Community Solar Operation Strategy for Smart Energy Communities Considering Resource Fairness

Abstract

This study proposes a community solar operation strategy for smart energy communities (SECs), which comprise members of an energy consumption group, to minimize the electricity bill of its members. When sharing resources within a group, resource distribution is a critical problem, and fairness in resource sharing is the main constraint for operation. The proposed community solar operation is formulated as a mixed-integer liner problem that can be optimally solved using centralized control and future time information. However, obtaining information of a future time is not causal. By decomposing the problem into individual problems that are solved by each member at each decision time, the proposed strategy operates the community solar in a distributed manner with partial information. The simulation results using the real dataset recorded in Korea show that the use of the proposed operation strategy results in a fair distribution of electricity bill savings with a marginal benefit reduction of 10% compared to the optimal operation that requires a centralized control and information on the future time. Moreover, a discussion on the tradeoff between the benefits of electricity bill savings and guarantee of fairness is provided. Based on the results, this study can serve as a reference for the design of community solar operations for SECs.

1. Introduction

With the consensus on global energy and environmental objectives, the development of renewable energy resources is rapidly growing [1]. However, the increase in renewable energy production has led to broad and significant impacts across energy systems [2]. In this regard, demand-side management is a cost-effective way of reducing the energy system burden compared with supply-side management such as unit commitment and bulk generation ramping control [3].

Smart energy communities (SECs) are regional demand-side organizations based on energy integration techniques [4]. They have self-organized energy service providers (SPs) or energy management systems (EMSs) and operate to achieve environmental, social, and economic objectives [5]. Demand-side management such as peak-demand reduction and the load-shifting of the SEC provides the benefit of electricity bill savings and increases the efficiency of the grid [6].

The basic concept of SECs for achieving economic benefits is the sharing of resources. Virtual power plants [7], virtual energy storage systems [6], and community solar power [8] are considered as shared resources. In the case of configuring a large-scale resource and sharing it, a price advantage as the unit price reduction is obtained compared to configuring resources individually [9]. Moreover, increasing the operational resources also enhances the efficiency of systems owing to an improvement in the operational diversity [10]. For an example, if two users operate with resources for which each resource size is one, they can operate at most one, respectively. However, if a sharing operation is performed, operation of 1.5 and 0.5 or 0.5 and 1.5 is possible as needed. However, sharing resources raises fairness issues regarding how the resources should be shared and the benefits received by each member of the SEC. It is essential to continuously maintain the service of SECs [11]. However, existing SEC research focuses on the benefits of SEC without considering fairness. Therefore, this study examines fairness based on how it should be considered and how it affects the operation of SECs when solar power is used as a shared resource.

Several studies on SECs have considered solar communities. Business models and directions for policy makers are outlined in various codes in [12,13,14]. Shakouri et al. showed the cost-effectiveness of community solar considering the solar generation uncertainty [15]. Schunder et al. presented the potential of community solar power using geographical information [16]. Huang et al. proposed a hierarchical design optimization method for solar sharing using distributed battery systems [17]. They demonstrated that the sharing process can reduce the required battery capacity and electricity loss. Lee et al. suggested a virtual community-owned solar and storage system for individually controlling the sharing of resources and showed that the individually controlled shared-resource system can achieve the same electricity bill savings as the centralized-controlled shared-resource system [18]. Cosic et al. formulated a community solar operation problem as a mixed-integer linear programming problem and experimentally showed that community solar operations can reduce the electricity bill and CO₂ emissions [19]. In fact, the state-of-the-art solar operation techniques reviewed in [20] can be used for community solar operations. However, these techniques do not consider fairness, which is a critical problem in resource sharing.

Few studies have been conducted on fairness in resource sharing. Tsaousoglou et al. formulated the problem of finding an optimal max-min fair allocation of the available energy using mixed-integer linear programming. This problem is minimized by the worst-off user’s disutility [21]. In [22], the authors modified the energy allocation problem into a flexibility allocation problem by using the same framework as that in [21]. In the modified problem, a distributed service operator can simultaneously achieve compatibility incentives and optimality for the max–min fairness objective. Hupez et al. proposed a collaborative framework for power exchanges inside a low-voltage community to minimize the total costs [23]. To share community costs in a fair manner, a cost compensation process was conducted after all power exchanges had been performed. Grzanic et al. presented a two-stage cost-sharing strategy to minimize all community members [24]. However, the cost was settled only after the operation process was completed. Oh introduced a community solar service strategy for commercial buildings, considering profit balancing between the service provider and participants [25]. Cost fairness is considered an aspect of proportional fairness. However, these studies suffer from two issues. First, the problems formulated in the studies considered the overall benefit as the objective because they were centrally operated. This simplifies the problem but requires additional processes such as settlement or weak fairness, as in the worst case only. Second, to optimally solve the problems formulated in the studies, perfect information that includes information on future time is required.

