The Optimal Configuration Scheme of the Virtual Power Plant Considering Benefits and Risks of Investors

A virtual power plant (VPP) is a special virtual unit that integrates various distributed energy resources (DERs) distributed in the generation and consumption sides. The optimal configuration scheme of the VPP needs to break the geographical restrictions to make full use of DERs, considering the uncertainties. First, the components of the DERs and the structure of the VPP are briefly introduced. Next, the cubic exponential smoothing method is adopted to predict the VPP load requirement. Finally, the optimal configuration of the DER capacities inside the VPP is calculated by using portfolio theory and genetic algorithms (GA). The results show that the configuration scheme can optimize the DER capacities considering uncertainties, guaranteeing economic benefits of investors, and fully utilizing the DERs. Therefore, this paper provides a feasible reference for the optimal configuration scheme of the VPP from the perspective of investors.


Introduction
The economic level and energy demand have continually increased, leading to deterioration of the ecological environment, global warming, fossil energy depletion, and many other serious problems for human survival and development.Such problems have become increasingly prominent.Thus, countries around the world have introduced innovative policies to encourage enterprises and units to optimize their energy structure and actively promote energy conservation and emission reduction to achieve sustainable development of the economy.In this new situation, the penetration of distributed energy resources (DERs) in the distribution network is increasing, attracting worldwide attention [1].DERs are composed of distributed power generations, distributed energy storages, demand side resources, etc.These DERs have the advantages of environmental protection, low energy consumption, investment savings, and improved power system flexibility [2].
The output characteristics of DERs are different, and their scales are generally small and scattered.The ability of a distribution network to absorb DER capacity is limited, and scheduling and control strategies are relatively scarce.If a large amount of DERs are directly connected to the network, it would cause a very large impact on the system, which could not meet the higher standards of power supply quality requirements [3].To solve the absorption problem of DERs, the development Energies 2017, 10, 968 3 of 12 micro-grid, including various generators in the generation side and demand side resources in the customer side.However, the micro-grid usually accepts distributed generators that are geographically close to the customer side with fewer DERs [23][24][25].
Currently, grid-connected and independent modes are the two main operating modes of micro-grids [26,27].To make full use of DERs and guarantee the reliability of the power supply, the operation mode of VPPs in this paper draws on the combined operation pattern of the independent mode, which indicates that the VPP could be an individual unit or serve the power grid if necessary.In this mode, the DER capacity allocation methods in the micro-grid usually focus on controllability, economic benefits, environmental protection and reliability, based on strategies of load analysis and optimal control [28].The objectives are minimizing the operation costs [29] and maximizing the permeation rate of clean DERs [30], and the constraints include reliability and security indices [31].Analytical methods, heuristic algorithms, and stochastic optimization algorithms are usually adopted to optimize the solution of the above configuration.However, micro-grids cannot be easily separated and reorganized, and their configuration scheme and operation strategy mostly concentrate on local application of DERs, which has certain limitations on the aggregation of large-scale and scattered DERs of VPPs.
The remainder of this paper is organized as follows: In Section 2, a variety of DERs are encapsulated into the VPP based on the information and communication technology to be coordinated and controlled.In Section 3, the exponential smoothing method is adopted in the forecast of the VPP sub-area yearly load density per hour in the long-term, and the optimal configuration of the DER capacities inside the VPP is calculated by using the portfolio theory.In Section 4, the case analysis provides an application example of the above models.In Section 5, a short conclusion is made, which shows that the mentioned optimal configuration scheme with portfolio theory can optimize the DER capacities inside the VPP considering the uncertainties of DER.

