# Optimal Allocation of Distributed Generators in Active Distribution Network considering TOU Price

Authors: Hongbo Liu; Shencheng Liu; Xueyang Gai; Yongfa Liu; Yutong Yan; Li Sun
Journal: International Journal of Antennas and Propagation
 (2023)

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## Abstract

As the distributed generators (DGs) are connected to active distribution network (ADN), it strengthens the communication interest between the customs and DGs and can facilitate energy integration. This article proposes hybrid pricing for DG configuration by taking advantage of fixed pricing and dynamic pricing. The time sequence scenario of wind-photovoltaic-load power can be got by k-means, which can balance the calculation burden with multiple scenarios. The planning model is built as the optimal objective for minimal investment in operation and maintenance of DGs, reduction of network loss, and decrease of voltage deviation. An improved simulated annealing particle swarm optimization algorithm is also proposed by refining the initialized population based on the niche fitness, introducing inertia weight with chaotic disturbance and accelerating local search with learning factor of dynamic parameter. The effectiveness and rationality of the proposed methodology are verified by simulation in the IEEE 69-bus system.


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## Body

## 1. Introduction

In recent years, renewable energy has been rapidly developed. Based on realization of rational energy allocation prospect and reduction of main pollutants emission, it is expected that the installed share of renewable energy will reach 38% in 2030 and 70% in 2050. Accordingly, the installed wind and photovoltaic power capacities will reach 1.44 billion kW and 2.16 billion kW, respectively [1]. At present, development of both centralized and decentralized renewable energy is equally important, though development of decentralized and distributed renewable energy has been encouraged first. Continuous transformation and construction of the distribution network improve coverage of distribution automation and enhance the acceptance capacity of distributed clean energy of the power grid [2].Active distribution network (ADN) [3] is flexible and controllable. It can improve utilization rate of green energy and carry out centralized management. ADN is compatible with large-scale and multi-form distributed power sources, changes the primary energy structure [4, 5], and copes with uncontrollability, randomness, and volatility caused by distributed power sources. Therefore, it is particularly important to formulate planning scheme of active distribution network to deal with various situations and fit the reality.The operation stochastic characteristics of each component in the active distribution network result in planning uncertainty. The planning scheme with consideration of uncertainty is more adaptable to the changes of future scenarios [6, 7]. The uncertainty factor is the difficulty in handling the planning scheme design. A planning scheme that deals with the uncertainty factor well is more suitable for the reality. Tang et al. [8] established a MEGA (micro energy grid aggregator) shaping potential range evaluation model to solve the uncertainty of source load.At present, the mathematical analysis method based on the probability model or scene analysis method is mainly used to consider uncertainty. Probabilistic models are highly accurate in some modeling objects, but they are poor at multiple time scales. Scene analysis is more advantageous in time-dependent simulation, but the simulation effect depends on the number of scenes.Huppertz et al. [9] took full advantage of the precision of probabilistic models, building probability models from cross-sectional data for specific points in time which are processed by probabilistic load flow along the time axis, creating highly diverse household load profiles.Sannigrahi et al. [10] proposed multi-scenario active distribution network planning under uncertain environment based on economy, technology, and green energy perspectives. The probabilistic model was utilized to simulate variation of wind speed and light intensity, and the clustering method was employed to establish the scene. However, since wind, light, and time were closely related, this method could result in non-obvious differences between the established scenes. The method of typical days in four seasons was utilized in [11, 12] to analyze and calculate the scenery temporal output. Although the scenario analysis method of selecting typical days could significantly improve the calculation speed, the number of selected scenarios was too brief. Using this method, the scene is prone to lack of diversity, and the adaptability of the scheme to future changes is poor. Accordingly, the scheme of selecting typical days was generally applied to the area with little environmental change, which was greatly affected by local conditions and was not a universal method. The Monte Carlo sampling method was used in [13, 14] to sample wind speed and light intensity. It was combined with the k-means method to generate typical wind and light output scenes. Although there was certain diversity in the established multiple scenes, the number of scene clusters was selected based on experience. Therefore, missing scene diversity due to improper selection of cluster number was still a problem.Different from the traditional net-load relationship, the high degree of user interaction is one of the prominent characteristics of active distribution network. Demand response (DR) is generated along with electricity consumption behavior of users, which is divided into incentive DR and price DR. Users can change their power consumption behavior by responding to incentive mechanisms or price signals, which can effectively enhance energy consumption. Active distribution network can make use of this advantage to effectively deal with the energy consumption problem caused by the high proportion of new energy access. In [15], the incentive-based DR was directly added into the optimization model for consumption of new energy. Liu et al. [16] suggested that conventional incentive DR lacks selectivity and proposed the stepped DR incentive mechanism to encourage users to participate in DR so as to better carry out peak cutting and valley filling.Although incentive DR is easier to realize than price-type DR, price-type DR can regulate the load on a large scale, leading to participation of more users and achievement of more advantages in energy consumption promotion. Among various price-type DRs, the DR based on TOU price has been widely used (both fixed and dynamic TOU prices). Yang et al. [17] established a quotation mechanism of incentive electricity price to achieve more flexible and accurate DR.Ren et al. [18] adopted the price-type demand response based on fixed TOU price to establish a model reflecting the relationship between TOU price and user demand. The fixed TOU price can help the system to cut the peak and fill the valley. However, if only fixed TOU price is adopted to deal with the access of distributed new energy, an excess energy situation can occur at a certain time, resulting in the increase of circuit voltage exceedance and serious network loss. The supply and demand relationship between short-termwind-power output and load was analyzed in [19], and the dynamic TOU price mechanism was addressed. The dynamic TOU price can fully realize coordination of wind-power supply timing output in order to promote energy consumption. However, there may be unreasonable electricity price when it is applied to long-term ADN planning.In this paper, a multi-objective programming model is established to minimize the investment operation of distributed power supply, reduce network loss and voltage offset, and reasonably locate and determine the capacity of distributed power supply. The main research of this paper is as follows:(1)
The planning scheme adopts the scenario analysis method to simulate the output of wind power and photovoltaic power using the measured data. Considering the contradiction between scene diversity and calculation burden, the k-means clustering method including Davies–Bouldin index is applied. It is compared with the scene generated by probability model simulation and Latin hypercube sampling to verify its superiority.(2)
The price-type demand response based on hybrid fixed and dynamic TOU prices is proposed to address limitation of the two TOU prices effectively.(3)
The modified simulated annealing particle swarm optimization algorithm is used to solve the model. The initial population of the niche fitness algorithm is introduced to enhance the calculation speed. Furthermore, the inertia weight and dynamic parameters are added to improve the local optimization ability of the algorithm.The IEEE 69-node system is simulated for verification purpose. The planning scheme in this paper is compared with those based on fixed TOU price and probability model generation scenario to verify superiority of the model. Particle swarm optimization (PSO), simulated annealing particle swarm optimization (SAPSO), and improved simulated annealing particle swarm optimization (ISAPSO) algorithms based on the niche fitness are employed to solve the model. The rationality of the improved algorithm is verified by comparing the fitness, convergence, and calculation speed.


## 2. ADN Mathematical Model

### 2.1. Output Model of Distributed Generators

The wind turbine generator (WTG) and photovoltaic generator (PVG) are greatly affected by the natural environment, such that the active power output is volatile and stochastic. The relationship between wind speed, light radiation, and active power output of generator is commonly expressed as equations (1) and (2) in engineering community [20, 21]:(1)pwtg=0,pratev−vivr−vi,prate,0≤v<vi,v>vo,vi≤v<vr,vr≤v≤vo,where vi and vo represent the cut-in and cut-out wind speeds, respectively, vr denotes rated wind speed, and prate indicates rated active power of wind turbine.(2)ppvg=prateIIr,prate,I≤Ir,I>Ir,where Ir and prate represent rated light intensity and rated active power of the PV unit, respectively.


### 2.2. Price-Type Demand Response Model Based on TOU Price

#### 2.2.1. Fixed TOU Price Model

As a special commodity, electric energy has the commodity commonality that price and demand are inversely proportional [22]. In economics, the ratio of load transfer rate to price transfer rate in a certain period is used to express the elasticity coefficient, nij, as follows:(3)ηij=λLiλpj,λLi=Li−L0iL0i,λpj=pj−p0jp0j,where λLi represents the load transfer rate at time i, λpj denotes the price transfer rate at time j, L0 and p0 are the load quantity and electricity price without considering the demand response, and L and P are the load quantity and electricity price considering the demand response, respectively. After calculation of the elastic coefficient, the elastic coefficient matrix Q can be formed according to the time period division, as follows:(4)Q=η11…η1j⋮⋱⋮ηi1⋯ηij.Wheni = j, nij is the autoelasticity coefficient, which is usually negative and indicates that with growth of electricity price, the user demand decreases. When i≠j, nij is the cross-elasticity coefficient, indicating that with decrease of the electricity price at time j, the user transfers part of the load from time i to time j.After computation of the elastic matrix,Q, the load transformation can be obtained based on consideration of the demand response, as given in the following equation:(5)L1⋮Lm=L01⋮L0m+L01⋯0⋮⋱⋮0⋯L0mQλp1⋮λpm.


