Solution of Combined Heat and Power Economic Dispatch Problem Using Direct Optimization Algorithm

This paper presents the solution to the combined heat and power economic dispatch problem using a direct solution algorithm for constrained optimization problems. With the potential of Combined Heat and Power (CHP) production to increase the efficiency of power and heat generation simultaneously having been researched and established, the increasing penetration of CHP systems, and determination of economic dispatch of power and heat assumes higher relevance. The Combined Heat and Power Economic Dispatch (CHPED) problem is a demanding optimization problem as both constraints and objective functions can be non-linear and non-convex. This paper presents an explicit formula developed for computing the system-wide incremental costs corresponding with optimal dispatch. The circumvention of the use of iterative search schemes for this crucial step is the innovation inherent in the proposed dispatch procedure. The feasible operating region of the CHP unit three is taken into account in the proposed CHPED problem model, whereas the optimal dispatch of power/heat outputs of CHP unit is determined using the direct Lagrange multiplier solution algorithm. The proposed algorithm is applied to a test system with four units and results are provided.

Robust optimal dispatch strategy of integrated energy system considering CHP-P2G-CCS

Integrated energy systems(IESs)can improve energy efficiency and reduce carbon emissions,essential for achieving peak carbon emissions and carbon neutrality.This study investigated the characteristics of the CHP model considering P2G and carbon capture systems,and a two-stage robust optimization model of the electricity-heat-gascold integrated energy system was developed.First,a CHP model considering the P2G and carbon capture system was established,and the electric-thermal coupling characteristics and P2G capacity constraints of the model were derived,which proved that the model could weaken the electric-thermal coupling characteristics,increase the electric power regulation range,and reduce carbon emissions.Subsequently,a two-stage robust optimal scheduling model of an IES was constructed,in which the objective function in the day-ahead scheduling stage was to minimize the start-up and shutdown costs.The objective function in the real-time scheduling stage was to minimize the equipment operating costs,carbon emission costs,wind curtailment,and solar curtailment costs,considering multiple uncertainties.Finally,after the objective function is linearized with a ψ-piecewise method,the model is solved based on the C&CG algorithm.Simulation results show that the proposed model can effectively absorb renewable energy and reduce the total cost of the system.

Combined Electric and Heat System Testbeds for Power Flow Analysis and Economic Dispatch

In combined electric and heat systems,selecting a suitable testbed for power flow analysis or economic dispatch is not easy:a large number of existing testbeds are not opensource,while others are difficult to be reused by other researchers due to the particularity of system scale,topology,and data.In this paper,we present three open-source testbeds with different scales based on practical combined electric and heat systems.To satisfy researchers"specific demands on the system topology and data,we also discuss how to modify testbeds based on existing topologies and data.Researchers can use the testbeds presented in this paper to test their innovative methods for power flow analysis and economic dispatch,and can also design their own testbeds based on the methodology in this paper,using published topologies and data.

Integrated Heat and Power Dispatch Model for Wind-CHP System with Solid Heat Storage Device Based on Robust Stochastic Theory

This paper built a combined heat and power（CHP） dispatch model for wind-CHP system with solid heat storage device（SHS） aiming at minimizing system coal consumption, and set system demand-supply balance and units＇ operation conditions as the operation constraints. Furthermore, robust stochastic optimization theory was used to describe wind power output uncertainty. The simulation result showed that SHS increased CHP peak-valley shifting capability and reduced abandoned wind rate from 12% to 6%, and reduced 5% coal consumption, compared with the original system operation by flexible charging electric power and heating. The payback period of employing SHS in wind-CHP system is far shorter than SHS expected service life.

Optimal Combined Heat and Power Economic Dispatch Using Stochastic Fractal Search Algorithm

Combined heat and power(CHP)generation is a valuable scheme for concurrent generation of electrical and thermal energies.The interdependency of power and heat productions in CHP units introduces complications and non-convexities in their modeling and optimization.This paper uses the stochastic fractal search(SFS)optimization technique to treat the highly non-linear CHP economic dispatch(CHPED)problem,where the objective is to minimize the total operation cost of both power and heat from generation units while fulfilling several operation interdependent limits and constraints.The CHPED problem has bounded feasible operation regions and many local minima.The SFS,which is a recent metaheuristic global optimization solver,outranks many current reputable solvers.Handling constraints of the CHPED is achieved by employing external penalty parameters,which penalize infeasible solution during the iterative process.To confirm the strength of this algorithm,it has been tested on two different test systems that are regularly used.The obtained outcomes are compared with former outcomes achieved by many different methods reported in literature of CHPED.The results of this work affirm that the SFS algorithm can achieve improved near-global solution and compare favorably with other commonly used global optimization techniques in terms of the quality of solution,handling of constraints and computation time.

