1. Introduction
In recent years, the energy crisis and deteriorating living environment have promoted the development of new energy resources. Compared with hydro, nuclear and wind power generation, photovoltaic power (PV) generation is less restricted by geography, resources, manufacturing materials and long-distance transmission. Thus, the PV industry has achieved rapid development. International Energy Agency (IEA) and the European Joint Research Centre (JRC) predicted that the global PV generation capacity would account for 2% of the total electricity power generation by 2020. This proportion will be even more than 10% by 2030.
The output power of PV generation is intermittent and random, which causes the difficulties and complexities of PV-based microgrid (PV-MG) [
1]. As for the island PV-MG, particularly with high penetration of PV, there is the problem of power supply reliability. For grid-connected PV-MG, is the bulk power system fault will lead to off-network operation. Therefore, battery energy storage system (BESS) is necessary to smooth and stabilize its output, meet the load demand, and improve the power quality. BESS has dual property of load and power resource. By virtue of flexible charge and discharge characteristics, BESS has prospects in smoothing and stabilizing the output of PV system, peak load shifting, operating reserve, improving power quality and scheduling flexibility of PV-MG. Therefore, optimal sizing of BESS with reasonable volume can significantly improve the efficiency of PV system and promote the local PV consumptive rate [
2].
Currently, due to the high price of BESS devices, the optimal sizing of BESS capacity should not be too large, which could significantly increase investment cost. However, excessively small energy optimal sizing cannot guarantee the stable operation of PV-MG and promote PV power consumption. Therefore, the reasonable optimal sizing of BESS system in PV-MG has become one of the focus researches of many scholars. At present, research of BESS capacity optimization is mainly focused on: (1) BESS optimal sizing method under two scenarios of single and hybrid BESS systems [
3,
4]; (2) BESS optimal sizing principle under the off-grid and gird-connected operation of MG [
5,
6]; (3) BESS optimization analysis methods, such as the difference supplement method, fluctuation smoothing analysis method [
7,
8]; (4) for particular types of PV-MG, such as industrial and commercial MG, quantitative analysis is carried out on the economic benefits of BESS system optimal sizing [
9,
10]. [
10] focused on the optimization of the capacities of components in the PV-based BSS (battery switch stations) with consideration of battery swapping requirement and maximally utilizing PV energy.
DR refers to the electricity consumers’ response on power price signal or incentive mechanism to change the market participation behavior of normal power consumption mode, which is an important means in optimal operation of PV-MG. Research of Pacific Northwest National Laboratory indicated that, under the condition of the fluctuant electricity price, users would be willing to change their consumption behaviors and adjust the power consumption of controllable equipment. Demand response technology can be used to optimize the operation of MG [
11,
12], frequency and connection line power [
13,
14], as well as support emergency fault [
15,
16]. DR can significantly improve the economy, reliability and flexibility of MG system [
17]. With the improvement of the electric power market and the widespread application of the communication, the load optimization of the demand response has become the important factor that can not be ignored in the MG’s planning and operation. Therefore, it is needed to consider the influence of the demand response when the energy storage optimal sizing is carried out.
In the BESS optimal configuration, in order to clarify the benefits and advantages of the proposed model, the features are compared to several related papers [
18,
19,
20,
21,
22], in terms of optimization objectives, constraints, solving algorithm, connected or disconnected to grid, whether the demand response factors are considered. The comparison result is shown in
Table 1 below. With respect to the optimization objectives, most contrastive papers focus on one specific function of BESS, such as compensate for power fluctuations, while this paper proposes multi-objectives optimal model of maximum PV consumptive rate and annual net profits. As the basic data and scenarios in these papers are different, their simulation constraints and solving algorithms are not comparable. In addition, the proposed model introduces DR and BESS simultaneously into the operation optimal scheduling of grid-connected PV-MG, and has a relatively superior guiding significance for the commercial investment of BESS in PV-MG.
