power Flow Solutions via Deep Reinforcement Learning

With the increasing penetration of renewable energy,power grid operators are observing both fast and large fluctuations in power and voltage profiles on a daily basis.Fast and accurate control actions derived in real time are vital to ensure system security and economics.To this end,solving alternating current(AC)optimal power flow(OPF)with operational constraints remains an important yet challenging optimization problem for secure and economic operation of the power grid.This paper adopts a novel method to derive fast OPF solutions using state-of-the-art deep reinforcement learning(DRL)algorithm,which can greatly assist power grid operators in making rapid and effective decisions.The presented method adopts imitation learning to generate initial weights for the neural network(NN),and a proximal policy optimization algorithm to train and test stable and robust artificial intelligence(AI)agents.Training and testing procedures are conducted on the IEEE 14-bus and the Illinois 200-bus systems.The results show the effectiveness of the method with significant potential for assisting power grid operators in real-time operations.

Scheduling Framework Using Dynamic Optimal Power Flow for Battery Energy Storage Systems

Battery energy storage systems(BESS)are instrumental in the transition to a low carbon electrical network with enhanced flexibility,however,the set objective can be accomplished only through suitable scheduling of their operation.This paper develops a dynamic optimal power flow(DOPF)-based scheduling framework to optimize the day(s)-ahead operation of a grid-scale BESS aiming to mitigate the predicted limits on the renewable energy generation as well as smooth out the network demand to be supplied by conventional generators.In DOPF,all the generating units,including the ones that model the exports and imports of the BESS,across the entire network and the complete time horizon are integrated on to a single network.Subsequently,an AC-OPF is applied to dispatch their power outputs to minimize the total generation cost,while satisfying the power balance equations,and handling the unit and network constraints at each time step coupled with intertemporal constraints associated with the state of charge(SOC).Furthermore,the DOPF developed here entails the frequently applied constant current-constant voltage charging profile,which is represented in the SOC domain.Considering the practical application of a 1 MW BESS on a particular 33 kV network,the scheduling framework is designed to meet the pragmatic requirements of the optimum utilization of the available energy capacity of BESS in each cycle,while completing up to one cycle per day.

Optimal power flow calculation in AC/DC hybrid power system based on adaptive simplified human learning optimization algorithm

This paper employs an efficacious analytical tool,adaptive simplified human learning optimization(ASHLO)algorithm,to solve optimal power flow(OPF)problem in AC/DC hybrid power system,considering valve-point loading effects of generators,carbon tax,and prohibited operating zones of generators,respectively.ASHLO algorithm,involves random learning operator,individual learning operator,social learning operator and adaptive strategies.To compare and analyze the computation performance of the ASHLO method,the proposed ASHLO method and other heuristic intelligent optimization methods are employed to solve OPF problem on the modified IEEE 30-bus and 118-bus AC/DC hybrid test system.Numerical results indicate that the ASHLO method has good convergent property and robustness.Meanwhile,the impacts of wind speeds and locations of HVDC transmission line integrated into the AC network on the OPF results are systematically analyzed.