#### 2.2.2. Dynamic TOU Price Model

Dynamic TOU price adds an interaction link to load on the basis of fixed TOU price. It changes the electricity price at each moment using equation (6) and then modifies the matrix Q to obtain the response load. Zhang et al. [19] used the net load to reflect the supply-demand relationship. In order to formulate the distributions of peak, valley, and flat price, the present paper takes 1 h as the interval to divide the step length and considers the ratio of net load at each moment to the maximum and minimum values in the same scene as the division basis. Accordingly, the following formula is adopted:(6)kt=kt,Ft−aPwt+bPptmaxFt−aPwt+bPpt>kt,kf,kl,Ft−aPwt+bPptminFt−aPwt+bPpt<kl,where kt and kl are the peak hour and valley hour of electricity price, respectively, Pwt and Ppt represent the outputs of wind power and photovoltaic power at the moment t, respectively, Ft denotes the total load of all nodes in the distribution network at the current time, a and b represent the installed number of wind and photovoltaic power units, respectively, and kt and kl are the thresholds for the division of peak and valley time, respectively.The main scheme of this paper is based on the price-type demand response with hybrid fixed and dynamic TOU prices. Accordingly, the fixed TOU price is used in the scenario in which distributed power supply output is very poor or even there is no output, and the dynamic TOU price is used in the scenario in which distributed power supply output is good. This avoids the situation that the dynamic TOU price is adopted in the whole scenario leading to unreasonable price.


## 2.1. Output Model of Distributed Generators

The wind turbine generator (WTG) and photovoltaic generator (PVG) are greatly affected by the natural environment, such that the active power output is volatile and stochastic. The relationship between wind speed, light radiation, and active power output of generator is commonly expressed as equations (1) and (2) in engineering community [20, 21]:(1)pwtg=0,pratev−vivr−vi,prate,0≤v<vi,v>vo,vi≤v<vr,vr≤v≤vo,where vi and vo represent the cut-in and cut-out wind speeds, respectively, vr denotes rated wind speed, and prate indicates rated active power of wind turbine.(2)ppvg=prateIIr,prate,I≤Ir,I>Ir,where Ir and prate represent rated light intensity and rated active power of the PV unit, respectively.


## 2.2. Price-Type Demand Response Model Based on TOU Price

### 2.2.1. Fixed TOU Price Model

As a special commodity, electric energy has the commodity commonality that price and demand are inversely proportional [22]. In economics, the ratio of load transfer rate to price transfer rate in a certain period is used to express the elasticity coefficient, nij, as follows:(3)ηij=λLiλpj,λLi=Li−L0iL0i,λpj=pj−p0jp0j,where λLi represents the load transfer rate at time i, λpj denotes the price transfer rate at time j, L0 and p0 are the load quantity and electricity price without considering the demand response, and L and P are the load quantity and electricity price considering the demand response, respectively. After calculation of the elastic coefficient, the elastic coefficient matrix Q can be formed according to the time period division, as follows:(4)Q=η11…η1j⋮⋱⋮ηi1⋯ηij.Wheni = j, nij is the autoelasticity coefficient, which is usually negative and indicates that with growth of electricity price, the user demand decreases. When i≠j, nij is the cross-elasticity coefficient, indicating that with decrease of the electricity price at time j, the user transfers part of the load from time i to time j.After computation of the elastic matrix,Q, the load transformation can be obtained based on consideration of the demand response, as given in the following equation:(5)L1⋮Lm=L01⋮L0m+L01⋯0⋮⋱⋮0⋯L0mQλp1⋮λpm.


### 2.2.2. Dynamic TOU Price Model

Dynamic TOU price adds an interaction link to load on the basis of fixed TOU price. It changes the electricity price at each moment using equation (6) and then modifies the matrix Q to obtain the response load. Zhang et al. [19] used the net load to reflect the supply-demand relationship. In order to formulate the distributions of peak, valley, and flat price, the present paper takes 1 h as the interval to divide the step length and considers the ratio of net load at each moment to the maximum and minimum values in the same scene as the division basis. Accordingly, the following formula is adopted:(6)kt=kt,Ft−aPwt+bPptmaxFt−aPwt+bPpt>kt,kf,kl,Ft−aPwt+bPptminFt−aPwt+bPpt<kl,where kt and kl are the peak hour and valley hour of electricity price, respectively, Pwt and Ppt represent the outputs of wind power and photovoltaic power at the moment t, respectively, Ft denotes the total load of all nodes in the distribution network at the current time, a and b represent the installed number of wind and photovoltaic power units, respectively, and kt and kl are the thresholds for the division of peak and valley time, respectively.The main scheme of this paper is based on the price-type demand response with hybrid fixed and dynamic TOU prices. Accordingly, the fixed TOU price is used in the scenario in which distributed power supply output is very poor or even there is no output, and the dynamic TOU price is used in the scenario in which distributed power supply output is good. This avoids the situation that the dynamic TOU price is adopted in the whole scenario leading to unreasonable price.


## 2.2.1. Fixed TOU Price Model

As a special commodity, electric energy has the commodity commonality that price and demand are inversely proportional [22]. In economics, the ratio of load transfer rate to price transfer rate in a certain period is used to express the elasticity coefficient, nij, as follows:(3)ηij=λLiλpj,λLi=Li−L0iL0i,λpj=pj−p0jp0j,where λLi represents the load transfer rate at time i, λpj denotes the price transfer rate at time j, L0 and p0 are the load quantity and electricity price without considering the demand response, and L and P are the load quantity and electricity price considering the demand response, respectively. After calculation of the elastic coefficient, the elastic coefficient matrix Q can be formed according to the time period division, as follows:(4)Q=η11…η1j⋮⋱⋮ηi1⋯ηij.Wheni = j, nij is the autoelasticity coefficient, which is usually negative and indicates that with growth of electricity price, the user demand decreases. When i≠j, nij is the cross-elasticity coefficient, indicating that with decrease of the electricity price at time j, the user transfers part of the load from time i to time j.After computation of the elastic matrix,Q, the load transformation can be obtained based on consideration of the demand response, as given in the following equation:(5)L1⋮Lm=L01⋮L0m+L01⋯0⋮⋱⋮0⋯L0mQλp1⋮λpm.


## 2.2.2. Dynamic TOU Price Model

Dynamic TOU price adds an interaction link to load on the basis of fixed TOU price. It changes the electricity price at each moment using equation (6) and then modifies the matrix Q to obtain the response load. Zhang et al. [19] used the net load to reflect the supply-demand relationship. In order to formulate the distributions of peak, valley, and flat price, the present paper takes 1 h as the interval to divide the step length and considers the ratio of net load at each moment to the maximum and minimum values in the same scene as the division basis. Accordingly, the following formula is adopted:(6)kt=kt,Ft−aPwt+bPptmaxFt−aPwt+bPpt>kt,kf,kl,Ft−aPwt+bPptminFt−aPwt+bPpt<kl,where kt and kl are the peak hour and valley hour of electricity price, respectively, Pwt and Ppt represent the outputs of wind power and photovoltaic power at the moment t, respectively, Ft denotes the total load of all nodes in the distribution network at the current time, a and b represent the installed number of wind and photovoltaic power units, respectively, and kt and kl are the thresholds for the division of peak and valley time, respectively.The main scheme of this paper is based on the price-type demand response with hybrid fixed and dynamic TOU prices. Accordingly, the fixed TOU price is used in the scenario in which distributed power supply output is very poor or even there is no output, and the dynamic TOU price is used in the scenario in which distributed power supply output is good. This avoids the situation that the dynamic TOU price is adopted in the whole scenario leading to unreasonable price.


## 3. ADN Programming Model

The location and capacity of distributed power supply are taken as control variables. The configuration scheme of optimal distributed power supply is established based on economy and environmental protection perspectives.


### 3.1. Objective Function

The objective function includes two parts, namely, the investment and installation cost of distributed power supply and the system operation cost. The system operation cost itself consists of two parts: cost and cost savings. The goal is to minimize the total cost of both of them, as follows:(7)minF=a1Finv+a2Fop,Fop=Fprofit+Fcost,where a1+a2=1 and a1=a2 consider the same weight for investment and system operation costs and Fcost and Fprofit are the system operation cost and cost savings after implementation of the scheme, respectively.


#### 3.1.1. Investment Cost of Distributed Generators

Finv can be calculated as follows:(8)Finv=d1+dn1+dn−1∑i∈NDGcDGnDGprate,where d is the discount rate, n is the service life of distributed power supply, NDG is the set of network nodes, cDG is the unit investment price of distributed power supply, and nDG indicates the number of installed distributed power supplies.


#### 3.1.2. System Operation Cost

The system operation cost consists of four parts, namely, the operation and maintenance cost of distributed power supply, the power purchase cost of main network, the voltage overlimit penalty cost, and the demand response implementation cost, as follows:(9)Fcost=Cope+Cmpur+Cvdev+Cdr.The calculation method of each part is as follows.(1)
Operation and maintenance cost of distributed generators:(10)Cope=365S∑s=1S∑t=1TcopnDGpDG.s.t,wheres indicates the number of scenarios, cop is unit operation and maintenance cost of distributed power supply, and pDG.s.t is the active power output of distributed power supply.(2)
Power purchase cost of the main network:(11)Cmpur=365S∑s=1S∑t=1Tcpupload.s.t+ploss.s.t−nDGpDG.s.t,wherecpu is the cost of electricity purchase from the main network, pload is the load demand, and ploss is the network loss.(3)
Penalty cost of voltage exceedance:(12)Cvdev=365S∑s=1S∑t=1T∑i=1NDGcvdev∆Ui.s.t,∆U=Ui−Ut,0,Ul−Ui,Ui>Ut,Ul<Ui<UtUi<Ul,,wherecvdev is the penalty cost per unit voltage exceedance, ∆U is the voltage overlimit degree, and Ut and Ul are the upper and lower voltage limits, respectively.(4)
Demand response implementation cost:(13)Cdr=365S∑s=1S∑t=1Tktpload.s.t−Kpload.s.t′,wherekt is TOU price, K is the original electricity price, and pload.s.t′ is the load demand before implementation of TOU price.