The Components of DERs
The DERs that form the VPP could be the same or different and may be centralized in a certain area or decentralized over a broad region.The various DERs with different characteristics could be divided into three classes, including distributed generation, demand-side resources, and distributed energy storage, as shown in Figure 1.
Energies 2017, 10, 968 3 of 12 Currently, grid-connected and independent modes are the two main operating modes of microgrids [26,27].To make full use of DERs and guarantee the reliability of the power supply, the operation mode of VPPs in this paper draws on the combined operation pattern of the independent mode, which indicates that the VPP could be an individual unit or serve the power grid if necessary.In this mode, the DER capacity allocation methods in the micro-grid usually focus on controllability, economic benefits, environmental protection and reliability, based on strategies of load analysis and optimal control [28].The objectives are minimizing the operation costs [29] and maximizing the permeation rate of clean DERs [30], and the constraints include reliability and security indices [31].Analytical methods, heuristic algorithms, and stochastic optimization algorithms are usually adopted to optimize the solution of the above configuration.However, micro-grids cannot be easily separated and reorganized, and their configuration scheme and operation strategy mostly concentrate on local application of DERs, which has certain limitations on the aggregation of large-scale and scattered DERs of VPPs.
The remainder of this paper is organized as follows: In Section 2, a variety of DERs are encapsulated into the VPP based on the information and communication technology to be coordinated and controlled.In Section 3, the exponential smoothing method is adopted in the forecast of the VPP sub-area yearly load density per hour in the long-term, and the optimal configuration of the DER capacities inside the VPP is calculated by using the portfolio theory.In Section 4, the case analysis provides an application example of the above models.In Section 5, a short conclusion is made, which shows that the mentioned optimal configuration scheme with portfolio theory can optimize the DER capacities inside the VPP considering the uncertainties of DER.

The Components of DERs
The DERs that form the VPP could be the same or different and may be centralized in a certain area or decentralized over a broad region.The various DERs with different characteristics could be divided into three classes, including distributed generation, demand-side resources, and distributed energy storage, as shown in Figure 1.The external features of the VPP include the overall characteristics of all DERs, and the control center ensures the coordinated operation inside.The information and communication technology, together with the high level software architecture, is employed by the VPP control center to centrally aggregate all types of DERs.The grid-connected structure and the distributed topology of DERs can remain the same, and it is unnecessary to build more power tie lines.Furthermore, the characteristics of different DERs, such as wind power and photovoltaic power, could be complementary, and the uncertainties could be offset to some degree.remain the same, and it is unnecessary to build more power tie lines.Furthermore, the characteristics of different DERs, such as wind power and photovoltaic power, could be complementary, and the uncertainties could be offset to some degree.

The Optimal Configuration Scheme of the VPP
The service regions of the VPP are divided based on the region types and load density characteristics, and the exponential smoothing method is adopted in the forecast of the sub-area yearly load density per hour in the long-term, which can be used to obtain the total load requirement of the VPP's service regions.On that basis, the optimal configuration of the DER capacities inside the VPP is calculated by the portfolio theory.

The Division of the Service Regions of the VPP
The major factors of the division include the region space, administrative level, load density, and user types.First, the rough ranges are decided by the region space and administrative level.Then, the refinement of the division is completed according to load density and user types.Some applicable protocols are used to guarantee the power distribution reliability and improve the economic and environmental benefits.
On the above basis, the service regions of the VPP can be divided into 11 classes, including residential, industrial, commercial, administrative, cultural, medical, educational, municipal, warehouse, traffic, and agricultural, as shown in Figure 2. The service regions of the VPP are divided based on the region types and load density characteristics, and the exponential smoothing method is adopted in the forecast of the sub-area yearly load density per hour in the long-term, which can be used to obtain the total load requirement of the VPP's service regions.On that basis, the optimal configuration of the DER capacities inside the VPP is calculated by the portfolio theory.

The Division of the Service Regions of the VPP
The major factors of the division include the region space, administrative level, load density, and user types.First, the rough ranges are decided by the region space and administrative level.
Then, the refinement of the division is completed according to load density and user types.Some applicable protocols are used to guarantee the power distribution reliability and improve the economic and environmental benefits.
On the above basis, the service regions of the VPP can be divided into 11 classes, including residential, industrial, commercial, administrative, cultural, medical, educational, municipal, warehouse, traffic, and agricultural, as shown in Figure 2.
where sk (k = 1,2, …, K, K = 11) is the area of the kth region; Sa is the total area of the VPP regions.
where βk is the yearly load density per hour of sk, with β1k and β2k its minimal and maximal values, respectively; E(βk) is the forecast value of the expectation of βk; and Pa is the total load requirement, which could be supplied by the DERs inside the VPP, together with the thermal power units, such as miniature gas turbines, in this paper.
where s k (k = 1,2, . . ., K, K = 11) is the area of the kth region; S a is the total area of the VPP regions.
Energies 2017, 10, 968 where β k is the yearly load density per hour of s k , with β 1k and β 2k its minimal and maximal values, respectively; E(β k ) is the forecast value of the expectation of β k ; and P a is the total load requirement, which could be supplied by the DERs inside the VPP, together with the thermal power units, such as miniature gas turbines, in this paper.

