# Multiobjective Optimal Dispatching Method of Generalized Power Active Distribution Network Based on Game Theory

Authors: Xiaoxiang Fan
Journal: Security and Communication Networks
 (2021)

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## Abstract

To improve the operating dependability of a generalized power active distribution network, a multiobjective optimal scheduling approach based on game theory is proposed. The active distribution network's multistakeholder coordinated and optimal dispatching mode is then established, and the game interaction between various stakeholders in the generalized power active distribution network is evaluated. Using the multistakeholder game coordinated and optimal dispatching strategy, manage and regulate the distribution firms, distributed generation operators, and users engaging in demand response in the active distribution network, to guarantee that the distribution system runs smoothly and fairly. The rate of renewable energy usage, network loss, and user satisfaction are all factored into the multiobjective optimum scheduling objective function of a generalized power active distribution network. Using the multistakeholder game coordinated and optimal dispatching strategy, manage and regulate the distribution firms, distributed generation operators, and demand response participants in the active distribution network, to make sure the distribution system runs smoothly and equitably. Taking into account the rate of renewable energy usage, network loss, and user satisfaction, a multiobjective optimum scheduling objective function for a generalized power active distribution network is thus created.


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## Body

## 1. Introduction

China's energy demand is increasing on a daily basis as the country's social economy expands, but fossil fuels are becoming scarce, and nuclear energy growth is limited. Traditional power generation, which relies mostly on coal and oil, has a variety of drawbacks, including resource sustainability, climate change, and pollution. As a result, the production and utilization of renewable energy will gradually become the sole alternative for socially sustainable growth [1–3]. Because of its distinctive environmental protection and economics, minimal investment, flexible power generation mode, and environmental compatibility, the generalized power supply provided by wind power and solar has become an important aspect of future energy. As a result, generalized power supply has sparked widespread interest and quick development [4]. As a result of the growth of distributed generation, countries all over the world have looked at active distribution networks. When investors diversify their portfolios, the dispersed generating operator develops and controls additional energy connections to the distribution network, reversing the previous pattern in which the power grid was in charge of the generalized power supply [5–7]. In addition, demand response participants become additional distribution network stakeholders, when the autonomous optimization based on various interests are executed, and each stakeholder's income is influenced by the decision variables of other stakeholders. As a result, in the current environment, achieving the effective and fair functioning of a distribution network with diverse stakeholders is an urgent issue. A complete and accurate assessment of the effects of the dispatch strategy on the optimal design configurations of possible permutations of solar power plants with storage is presented [8] to examine four dispatch statuses (baseload, daylight, night, and daylight and evening), as well as four technology combinations, including a solar PV plant with batteries, a CSP plant with Thermal Storage (TES), and a hybrid CSP plant with TES. This study offers a two-stage multiobjective optimum scheduling technique (TMOS) in the integrated energy system based on the novel mathematical model of We-Energy (WE) (IES). As a new style energy unit with fully duplex and multienergy carrier coupling connection, a mathematical model is required to address the schema interpretation problem for WE scheduling. Two example scenarios are used to exemplify the suggested method, in which the performance of the TMOS is observed. In light of the energy exchanges with networks and the outputs of elements in the provided circumstance, the ramifications of the instances are examined [9]. This work presented an electric vehicle cluster dispatching strategy that considers demand response and uses Vehicle to Grid (V2G) technology to control charging and discharging behavior and provide forms of assistance for the power system, in light of the load fluctuations caused by large-scale access of electric vehicles to the power grid. The experiments show that when dispatching with the maximum profit of the user, after increasing the V2G response subsidy under the tiered power demand mode, the grid-side peak-to-valley ratio can be reduced by 2.99 percent, and the variance can be reduced by 9.52%, achieving the multiobjective optimization of V2G participation in power response [10]. The emphasis and challenge of microgrid optimization operation is how to effectively absorb renewable energy in the face of national carbon neutrality regulations. The previous optimization method, which focused solely on electricity generating cost, has struggled to satisfy current demand. As a result, the optimization objectives in this study are generation cost, environmental cost, and system resilience. The trials indicate that the algorithm and model are successful in increasing the share of renewable energy usage [11]. The optimized reactive power dispatch (ORPD) problem is important for the successful and dependable functioning of power systems, which is dependent on the appropriate coordination of multiple devices. A an improved salp swarm method is presented to resolve the ORPD issue for IEEE-14 and IEEE-30 bus systems by treating reactive power planning as a single- and multiobjective problem with the goal of reducing actual power losses and bus voltage variations [12]. Optimal operation in islanded microgrids is a fundamental and well-known nonlinear optimization issue that has been studied with new/different objective(s) in light of adaptive system limitations for successful power dispatch. In islanded microgrids, this study proposes a unique optimization approach with separate targets for optimum dispatch of both real and reactive power from Distributed Generations (DGs). The proposed technique does this by optimizing droop parameters in dispatchable DGs in order to achieve the best dispatch strategy for each DG in the microgrid [13]. Microgrids and combined cooling, heating, and power (CCHP) systems can work together to improve energy efficiency. This study offers a multiobjective optimum scheduling model for CCHP microgrids integrated with renewable energy, energy storage system, and incentive-based demand response in order to accomplish economic optimization and peak-load reduction of the CCHP microgrids model. Finally, a sensitivity analysis is performed, and the findings show that the prices of electricity, natural gas, and PV efficiency have various degrees of influence on model performance [14].


