#### 4.2.1. Introduction to the Methods

(1) The Promotion Path of Resource Use Efficiency Based on the Optimization of Siting and Sizing

Due to the great influence of the location and capacity on the absorption and utilization of solar energy, the technology of siting and sizing of distributed photovoltaic plays an important role in its operation and development [

19]. Under dual restrictions of cost and technology, optimizing dynamic multi-objective and finding the best position, which is lowest-cost power generation, will enhance the efficiency of light use and give full play to distributed photovoltaic’s advantages of economy, technology and environment [

20].

Siting and sizing for distributed photovoltaic is a nonlinear, multi-objective, multi-dimensional and multi-constrained optimization problem. On the basis of existing research results, this paper constructed the multi-objective optimization model by taking the lowest running costs and carbon emissions as objectives, taking the node voltage, branch power and power conservation as constraints and considering the economic and environmental efficiency of distributed photovoltaic.

(i) The Objective Function

where

$\Delta {C}_{LOSS}$ represents the changes of network loss cost after distributed photovoltaic accessing to network, and

$\Delta {C}_{P}$ represents the changes of purchase cost after distributed photovoltaic accessing to network.

where

${C}_{PUN}$ represents carbon emissions penalty, 9.75 Yuan/t; and

$E({\sum}_{i=1}^{DP}{\tau}_{DP,i}{P}_{DG,i})$ represents equivalent reduction of CO

_{2} emissions after the distributed photovoltaic accessing to network.

(ii) The Constraint Condition

- (a)
The Branch Power Constraint

where

${S}_{ij}$ represents the branch power;

i and

j represent the first and last branch node, respectively; and

${S}_{ij,max}$ represents the upper limit of branch power.

- (b)
The Node Voltage Constraint

where

${U}_{i}$ represents voltage amplitude of the node i, and

${U}_{i,min}$ and

${U}_{i,max}$ represent the upper and lower limit of the voltage node respectively.

- (c)
Distributed Photovoltaic Capacity Constraint

where

${P}_{NE,i}$ represents the active output of the

i-node, and

${P}_{NE,i,max}$ represents the maximum capacity of i-node which can access to distributed photovoltaic, measured in MW.

From the perspective of resource-side, the optimization path of siting and sizing proposed in this paper can determine the best location and capacity of distributed photovoltaic plant by technical means, which can ensure safe operation, taking economic and environmental benefits into account, and improve the utilization efficiency of solar energy.

(2) The Promotion Path of Resource Conversion Efficiency Based on the Optimization of Power Generation Dispatching

Solar energy has the characteristics of richness and environmental friendliness, so distributed photovoltaic can maximize resource value of solar energy in its application. However, solar randomness and volatility pose a serious challenge to the stability of a distributed photovoltaic system. Therefore, we should seriously take cost control and energy-saving and emission reduction into consideration and improve the energy conversion efficiency by optimizing generation dispatching [

21,

22].

Two-stage dispatching optimization model of distributed photovoltaic is proposed in this paper by taking into account the following factors: energy, economy and environment. The model divides the dispatching program into two stages: day-ahead dispatching and real-time dispatching. The day-ahead dispatching is responsible for generation scheduling. The real-time dispatching corrects the operation mode in the next interval and the day-ahead makes output plan based on forecast results. The entire dispatching process is presented in

Figure 5.

Optimization of two-stage dispatching will reduce the effect of uncertainty of solar energy effectively and reduce the distributed photovoltaic’s needs of operational reserve, thus it will optimize conversion efficiency of distributed photovoltaic in terms of economy and environmental protection.

(3) The Promotion Path of Demand-side Utilization Efficiency Based on the Optimization of Demand Response

Demand response refers to the behavior of electricity users for changing the existing electricity consumption patterns according to market price signals or incentive mechanism [

23]. An important prerequisite for the implementation of demand response is whether electricity users respond to the plans of power use and measures of demand response. Users will reduce electricity consumption during peak. Transferring the electricity tariff periods to a lower point and decreasing electricity costs aim to bring economic benefits for electricity users [

24]. This paper selects two response measures from demand-side: time-of-use electricity price and economic demand response based on incentive. Load model was built under the principle of maximizing benefits, so the overall operational level of distributed photovoltaic should be optimized and promoted from the demand-side.

(i) Demand Response Based on Time-of-use Electricity Price

The expression of self-elasticity coefficient and cross-elasticity coefficient are as follows:

The amount load changes caused by day-ahead price error as users expected is expressed as follows:

where

$\Delta {d}_{i}$ represents the load change of time

i;

${E}_{ij}$ represents the coefficient of elasticity, and, when

i =

j its value represents the self-elasticity coefficient, whereas, when

i ≠

j, the value represents the cross-elasticity coefficient; and

$\Delta {p}_{j}$ represents the error value which is the users’ desired price at point

j.