Stochastic Accelerated Alternating Direction Method of Multipliers for Hedging Communication Noise in Combined Heat and Power Dispatch

Combined heat and power dispatch(CHPD)opens a new window for increasing operational flexibility and reducing wind power curtailment.Electric power and district heating systems are independently controlled by different system operators;therefore,a decentralized solution paradigm is necessary for CHPD,in which only minor boundary information is required to be exchanged via a communication network.However,a nonideal communication environment with noise could lead to divergence or incorrect solutions of decentralized algorithms.To bridge this gap,this paper proposes a stochastic accelerated alternating direction method of multipliers(SA-ADMM)for hedging communication noise in CHPD.This algorithm provides a general framework to address more types of constraint sets and separable objective functions than the existing stochastic ADMM.Different from the single noise sources considered in the existing stochastic approximation methods,communication noise from multiple sources is addressed in both the local calculation and the variable update stages.Case studies of two test systems validate the effectiveness and robustness of the proposed SAADMM.

Dispatch Model for Integrated Heat and Power Systems Considering Internal Composition of CHP Plants

An integrated heat and power system(IHPS)is a promising approach for alleviating wind curtailment problems.In an IHPS,the combined heat and power(CHP)plant is the key component,which supplies both heat and electric loads,and couples the thermal system and power system.However,existing research commonly ignores or simplifies the internal composition of CHP plants,which could lead to some unavoidable errors.This paper focuses on the internal composition of CHP plants,and models the physical processes in different components and flexible resources in the CHP plant.Furthermore,a joint dispatch problem of an IHPS with the above CHP plant models is formulated,and an iterative algorithm is developed to handle the nonlinearity in this problem.Case studies are performed based on a real CHP plant in Northern China,and the results indicate that the synergistic effect of different energy resources in the CHP plant is realized by the joint dispatch model,which promotes wind power accommodation and reduces fossil fuel consumption.

考虑外送输电容量限制的梯级水光互补日前鲁棒调峰调度方法

水光联合外送可促进新能源消纳,但光伏出力预测的不确定性会影响水光互补优化调度的经济性和安全性。提出一种考虑外送输电容量限制的梯级水光互补联合发电系统日前鲁棒调度方法。考虑光伏出力不确定性,构建水光互补联合发电系统的日前调峰鲁棒优化调度模型,该模型以最小化受端电网剩余负荷峰谷差为目标,计及梯级水电的上、下游水力耦合约束。采用高效线性化方法对梯级水电运行的非线性模型进行处理,并利用对偶方法实现鲁棒模型的确定性转化。算例仿真结果表明,利用所提方法制定的梯级水电发电计划能充分考虑光伏出力的不确定性,兼顾联合发电系统调峰效果和光伏消纳,实现梯级水电和光伏的互补运行。

基于CHP机组碳排放分析的综合能源系统低碳调度优化方法

针对现有研究对于热电联产(CHP)机组碳排放计算不符合实际物理特性的问题,提出了基于CHP碳排放分析的综合能源系统(IES)低碳调度优化方法。从CHP机组内部结构入手,分析CHP机组内部各部分之间能量的传递过程,绘制CHP机组功率与碳排流向图,列写各个部分的功率平衡方程,得到CHP机组排放废气的等效热功率;计及碳排放量与废气排放速率的关系,结合废气排放的热力学方程,得到CHP机组废气排放速率与输入气流量及输出功率的关系;提出基于CHP机组碳排放分析的IES低碳调度优化模型,以总运行成本最小为目标,求解IES低碳调度优化结果;通过算例分析不同CHP机组运行方式下的优化调度结果,并与现有方法进行对比,验证了所提模型在降低碳排放方面的有效性。

Q学习差分进化算法求解热电动态经济排放调度

热电联产动态经济排放调度同时考虑了燃料成本花费和污染气体排放两个目标值,且下一时间段的热电产量受当前时间段热电产量的影响,这是近年来电力系统运行中的一个重要问题。文中提出一种基于Q学习强化多目标差分进化(Q Learning Multi-Objective Differential Evolution,QLMODE)算法,以此求解热电联产动态经济排放调度(Combined Heat and Power Dynamic Economic Emission Dispatch,CHPDEED)问题。在QLMODE中,采用Q学习技术调整算法的比例因子参数,即在迭代过程中利用子代解和父代解之间的支配关系确定动作奖励和惩罚,并通过Q学习调整参数值,以获得最适合环境模型的算法参数。文中将所提QLMODE用于求解11机组和33机组的热电联产动态经济排放调度问题。仿真结果表明,与4种成熟的多目标优化算法相比,QLMODE算法燃料成本最小,污染气体排放最少,收敛性和多样性指标优于其他4种算法,且QLMODE在两组问题上都获得了更好的Pareto最优前沿。