#### 3.1.3. System Operation Revenue

System operation revenue includes two parts, namely, network loss reduction cost savings and environmental protection cost savings:(14)Fprofit=−Crloss−Cep.These two parts can be calculated as follows.(1)
Network loss reduction cost savings:(15)Crloss=365S∑s=1S∑t=1Tcrlossploss.s.t′−ploss.s.t,wherecloss is the unit net loss reduction income and ploss′ is the network loss before connection of distributed power supply.(2)
Environmental cost savings:(16)Cep=365S∑s=1S∑t=1TαiβinDGpDG.s.t,whereαi and βi are the emission coefficient and treatment cost of the ith pollutant.


### 3.2. Constraints

The access of distributed power supply is constrained by safe operation of the system, which can be categorized into equality and inequality constraints, as follows(1)
Equality Constraint. The power balance equation should be satisfied for either the nodes connected to distributed power supply or other nodes, as follows:(17)PGi−PLi−Ui∑j∈kUjGijcosθij+Bijsinθij=0,QGi−QLi−Ui∑j∈kUjGijsinθij−Bijcosθij=0,wherePGi and QGi are the active and reactive powers of the ith node, PLi and QLi are the active and reactive power loads of the ith node, respectively, Ui is the voltage of the ith node, and Gij, Bij, and θij are the conductance, susceptance, and phase angle difference between nodes i and j, respectively.(2)
Inequality Constraints. There are three inequality constraints, as follows.(a)
Node voltage constraints:(18)Uimin≤Ui≤Uimax,whereUimin and Uimax represent the lower and upper limits of voltage at the ith node, respectively.(b)
Branch power constraints of the system:(19)Sij≤Sij,max,whereSij,max is the maximum apparent power allowed by the branch.(c)
Constraints on the number of distributed generators to be installed:(20)ni.s.tWTG≤NiWTG,ni.s.tPVG≤NiPVG,whereNiWTG and NiPVG represent the maximum number of installed wind turbines and photovoltaic units, respectively.


## 3.1. Objective Function

The objective function includes two parts, namely, the investment and installation cost of distributed power supply and the system operation cost. The system operation cost itself consists of two parts: cost and cost savings. The goal is to minimize the total cost of both of them, as follows:(7)minF=a1Finv+a2Fop,Fop=Fprofit+Fcost,where a1+a2=1 and a1=a2 consider the same weight for investment and system operation costs and Fcost and Fprofit are the system operation cost and cost savings after implementation of the scheme, respectively.


### 3.1.1. Investment Cost of Distributed Generators

Finv can be calculated as follows:(8)Finv=d1+dn1+dn−1∑i∈NDGcDGnDGprate,where d is the discount rate, n is the service life of distributed power supply, NDG is the set of network nodes, cDG is the unit investment price of distributed power supply, and nDG indicates the number of installed distributed power supplies.


### 3.1.2. System Operation Cost

The system operation cost consists of four parts, namely, the operation and maintenance cost of distributed power supply, the power purchase cost of main network, the voltage overlimit penalty cost, and the demand response implementation cost, as follows:(9)Fcost=Cope+Cmpur+Cvdev+Cdr.The calculation method of each part is as follows.(1)
Operation and maintenance cost of distributed generators:(10)Cope=365S∑s=1S∑t=1TcopnDGpDG.s.t,wheres indicates the number of scenarios, cop is unit operation and maintenance cost of distributed power supply, and pDG.s.t is the active power output of distributed power supply.(2)
Power purchase cost of the main network:(11)Cmpur=365S∑s=1S∑t=1Tcpupload.s.t+ploss.s.t−nDGpDG.s.t,wherecpu is the cost of electricity purchase from the main network, pload is the load demand, and ploss is the network loss.(3)
Penalty cost of voltage exceedance:(12)Cvdev=365S∑s=1S∑t=1T∑i=1NDGcvdev∆Ui.s.t,∆U=Ui−Ut,0,Ul−Ui,Ui>Ut,Ul<Ui<UtUi<Ul,,wherecvdev is the penalty cost per unit voltage exceedance, ∆U is the voltage overlimit degree, and Ut and Ul are the upper and lower voltage limits, respectively.(4)
Demand response implementation cost:(13)Cdr=365S∑s=1S∑t=1Tktpload.s.t−Kpload.s.t′,wherekt is TOU price, K is the original electricity price, and pload.s.t′ is the load demand before implementation of TOU price.


### 3.1.3. System Operation Revenue

System operation revenue includes two parts, namely, network loss reduction cost savings and environmental protection cost savings:(14)Fprofit=−Crloss−Cep.These two parts can be calculated as follows.(1)
Network loss reduction cost savings:(15)Crloss=365S∑s=1S∑t=1Tcrlossploss.s.t′−ploss.s.t,wherecloss is the unit net loss reduction income and ploss′ is the network loss before connection of distributed power supply.(2)
Environmental cost savings:(16)Cep=365S∑s=1S∑t=1TαiβinDGpDG.s.t,whereαi and βi are the emission coefficient and treatment cost of the ith pollutant.


## 3.1.1. Investment Cost of Distributed Generators

Finv can be calculated as follows:(8)Finv=d1+dn1+dn−1∑i∈NDGcDGnDGprate,where d is the discount rate, n is the service life of distributed power supply, NDG is the set of network nodes, cDG is the unit investment price of distributed power supply, and nDG indicates the number of installed distributed power supplies.


## 3.1.2. System Operation Cost

The system operation cost consists of four parts, namely, the operation and maintenance cost of distributed power supply, the power purchase cost of main network, the voltage overlimit penalty cost, and the demand response implementation cost, as follows:(9)Fcost=Cope+Cmpur+Cvdev+Cdr.The calculation method of each part is as follows.(1)
Operation and maintenance cost of distributed generators:(10)Cope=365S∑s=1S∑t=1TcopnDGpDG.s.t,wheres indicates the number of scenarios, cop is unit operation and maintenance cost of distributed power supply, and pDG.s.t is the active power output of distributed power supply.(2)
Power purchase cost of the main network:(11)Cmpur=365S∑s=1S∑t=1Tcpupload.s.t+ploss.s.t−nDGpDG.s.t,wherecpu is the cost of electricity purchase from the main network, pload is the load demand, and ploss is the network loss.(3)
Penalty cost of voltage exceedance:(12)Cvdev=365S∑s=1S∑t=1T∑i=1NDGcvdev∆Ui.s.t,∆U=Ui−Ut,0,Ul−Ui,Ui>Ut,Ul<Ui<UtUi<Ul,,wherecvdev is the penalty cost per unit voltage exceedance, ∆U is the voltage overlimit degree, and Ut and Ul are the upper and lower voltage limits, respectively.(4)
Demand response implementation cost:(13)Cdr=365S∑s=1S∑t=1Tktpload.s.t−Kpload.s.t′,wherekt is TOU price, K is the original electricity price, and pload.s.t′ is the load demand before implementation of TOU price.


## 3.1.3. System Operation Revenue

System operation revenue includes two parts, namely, network loss reduction cost savings and environmental protection cost savings:(14)Fprofit=−Crloss−Cep.These two parts can be calculated as follows.(1)
Network loss reduction cost savings:(15)Crloss=365S∑s=1S∑t=1Tcrlossploss.s.t′−ploss.s.t,wherecloss is the unit net loss reduction income and ploss′ is the network loss before connection of distributed power supply.(2)
Environmental cost savings:(16)Cep=365S∑s=1S∑t=1TαiβinDGpDG.s.t,whereαi and βi are the emission coefficient and treatment cost of the ith pollutant.


## 3.2. Constraints

The access of distributed power supply is constrained by safe operation of the system, which can be categorized into equality and inequality constraints, as follows(1)
Equality Constraint. The power balance equation should be satisfied for either the nodes connected to distributed power supply or other nodes, as follows:(17)PGi−PLi−Ui∑j∈kUjGijcosθij+Bijsinθij=0,QGi−QLi−Ui∑j∈kUjGijsinθij−Bijcosθij=0,wherePGi and QGi are the active and reactive powers of the ith node, PLi and QLi are the active and reactive power loads of the ith node, respectively, Ui is the voltage of the ith node, and Gij, Bij, and θij are the conductance, susceptance, and phase angle difference between nodes i and j, respectively.(2)
Inequality Constraints. There are three inequality constraints, as follows.(a)
Node voltage constraints:(18)Uimin≤Ui≤Uimax,whereUimin and Uimax represent the lower and upper limits of voltage at the ith node, respectively.(b)
Branch power constraints of the system:(19)Sij≤Sij,max,whereSij,max is the maximum apparent power allowed by the branch.(c)
Constraints on the number of distributed generators to be installed:(20)ni.s.tWTG≤NiWTG,ni.s.tPVG≤NiPVG,whereNiWTG and NiPVG represent the maximum number of installed wind turbines and photovoltaic units, respectively.


## 4. Scene Generation and Model Solution

### 4.1. Generation of Wind-Photovoltaic-Load Timing Sequence Scenario

In order to make the planning scheme as close as possible to the reality, the required scenarios for the analysis in the scheme should be diversified, and a large variety of possible working conditions should be presented. A large number of local actual wind speed and illumination data are considered the first choice for scene generation. Existence of numerous scenes results in dimensional disaster in the algorithm, while blind reduction of scenes considering the computational burden may lose scene diversity.The k-means clustering algorithm can be divided into different categories according to samples’ characteristics. Samples of the same category have good similarity, while samples of different kinds are characterized by greater difference. Moreover, k-means clustering algorithm has the advantages of simplicity, effectiveness, and high efficiency, which can alleviate the computational cost [23]. At the same time, the cluster validity index of Davies and Bouldin (IDB) is introduced as the basis for the number of scene clusters in the k-means clustering algorithm. This can avoid the lack of scene diversity caused by subjective selection of the cluster center number. The relation between Euclidean distance of different cluster centers and the degree of separation indicates that the Davis Bolding index determines the best number of clusters leading to generation of diverse and representative scenes [24]. The procedure of cluster generation scenario is presented in Figure 1.Figure 1
Generation of scenarios based on k-means with IDB.