There are mainly two kinds of methods to analyze DR of users: one is fitting DR curve through historical data [
23,
24]; the other is by obtaining elastic matrix to analyze the response of users to the price change [
25,
26,
27]. Since the latter is more suitable for quantitative analysis, it is widely used in the analysis of DR. [
25] described how the consumers behavior can be modeled using a matrix of self and cross elasticity, and how elasticity can be taken into consideration when scheduling generation and setting the price of electricity in a pool based electricity market. [
26] introduced the impact of price elasticity matrix of demand side on power purchase decision-making under time-of-use (TOU) price into the optimization of power supply company power purchase from weekly market. However, the elasticity coefficients in these papers are artificially given without calculation through reasonable method or model. [
27] established multiple regression model of electricity consumption and price based on the electricity market statistics, and analyzes the price elasticity of electricity demand by the difference between SD and control group LADWP. However, it only considers self-elasticity, not cross-elasticity. Given the BESS configuration is made at the planning stage of PV-MG, so it demands less on real-time performance and TOU is the most principle DR project implemented. Thus, this paper explores the DR’s influence on BESS configuration under TOU price scenario.
Based on the above analysis, this paper establishes multi-period DR model based on price elasticity matrix under TOU price and introduces DR and BESS system operation into PV-MG scheduling optimization to analyze the impact of DR on BESS optimal sizing, which is of significant effect on commercial investment decisions of PV-MG. The contribution mainly includes following aspects.
- (1)
The multi-period DR model based on price elasticity matrix under TOU price is established, which can reflect the impact of TOU price on users’ electricity consumption.
- (2)
The DR and BESS system operation are included into PV-MG scheduling optimization to build the MG investment profit model, and the PV consumptive rate and annual net profits are taken as greatest objectives.
- (3)
Considering the constraint conditions such as power supply and demand balance, side electricity price elasticity, loss of BESS systems, NSGA-II algorithm is utilized to solve the DR-based BESS capacity optimize optimal sizing model in PV-MG.
3. Demand Response Model
DR projects include electricity price mechanism and compensation incentive mechanism, and both means change electricity consumption by price change or economic compensation. As a special commodity, the price change of electricity will affect consumption behaviour. When users participate in market electricity price response, the demand curve will be left oblique and bending, as shown in
Figure 2.
[
36] pointed out that, based on the balance of commodity supply and demand elasticity, commodity price and deal quantity (correspond to electricity price and electricity consumption separately in this paper) present linear relation near the electric power market equilibrium point. Its expression is
Based on the equilibrium relationship between commodity supply and elastic demand as well as the price elasticity matrix of electricity price in multi time period, the users’ DR behaviors can be more accurately and comprehensively described under TOU price. Electricity price elasticity refers to the function relationship between electricity consumption change rate and electricity price change rate. The actual function expression of the typical demand curve usually needs to be considered in different factors for regression analysis. In order to simplify this complex process, it is treated as a linear function.
In practical, users will not only consider the electricity prices at current and other moments. Self-elasticity coefficient is utilized to express the impact of current moment electricity price change rate on current moment electricity consumption, while cross-elasticity coefficient means the impact that on the other moment electricity consumption. The formula for the relationship between the change rates the electricity quantity and electricity prices expressed in elasticity coefficient is as follows:
For time periods
, the elastic matrix can be constructed as:
This paper takes the assumption in [
37] that the elastic matrix is symmetrical to the y diagonal, which means electricity price has the same effect on electricity consumption between two time periods with the same distance.
Theoretically, the price tariff can be divided into single pricing, TOU pricing, real time pricing, critical peak pricing and so on, which can be implemented in the PV-MG and have influence on the BESS optimal sizing considering the demand response. Real time pricing is ideal instantaneous dynamic prices in space, which requires almost instantaneous match of price and cost in power grid, and users can’t timely and effectively arrange their loads in the short term [
38]. Thus, quasi real time pricing is generally implemented, and can effectively mobilize the users’ DR to real time pricing. Quasi real time pricing means that, the time interval division and price scheme of 24 h in
D day is set based on data mastered in
days, put on execution at 0:00 in
D, thus users can arrange their consumptions more effectively. Then, the prices corresponding to loads in each time point is:
where
is the price at time
t with time intervals of 15 min,
and
is the load at time
t with time intervals of 15 min and one hour respectively,
is the single price,
is the daily average load in
day,
is the floating rate of quasi real time pricing at time
t.
