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.

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.

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.

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.

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.

Optimal power allocation for amplify-and-forward in single relay non-cooperative systems

For a single-relay amplify-and-forward (AF) non-cooperative system,an optimal power proportionbetween source and relay is considered.Aiming to minimize end-to-end bit error rate (BER) and maximizeattainable rate,both large-scale path loss and small-scale Rayleigh fading are taken into account.Aclosed form expression to allocate power in optimal proportion at source is obtained.Simulation resultsshow that the proposed scheme to distribute power can minimize BER under any channel conditions.

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.

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.

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.

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.

Two-stage Transient-stability-constrained Optimal Power Flow for Preventive Control of Rotor Angle Stability and Voltage Sags

In practice,an equilibrium point of the power system is considered transiently secure if it can withstand a specified contingency by maintaining transient evolution of rotor angles and voltage magnitudes within set bounds.A novel sequential approach is proposed to obtain transiently stable equilibrium points through the preventive control of transient stability and transient voltage sag(TVS)problems caused by a severe disturbance.The proposed approach conducts a sequence of non-heuristic optimal active power re-dispatch of the generators to steer the system toward a transiently secure operating point by sequentially solving the transient-stability-constrained optimal power flow(TSC-OPF)problems.In the proposed approach,there are two sequential projection stages,with the first stage ensuring the rotor angle stability and the second stage removing TVS in voltage magnitudes.In both projection stages,the projection operation corresponds to the TSC-OPF,with its formulation directly derived by adding only two steady-state variable-based transient constraints to the conventional OPF problem.The effectiveness of this approach is numerically demonstrated in terms of its accuracy and computational performance by using the Western System Coordinated Council(WSCC)3-machine 9-bus system and an equivalent model of the Mexican 46-machine 190-bus system.

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.

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.

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.

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.