### 4.2. Improved Simulated Annealing Particle Swarm Optimization Algorithm

The traditional particle swarm optimization (PSO) algorithm starts with random solution and searches for the optimal solution through continuous iteration. This is performed by pursuit of the optimal value of the current search to find the global optimal solution. Completely random movement of the particles without a clear purpose may cause failure in finding the global optimal position. In such condition, the algorithm chooses the same position to be replaced with the current optimal position without any change, leading to a local optimum.By integration with simulated annealing algorithm, the local search ability of traditional PSO algorithm is improved. Simulated annealing algorithm can control the temperature and accept relatively poor solutions under a certain probability. It can search for the optimal position in the region repeatedly. In the SAPSO algorithm, the speed and position are updated as follows:(21)Vik+1=ωVik+c1randpbest−Xik+c2randgbest−Xik,Xik+1=Xik+Vik+1,c1=cmax+cmin−cmaxT,c2=cmax+cmin−cmaxT,e−fpi−fgbest/T∑i=1N−fpi−fgbest/T,where Vik and Xik are the velocity and position of the ith particle at the kth iteration, respectively, c1 and c2 are learning factors, ω represents inertia weight, pbest is the individual optimal solution of the traditional PSO algorithm, pbbest is the optimal solution of SAPSO algorithm, and gbest is the global optimal solution. Equation (22) is used to select pbbest based on the neighborhood search principle, where fpi and fgbest are fitness of the ith individual and fitness of the global best position, respectively, and T is the current temperature.Although the SAPSO algorithm improves the local search ability of PSO algorithm, it weakens the advantages of PSO algorithm at the same time. Regarding partial limitations of the algorithm, the following improvements are made.(1)
Optimization of the initial population based on niche fitness: SAPSO is slower in convergence than PSO. Excellent local search mechanism of the simulated annealing algorithm also reduces computational speed of the whole algorithm. In the niche fitness optimization, each generation of individuals is classified and some representative individuals with good fitness are selected as elite population. The next generation of operation is produced on the basis of this elite group. At the same time, the preselection and sharing mechanisms are applied to maintain the diversity of population and obtain a better initial population [25, 26]. It can not only improve the convergence speed but also effectively avoid the blind search of particles and enhance the calculation speed. The niche fitness is expressed as follows:(22)Fi=1∑j=1Njyfjydijj=1,2,3,⋯,Njy,(23)fjydij=1−dijδshareα0,0<dij<δshare,dij>δshare,whereFi is niche fitness, fjydij is the shared fitness function of individuals i and j, Njy is the number of particles in elite set, dij is the Euclidean distance between different individuals, α is the shape parameter, and δshare is the shared distance.(2)
Improvement of inertia weight and learning factor: The SAPSO algorithm may fail to find the global optimum in a limited number of iterations due to the mechanism of finding the local optimum. Therefore, the speed update formula of PSO is modified to further improve the local search capability and quickly find the optimal solution. The inertia weight in the formula represents ability of the offspring to inherit velocity of the previous generation. The large inertia value is suitable for global search, while its small value is appropriate for local search. The present paper adopts inertia weight with chaotic disturbance [27, 28] with the following setting:(24)ωt=ωmax−ωmax−ωminSt+ω¯γωmax−ωmax−ωminStδ2≤ε,δ2>ε,γi+1=4γi1−γi,δ2=1N∑iNfti−f¯f,f=max1,fti−f¯,whereSt is the sigmoid function, which is sensitive to subtle changes and can be used to control variation of inertia weight, ϖ represents the mean value of the maximum and minimum inertia weight, γ denotes the chaotic disturbance represented by the logistic mapping model, which can slightly change the inertia weight, affect the subsequent orbit, and effectively prevent falling into local minimum, δ2 is population fitness variance, fti is fitness of the ith particle, and f¯ is the mean of particle fitness in the current particle swarm.The learning factor in the velocity update formula of PSO represents the ability of particles to accumulate and learn from excellent individuals in the group, which can cause faster movement of particles to proximity of the best point in the group or the field. In this paper, dynamic parameters are adopted to strengthen the adaptive ability of learning factors, as follows:(25)c1=cmax+cmin−cmaxtT,c2=cmin+cmin−cmaxtT,where cmin and cmax are the minimum and maximum values of learning factors, t is the current iteration number, and T is the maximum number of iterations.The computational process flow of the improved simulated annealing particle swarm optimization algorithm is presented in Figure2.Figure 2
Computational process flow of improved simulated annealing particle swarm optimization algorithm.


## 4.1. Generation of Wind-Photovoltaic-Load Timing Sequence Scenario

In order to make the planning scheme as close as possible to the reality, the required scenarios for the analysis in the scheme should be diversified, and a large variety of possible working conditions should be presented. A large number of local actual wind speed and illumination data are considered the first choice for scene generation. Existence of numerous scenes results in dimensional disaster in the algorithm, while blind reduction of scenes considering the computational burden may lose scene diversity.The k-means clustering algorithm can be divided into different categories according to samples’ characteristics. Samples of the same category have good similarity, while samples of different kinds are characterized by greater difference. Moreover, k-means clustering algorithm has the advantages of simplicity, effectiveness, and high efficiency, which can alleviate the computational cost [23]. At the same time, the cluster validity index of Davies and Bouldin (IDB) is introduced as the basis for the number of scene clusters in the k-means clustering algorithm. This can avoid the lack of scene diversity caused by subjective selection of the cluster center number. The relation between Euclidean distance of different cluster centers and the degree of separation indicates that the Davis Bolding index determines the best number of clusters leading to generation of diverse and representative scenes [24]. The procedure of cluster generation scenario is presented in Figure 1.Figure 1
Generation of scenarios based on k-means with IDB.


## 4.2. Improved Simulated Annealing Particle Swarm Optimization Algorithm

The traditional particle swarm optimization (PSO) algorithm starts with random solution and searches for the optimal solution through continuous iteration. This is performed by pursuit of the optimal value of the current search to find the global optimal solution. Completely random movement of the particles without a clear purpose may cause failure in finding the global optimal position. In such condition, the algorithm chooses the same position to be replaced with the current optimal position without any change, leading to a local optimum.By integration with simulated annealing algorithm, the local search ability of traditional PSO algorithm is improved. Simulated annealing algorithm can control the temperature and accept relatively poor solutions under a certain probability. It can search for the optimal position in the region repeatedly. In the SAPSO algorithm, the speed and position are updated as follows:(21)Vik+1=ωVik+c1randpbest−Xik+c2randgbest−Xik,Xik+1=Xik+Vik+1,c1=cmax+cmin−cmaxT,c2=cmax+cmin−cmaxT,e−fpi−fgbest/T∑i=1N−fpi−fgbest/T,where Vik and Xik are the velocity and position of the ith particle at the kth iteration, respectively, c1 and c2 are learning factors, ω represents inertia weight, pbest is the individual optimal solution of the traditional PSO algorithm, pbbest is the optimal solution of SAPSO algorithm, and gbest is the global optimal solution. Equation (22) is used to select pbbest based on the neighborhood search principle, where fpi and fgbest are fitness of the ith individual and fitness of the global best position, respectively, and T is the current temperature.Although the SAPSO algorithm improves the local search ability of PSO algorithm, it weakens the advantages of PSO algorithm at the same time. Regarding partial limitations of the algorithm, the following improvements are made.(1)
Optimization of the initial population based on niche fitness: SAPSO is slower in convergence than PSO. Excellent local search mechanism of the simulated annealing algorithm also reduces computational speed of the whole algorithm. In the niche fitness optimization, each generation of individuals is classified and some representative individuals with good fitness are selected as elite population. The next generation of operation is produced on the basis of this elite group. At the same time, the preselection and sharing mechanisms are applied to maintain the diversity of population and obtain a better initial population [25, 26]. It can not only improve the convergence speed but also effectively avoid the blind search of particles and enhance the calculation speed. The niche fitness is expressed as follows:(22)Fi=1∑j=1Njyfjydijj=1,2,3,⋯,Njy,(23)fjydij=1−dijδshareα0,0<dij<δshare,dij>δshare,whereFi is niche fitness, fjydij is the shared fitness function of individuals i and j, Njy is the number of particles in elite set, dij is the Euclidean distance between different individuals, α is the shape parameter, and δshare is the shared distance.(2)
Improvement of inertia weight and learning factor: The SAPSO algorithm may fail to find the global optimum in a limited number of iterations due to the mechanism of finding the local optimum. Therefore, the speed update formula of PSO is modified to further improve the local search capability and quickly find the optimal solution. The inertia weight in the formula represents ability of the offspring to inherit velocity of the previous generation. The large inertia value is suitable for global search, while its small value is appropriate for local search. The present paper adopts inertia weight with chaotic disturbance [27, 28] with the following setting:(24)ωt=ωmax−ωmax−ωminSt+ω¯γωmax−ωmax−ωminStδ2≤ε,δ2>ε,γi+1=4γi1−γi,δ2=1N∑iNfti−f¯f,f=max1,fti−f¯,whereSt is the sigmoid function, which is sensitive to subtle changes and can be used to control variation of inertia weight, ϖ represents the mean value of the maximum and minimum inertia weight, γ denotes the chaotic disturbance represented by the logistic mapping model, which can slightly change the inertia weight, affect the subsequent orbit, and effectively prevent falling into local minimum, δ2 is population fitness variance, fti is fitness of the ith particle, and f¯ is the mean of particle fitness in the current particle swarm.The learning factor in the velocity update formula of PSO represents the ability of particles to accumulate and learn from excellent individuals in the group, which can cause faster movement of particles to proximity of the best point in the group or the field. In this paper, dynamic parameters are adopted to strengthen the adaptive ability of learning factors, as follows:(25)c1=cmax+cmin−cmaxtT,c2=cmin+cmin−cmaxtT,where cmin and cmax are the minimum and maximum values of learning factors, t is the current iteration number, and T is the maximum number of iterations.The computational process flow of the improved simulated annealing particle swarm optimization algorithm is presented in Figure2.Figure 2
Computational process flow of improved simulated annealing particle swarm optimization algorithm.