## 2. Construction of Multiobjective Coordinated Optimization Game Model for Generalized Power Active Distribution Network

Under the centralized dispatching mode of transmission, all generalized power sources are allocated to the distribution network, and the power output is globally regulated by the power distribution network [15]. After gathering data from each terminal in the distribution grid region under its authority, the dispatching center will uniformly send the dispatching results obtained by solving the optimum dispatching model to each terminal in the form of control instructions. The generalized power active distribution network's multiobjective scheduling optimization game model established performs targeted optimal scheduling based on the current power situation to improve the operation effect of each terminal [16]. The expression of multiobjective coordination optimization game model is(1)maxfx1,…,xi,…xn,s.t.Gx1,…,xi,…xn,Hx1,…,xi,…xn≤0,xi,min≤xi≤xi,max,where xi represents the optimization variables in the scheduling model, xi,min and xi,max represent the minimum and maximum values of the optimization variables, respectively, G represents the equality constraints to be satisfied in the scheduling model, and H represents the inequality constraints to be satisfied in the scheduling model.On the basis of ensuring the safe functioning of the generalized power distribution network, give the generalized power supply and users some autonomy, and study the coordinated optimum scheduling of the generalized power supply, users, and distribution network [17]. New stakeholders, such as generic power providers and consumers, are actively specifying power generating and use plans, participating in power grid dispatching, and reaping economic benefits as a consequence. Furthermore, by delegating the power grid's dispatching control authority over generalized power generation to each distributed generating operator for autonomous management, the enormous scale and complex control challenges of generalized power generation optimization may be handled [18–20]. On the other hand, each stakeholder has its own power generating and consumption plan as well as optimization objectives. To achieve consistency, mechanisms to coordinate and regulate the conflict variables of diverse stakeholders must be developed. The multiobjective optimal dispatching model of generalized power distribution network under the coordinated optimization mode of multistakeholders is provided as follows:(2)maxf1,1x1,…,xn,…,fm,sx1,…,xn,s.tGx1,…,xn=0,Hx1,…,xn≤0,xi,min≤xi≤xi,max,where m represents the number of stakeholders in the distribution network and s represents the number of optimization objectives of n among stakeholders. Multiple optimization objectives can be considered based on the actual situation of different stakeholders.The three parties in this study are demand response operators, distribution firms, and users. The operator anticipates benefiting from the generalized power output as a new interest topic in the distribution network with a desire to make choices first. Furthermore, the distribution company must modify tie line power or real-time electricity pricing in accordance with the operator's decision output, regardless of whether it adjusts tie line power or real-time electricity pricing. As a result, the operator is the higher subject in the game model. The operator's decision variable is the controllable generalized power output in each optimal dispatching period; based on the upper-level decision-making information, the distribution company guides its own tie line power adjustment, real-time electricity price, and incentive information of interruptible load; after receiving real-time electricity price information and incentive information, the distribution company guides its own tie line power adjustment, real-time electricity price, and incentive information of interruptible load. One of the basic causes for the game is the conflict between generalized power output and tie line power, which must be synchronized [21, 22]. In particular, if the distribution company's behavior is not taken into account when determining the generalized power supply's output, the operator may mistakenly believe that the distribution company is highly dependent on the main network's power supply and has less power demand, causing the generalized power supply's output to be too conservative. As can be seen, the generalized power output decision must be coordinated with the tie line power. Figure 1 depicts the game connection between the three parties.Figure 1
Game relationship among stakeholders.