The Forecast of Yearly Load Density per Hour
The optimal configuration of the DER capacities inside the VPP must consider the growth of load requirements in the long-term.Therefore, E(β k ) is a vital factor.According to the development tendency of the economic level and developmental characters of the load, the cubic exponential smoothing method of the time sequence model, which overcomes the disadvantages of the single rising tendency and lag [32], is adopted to predict E(β k ) to simulate the development of the load.
where y t is the time series; R is the number of y t ; α ∈ (0, 1) is the weighting coefficient (default: 0.2); and d t (1) , d t (2) , and d t (3) are values of single, double, and cubic exponential smoothing.
The forecast model of the cubic exponential smoothing method is shown in Equation ( 4): t − 3d where Y t+l is the lth forecast value; and L is the total number of forecast values.
Select several forecast values of each β k to obtain its mean value, which could represent E(β k ), and calculate the P a of all the regions of the VPP according to Equation (2).

The Optimal Configuration of the VPP Based on the Portfolio Theory
The Markowitz portfolio theory of modern finance is introduced to allocate the DER capacities inside the VPP in the long-term, and the expectation and variance of the rate of return are the metrics of benefits and risk.Based on the average value-variance model, the optimal configuration of the VPP intends to minimize the variance while maintaining the expected revenue or maximize the expected revenue while maintaining the variance [33].
The fluctuation of the expected revenue is mainly generated by the uncertainties of various DERs inside the VPP.Therefore, thermal power units are needed to stabilize the fluctuation caused by the DERs and fulfill the total load requirement.
From the macroscopic perspective, the uncertainties of different DERs are mapped to the price fluctuations in the portfolio problem: where ϕ v is the rate of return of unit capacity of the VPP; m is the number of DERs inside the VPP; η i is the capacity ratio of DER i ; and p i , g i and a i are the output, electrovalence, and cost of unit capacity of DER i .
If the ratio of the load requirement fulfilled by the VPP is µ, then the ratio of the thermal power units is 1 − µ.The optimal total capacity ratio of the VPP is µ*, and the optimal capacity proportions of the DERs inside the VPP are µ*•η i * (I = 1, 2, ..., m), which could be calculated by Equations ( 8)-( 11): where ϕ G is the rate of return of unit capacity of the thermal power unit (unit G); p G , g G and a G are the output, electrovalence, and cost of unit capacity of unit G; a Gf is the generating cost; a Ge is the penalty cost of pollution emission; a Gc is the cost of carbon emission; a Ge0 is the basic emission cost; and α F-H is the proportionality coefficient of the emission penalty considering fog and haze, which is an empirical value established by the air quality and government policy: where k v is the Sharpe Ratio, which reflects the extraneous income of risk.The objective of the investor is to achieve the utility maximization: where A ∈ [2,6] reflects the aversion degree of the investor toward risk.A < 4 indicates a preference for risk, A > 4 indicates an aversion to risk, and A = 4 indicates risk neutral.The default value of A is 6 in this paper, which indicates risk aversion in the model.The result of Equation ( 10) is shown in Equation ( 11): Therefore, µ*, 1 − µ* and µ*•η i * (I = 1, 2, ..., m) can be obtained.

The Solving Procedure
First, the yearly load density is forecast by the cubic exponential smoothing method, and then the portfolio theory is adopted to calculate the optimal configuration of the DER capacities inside the VPP, as shown in Figure 3.

The Forecast of Yearly Load Density of Each Service Region of the VPP
Based on the historical data of the 11 service regions of the VPP in a certain city from 2005 to 2015, the forecast values from 2016 to 2018 are obtained, as shown in the curves in Figure 4.    Here, the left of the black vertical line in Figure 4 is the region of historical data and the right is the region of forecast data.
The mean values of the load density from 2016 to 2018 are shown in column 4 of Table 1.The acreage and its load requirement are shown in column 3 and column 5 of Table 1.