This study focuses on a community solar operation strategy for an SEC that considers resource fairness. The main objective is to solve the existing problems in conventional studies including centralized control for the overall benefit and perfect information usage such as including future time information. The main contributions of this study are summarized as follows.

• Distributed operation: The baseline problem is formulated as a mixed-integer linear programming problem that considers the minimization of the overall electricity bill and resource fairness. To design the distributed operation, the problem is decomposed into two problems using the slack variable, for the community smart energy service provider (SESP) and community members. Each member solves the community solar operation problem by minimizing their own electricity bill using resource constraints. The SESP manages the required operational results, as shown in Figure 1. It is converged in an iterative manner based on information exchange between the SESP and the members.
• Partial information usage: To select the correct operation while considering resource fairness, information on the future time is required. This is because the priority of all decision times must be measured to determine the optimal solution. In this study, the forecasted values of the demand and generation were obtained using forecasting techniques. Due to forecast errors, a mismatch occurs between the resource allocation constraint and actual allocation. It is defined as the residual allocation factor. This factor is used as a priority factor to determine the operation at each decision time. Therefore, community solar operations are decided at each decision time and not for all decision times.
• Experimental results and discussions on a real data set: The proposed community solar operation was performed using a real data set obtained in Korea. To verify its performance, the overall electricity bill savings, distribution of electricity bill savings, performance gap with respect to the baseline problem, and fairness indices were measured by varying the community solar capacity. The experimental results show that by using the proposed operation, members in the SEC can achieve fairly distributed electricity bill savings, and the benefit reduction of the overall electricity bill saving is marginally less than 10% compared to the baseline operation that requires a centralized controller and perfect information, including the future time. Moreover, the effects of fairness and future research prospects of community solar operations are also discussed.

Based on the main contributions of distributed operation and partial information usage, the conceptual comparison between the conventional method and the proposed method can be illustrated as shown in Figure 1.

2. Method

2.1. Model

The proposed community solar system for the SEC consists of three parts: SEC, community solar, and utility grid, as shown in Figure 2. The SEC is a customer group comprising commercial or residential units, and the SESP is a demand aggregator for the community members. The SESP manages the energy transactions between the members and energy producers of the community solar and utility grids. Community solar can be implemented such that the SESP installs and operates it by themselves or rents it out to a third-party service provider [26]. Moreover, the resource of community solar is configured in various ways such as aggregating the solar resources of members and implementing a solar farm. From an operational point of view, because solar generation is determined according to the solar capacity, there is no difference between installing and renting. In this study, it was assumed that community solar power was implemented as a solar farm by the SESP, as shown in Figure 2. Therefore, the SESP monitors community solar generation and allocates the generated energy to each member according to the objectives and constraints. Moreover, the utility grid is connected to the SESP to balance the energy supplied to the community members.

2.2. Problem Formulation

The main purpose of participating in community solar services is to reduce electricity bills.

This study adopts a Time-of-Use (ToU) tariff for billing. Therefore, taking $d_{m,t}$ as the demand for member $m$ at a time $t$, the electricity bill of member $m$ is measured as:

$$\begin{array}{rr}\hfill B_m\left(\cdot \right)& \hfill =p_d\underset{t\in \mathcal{T}}{\max }{d}_{m,t}+{\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{p}_{e,t}{d}_{m,t},\end{array}$$

(1)

where $\mathcal{T}=\left\{1,\dots ,t,\dots ,T\right\}$ is the billing period such as one month, $p_d$ is the demand price for the billing period, and $p_{e,t}$ is the energy price at time $t$. This study assumes that all members use the same electricity tariff. The demand price is the price charged for peak demand that occurs during the billing period and is the factor that lowers peak demand. The energy price is a charge imposed on energy usage during the billing period, and it has the effect of demand shifting by setting the price for each time differently.