### 2.1. Operator Benefit Function

As a new investor in the distribution network, the power production operator of the generalized power distribution network constructs and manages fans, solar, mini gas turbines, and diesel generators and gets advantages by selling electric energy to the distribution network. Starting with the economy and seeking to maximize operator interests:(3)maxUDGO=CS+CSUB−COM−CCDG,where UDGO and CS represent the operator's revenue and operator's power sales revenue, respectively, CSUB represents the government subsidy for new energy power generation, COM are the operation and maintenance cost of generalized power supply, and CCDG represents the power generation cost of generalized power supply, of which(4)CS=∑i=1N∑t=1HCsell⋅PDG,i,t,where Csell represents the price of electricity sold by the operator to the distribution network, PDG,i,t represents the active output of the i-th generalized power supply in period t, H represents the number of divided periods of a complete operation cycle, and N represents the number of generalized power supplies.(5)CSUB=∑i=1NWT∑j=1HPV∑t=1HCsubPWT,i,t+PPV,i,t,where Csub represents the government subsidy coefficient for unit power generation of new energy, PWT,i,t represents the active output of the i-th wind turbine in period t, and PPV,i,t represents the active output of the j-th photovoltaic unit in period t.(6)COM=∑i=1N∑t=1HCom⋅PDG,i,t,where Com represents the unit operation and maintenance cost of generalized power supply.(7)CCDG=CMT+CDIE,where CMT represents the power generation cost of micro gas turbine and CDIE represents the power generation cost of diesel generator.(8)CMT=∑i=1NMT∑t=1HCfuelPMT,i,tηi,where Cfuel represents the fuel price of the micro gas turbine, ηi represents the conversion efficiency of the micro gas turbine, and PMT,i,t represents the active output of the i-th micro gas turbine in period t.(9)CDIE=∑i=1NDIE∑t=1Hai⋅PDIE,i,t2+bi⋅PDIE,i,t+ci,where ai, bi, and ci represent the fuel cost coefficient of diesel generator and PDIE,i,t represents the active output of the i-th diesel generator in period t.Constraints are as follows.The output constraints of micro gas turbine and diesel generator are(10)PMT,tmin≤PMT,t≤PMT,tmax,PDIE,tmin≤PDIE,t≤PDIE,tmax,where PMT,tmin and PMT,tmax, respectively, represent the upper and lower limits of output of micro gas turbine and PDIE,tmin and PDIE,tmax, respectively, represent the upper and lower limits of output of diesel generator.The climbing constraints of micro gas turbine and diesel generator are(11)−RMT,tdown≤PMT,t−PMT,t−1≤RMT,tup,−RDIE,tdown≤PDIE,t−PDIE,t−1≤RDIE,tup,where RMT,tdown and RMT,tup represent the limit value of climbing power of micro gas turbine in each period and RDIE,tdown and RDIE,tup represent the limit value of climbing power of diesel generator in each period.In this study, it is assumed that the electric energy stored by the energy storage device is equal at the beginning and the end of a complete operation time. The constraints of the energy storage device are(12)Et=Et−1+Pess,tchThηch−Pess,tdThηd,EESS,0=EESS,TH,PESS,Tmin≤PESS,T≤PESS,Tmax,where PESS,Tmin and PESS,Tmax represent the upper and lower limits of the charging and discharging power of the energy storage device in the t period, ηch and ηd represent the charging and discharging efficiency of the energy storage device, and EESS,t represents the energy stored by the energy storage device in the t period.