## 5. Experiment Analyses

The IEEE 69-node distribution system with actual measured data is taken as the research experiment. Its topology is shown in Figure3. The reference power and voltage of the system are 10 MVA and 10 kV, respectively. The change of load trend with scenario reduction is illustrated in Figure 4.Figure 3
IEEE 69-node distribution network.Figure 4
Temporal change of load trend with scenario.In the node system, all except one node is residential load, and distributed power supply can be installed in all other 2–69 nodes. The WTG unit capacity is 200 kW, and the rated, inlet, and outlet wind speeds are 14 m/s, 4.5 m/s, and 28 m/s. The unit investment cost is 8000 yuan/set, the upper limit for each node is set to 6 sets, and the operation and maintenance cost is 0.25 yuan/kWh. In the case of PVG unit, the capacity is 100 kW, rated radiation is 500 W/m2, unit investment cost is 6000 yuan/unit, installation limit of each node is set to 8 units, and operation and maintenance cost is 0.2 yuan/kWh. These two distributed power supplies have 20-year lifespan and 10% discount rate. The unit cost of power purchase for the main network is 0.4 yuan/kWh, and the loss reduction benefit is 0.5 yuan/kWh. Emission factors of NOx, CO2, and SO2 emission factor are 1.6 g/kWh, 889 g/kWh, and 1.8 g/kWh, and the respective treatment costs are 62.964 yuan/kg, 0.21 yuan/kg, and 14.842 yuan/kg. The upper and lower limits of node voltage are 1.1 p.u and 0.9 p.u, respectively.In terms of demand response, when the fixed TOU price is adopted, the price variations are given in Table1.Table 1
Time-dependent electricity price.
TypePeak and valley periodPrice (yuan/kWh)The peak times12 : 00∼14 : 000.74319 : 00∼22 : 00The flat times9 : 00∼11 : 000.5515 : 00∼18 : 0023 : 00∼24 : 00The valley times1 : 00∼8 : 000.288According to the historical load data and electricity price information, the elasticity price coefficient of the region is presented in Table2.Table 2
Elastic coefficient matrix.
PeriodPeakFlatValleyPeak−0.10.010.02Flat0.01−0.10.01Valley0.020.01−0.1In terms of the modified simulated annealing PSO algorithm based on the niche fitness, the number of population particles and the maximum number of iterations are set to 20 and 60, respectively. Furthermore, the annealing constant is 0.9, the maximum and minimum inertia weights for the velocity update formula are 0.9 and 0.4, and the maximum and minimum learning factors are 2.5 and 0.5, respectively.


### 5.1. Results

#### 5.1.1. Comparison of Generated Scenarios

Considering the balance between scene diversity and calculation cost, the number of clusters is defined in the range of [10, 50]. In Figure5, the scene is divided into 24 categories and the Davis Bolding index is the smallest. So, it is reasonable to select the cluster scene as 24 for this group of data.Figure 5
Davis Bolding index distribution.Regarding comparison of the scene diversity, Figures6(a) and 6(c) illustrate the Weibull and beta distributions, obtained from statistical data of wind speed and light intensity, respectively. The output is then simulated by Latin hypercube sampling. Figures 6(b) and 6(d) present the output scenes generated by clustering of actual wind speed and light radiance at each moment. The wind speed and optical radiation data used are shown in Figure 7. The wind turbine cannot reach the maximum power, which is about 150 kW.Figure 6
Wind-photovoltaic scenarios based on probabilistic model or time. (a) Wind power scenario based on probability model. (b) Time series-based wind power scenario. (c) PV power scenario based on probabilistic model. (d) Time series-based PV power scenario.
(a)(b)(c)(d)Figure 7
Regional measurement data. (a) Wind speed. (b) Optical radiation.
(a)(b)In comparison with the scenario obtained by the probability model, in the scenario based on the actual wind speed simulation, the wind turbines’ output mostly increases from noon to the highest value in the evening. There are also particular scenarios in which no power is generated in a windless day, or significant power is generated in an entirely windy day.In terms of PV unit output and in comparison with the probabilistic model scenario, in the scenario obtained by the actual luminous radiance simulation, the PV unit can reach the full output at noon lasting for a period of time. There are also scenarios with oscillating output caused by cloudy weather and poor output on the cloudy days.Comparison of the results indicates that the scene generated by the k-means clustering method including IDB on the actual wind speed and light intensity is closely time-dependent, fits to the reality, and involves good scene diversity. The planning scheme based on such a scene is more reliable and flexible.


#### 5.1.2. Analysis of Planning Results

In this paper, three planning schemes are considered for comparative analysis. Scheme 1 uses the actual wind speed and light intensity for scene generation and adopts the demand response based on hybrid dynamic and fixed TOU prices. In Scheme 2, the actual wind speed, light generation scenario, and demand response based on fixed TOU price are used to optimize the distributed power supply allocation. Scheme 3 utilizes the probability model to generate the scenario and the demand response based on the fixed TOU price to carry out the scheme planning. The planning results, cost data, and total costs based on these three schemes are presented in Tables3 and 4.Table 3
Program results.
Planning schemePlan 1Plan 2Plan 3WTG location (number)23 (1), 65 (4)59 (4), 64 (2)59 (3), 60 (1)PVG location (number)64 (6), 65 (1)11 (4), 31 (1)61 (6), 65 (3)Table 4
Cost data.
Type (unit/ten thousand yuan)Plan 1Plan 2Plan 3Network loss reduction cost savings45.6830.4126.64Demand response cost42.57143.16143.16Environmental cost savings125.05120.2469.02Distributed power investment136.25131.56140.95Operation and maintenance cost58.9847.0638.57Electricity purchase cost of the main network1867.031889.111957.34Voltage limit (p.u)46.0581.5482.54Total cost1980.162011.102127.08In plan one, a wind turbine generator is installed on node 23, six photovoltaic units are installed on node 64, and one photovoltaic unit and four wind turbine generators are installed on node 65. A total of 12 distributed generators are installed.In plan two, four photovoltaic units are installed on node 11, one photovoltaic unit is installed on node 31, four wind turbine generators are installed on node 59, and two wind turbine generators are installed on node 64. A total of 11 distributed generators are installed.In plan three, three wind turbine generators are installed on node 59, one wind turbine generators is installed on node 64, six photovoltaic units are installed on node 61, and three photovoltaic units are installed on node 65. A total of 13 distributed generators are installed.The investment costs of plans 1, 2, and 3 are 1.36, 1.316, and 1.4095 million yuan, respectively. The voltage limit cost is the sum of the off-limit cost of all nodes. According to specific quantity of installation, it can be seen that after connection of the same distribution network with an approximate quantity of distributed power supply, the loss reduction effect of Scheme 1 is better than that of Scheme 2 with fixed TOU price, and the network loss saving cost of Schemes 1 and 2 is 456,800 and 304,100 yuan, such that the revenue of Scheme 1 is 1.5 times greater than that of Scheme 2. At the same time, when the total number of distributed power supplies in Scheme 1 is slightly higher than that of Scheme 2, the voltage overlimit is only 56% of that in Scheme 2.Because of interaction between demand response and distributed power supply, site selection and capacity determination in Scheme 1 are performed according to the time series output characteristics of wind power and photovoltaic distributed power supply. This makes the access to distributed power supply more reasonable. It meets the system requirements and leads to suitable performance in reduction of network loss and voltage quality. In addition, after reasonable planning, Scheme 1 is capable to accommodate a larger scale of distributed power supply access compared to that of Scheme 2.The demand response cost of plans 1, 2, and 3 is 0.43, 1.432, and 1.432 million yuan, respectively. Both Schemes 2 and 3 adopt fixed TOU price, which is costly in terms of demand response implementation. At the same time, it is possible that users consume electricity in the period of low electricity price for a long time, which increases the cost again and further reduces the scheme economy. In Scheme 1, the hybrid TOU price can not only decrease energy consumption but also greatly reduces the cost of demand response implementation. Compared to Schemes 2 and 3, the cost of Scheme 1 is reduced by 70.2%. Scheme 1 can also reduce the demand response cost on the basis of more detailed division of scenes and electricity prices.The environmental cost savings of plans 2 and 3 are 1.20 and 0.69 million yuan, and the operation and maintenance cost of Schemes 2 and 3 is 470,600 and 385,700 yuan.Although the number of installed distributed power supplies in Schemes 2 and 3 is roughly the same, the environmental cost savings and operation and maintenance costs of them are quite different. These two objective functions should be increased with the increase of the number of DG access. However, in comparison with Scheme 2, Scheme 3 includes more DGs and smaller environmental cost savings and operation and maintenance costs. This is because the probabilistic model simulates the output inaccurate and mainly simulates the uncertainty. Moreover, the diversity of simulated output scenarios obtained by sampling based on the probabilistic model is low. Therefore, the two objective functions lead to opposite results, though they are closely related to the output.