计及改进阶梯型碳交易和热电联产机组灵活输出的园区综合能源系统低碳调度

为了进一步降低园区综合能源系统(park-level integrated energy system,PIES)碳排放量,优化热电联产(combined heat and power,CHP)机组出力的灵活性,提出一种考虑改进阶梯型碳交易和CHP热电灵活输出的PIES低碳经济调度策略。首先,将遗传算法与模糊控制相结合,设计一种遗传模糊碳交易参数优化器,从而对现有阶梯型碳交易机制进行改进,实现该机制参数的自适应变化;其次,在传统CHP中加入卡琳娜(Kalina)循环与电锅炉(electricboiler,EB),构造CHP热电灵活输出模型,以同时满足电、热负荷的不同需求;然后,提出一种柔性指标——电、热输出占比率,进而计算出电、热输出占比率区间,以衡量CHP运行灵活性;最后,将改进阶梯型碳交易机制和CHP热电灵活输出模型协同优化,以系统运行成本和碳交易成本之和最小为目标,构建PIES低碳经济优化模型。算例分析表明,所提策略可有效降低经济成本和碳排放量,同时还可扩展CHP灵活输出调节范围,能够为PIES低碳经济调度提供参考。

计及蓄热罐与管网虚拟储能热电联供系统的经济运行优化分析

本文建立计及蓄热罐与管网虚拟储能热电联供系统模型,探讨不同储能装置配置(如无储能装置、含虚拟储能、含蓄热罐、含蓄热罐与虚拟储能)下负荷场景、燃煤价格、管网长度对系统运行成本的影响。结果表明:含蓄热罐与虚拟储能的储能配置使得热电联供系统的运行成本大幅降低,且当热电负荷波动较大时,运行成本降幅更大,如工业负荷场景下降幅达26.12%;燃料价格上涨使得系统运行成本线性增加,但相比于无储能装置,含储能装置系统的运行成本仍然较低,经济性更好;由于管网储能容量限制以及管网热损的影响,存在一个最佳管长使得系统运行成本最小。

电-热-氢综合能源系统鲁棒区间优化调度

储能技术与风电相结合实现电能的时空平移是解决系统运行稳定性问题的有效手段。氢储能具有储存容量大、可实现电热联产联供的优点,具有很大的发展潜能。然而由于风电存在不确定性,氢储能系统在频繁切换工作模式时面临着不确定的热能需求。因此,文中综合考虑氢储能在间歇模式下的热能需求,首先,介绍了氢储能系统接入的电-热综合能源系统基本结构,将风电场与氢储能相结合构成风-氢混合系统;然后,提出考虑风-氢混合系统热平衡需求不确定性的电-热综合能源系统鲁棒区间优化调度模型;最后,基于对偶理论,对所提出的模型转化求解,通过算例对比分析各类情况优化结果,验证了氢储能在促进风电消纳、提高系统能源综合利用率方面的有效性,并证明了考虑电解槽和燃料电池工作温度能提高系统的工作效率并提高风电场并网功率。

多市场参与下热电联产虚拟电厂低碳经济协同调度方法

热电联产(combined heat and power,CHP)机组与虚拟电厂(virtual power plant,VPP)结合,可以有效提高能源利用效率,增强电力系统运行的可靠性及稳定性。为保证CHP-VPP灵活、低碳、经济运行,文中提出一种聚合风电、光伏、CHP机组、锅炉、碳捕集设备、燃气轮机、燃料电池、储能及电、热负荷的综合能源VPP,并在参与电-热-旋转备用-碳等多市场下,研究其低碳经济协同调度问题。首先,以各时刻VPP在多市场下整体净收益最大为目标,建立其CHP-VPP两阶段鲁棒优化调度模型;然后,考虑新能源出力、市场价格及负荷的不确定性,利用蒙特卡洛法进行场景削减,从而降低系统风险,增强其鲁棒性;最后,采用列与约束生成算法对模型进行求解,得到最恶劣场景下系统运行的经济性最优调度方案。仿真结果表明:所提综合能源VPP结构合理,可通过动态调整碳捕集设备及储能电池,达到平抑新能源出力波动的效果,从而实现碳排放的大幅降低;所提调度策略可有效保证源-荷-储多侧电、热资源的协同优化运行,提高VPP的灵活性、经济性和低碳性。