### 2.2. Distribution Company Benefit Function

As the power grid's operation manager, the distribution firm considers the power grid's safety as a restriction and its economic operation as a goal, with the benefit function being(13)maxUDN=Cuser−Closs+CS+CDR,where UDN represents the total revenue of the distribution company, Cuser represents the power purchase cost of the user, Closs represents the economic loss caused by network loss, CS represents the cost of power purchase from the operator by the distribution network, and CDR is the cost of adopting demand response, which includes the cost of managing the demand response project as well as the cost of compensating consumers with medium load interruptions.(14)Closs=∑t=1HCload,t⋅Ploss,t,where Cload,t represents the real-time price of electricity sold by the distribution company to users in time period t and Ploss,t represents the network loss of the distribution network in time period t.(15)CDR=CDRM+Cil,CCDR=∑t=1HCdrm⋅PIL,t+PTL,t,CCDR=∑t=1HCdrm⋅PIL,t+PTL,t,CIL=∑t=1HCil⋅PIL,t,where Cdrm represents the unit management cost of demand response project and Cil represents the unit compensation cost of interruptible load, i.e., incentive information, PIL,t represents the interruption power of interruptible load in time period t, and PTL,t represents the transfer power of transferable load in time period t.The functioning of the distribution network must respect the network's power balance, as well as node voltage and branch transmission capacity constraints:(16)PMIN,t+PDGO,t−Ploss,t−Pload,t=0,Ploss,t=Vi,t∑j∈iVj,tGijcosθij+Bijsinθij,Vimin≤Vi,t≤Vimax,Pij,t≤Pijmax,Ppcc,min≤Ppcc,t≤Ppcc,max,where PMIN,t represents the power transmitted from the superior power grid to the distribution network in t period, PDGO,t represents the electric energy sold by the microgrid under the jurisdiction of the operator to the distribution network in period t, Ploss,t represents the network loss in period t, Pload,t represents the electric load power in period t, Vi,t and Vj,t represent the voltage amplitude of node i and node j in t period, respectively, Gij and Bij represent the conductivity and admittance between node i and node j, θij represents the voltage phase difference between node i and node j, Vimin and Vimax represent the upper and lower limits of node i voltage amplitude, Pij,t represents the transmission power of the line between node i and node j in period t, Pijmax represents the limit value of line output power, and Ppcc,t represents the transmission power of distribution network and microgrid under the jurisdiction of the operator in t period.


### 2.3. User Benefit Model

Demand response, which is divided into interrupted load and transferable load in this study, is believed to include certain customers. Users of interruptible loads, for example, agree to allow the distribution company to reduce their power load for a set period of time in exchange for compensation for the reduced load power; users of transferable loads, on the other hand, transfer their own load according to the distribution company's real-time electricity price in order to save money on electricity. The user's benefit function is(17)maxUL=CIL+CDRL−Cload,where UL represents the user's income, Cload represents the user's power consumption cost, CIL represents the compensation cost obtained by interruptible load, and CDRL represents the reduced power consumption cost due to participating in demand response.(18)CIL=∑t=1HCil⋅PIL,t,CDRL=∑t=1HCload,tPIL,t+PTL,t,where Cil represents the unit compensation cost of interruptible load, Cload,t indicates the real-time price of electricity sold by the distribution company to users in period t, PIL,t represents the interruption power of interruptible load in period t, and PTL,t is the transfer power of transferable load in period t.Even though the transferable load participating in the price demand response can select whether to raise or reduce power consumption in each period based on the electricity price, the overall power consumption in a single day must stay constant. According to the agreement signed by the incentive demand response, the interruptible load in each period must have upper and lower restrictions:(19)PTL,tmin≤PTL,t≤PTL,tmax,∑t=1HPTL,t=0,PIL,tmin≤PIL,t≤PIL,tmax,where PTL,tmin and PTL,tmax represent the upper and lower limits of load transferable power in period t. PIL,tmin and PIL,tmax represent the upper and lower limits of interruptible power during the t period.This section establishes the operator model, distribution business model, and participatory demand response user model. The operator model is a generation planning problem in which the output of controlled generic power sources (micro gas turbines, diesel generators, and so on) is the decision variable and the optimization goal is to have the lowest operating cost. The distribution company model is an optimization problem with real-time electricity price and tie line power adjustment as decision variables and the minimum comprehensive operation cost as the goal; the participating demand response user model is an optimization problem with real-time electricity price and tie line power adjustment as decision variables and the minimum comprehensive operation cost as the goal. Simultaneously, two forms of incentive demand response and price demand response are being investigated to assist consumers in improving their power usage patterns by altering energy costs.