#### 5.1.3. Analysis of Representative Scenarios

Among the 24 scenarios in Scheme 1, there are 2 scenarios with fixed TOU price, as shown in Figure8(a). In such scenarios, the distributed power supply is a special scenario with almost no output. Although the effect of guiding load by dynamic TOU mechanism is similar to that of fixed TOU price mechanism, its effect is not as good as that of fixed TOU price. Therefore, in such scenarios, it is more reasonable to adopt fixed TOU price without interaction with distributed power output to guide load changes. The other 22 scenarios adopt the dynamic TOU price mechanism. One scenario with frequent price changes is taken as shown in Figure 8(b).Figure 8
Classification of the TOU price. (a) Change of electricity price, load, and DG output in the scenario with fixed TOU price. (b) Change of electricity price, load, and DG output in the scenario with dynamic TOU price.
(a)(b)Figure9 shows the scenario with favorable output of the distributed power supply, where Figure 9(a) shows the scenario of Scheme 1. In the current scenario, the peak load, valley load, and peak-valley difference after demand response are 5.289 MW, 3.795 MW, and 1.494 MW, respectively. The respective original values are 5.289 MW, 3.438 MW, and 1.851 MW. Scheme 1 mainly leads to peak shifting and valley filling in this scene. Figure 9(b) presents the scenario of Scheme 2. The peak load, valley load, and peak-valley difference after demand response are 5.217 MW, 3.771 MW, and 1.446 MW, respectively. Scheme 2 plays the role of peak cutting and valley filling slightly better than that of Scheme 1. However, the load variation trend of Scheme 1 is similar to that of DG output, such that the peak load is shifted to the moment with better DG output, which is favorable for energy consumption. In comparison, when DG output is the best, the change of electricity price in Scheme 2 limits the users’ electricity consumption. This is the reason for the increase of voltage overlimit index of plan 2 in the above planning results.Figure 9
Load and electricity price changes of the three schemes in the scenario with better DG output. (a) Scheme 1. (b) Scheme 2. (c) Scheme 3.
(a)(b)(c)Figure10 shows the scenario with large peak-valley difference, where Figure 10(a) belongs to the scenario of Scheme 1. The peak load, valley load, and peak-valley difference after demand response are 6.498 MW, 4.581 MW, and 1.917 MW, respectively. Figure 10(b) presents the scenario corresponding to Scheme 2. The peak load, valley load, and peak-valley difference after demand response are 6.774 MW, 4.552 MW, and 2.222 MW, respectively. The respective original values are 6.837 MW, 4.151 MW, and 2.686 MW. In Scheme 2, the peak cutting effect is not obvious in the scene with large peak-valley difference. Furthermore, the overall load adjustment effect is not evident in this scheme, while the load fluctuation is considerable. In comparison with Scheme 2, Scheme 1 is characterized by better peak cutting and valley filling effects as well as stable and relatively gentle adjusted load curve in the scene with large peak-valley difference.Figure 10
Load and electricity price changes of the three schemes in the scenario with large peak-valley difference. (a) Scheme 1. (b) Scheme 2. (c) Scheme 3.
(a)(b)(c)Figures9(c) and 10(c) correspond to the scene of Scheme 3. It can be seen that DG output in Scheme 3 is fluctuative without any obvious temporal characteristics. Moreover, output scenes are highly similar, and the scene diversity is poor. As a result, part of the revenue and cost in the planning results of Scheme 3 (in the previous subsection) are inconsistent with the actual situation. Such planning scheme causes a series of disadvantages such as unexpected changes in various economic indicators and increased network losses during actual implementation. More complex factors should be considered in plan 3 in order to achieve the approximate effect with plans 1 and 2, in which loss outweighs the gain.


#### 5.1.4. Comparison of Algorithm Improvement

In this paper, traditional PSO, SAPSO, and ISAPSO algorithms based on niche fitness were used to calculate Scheme 1. The convergence speed, calculation speed, fitness, and local search ability were compared and analyzed. The fitness obtained by the three algorithms is shown in Figure11. As can be seen, convergence speed of the traditional PSO is the main advantage of this algorithm. It converges to the optimal value in the 19th generation, and it can be seen that further increase of the number of iterations does not results in finding a better solution. Since the local search ability is poor, it falls into the local optimum. The SAPSO has higher requirements on the initial population, which affects its convergence speed, such that it converges to the optimal value in the 42nd generation. Although the mechanism of finding the optimal solution in the SAPSO leads to better results than the PSO algorithm, the local search mechanism of this algorithm is still similar to the optimization method of PSO algorithm. So, more iteration also falls into the local optimum. In contrast, convergence speed of the ISAPSO algorithm based on the niche fitness lies between the two mentioned algorithms, such that it converges to the optimal value in the 35th generation. It can also be seen that through the improvement of the inertia weight and learning factor in the local search mechanism of PSO, the local search ability of the proposed algorithm has been significantly improved, and it can search for relatively better solutions within a limited number of iterations. The calculation time of PSO and simulated annealing PSO is 1.5 and 1.8 times larger than that of the ISAPSO based on the niche fitness, respectively. The above enhancements reveal that the ISAPSO algorithm has the advantages of the two other algorithms and additionally improves the disadvantages of these algorithms.Figure 11
Comparison of algorithms implemented in the present study.


## 5.1. Results

### 5.1.1. Comparison of Generated Scenarios

Considering the balance between scene diversity and calculation cost, the number of clusters is defined in the range of [10, 50]. In Figure5, the scene is divided into 24 categories and the Davis Bolding index is the smallest. So, it is reasonable to select the cluster scene as 24 for this group of data.Figure 5
Davis Bolding index distribution.Regarding comparison of the scene diversity, Figures6(a) and 6(c) illustrate the Weibull and beta distributions, obtained from statistical data of wind speed and light intensity, respectively. The output is then simulated by Latin hypercube sampling. Figures 6(b) and 6(d) present the output scenes generated by clustering of actual wind speed and light radiance at each moment. The wind speed and optical radiation data used are shown in Figure 7. The wind turbine cannot reach the maximum power, which is about 150 kW.Figure 6
Wind-photovoltaic scenarios based on probabilistic model or time. (a) Wind power scenario based on probability model. (b) Time series-based wind power scenario. (c) PV power scenario based on probabilistic model. (d) Time series-based PV power scenario.
(a)(b)(c)(d)Figure 7
Regional measurement data. (a) Wind speed. (b) Optical radiation.
(a)(b)In comparison with the scenario obtained by the probability model, in the scenario based on the actual wind speed simulation, the wind turbines’ output mostly increases from noon to the highest value in the evening. There are also particular scenarios in which no power is generated in a windless day, or significant power is generated in an entirely windy day.In terms of PV unit output and in comparison with the probabilistic model scenario, in the scenario obtained by the actual luminous radiance simulation, the PV unit can reach the full output at noon lasting for a period of time. There are also scenarios with oscillating output caused by cloudy weather and poor output on the cloudy days.Comparison of the results indicates that the scene generated by the k-means clustering method including IDB on the actual wind speed and light intensity is closely time-dependent, fits to the reality, and involves good scene diversity. The planning scheme based on such a scene is more reliable and flexible.


### 5.1.2. Analysis of Planning Results

In this paper, three planning schemes are considered for comparative analysis. Scheme 1 uses the actual wind speed and light intensity for scene generation and adopts the demand response based on hybrid dynamic and fixed TOU prices. In Scheme 2, the actual wind speed, light generation scenario, and demand response based on fixed TOU price are used to optimize the distributed power supply allocation. Scheme 3 utilizes the probability model to generate the scenario and the demand response based on the fixed TOU price to carry out the scheme planning. The planning results, cost data, and total costs based on these three schemes are presented in Tables3 and 4.Table 3
Program results.
Planning schemePlan 1Plan 2Plan 3WTG location (number)23 (1), 65 (4)59 (4), 64 (2)59 (3), 60 (1)PVG location (number)64 (6), 65 (1)11 (4), 31 (1)61 (6), 65 (3)Table 4
Cost data.
Type (unit/ten thousand yuan)Plan 1Plan 2Plan 3Network loss reduction cost savings45.6830.4126.64Demand response cost42.57143.16143.16Environmental cost savings125.05120.2469.02Distributed power investment136.25131.56140.95Operation and maintenance cost58.9847.0638.57Electricity purchase cost of the main network1867.031889.111957.34Voltage limit (p.u)46.0581.5482.54Total cost1980.162011.102127.08In plan one, a wind turbine generator is installed on node 23, six photovoltaic units are installed on node 64, and one photovoltaic unit and four wind turbine generators are installed on node 65. A total of 12 distributed generators are installed.In plan two, four photovoltaic units are installed on node 11, one photovoltaic unit is installed on node 31, four wind turbine generators are installed on node 59, and two wind turbine generators are installed on node 64. A total of 11 distributed generators are installed.In plan three, three wind turbine generators are installed on node 59, one wind turbine generators is installed on node 64, six photovoltaic units are installed on node 61, and three photovoltaic units are installed on node 65. A total of 13 distributed generators are installed.The investment costs of plans 1, 2, and 3 are 1.36, 1.316, and 1.4095 million yuan, respectively. The voltage limit cost is the sum of the off-limit cost of all nodes. According to specific quantity of installation, it can be seen that after connection of the same distribution network with an approximate quantity of distributed power supply, the loss reduction effect of Scheme 1 is better than that of Scheme 2 with fixed TOU price, and the network loss saving cost of Schemes 1 and 2 is 456,800 and 304,100 yuan, such that the revenue of Scheme 1 is 1.5 times greater than that of Scheme 2. At the same time, when the total number of distributed power supplies in Scheme 1 is slightly higher than that of Scheme 2, the voltage overlimit is only 56% of that in Scheme 2.Because of interaction between demand response and distributed power supply, site selection and capacity determination in Scheme 1 are performed according to the time series output characteristics of wind power and photovoltaic distributed power supply. This makes the access to distributed power supply more reasonable. It meets the system requirements and leads to suitable performance in reduction of network loss and voltage quality. In addition, after reasonable planning, Scheme 1 is capable to accommodate a larger scale of distributed power supply access compared to that of Scheme 2.The demand response cost of plans 1, 2, and 3 is 0.43, 1.432, and 1.432 million yuan, respectively. Both Schemes 2 and 3 adopt fixed TOU price, which is costly in terms of demand response implementation. At the same time, it is possible that users consume electricity in the period of low electricity price for a long time, which increases the cost again and further reduces the scheme economy. In Scheme 1, the hybrid TOU price can not only decrease energy consumption but also greatly reduces the cost of demand response implementation. Compared to Schemes 2 and 3, the cost of Scheme 1 is reduced by 70.2%. Scheme 1 can also reduce the demand response cost on the basis of more detailed division of scenes and electricity prices.The environmental cost savings of plans 2 and 3 are 1.20 and 0.69 million yuan, and the operation and maintenance cost of Schemes 2 and 3 is 470,600 and 385,700 yuan.Although the number of installed distributed power supplies in Schemes 2 and 3 is roughly the same, the environmental cost savings and operation and maintenance costs of them are quite different. These two objective functions should be increased with the increase of the number of DG access. However, in comparison with Scheme 2, Scheme 3 includes more DGs and smaller environmental cost savings and operation and maintenance costs. This is because the probabilistic model simulates the output inaccurate and mainly simulates the uncertainty. Moreover, the diversity of simulated output scenarios obtained by sampling based on the probabilistic model is low. Therefore, the two objective functions lead to opposite results, though they are closely related to the output.