Therefore, the amount of 24-h load change is expressed as follows:

where

$\Delta \mathrm{d}$ represents the vector of 24-h load variation; E represents the elastic matrix; and

$\Delta \mathrm{p}$ represents price error vector.

(ii) The Economic Demand Response Based on Incentive

Economic demand response refers to the fact that the power company compensates the users who actively participate in load reduction as an incentive. Due to the uncertainty of the load reduction amount of distributed photovoltaic, demand response can be used to forecast the number of pre-agreed reduced load and stipulate disincentive measures of failing to respond, thus the electricity price can be controlled and maintained at the normal level.

Optimal system of demand response for distributed photovoltaic from the perspective of demand-side was built in this paper. It can be used to quantify users’ responses to the electricity price and incentives. Power load curve can be stabilized by analyzing and controlling the changes of electricity demand. Therefore, the problem of supply instability of distributed photovoltaic can be solved and then demand-side utilization efficiency and users’ satisfaction will be improved.

#### 4.2.2. The Example Simulation

(1) The Process of Simulation

This paper performed simulations using a typical example of IEEE33-node distribution network wiring. Suppose the operation time of the project is 50 years, the maximum annual load loss is 4500 h, the maximum utilization time is 1800 h, and the range of maximum capacity of each node is 50–150 kW. The electricity price of power distribution is 0.7 Yuan/kWh, and the operation cost is 0.72 Yuan/kWh. Photovoltaic power generation is 10,000 Yuan/kW, which is equivalent to the annual construction costs 200 Yuan per kW. Over the same period, coal-fired power plant emits 950 g CO_{2} when it generates one kilowatt electricity energy.

To optimize the siting and sizing, applying Equations (9)–(14), and using the algorithm of Particle Swarm Optimization (PSO), let 40 particles get iterated for 1000 times, this paper obtained the results of siting and sizing shown in

Figure 6. As

Figure 6 shows, applying 60 kW, 100 kW, 90 kW, 100 kW, 120 kW, and 100 kW capacity of photovoltaic equipment in 12, 14, 18, 25, 30, and 32 nodes, respectively, is the best location and optimal capacity of distributed photovoltaic when taking economic and environmental performances into account.

To optimize the generation dispatching, the load at other times of day was adjusted on the basis of the total load of the reference case. The 24-h load and price forecast based on the photovoltaic power generation price in China are shown in

Figure 7.

The ultra-short term photovoltaic output can be obtained by analyzing the flow chart in

Figure 5 and the data of reference case, and the results are as follows.

The figure of photovoltaic active power forecast shows the power trend of photovoltaic devices within 24 h. As can be seen in

Figure 8, the distributed photovoltaic system has output during 5:00 a.m.–20:00 p.m. and the output between 9:00 a.m. and 14:00 p.m. was above 100 kW which was the peak period. Arranging the output of photovoltaic power generation on the basis of forecast will reduce the influence of uncertain factors on the level and capacity of system generation, which provides effective support for revising the previous generation output and making the plan of day-ahead output dispatching.

To optimize the demand response, it is assumed that the distributed photovoltaic users in the case are residential users, and the load characteristics of the residential users and the price fluctuation of time-of-use (TOU) are shown in

Table 3 and

Table 4.

Changes of total load before and after the implementation of TOU price policy can be obtained by analyzing the existing data and Equations (15)–(17).

Figure 9 shows the results.

It can be seen in

Figure 9 that the load peak period is cut down obviously after the residential users participating in the campaign of demand response, and the total load curve is smoother. Referring to the changes of the load in peak or valley period, residential users can reasonably arrange electricity plans, and power companies will take incentives or punitive measures to promote rational use of photovoltaic power generation and guarantee the stable price on the basis of satisfying users’ demand.

(2) The Conclusions of Simulation

In this paper, the IEEE33-node distribution network wiring is selected as the research object. This paper did simulation experiments by using the methods of sitting and sizing, generation dispatching and demand response. The simulation results show that the optimization paths proposed in

Section 4.2.1 can be used to select the best location and determine the optimized capacity of photovoltaic generation. Moreover, it will enhance the ability of energy absorption of the distributed photovoltaic generation by forecasting the output of photovoltaic units. The relationship between photovoltaic generation and users’ demand can be coordinated by analyzing the effects of TOU on demand response or applying price incentive measures. The optimization methods proposed in this paper from the supply side, energy conversion and demand side provide technical support for improving the comprehensive efficiency of distributed photovoltaic.