## 2.1. Operator Benefit Function

As a new investor in the distribution network, the power production operator of the generalized power distribution network constructs and manages fans, solar, mini gas turbines, and diesel generators and gets advantages by selling electric energy to the distribution network. Starting with the economy and seeking to maximize operator interests:(3)maxUDGO=CS+CSUB−COM−CCDG,where UDGO and CS represent the operator's revenue and operator's power sales revenue, respectively, CSUB represents the government subsidy for new energy power generation, COM are the operation and maintenance cost of generalized power supply, and CCDG represents the power generation cost of generalized power supply, of which(4)CS=∑i=1N∑t=1HCsell⋅PDG,i,t,where Csell represents the price of electricity sold by the operator to the distribution network, PDG,i,t represents the active output of the i-th generalized power supply in period t, H represents the number of divided periods of a complete operation cycle, and N represents the number of generalized power supplies.(5)CSUB=∑i=1NWT∑j=1HPV∑t=1HCsubPWT,i,t+PPV,i,t,where Csub represents the government subsidy coefficient for unit power generation of new energy, PWT,i,t represents the active output of the i-th wind turbine in period t, and PPV,i,t represents the active output of the j-th photovoltaic unit in period t.(6)COM=∑i=1N∑t=1HCom⋅PDG,i,t,where Com represents the unit operation and maintenance cost of generalized power supply.(7)CCDG=CMT+CDIE,where CMT represents the power generation cost of micro gas turbine and CDIE represents the power generation cost of diesel generator.(8)CMT=∑i=1NMT∑t=1HCfuelPMT,i,tηi,where Cfuel represents the fuel price of the micro gas turbine, ηi represents the conversion efficiency of the micro gas turbine, and PMT,i,t represents the active output of the i-th micro gas turbine in period t.(9)CDIE=∑i=1NDIE∑t=1Hai⋅PDIE,i,t2+bi⋅PDIE,i,t+ci,where ai, bi, and ci represent the fuel cost coefficient of diesel generator and PDIE,i,t represents the active output of the i-th diesel generator in period t.Constraints are as follows.The output constraints of micro gas turbine and diesel generator are(10)PMT,tmin≤PMT,t≤PMT,tmax,PDIE,tmin≤PDIE,t≤PDIE,tmax,where PMT,tmin and PMT,tmax, respectively, represent the upper and lower limits of output of micro gas turbine and PDIE,tmin and PDIE,tmax, respectively, represent the upper and lower limits of output of diesel generator.The climbing constraints of micro gas turbine and diesel generator are(11)−RMT,tdown≤PMT,t−PMT,t−1≤RMT,tup,−RDIE,tdown≤PDIE,t−PDIE,t−1≤RDIE,tup,where RMT,tdown and RMT,tup represent the limit value of climbing power of micro gas turbine in each period and RDIE,tdown and RDIE,tup represent the limit value of climbing power of diesel generator in each period.In this study, it is assumed that the electric energy stored by the energy storage device is equal at the beginning and the end of a complete operation time. The constraints of the energy storage device are(12)Et=Et−1+Pess,tchThηch−Pess,tdThηd,EESS,0=EESS,TH,PESS,Tmin≤PESS,T≤PESS,Tmax,where PESS,Tmin and PESS,Tmax represent the upper and lower limits of the charging and discharging power of the energy storage device in the t period, ηch and ηd represent the charging and discharging efficiency of the energy storage device, and EESS,t represents the energy stored by the energy storage device in the t period.


## 2.2. Distribution Company Benefit Function

As the power grid's operation manager, the distribution firm considers the power grid's safety as a restriction and its economic operation as a goal, with the benefit function being(13)maxUDN=Cuser−Closs+CS+CDR,where UDN represents the total revenue of the distribution company, Cuser represents the power purchase cost of the user, Closs represents the economic loss caused by network loss, CS represents the cost of power purchase from the operator by the distribution network, and CDR is the cost of adopting demand response, which includes the cost of managing the demand response project as well as the cost of compensating consumers with medium load interruptions.(14)Closs=∑t=1HCload,t⋅Ploss,t,where Cload,t represents the real-time price of electricity sold by the distribution company to users in time period t and Ploss,t represents the network loss of the distribution network in time period t.(15)CDR=CDRM+Cil,CCDR=∑t=1HCdrm⋅PIL,t+PTL,t,CCDR=∑t=1HCdrm⋅PIL,t+PTL,t,CIL=∑t=1HCil⋅PIL,t,where Cdrm represents the unit management cost of demand response project and Cil represents the unit compensation cost of interruptible load, i.e., incentive information, PIL,t represents the interruption power of interruptible load in time period t, and PTL,t represents the transfer power of transferable load in time period t.The functioning of the distribution network must respect the network's power balance, as well as node voltage and branch transmission capacity constraints:(16)PMIN,t+PDGO,t−Ploss,t−Pload,t=0,Ploss,t=Vi,t∑j∈iVj,tGijcosθij+Bijsinθij,Vimin≤Vi,t≤Vimax,Pij,t≤Pijmax,Ppcc,min≤Ppcc,t≤Ppcc,max,where PMIN,t represents the power transmitted from the superior power grid to the distribution network in t period, PDGO,t represents the electric energy sold by the microgrid under the jurisdiction of the operator to the distribution network in period t, Ploss,t represents the network loss in period t, Pload,t represents the electric load power in period t, Vi,t and Vj,t represent the voltage amplitude of node i and node j in t period, respectively, Gij and Bij represent the conductivity and admittance between node i and node j, θij represents the voltage phase difference between node i and node j, Vimin and Vimax represent the upper and lower limits of node i voltage amplitude, Pij,t represents the transmission power of the line between node i and node j in period t, Pijmax represents the limit value of line output power, and Ppcc,t represents the transmission power of distribution network and microgrid under the jurisdiction of the operator in t period.