### 5.1.3. Analysis of Representative Scenarios

Among the 24 scenarios in Scheme 1, there are 2 scenarios with fixed TOU price, as shown in Figure8(a). In such scenarios, the distributed power supply is a special scenario with almost no output. Although the effect of guiding load by dynamic TOU mechanism is similar to that of fixed TOU price mechanism, its effect is not as good as that of fixed TOU price. Therefore, in such scenarios, it is more reasonable to adopt fixed TOU price without interaction with distributed power output to guide load changes. The other 22 scenarios adopt the dynamic TOU price mechanism. One scenario with frequent price changes is taken as shown in Figure 8(b).Figure 8
Classification of the TOU price. (a) Change of electricity price, load, and DG output in the scenario with fixed TOU price. (b) Change of electricity price, load, and DG output in the scenario with dynamic TOU price.
(a)(b)Figure9 shows the scenario with favorable output of the distributed power supply, where Figure 9(a) shows the scenario of Scheme 1. In the current scenario, the peak load, valley load, and peak-valley difference after demand response are 5.289 MW, 3.795 MW, and 1.494 MW, respectively. The respective original values are 5.289 MW, 3.438 MW, and 1.851 MW. Scheme 1 mainly leads to peak shifting and valley filling in this scene. Figure 9(b) presents the scenario of Scheme 2. The peak load, valley load, and peak-valley difference after demand response are 5.217 MW, 3.771 MW, and 1.446 MW, respectively. Scheme 2 plays the role of peak cutting and valley filling slightly better than that of Scheme 1. However, the load variation trend of Scheme 1 is similar to that of DG output, such that the peak load is shifted to the moment with better DG output, which is favorable for energy consumption. In comparison, when DG output is the best, the change of electricity price in Scheme 2 limits the users’ electricity consumption. This is the reason for the increase of voltage overlimit index of plan 2 in the above planning results.Figure 9
Load and electricity price changes of the three schemes in the scenario with better DG output. (a) Scheme 1. (b) Scheme 2. (c) Scheme 3.
(a)(b)(c)Figure10 shows the scenario with large peak-valley difference, where Figure 10(a) belongs to the scenario of Scheme 1. The peak load, valley load, and peak-valley difference after demand response are 6.498 MW, 4.581 MW, and 1.917 MW, respectively. Figure 10(b) presents the scenario corresponding to Scheme 2. The peak load, valley load, and peak-valley difference after demand response are 6.774 MW, 4.552 MW, and 2.222 MW, respectively. The respective original values are 6.837 MW, 4.151 MW, and 2.686 MW. In Scheme 2, the peak cutting effect is not obvious in the scene with large peak-valley difference. Furthermore, the overall load adjustment effect is not evident in this scheme, while the load fluctuation is considerable. In comparison with Scheme 2, Scheme 1 is characterized by better peak cutting and valley filling effects as well as stable and relatively gentle adjusted load curve in the scene with large peak-valley difference.Figure 10
Load and electricity price changes of the three schemes in the scenario with large peak-valley difference. (a) Scheme 1. (b) Scheme 2. (c) Scheme 3.
(a)(b)(c)Figures9(c) and 10(c) correspond to the scene of Scheme 3. It can be seen that DG output in Scheme 3 is fluctuative without any obvious temporal characteristics. Moreover, output scenes are highly similar, and the scene diversity is poor. As a result, part of the revenue and cost in the planning results of Scheme 3 (in the previous subsection) are inconsistent with the actual situation. Such planning scheme causes a series of disadvantages such as unexpected changes in various economic indicators and increased network losses during actual implementation. More complex factors should be considered in plan 3 in order to achieve the approximate effect with plans 1 and 2, in which loss outweighs the gain.


### 5.1.4. Comparison of Algorithm Improvement

In this paper, traditional PSO, SAPSO, and ISAPSO algorithms based on niche fitness were used to calculate Scheme 1. The convergence speed, calculation speed, fitness, and local search ability were compared and analyzed. The fitness obtained by the three algorithms is shown in Figure11. As can be seen, convergence speed of the traditional PSO is the main advantage of this algorithm. It converges to the optimal value in the 19th generation, and it can be seen that further increase of the number of iterations does not results in finding a better solution. Since the local search ability is poor, it falls into the local optimum. The SAPSO has higher requirements on the initial population, which affects its convergence speed, such that it converges to the optimal value in the 42nd generation. Although the mechanism of finding the optimal solution in the SAPSO leads to better results than the PSO algorithm, the local search mechanism of this algorithm is still similar to the optimization method of PSO algorithm. So, more iteration also falls into the local optimum. In contrast, convergence speed of the ISAPSO algorithm based on the niche fitness lies between the two mentioned algorithms, such that it converges to the optimal value in the 35th generation. It can also be seen that through the improvement of the inertia weight and learning factor in the local search mechanism of PSO, the local search ability of the proposed algorithm has been significantly improved, and it can search for relatively better solutions within a limited number of iterations. The calculation time of PSO and simulated annealing PSO is 1.5 and 1.8 times larger than that of the ISAPSO based on the niche fitness, respectively. The above enhancements reveal that the ISAPSO algorithm has the advantages of the two other algorithms and additionally improves the disadvantages of these algorithms.Figure 11
Comparison of algorithms implemented in the present study.


## 5.1.1. Comparison of Generated Scenarios

Considering the balance between scene diversity and calculation cost, the number of clusters is defined in the range of [10, 50]. In Figure5, the scene is divided into 24 categories and the Davis Bolding index is the smallest. So, it is reasonable to select the cluster scene as 24 for this group of data.Figure 5
Davis Bolding index distribution.Regarding comparison of the scene diversity, Figures6(a) and 6(c) illustrate the Weibull and beta distributions, obtained from statistical data of wind speed and light intensity, respectively. The output is then simulated by Latin hypercube sampling. Figures 6(b) and 6(d) present the output scenes generated by clustering of actual wind speed and light radiance at each moment. The wind speed and optical radiation data used are shown in Figure 7. The wind turbine cannot reach the maximum power, which is about 150 kW.Figure 6
Wind-photovoltaic scenarios based on probabilistic model or time. (a) Wind power scenario based on probability model. (b) Time series-based wind power scenario. (c) PV power scenario based on probabilistic model. (d) Time series-based PV power scenario.
(a)(b)(c)(d)Figure 7
Regional measurement data. (a) Wind speed. (b) Optical radiation.
(a)(b)In comparison with the scenario obtained by the probability model, in the scenario based on the actual wind speed simulation, the wind turbines’ output mostly increases from noon to the highest value in the evening. There are also particular scenarios in which no power is generated in a windless day, or significant power is generated in an entirely windy day.In terms of PV unit output and in comparison with the probabilistic model scenario, in the scenario obtained by the actual luminous radiance simulation, the PV unit can reach the full output at noon lasting for a period of time. There are also scenarios with oscillating output caused by cloudy weather and poor output on the cloudy days.Comparison of the results indicates that the scene generated by the k-means clustering method including IDB on the actual wind speed and light intensity is closely time-dependent, fits to the reality, and involves good scene diversity. The planning scheme based on such a scene is more reliable and flexible.