Moreover, when $e_{m,t}$ is the solar generation allocated to member $m$ at time $t$, the electricity bill is modified as

$$\begin{array}{r}\hfill B_m\left(e_{m,t}\right)=p_d\underset{t\in \mathcal{T}}{\max }\left(d_{m,t}-e_{m,t}\right)+{\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{p}_{e,t}\left(d_{m,t}-e_{m,t}\right).\end{array}$$

(2)

Subsequently, the SESP allocates the solar generation to minimize the overall electricity bill. Letting $\mathcal{M}=\left\{1,\dots ,m,\dots ,M\right\}$ be a community member set, the objective function is expressed as:

$$\mathcal{O}\left(e_{m,t}\right)={\displaystyle \sum }_{m\in \mathcal{M}}{B}_m\left(e_{m,t}\right).$$

(3)

The objective, the electricity bill, is reduced by the allocation of the solar generation. However, the utility of solar generation that is the electricity bill saving varies with time. This is because the energy price at each time is difference. Moreover, if the time at which peak demand occurs is different for each member, the utility of solar generation for each member will also be different. This is because the electricity bill is determined by peak demand as well as energy consumption. Therefore, even if the same amount of solar generation is used, the electricity bill saving of each member depends on when it is allocated. As a result, the community solar operation to minimize the electricity bill presented as the objective function in Equation (3) is the solar generation resource allocation problem that can be formulated as a mixed-integer linear programming problem [27].

The allocation for each member should be less than the solar generation. Therefore, the generation constraint is considered as:

$${\displaystyle \sum }_{m\in \mathcal{M}}{e}_{m,t}\le g_t,||\forall |t\in \mathcal{T},$$

(4)

where $g_t$ is the solar generation at time $t$.

Moreover, resource fairness was considered in this study. Resource fairness is defined as the resource allocation of a member proportional to some pre-existing claims [28]. The pre-existing claim can be set to various values such as total demand and investment cost. In this study, it is assumed that the resource, i.e., the solar generation, is allocated in proportion to the total demand of each member.

Letting ${\gamma }_m$ be the resource indicator for member $m$ that is the fraction of total solar generation distributed to each member during the billing period, and ${\displaystyle {\displaystyle \sum }_{m\in \mathcal{M}}}{\gamma }_m=1$, the resource fairness constraint is expressed as:

$${\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{e}_{m,t}={\gamma }_m{\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{g}_t,||\forall |m\in \mathcal{M}.$$

(5)

Using Equations (3)–(5), the community solar operation problem is:

$$\begin{array}{cc}\hfill \mathrm{P}0:||||||||||\underset{e_{m,t}}{\min }|& {\displaystyle {\displaystyle \sum }_{m\in \mathcal{M}}}{B}_m\left(e_{m,t}\right)\hfill \\ \hfill \mathrm{subject} \mathrm{to}|& {\displaystyle {\displaystyle \sum }_{m\in \mathcal{M}}}{e}_{m,t}\le g_t,||\forall |t\in \mathcal{T},\hfill \\ & {\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{e}_{m,t}={\gamma }_m{\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{g}_t,||\forall |m\in \mathcal{M}.\hfill \end{array}$$

(6)

This equation represents a mixed-integer linear programming problem that is the electricity bill minimization problem of allocating solar generation to each member considering resource fairness within the billing period. This problem satisfies convexity [29]. Therefore, it can be solved iteratively using the gradient method [30].

However, the solution of P0 has two problems. First, the solution minimizes the overall electricity bill of the members, but it does not guarantee the minimization of the individual bills of each member. For problem P0, the objective function is rewritten as follows:

$$\begin{array}{ccc}\hfill {\displaystyle \sum }_{m\in \mathcal{M}}{B}_m\left(e_{m,t}\right)& =\hfill & {\displaystyle \sum }_{m\in \mathcal{M}}\left\{p_d\underset{t\in \mathcal{T}}{\max }\left(d_{m,t}-e_{m,t}\right)+{\displaystyle \sum }_{t\in \mathcal{T}}{p}_{e,t}\left(d_{m,t}-e_{m,t}\right)\right\}\hfill \\ & =\hfill & {\displaystyle \sum }_{m\in \mathcal{M}}{p}_d\underset{t\in \mathcal{T}}{\max }\left(d_{m,t}-e_{m,t}\right)+{\displaystyle \sum }_{m\in \mathcal{M}}{\displaystyle \sum }_{t\in \mathcal{T}}{p}_{e,t}\left(d_{m,t}-e_{m,t}\right)\hfill \\ & =\hfill & p_d{\displaystyle \sum }_{m\in \mathcal{M}}\underset{t\in \mathcal{T}}{\max }\left(d_{m,t}-e_{m,t}\right)+{\displaystyle \sum }_{t\in \mathcal{T}}{p}_{e,t}\left({\displaystyle \sum }_{m\in \mathcal{M}}{d}_{m,t}-{\displaystyle \sum }_{m\in \mathcal{M}}{e}_{m,t}\right)\hfill \\ & =\hfill & p_d{\displaystyle \sum }_{m\in \mathcal{M}}\underset{t\in \mathcal{T}}{\max }\left(d_{m,t}-e_{m,t}\right)+{\displaystyle \sum }_{t\in \mathcal{T}}{p}_{e,t}\left({\displaystyle \sum }_{m\in \mathcal{M}}{d}_{m,t}-g_t\right)\hfill \\ & & \propto {\displaystyle \sum }_{m\in \mathcal{M}}\underset{t\in \mathcal{T}}{\max }\left(d_{m,t}-e_{m,t}\right).\hfill \end{array}$$

(7)

This shows that the overall bill minimization problem in P0 is operated as a peak-shaving problem of the total demand.