## 2.3. User Benefit Model

Demand response, which is divided into interrupted load and transferable load in this study, is believed to include certain customers. Users of interruptible loads, for example, agree to allow the distribution company to reduce their power load for a set period of time in exchange for compensation for the reduced load power; users of transferable loads, on the other hand, transfer their own load according to the distribution company's real-time electricity price in order to save money on electricity. The user's benefit function is(17)maxUL=CIL+CDRL−Cload,where UL represents the user's income, Cload represents the user's power consumption cost, CIL represents the compensation cost obtained by interruptible load, and CDRL represents the reduced power consumption cost due to participating in demand response.(18)CIL=∑t=1HCil⋅PIL,t,CDRL=∑t=1HCload,tPIL,t+PTL,t,where Cil represents the unit compensation cost of interruptible load, Cload,t indicates the real-time price of electricity sold by the distribution company to users in period t, PIL,t represents the interruption power of interruptible load in period t, and PTL,t is the transfer power of transferable load in period t.Even though the transferable load participating in the price demand response can select whether to raise or reduce power consumption in each period based on the electricity price, the overall power consumption in a single day must stay constant. According to the agreement signed by the incentive demand response, the interruptible load in each period must have upper and lower restrictions:(19)PTL,tmin≤PTL,t≤PTL,tmax,∑t=1HPTL,t=0,PIL,tmin≤PIL,t≤PIL,tmax,where PTL,tmin and PTL,tmax represent the upper and lower limits of load transferable power in period t. PIL,tmin and PIL,tmax represent the upper and lower limits of interruptible power during the t period.This section establishes the operator model, distribution business model, and participatory demand response user model. The operator model is a generation planning problem in which the output of controlled generic power sources (micro gas turbines, diesel generators, and so on) is the decision variable and the optimization goal is to have the lowest operating cost. The distribution company model is an optimization problem with real-time electricity price and tie line power adjustment as decision variables and the minimum comprehensive operation cost as the goal; the participating demand response user model is an optimization problem with real-time electricity price and tie line power adjustment as decision variables and the minimum comprehensive operation cost as the goal. Simultaneously, two forms of incentive demand response and price demand response are being investigated to assist consumers in improving their power usage patterns by altering energy costs.


