【正文】 the value of objective function. MAPSO applied to optimal reactive power dispatch is evaluated on an IEEE 30bus power system and a practical 118bus power system. Simulation results show that the proposed approach converges to better solutions much faster than the earlier reported approaches. The optimization strategy is general and can be used to solve other power system optimization problems as well. Index Terms—Multiagent system, particle swarm optimization (PSO), power system, reactive power dispatch NOMENCLATURE Voltage angle difference between buses and (rad). Transfer susceptance between bus and (.). Active power loss in work (.). Transfer conductance between bus and (.). Conductance of branch (.). Set of numbers of total buses excluding slack bus. Set of numbers of total buses. Set of numbers of possible reactive power source installation buses. Set of numbers of power demand buses. Set of numbers of work branches. Set of numbers of generator buses. Set of numbers of buses adjacent to bus , including bus . Set of numbers of buses. Set of numbers of buses. Set of numbers of buses on which injected reactive power outside limits. Set of numbers of transformer branches. Set of numbers of buses on which voltages outside limits. Demanded active power at bus (.). 7 Injected active power at bus (.). Active power loss in branch (.). Power flow in branch (.). Injected active power at slack bus (.). Reactive power source installation at bus (.). Demanded reactive power at bus (.). Injected reactive power at bus (.). Tap position of transformer . Voltage magnitude of bus (.). Voltage vectors of buses (.). Voltage vectors of buses (.). Manuscript received August 13, 2020。 所有代理程式都像住在格子中一樣，與每個(gè)代理程式一起在每一個(gè)格點(diǎn)上定盤(pán)。粒子群最優(yōu)化（ PSO）是進(jìn)化估算技術(shù)的一種。 VPVPV 總線 PV 的電壓矢量（ .)。 NPQ 設(shè)定的 PQ 總線的數(shù)量。為了更好地利用主體和主體之間的反互相作用和 PSO 的發(fā)展構(gòu)造， MAPSO 充分認(rèn)識(shí)到了這種積極反應(yīng)的價(jià)值。這種最優(yōu)化方案適用性較廣，可以用于解決其他能源結(jié)構(gòu)的最優(yōu)化問(wèn) 題。 NT 設(shè)定的變壓器支線的數(shù)量。在滿足一個(gè)物質(zhì)的既定設(shè)置和操作系統(tǒng)參數(shù)時(shí)，傳送損失最低估計(jì)和其它適當(dāng)客觀的作用。盡管 PSO 看起來(lái)比一些重量和參數(shù)的調(diào)整更容易受影響，許多研究仍然在解決 復(fù)雜的能源系統(tǒng)問(wèn)題 上證明它的可能性的進(jìn)程。 MAPSO 被用來(lái)計(jì)算一個(gè)電器最佳的無(wú)功功率，并且在國(guó)際電子工程師協(xié)會(huì)上評(píng)估出的 30 總線的能量系統(tǒng)和一個(gè)實(shí)際的 118總線能量系統(tǒng)。 ). Digital Object Identifier I. INTRODUCTION THE reactive power dispatch problem has a significant influence on secure and economic operation of power systems. Reactive power optimization is a subproblem of theoptimal powerflow (OPF) calculation, which determines all kinds of controllable variables, such as reactivepower outputs of generators and static reactive power pensators, tap ratios of transformers, outputs of shunt capacitors/reactors, etc., and minimizes transmission losses or other appropriate objective functions, while satisfying a given set of physical and operating constraints. Since transformer tap ratios and outputs of shunt capacitors/reactors have a discrete nature, while reactive power outputs of generators and static VAR pensators, busvoltage magnitudes, and angles are, on the other hand, continuous variables, the reactive power 8 optimization problem can be exactly formulated using a mixedinteger/nonlinea