The Optimal Configuration of DER Capacities inside the VPP
Take a VPP demonstration project as an example, which contains wind turbine (WT), photovoltaic unit (PV), and interruptible load (IL).The basic data are shown in Table 2.The cost of a thermal power unit in Table 2 includes the generating cost, the cost of pollution emission taking into account the effects of fog and haze, and the cost of carbon emission.Thus, the Here, the left of the black vertical line in Figure 4 is the region of historical data and the right is the region of forecast data.
The mean values of the load density from 2016 to 2018 are shown in column 4 of Table 1.The acreage and its load requirement are shown in column 3 and column 5 of Table 1.Take a VPP demonstration project as an example, which contains wind turbine (WT), photovoltaic unit (PV), and interruptible load (IL).The basic data are shown in Table 2.  Case 1: The standard deviation of the WT in Case 0 is larger (0.0800), second only to PV.In recent years, the development of wind power is better than that of photovoltaic power.One of the reasons for this is that the uncertainty controllability of WT is stronger than that of PV.Therefore, when the standard deviation of WT unit capacity output is significantly reduced (−50.50%),its capacity ratio increases slightly (by only +0.67%).However, the E(ϕv) and σv 2 of the VPP increase to a larger degree with respect to Case 0 (+1.75% and +3.22%), while U remains unchanged.Case 1: The standard deviation of the WT in Case 0 is larger (0.0800), second only to PV.In recent years, the development of wind power is better than that of photovoltaic power.One of the reasons for this is that the uncertainty controllability of WT is stronger than that of PV.Therefore, when the standard deviation of WT unit capacity output is significantly reduced (−50.50%),its capacity ratio increases slightly (by only +0.67%).However, the E(ϕ v ) and σ v 2 of the VPP increase to a larger degree with respect to Case 0 (+1.75% and +3.22%), while U remains unchanged.Case 2: PV output has more uncertainty than WT and IL in Case 0, and the standard deviation of the unit capacity is the largest (0.0960).Investors are more inclined to opt for WT and IL in decision-making.When the PV unit capacity output standard deviation is significantly reduced (−72.71%),that is, its risk is obviously decreased, the benefits of investment in PV become prominent, and investors tend to choose PV (capacity increased by 20.84%).However, the uncertainty of PV is still large, and the σ v 2 of VPP is the largest (0.1528).Therefore, the E(ϕ v ) is small (0.2647) and the investor's utility is smaller (0.0032) when the PV ratio is large.Case 3: IL, itself, has a small output variance, less uncertainty, and less impact on investor decision-making.When the standard deviation of IL output decreased (−58.00%), the capacity ratio of WT and PV decreased (−8.40% and −1.35%), and the capacity of IL increased significantly (+9.75).The use of IL in VPPs is mainly to implement the corresponding optimal control strategy at the load end when WT and PV uncertainties are difficult to control, mainly for auxiliary service.Therefore, when the IL capacity increases, the uncertainty risk is more effectively controlled, and σ v 2 can be significantly reduced (−34.66%).However, the economic benefits are not obvious when IL is used for auxiliary services, resulting in the minimum E(ϕ v ) (only 0.2529).

Conclusions
Based on the brief introduction of the classification of DERs and the construction of the VPP, this paper first divides the VPP service regions according to the region space, administrative level, load density, and user types, and employs the cubic exponential smoothing method to forecast the annual average hourly load density of each VPP to obtain the average hourly load demand of the entire area.Based on this, the optimal capacity configuration of various DERs inside the VPP is calculated by using the portfolio theory.The results show that the uncertainties of DERs are the key factors that affect their ratios of capacity allocation.When the uncertainty of a certain DER is reduced, its capacity will increase correspondingly.The configuration scheme can optimize the DER capacities from the perspective of investors, guarantee the economic benefits, make full use of clean DERs, and satisfy the load requirement.

Figure 2 .
Figure 2. The division of the service regions of the VPP. a

Figure 2 .
Figure 2. The division of the service regions of the VPP.

Figure 3 .
Figure 3.The flowchart of the solving procedure.

Figure 3 .
Figure 3.The flowchart of the solving procedure.

4. 3 .
The Forecast of Yearly Load Density of Each Service Region of the VPP Based on the historical data of the 11 service regions of the VPP in a certain city from 2005 to 2015, the forecast values from 2016 to 2018 are obtained, as shown in the curves in Figure 4.

Figure 4 .
Figure 4.The forecast curves of the load density of each service region of the VPP.

Figure 4 .
Figure 4.The forecast curves of the load density of each service region of the VPP.

Figure 5 .
Figure 5.The values of the configuration capacity for different cases.

Figure 5 .
Figure 5.The values of the configuration capacity for different cases.

Table 1 .
The acreage, mean values of load density, and load requirement of each service region of the VPP.

Table 2 .
Basic data of the DERs inside the VPP and the thermal power unit.

Table 1 .
The acreage, mean values of load density, and load requirement of each service region of the VPP.

Table 2 .
Basic data of the DERs inside the VPP and the thermal power unit.