## 3. Multiobjective Optimal Dispatching of Generalized Power Active Distribution Network

The utilization rate of renewable energy, network loss, and customer satisfaction are all taken into account in this study. The following is a summary of the objective function:(20)F=minf1AR,f2PLOSS,f3S.The analytic hierarchy process is a subjective and experience-based approach for calculating weights. The entropy weight technique is commonly used for assessing the objective weight of indicators. Using an analytic hierarchy process and the entropy weight approach, this work blends subjectivity and objectivity and provides a comprehensive index determination method:(21)λSy−i=λAHP−i+λEM−i∑λAHP−i+λEM−i,where λSy−i, λAHP−i, and λEM−i, respectively, represent the comprehensive weight, AHP weight, and entropy weight of the comprehensive objective function occupied by the i-th subobjective.Using the technique outlined above, the weight of each subgoal can be determined, and the dimension of each subobjective function may be unified. The following is a summary of the objective function's expression:(22)F=minλSy−11−AR+λSy−2PLOSSPg+λSy−31−S,where λSy−1, λSy−2, and λSy−3 are the weight coefficients of each subobjective function and meet λSy−1+λSy−2+λSy−3=1 and Pg is the total power generation of the power generation unit in a complete dispatching cycle. The difficulty of solving a large number of nonsplitting sets may be avoided using the comprehensive objective function of formula (22), and dimensional consistency is ensured. The optimum dispatching of a generalized distribution network should take into consideration the constraints of each time period during the dispatching cycle, since the general optimal power flow is time independent. In addition to the typical node voltage limitations and power flow equation constraints, this research must take into consideration the state of charge restrictions of energy storage devices as well as the power limits of flexible loads.(1)
Power flow equation and generator output constraint is as follows:(23)∑PGt=∑Plt−Plxt+Pdt+PESSt,wherePGt represents the active output of the power generation unit, Plt is the active loss of the network, Plxt indicates the reduced power that can reduce the load, Pdt denotes the load power, PESSt represents the charge and discharge power of energy storage, charging is positive, and discharge is negative.(24)PKF−kmin≤PKF−k≤PKF−kmax,wherePKF−k represents the active output of the k-kth power generation unit, which shall meet its upper- and lower-limit constraints.(2)
Node voltage limit is as follows:(25)Uimin≤Ui≤Uimax.(3)
Load reduction limit constraint is as follows:(26)Pcjmin≤Pcj,wherePcj represents the active output of the j-th reducible load.(4)
Energy storage power constraint, state of charge constraint, and energy balance are as follows:(27)PEss−nmin≤PEss−n≤PEss−nmax,wherePEss−n represents the charge discharge power of the n-th energy storage device.(28)SOCnmin≤SOCn≤SOCnmax,whereSOCn represents the state of charge of the n-th energy storage device.(29)EEss−n0=EEss−n96,whereEEss−n0 represents the initial energy stored by the energy storage device and EEss−n96 represents the residual energy of the energy storage device at the end of the dispatching cycle. In the whole dispatching cycle, the energy conservation of the energy storage device shall be ensured.In this study, the decision variables include not only continuous variables such as power generation unit outputPKF, charge and discharge power PESS of energy storage device, and load reduction power PL, but also discrete control variables such as translational load power consumption time period Tl and renewable power generation PWG and PPV. The mathematical model for optimization is basically a mixed integer nonlinear constraint programming issue. In order to solve the problem of discrete variable computation, when generating the choice variables, the coefficient matrix and corresponding discrete variable model are introduced, resulting in the decision vector of optimum scheduling being represented as PKF,PESS,PL,λTl,PWG,PPV and λ as the coefficient matrix, and the penalty function is constructed to solve the constraint problem.The particle swarm optimization method is a swarm intelligence optimization approach used in intelligent computing. It has the benefits of being easy to implement and producing quick convergence. It is commonly used in areas like energy storage system optimal configuration, generalized power capacity and placement, distribution network reconstruction, and microgrid economic operation among others. On the other hand, the particle swarm optimization technique has problems with discrete optimization and is prone to local optimization. To solve this problem, the method in this work includes a nonlinear inertia reduction weight to ensure that the search range is balanced before and after optimization. In order to better balance the algorithm's global and local search abilities, quadratic nonlinear decreasing inertia weight is introduced in the iterative process to ensure that the algorithm has better global search ability in the initial stage of optimization and better local search ability in the later stage. This method outperforms linear decreasing inertia weight in terms of jumping out of bad solutions. The following is the revised particle swarm optimization equation:(30)Vidk+1=ωkVidk+c1r1Pidk−Xidk+c2r2Pgdk−Xidk,Xidk+1=Xidk+Vidk+1,ωk+1=ωstart−ωstart−ωendkTmax2,where Vid represents the particle velocity, k and ω represent the current iteration and inertia weight coefficient, respectively, both c1 and c2 represent the learning factors of particles, which are related to self-cognition and social cognition, Pid represents the best historical value of i particle search, Xid is the current position of the particle, both r1 and r2 are all random numbers in [0,1] interval, Pgd represents the optimal solution currently searched by all particles, ωstart denotes the initial inertia weight, ωend represents the inertia weight when iterating to the maximum number of times, and Tmax represents the maximum number of iterations. The algorithm contains a big optimization step in the early stages after improvement, and the particles tend to hunt for the best answer throughout a wide range. The particles carry out deep mining near the current optimal solution in the final stages of iteration.


## 4. Experimental Verification

Quadratic nonlinear decreasing inertia weight is introduced in the iterative process to better balance the algorithm's global and local search abilities, ensuring that the algorithm has better global search ability in the initial stage of optimization and better local search ability in the later stage. In terms of leaping out of poor solutions, this technique surpasses linear decreasing inertia weight. The updated particle swarm optimization equation is as follows: Tables1–3 illustrate the exact parameters of the operator's internal power supply, the electricity price constructed by the distribution network from the superior power grid, and the operator, respectively. The peak hours are 10 am to 12 pm and 17 pm to 20 pm; the normal hours are 6 : 00 to 9 : 00, 13 : 00 to 16 : 00, and 21 : 00 to 24 : 00; and the valley hours are 1 am to 5 am.Table 1
Operator parameters 1.
Power supplyUnit electricity subsidy value (yuan/kW h)Unit power operation and maintenance coefficient (yuan/kW h)Installed capacity (kW)Installation quantity (set)Wind power0.100.033003Photovoltaic0.420.015006Micro gas turbine00.035001Diesel generator00.083001Energy storage device00.016001Table 2
Operator parameters 2.
Power supplyUnit electricity subsidy value (yuan/kW h)Unit power operation and maintenance coefficient (yuan/kW h)Installed capacity (kW)Installation quantity (set)Wind power0.100.0273502Photovoltaic0.420.0154006Micro gas turbine00.0355002Diesel generator00.0884501Energy storage device00.00134001Table 3
Electricity price parameters.
TypePrice (yuan/kWh)Build from superior power gridPeak: 0.58; flat: 0.42; valley: 0.32Build from operator0.4