## 5.1.2. Analysis of Planning Results

In this paper, three planning schemes are considered for comparative analysis. Scheme 1 uses the actual wind speed and light intensity for scene generation and adopts the demand response based on hybrid dynamic and fixed TOU prices. In Scheme 2, the actual wind speed, light generation scenario, and demand response based on fixed TOU price are used to optimize the distributed power supply allocation. Scheme 3 utilizes the probability model to generate the scenario and the demand response based on the fixed TOU price to carry out the scheme planning. The planning results, cost data, and total costs based on these three schemes are presented in Tables3 and 4.Table 3
Program results.
Planning schemePlan 1Plan 2Plan 3WTG location (number)23 (1), 65 (4)59 (4), 64 (2)59 (3), 60 (1)PVG location (number)64 (6), 65 (1)11 (4), 31 (1)61 (6), 65 (3)Table 4
Cost data.
Type (unit/ten thousand yuan)Plan 1Plan 2Plan 3Network loss reduction cost savings45.6830.4126.64Demand response cost42.57143.16143.16Environmental cost savings125.05120.2469.02Distributed power investment136.25131.56140.95Operation and maintenance cost58.9847.0638.57Electricity purchase cost of the main network1867.031889.111957.34Voltage limit (p.u)46.0581.5482.54Total cost1980.162011.102127.08In plan one, a wind turbine generator is installed on node 23, six photovoltaic units are installed on node 64, and one photovoltaic unit and four wind turbine generators are installed on node 65. A total of 12 distributed generators are installed.In plan two, four photovoltaic units are installed on node 11, one photovoltaic unit is installed on node 31, four wind turbine generators are installed on node 59, and two wind turbine generators are installed on node 64. A total of 11 distributed generators are installed.In plan three, three wind turbine generators are installed on node 59, one wind turbine generators is installed on node 64, six photovoltaic units are installed on node 61, and three photovoltaic units are installed on node 65. A total of 13 distributed generators are installed.The investment costs of plans 1, 2, and 3 are 1.36, 1.316, and 1.4095 million yuan, respectively. The voltage limit cost is the sum of the off-limit cost of all nodes. According to specific quantity of installation, it can be seen that after connection of the same distribution network with an approximate quantity of distributed power supply, the loss reduction effect of Scheme 1 is better than that of Scheme 2 with fixed TOU price, and the network loss saving cost of Schemes 1 and 2 is 456,800 and 304,100 yuan, such that the revenue of Scheme 1 is 1.5 times greater than that of Scheme 2. At the same time, when the total number of distributed power supplies in Scheme 1 is slightly higher than that of Scheme 2, the voltage overlimit is only 56% of that in Scheme 2.Because of interaction between demand response and distributed power supply, site selection and capacity determination in Scheme 1 are performed according to the time series output characteristics of wind power and photovoltaic distributed power supply. This makes the access to distributed power supply more reasonable. It meets the system requirements and leads to suitable performance in reduction of network loss and voltage quality. In addition, after reasonable planning, Scheme 1 is capable to accommodate a larger scale of distributed power supply access compared to that of Scheme 2.The demand response cost of plans 1, 2, and 3 is 0.43, 1.432, and 1.432 million yuan, respectively. Both Schemes 2 and 3 adopt fixed TOU price, which is costly in terms of demand response implementation. At the same time, it is possible that users consume electricity in the period of low electricity price for a long time, which increases the cost again and further reduces the scheme economy. In Scheme 1, the hybrid TOU price can not only decrease energy consumption but also greatly reduces the cost of demand response implementation. Compared to Schemes 2 and 3, the cost of Scheme 1 is reduced by 70.2%. Scheme 1 can also reduce the demand response cost on the basis of more detailed division of scenes and electricity prices.The environmental cost savings of plans 2 and 3 are 1.20 and 0.69 million yuan, and the operation and maintenance cost of Schemes 2 and 3 is 470,600 and 385,700 yuan.Although the number of installed distributed power supplies in Schemes 2 and 3 is roughly the same, the environmental cost savings and operation and maintenance costs of them are quite different. These two objective functions should be increased with the increase of the number of DG access. However, in comparison with Scheme 2, Scheme 3 includes more DGs and smaller environmental cost savings and operation and maintenance costs. This is because the probabilistic model simulates the output inaccurate and mainly simulates the uncertainty. Moreover, the diversity of simulated output scenarios obtained by sampling based on the probabilistic model is low. Therefore, the two objective functions lead to opposite results, though they are closely related to the output.


## 5.1.3. Analysis of Representative Scenarios

Among the 24 scenarios in Scheme 1, there are 2 scenarios with fixed TOU price, as shown in Figure8(a). In such scenarios, the distributed power supply is a special scenario with almost no output. Although the effect of guiding load by dynamic TOU mechanism is similar to that of fixed TOU price mechanism, its effect is not as good as that of fixed TOU price. Therefore, in such scenarios, it is more reasonable to adopt fixed TOU price without interaction with distributed power output to guide load changes. The other 22 scenarios adopt the dynamic TOU price mechanism. One scenario with frequent price changes is taken as shown in Figure 8(b).Figure 8
Classification of the TOU price. (a) Change of electricity price, load, and DG output in the scenario with fixed TOU price. (b) Change of electricity price, load, and DG output in the scenario with dynamic TOU price.
(a)(b)Figure9 shows the scenario with favorable output of the distributed power supply, where Figure 9(a) shows the scenario of Scheme 1. In the current scenario, the peak load, valley load, and peak-valley difference after demand response are 5.289 MW, 3.795 MW, and 1.494 MW, respectively. The respective original values are 5.289 MW, 3.438 MW, and 1.851 MW. Scheme 1 mainly leads to peak shifting and valley filling in this scene. Figure 9(b) presents the scenario of Scheme 2. The peak load, valley load, and peak-valley difference after demand response are 5.217 MW, 3.771 MW, and 1.446 MW, respectively. Scheme 2 plays the role of peak cutting and valley filling slightly better than that of Scheme 1. However, the load variation trend of Scheme 1 is similar to that of DG output, such that the peak load is shifted to the moment with better DG output, which is favorable for energy consumption. In comparison, when DG output is the best, the change of electricity price in Scheme 2 limits the users’ electricity consumption. This is the reason for the increase of voltage overlimit index of plan 2 in the above planning results.Figure 9
Load and electricity price changes of the three schemes in the scenario with better DG output. (a) Scheme 1. (b) Scheme 2. (c) Scheme 3.
(a)(b)(c)Figure10 shows the scenario with large peak-valley difference, where Figure 10(a) belongs to the scenario of Scheme 1. The peak load, valley load, and peak-valley difference after demand response are 6.498 MW, 4.581 MW, and 1.917 MW, respectively. Figure 10(b) presents the scenario corresponding to Scheme 2. The peak load, valley load, and peak-valley difference after demand response are 6.774 MW, 4.552 MW, and 2.222 MW, respectively. The respective original values are 6.837 MW, 4.151 MW, and 2.686 MW. In Scheme 2, the peak cutting effect is not obvious in the scene with large peak-valley difference. Furthermore, the overall load adjustment effect is not evident in this scheme, while the load fluctuation is considerable. In comparison with Scheme 2, Scheme 1 is characterized by better peak cutting and valley filling effects as well as stable and relatively gentle adjusted load curve in the scene with large peak-valley difference.Figure 10
Load and electricity price changes of the three schemes in the scenario with large peak-valley difference. (a) Scheme 1. (b) Scheme 2. (c) Scheme 3.
(a)(b)(c)Figures9(c) and 10(c) correspond to the scene of Scheme 3. It can be seen that DG output in Scheme 3 is fluctuative without any obvious temporal characteristics. Moreover, output scenes are highly similar, and the scene diversity is poor. As a result, part of the revenue and cost in the planning results of Scheme 3 (in the previous subsection) are inconsistent with the actual situation. Such planning scheme causes a series of disadvantages such as unexpected changes in various economic indicators and increased network losses during actual implementation. More complex factors should be considered in plan 3 in order to achieve the approximate effect with plans 1 and 2, in which loss outweighs the gain.


## 5.1.4. Comparison of Algorithm Improvement

In this paper, traditional PSO, SAPSO, and ISAPSO algorithms based on niche fitness were used to calculate Scheme 1. The convergence speed, calculation speed, fitness, and local search ability were compared and analyzed. The fitness obtained by the three algorithms is shown in Figure11. As can be seen, convergence speed of the traditional PSO is the main advantage of this algorithm. It converges to the optimal value in the 19th generation, and it can be seen that further increase of the number of iterations does not results in finding a better solution. Since the local search ability is poor, it falls into the local optimum. The SAPSO has higher requirements on the initial population, which affects its convergence speed, such that it converges to the optimal value in the 42nd generation. Although the mechanism of finding the optimal solution in the SAPSO leads to better results than the PSO algorithm, the local search mechanism of this algorithm is still similar to the optimization method of PSO algorithm. So, more iteration also falls into the local optimum. In contrast, convergence speed of the ISAPSO algorithm based on the niche fitness lies between the two mentioned algorithms, such that it converges to the optimal value in the 35th generation. It can also be seen that through the improvement of the inertia weight and learning factor in the local search mechanism of PSO, the local search ability of the proposed algorithm has been significantly improved, and it can search for relatively better solutions within a limited number of iterations. The calculation time of PSO and simulated annealing PSO is 1.5 and 1.8 times larger than that of the ISAPSO based on the niche fitness, respectively. The above enhancements reveal that the ISAPSO algorithm has the advantages of the two other algorithms and additionally improves the disadvantages of these algorithms.Figure 11
Comparison of algorithms implemented in the present study.


## 6. Conclusions

This paper proposed the price-type demand response of hybrid dynamic and fixed TOU. The actual wind speed and photovoltaic data were used to generate the scene based on k-means clustering. The optimized allocation scheme of distributed power supply with the minimum cost was obtained by using the improved simulated annealing particle swarm optimization algorithm based on the niche fitness. The conclusions are as follows:(1)
In order to simulate the uncertainty of wind and photovoltaic generator output in as much detail as possible, two different multi-scene modeling methods are compared to conclude the following. Based on actual wind speed and radiance data and using the k-means clustering algorithm containing IDB, the limitation of empirical classification can be avoided. Furthermore, various scenes with reasonable differences can be generated, while the contradiction between computational cost and scene diversity can be balanced.(2)
The hybrid TOU price mechanism is proposed to solve the energy consumption problem and provide a thinking direction for the transition to real-time price in the future. This paper also verifies that compared with traditional fixed TOU price, it also achieves similar or better effect.(3)
The algorithm in this paper is improved from the convergence speed, accuracy, and solving speed of the solution. It was verified that after optimizing the initial population and improving the velocity and position update formula, the simulated annealing particle swarm optimization algorithm can result in advantages like fast convergence speed, improved calculation speed, and enhanced local optimization ability. The convergence speed is between the two algorithms, and the calculation speed is 1.8 times the original algorithm.(4)
Reactive power compensation device can be added to further adjust the voltage and reduce the occurrence of voltage overlimit. Therefore, the location and capacity determination of distributed power supply and reactive power compensation device should be further studied on the basis of this planning scheme.



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*Source: 7471214-2023-03-23.xml*