考虑风电消纳的电热联合系统优化调度模型

电热联合系统能够有效整合电能和热能,具有显著的能源利用优势。为了分析电热联合调度的经济节能效果,在分时电价以及负荷波动的条件下,建立了包含风电场、能源集线器(energy hub,EH)、热泵和蓄热罐的电热联合系统优化调度模型。电热联合系统以日运行成本最小为目标,考虑了稳态电热联合潮流、储能设备动态特性、管道温度降方程等实际约束条件。为提高优化效率,采用方程线性化和分段McCormick凸包络技术处理约束中的非线性项,将原本的非凸优化问题转化为混合整数二次规划(mixed integer quadratic programming,MIQP)问题求解。通过算例分析验证了所提模型的有效性,在4种场景下比较了风电制热以及热网传输损耗对系统日运行成本和弃风量的影响,并确定了风电场接入热网的最佳节点。结果表明,电热联合系统能够将不稳定的风能转化为稳定的热能,从而有效提升风电消纳空间和系统经济效益。

绿证与改进型阶梯式碳交易互动机制下的CHP系统低碳经济调度研究

为了进一步降低热电联产型源荷系统的碳排放量,同时兼顾经济效益,文章改进了普通阶梯式碳交易的交易模型,提出了一种绿证与改进型阶梯式碳交易互动机制下的CHP型源荷系统低碳经济调度策略。构建热电联供型能源系统模型,确定能源测、转换侧、负荷侧模型,同时构建需求响应机制;在数学模型的基础上构建双层调度模型,上层模型是改进型阶梯式碳交易优化模型,利用差分进化算法来实现阶梯式碳交易参数自适应变化;下层源荷系统调度仿真模型,以系统运行成本为目标函数,耦合了碳交易机制和绿证策略,实现直接、间接同时减排,同时利用Cplex求解器进行最优化求解。最后,建立四种典型场景,对比分析得出所提策略能显著降低碳排放量,同时具有较好的经济效益,能够为源荷系统低碳经济调度提供参考。

考虑个体自私的热电联产系统完全分布式经济调度

针对传统集中式经济调度策略需要获取全局信息以及无法适应系统灵活拓扑的缺陷,同时考虑能量以电能和热量形式并存出现的情况,基于一致性算法提出了一种完全分布式热电联产经济调度策略.将热电联产系统中各机组电价和热价的增量成本作为一致性变量进行迭代计算,直至增量成本达到收敛,实现系统经济最优.此外,还分析了个别机组为了提升自身利益,向相邻机组传输带有偏差增量成本值的情况,设计了一个增量成本补偿项来消除该自私行为的影响.在3个仿真算例中得到的结果表明,所提策略在解决热电联产系统经济调度问题中具有有效性和可行性.

交直流电力系统与供热系统联合经济调度

随着热电联产等技术的广泛应用,电力系统和供热系统耦合日益紧密,电热联合调度得到了广泛的关注,但现有电热联合调度忽略了热网供电来源的多样性,由此提出了交直流电力系统与供热系统联合经济调度方法。首先,建立交直流电力系统模型,并提出一种线性近似方法对电压源变换器模型所带来的强非线性进行处理;然后,以运行成本最低为目标,建立考虑热网热惯性的交直流电力系统与供热系统联合调度模型,该模型中供热系统通过热电联产机组和交流电锅炉与交流电网耦合,通过直流电锅炉与直流电网耦合;最后,通过算例仿真验证了所提方法的有效性并说明了在电热联合调度中考虑交直流电源的必要性。

Dynamic scheduling of market price-based combined heat–power-constrained renewable microgrid

In this paper,a market price-based combined heat–power dynamic dispatch model for a microgrid is presented.The microgrid comprises cogeneration units and wind and solar power-generation units.A battery and a heat storage tank are incorporated to optimally balance variations in heat-and-power load demands.The proposed model explores the impact of market prices of electricity,heat supply and load variability on the optimal schedule such that profit maximizes and emission,loss and waste heat are minimized.The Weibull probability distribution function is applied to characterize the uncertain renewable power variable in the model and to find the over-and under-scheduling costs.The problem is solved using an improved differential evolution algorithm in which a fuzzy membership module is appended to obtain a solution having the highest attainment for the selected multiple objectives.The results show that the proposed model can handle uncertain heat–power demand and price scenarios to produce feasible and optimal schedules with owner profits,heat utilization and renewable share varying between 10.55–115.97%,72.51–90.39%and 26.82–38.05%,respectively.

含储热的电力系统电热综合调度模型

分析了热电机组配置储热前后运行特性与调峰能力的变化情况,讨论了利用储热消纳弃风的基本运行机理,建立了含储热的电力系统电热综合调度模型。与传统模型相比,新模型增加了系统热平衡约束、热电机组的热电耦合约束、储热装置运行约束等,且模型目标扩展为供电和供热总煤耗最低。算例分析表明:所提模型是有效的;在热电厂中配置储热可有效提高电网的风电消纳水平,且消纳单位电量风电的节煤量要高于电锅炉消纳方案。