### 4.1. Game Optimization Effect Analysis

The load curve after game optimization is shown in Figure2.Figure 2
Load curve after game optimization.As indicated in the picture, the technique in this study conducts peak shaving and valley filling, and the adjusted load curve is more in line with the curve of renewable energy power generation, boosting new energy consumption and exploitation.


### 4.2. Analysis of Network Loss Convergence Effect

The network loss convergence curve before and after the improvement of the algorithm is shown in Figure3.Figure 3
Network loss convergence curve before and after algorithm improvement.The network loss is minimized during the game, as seen in Figure3. The enhanced method decreases network loss by 2.2% when compared to the best response approach.


### 4.3. Analysis of Distribution Network Output and Daily Load Output Curve before and after Optimization

When the energy storage and flexible load are configured not to participate in the distribution network scheduling, according to the recommended optimization method, the operation state of the distribution network before optimization is illustrated in Figure4.Figure 4
Output and daily load curve of power generation units of distribution network before optimization.Figure5 depicts the power generation curves of each power generation unit, the power of energy storage units, and the daily load curve after optimization for the whole dispatching cycle.Figure 5
Output and daily load curve of each generation unit of distribution network after optimization.Under the coordination of energy storage and flexible load, the output of renewable energy has a high degree of fit with the target output curve, the steepness of the improved daily load curve is reduced, and it is closely related to the power generation curve of renewable power generation units, as shown in Figure5.


## 4.1. Game Optimization Effect Analysis

The load curve after game optimization is shown in Figure2.Figure 2
Load curve after game optimization.As indicated in the picture, the technique in this study conducts peak shaving and valley filling, and the adjusted load curve is more in line with the curve of renewable energy power generation, boosting new energy consumption and exploitation.


## 4.2. Analysis of Network Loss Convergence Effect

The network loss convergence curve before and after the improvement of the algorithm is shown in Figure3.Figure 3
Network loss convergence curve before and after algorithm improvement.The network loss is minimized during the game, as seen in Figure3. The enhanced method decreases network loss by 2.2% when compared to the best response approach.


## 4.3. Analysis of Distribution Network Output and Daily Load Output Curve before and after Optimization

When the energy storage and flexible load are configured not to participate in the distribution network scheduling, according to the recommended optimization method, the operation state of the distribution network before optimization is illustrated in Figure4.Figure 4
Output and daily load curve of power generation units of distribution network before optimization.Figure5 depicts the power generation curves of each power generation unit, the power of energy storage units, and the daily load curve after optimization for the whole dispatching cycle.Figure 5
Output and daily load curve of each generation unit of distribution network after optimization.Under the coordination of energy storage and flexible load, the output of renewable energy has a high degree of fit with the target output curve, the steepness of the improved daily load curve is reduced, and it is closely related to the power generation curve of renewable power generation units, as shown in Figure5.


## 5. Conclusion

In order to improve the network's operation efficiency, this paper uses game theory to solve the multiobjective optimal scheduling problem of a generalized power active distribution network, establishes a game mathematical model reflecting conflict of interest, and performs simulation verification using the ieee33 node distribution system. The multistakeholder game coordination optimization model is divided into three parts: the operator layer model is the power generation decision-making issue for distributed energy operators, the distribution network layer constructs an objective function with the minimum comprehensive operation cost of the distribution network to optimize the electricity price, and the optimal scheduling of controllable distributed generation is carried out with the goal of minimizing fuel cost and maintenance cost under the given conditions of wind power and photovoltaic output prediction and load curve. At the user layer, adjusting power use is a difficulty. Using real-time electricity pricing, the power load is adjusted in order to maximize user income. According on experimental results, the proposed method has high convergence and may significantly minimize network loss.



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*Source: 2559449-2021-10-29.xml*