One day is divided into 24 time intervals, and then the elastic matrix can be constructed as:
where
and
is the electricity consumption before and after DR of quasi real time pricing.
Substitute Equation (8) into Equation (7), then:
Based on the definition of quasi real time pricing, there is:
Substitute Equation (10) into Equation (9), then:
The elastic coefficient in the elastic matrix can be obtained by using the relevant historical electricity consumption and the historical electricity price coefficient of the power supply department, or the data obtained from the user survey. Then, we can obtain the load curve before and after DR with the implement of quasi real time pricing, and the influence of quasi real time on the BESS optimal configuration can be analyzed through the multi-objectives model proposed in this paper.
Given the BESS configuration is made at the planning stage of PV-MG, so it demands less on real-time performance and TOU is the most principle DR project implemented. Thus, this paper explores the DR’s influence on BESS configuration under TOU price scenario. Then, the following formula can be constructed:
Set the flat price as reference value, and simplify the parameters in Equation (6).
represents the difference between peak and flat price instead of
,
represents the difference between valley and flat price instead of
, and set
for simplification. Then, it can be constructed as:
In order to simplify the problem, this paper assumes that electricity consumption only shits before and after TOU power price, and the total electric quantity will stay constant. The reduced electricity consumption in peak price period can be transferred to flat and valley price period:
Equation (13) can be expressed as:
where
,
,
is the electricity consumption transferred from peak to flat period,
is the electricity consumption transferred from peak to valley period.
Simultaneously, the electricity consumption increased in flat price period increased is from the peak period, and part of the load is transferred to the valley price period.
where
.
According to consumer psychology, the users have minimum and maximum value of electricity price, namely the lower and upper limit of threshold. When the price is lower than the minimum threshold, users won’t respond to price, and when price is higher than the maximum threshold, they will also not further respond to the upper price. Based on this, the transfer rate can be modified as follow:
where
,
,
,
is taken as the reference value 1.
Thus the loads in peak, valley and flat price period after the application of TOU power price strategy are:
8. Conclusions
Research on the impact of DR on BESS optimal sizing has a significant effect on commercial investment decisions of PV-MG. This paper established multi-period DR model based on price elasticity matrix under TOU price. Besides, the DR and BESS system operation are included into PV-MG scheduling optimization to build the MG investment profit model. Considering the constraint conditions such as power supply and demand balance, side electricity price elasticity, loss of BESS systems, the PV consumptive rate and annual net profits are taken as greatest objectives to utilize NSGA-II algorithm to solve the DR-based BESS capacity optimize optimal sizing model in PV-MG.
Simulation results show that, in the electricity market environment, the needed rigid BESS capacity and PV consumptive rate decrease after DR. Thus, more capacity of flexible BESS should be configure d to contribute the midday PV consumption and achieve the same PV consumptive rate goal. This paper applies an optimization method to a practical MG in Guangdong to verify the reasonability of the proposed model and algorithm, which can be a significant reference on commercial investment decisions of PV-MG.
In order to solve the influence of uncertain PV on the stable operation of PV-MG, DR and BESS are introduced simultaneously into the operation optimal scheduling of PV-MG, and the uncertainties PV can be suppressed so as to improve the PV consumptive level, which is of great guiding significance for BESS optimal sizing under this situation. The net profits of PV-MG is poor with relatively expensive BESS module cost at present stage. With the decrease of BESS cost or further drive of the energy storage subsidy policy, business investment potential of PV-MG with BESS will be further enhanced.