The second problem is related to information usage. To find the optimal solution for P0, future information is required; for example, to solve the problem at $t=1$, the information $g_i$ at $i\in \left\{2,\dots ,T\right\}$ is required.

To reduce the first problem, the proposed community solar operation strategy decomposes the overall electricity bill minimization problem into an individual electricity bill minimization problem, which represents a form of selfish operation by each member and coordination by SESP. For the second problem, the proposed strategy decides the operation at each decision time $t$ using the decision information of the previous time ${\mathcal{T}}^{-}=\left\{1,\dots ,T-1\right\}$ and forecasting information of the future time ${\mathcal{T}}^{+}=\left\{\mathrm{t}+1,\dots ,T\right\}$.

3. Proposed Community Solar Operation Strategy for SEC

As discussed above, the proposed community solar operation strategy is implemented by each member to minimize their electricity bill in a distributed manner. For this purpose, the problem in P0 should be decomposed into a problem for individual members.

Applying the slack variable ${\lambda }_{m,t}$, the problem in P0 is rewritten as:

$$\begin{array}{cc}\hfill \underset{e_{m,t},{\lambda }_{m,t}}{\min }|& {\displaystyle {\displaystyle \sum }_{m\in \mathcal{M}}}{B}_m\left(e_{m,t}\right)\hfill \\ \hfill \mathrm{subject} \mathrm{to}|& {\displaystyle {\displaystyle \sum }_{m\in \mathcal{M}}}{\lambda }_{m,t}\le g_t,||\forall |t\in \mathcal{T},\hfill \\ & e_{m,t}\le {\lambda }_{m,t},||\forall |t\in \mathcal{T},\forall |m\in \mathcal{M},\hfill \\ & {\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{e}_{m,t}={\gamma }_m{\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{g}_t,||\forall |m\in \mathcal{M}.\hfill \end{array}$$

(8)

Subsequently, the problem in (8) can be divided into two problems: the problem for individual member $m$,

$$\begin{array}{cc}\hfill \underset{e_{m,t}}{\min }|& B_m\left(e_{m,t}\right)\hfill \\ \hfill \mathrm{subject} \mathrm{to}|& e_{m,t}\le {\lambda }_{m,t},||\forall |t\in \mathcal{T},\hfill \\ & {\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{e}_{m,t}={\gamma }_m{\displaystyle {\displaystyle \sum }_{t\in \mathcal{T}}}{g}_t,\hfill \end{array}$$

(9)

and the problem for SESP,

$$\begin{array}{cc}\hfill \underset{{\lambda }_{m,t}}{\min }|& c\hfill \\ \hfill \mathrm{subject} \mathrm{to}|& e_{m,t}\le {\lambda }_{m,t},||\forall |t\in \mathcal{T},\hfill \\ & {\displaystyle {\displaystyle \sum }_{m\in \mathcal{M}}}{\lambda }_{m,t}\le g_t,||\forall |t\in \mathcal{T},\hfill \end{array}$$

(10)

where $c$ is the constant value.

The problems in Equations (9) and (10) are solved through information exchange between the community members and SESP, as shown in Figure 3. At each decision time $t$, each community member individually solves the problem in Equation (9) and sends the solution $e_{m,t}$ to the SESP. The SESP aggregates $e_{m,t}$, calculates ${\lambda }_{m,t}$, and sends it back to each member, and the solution is converged through an iterative information exchange.

The solution of the problem in Equation (10) is simply achieved through:

$${\lambda }_{m,t}=\frac{e_{m,t}}{{{\displaystyle \sum }}_{m\in \mathcal{M}}{e}_{m,t}}{g}_t.$$

(11)

To solve the problem in Equation (9), the equation can be relaxed using Lagrangian relaxation [29] as follows:

$$\mathcal{L}\left(e_{m,t},{\nu }_m,{\eta }_{m,t}\right)=B_m\left(e_{m,t}\right)+{\nu }_m\left({\displaystyle \sum }_{t\in \mathcal{T}}{e}_{m,t}-{\gamma }_m{\displaystyle \sum }_{t\in \mathcal{T}}{g}_t\right)+{\displaystyle \sum }_{t\in \mathcal{T}}{\eta }_{m,t}\left(e_{m,t}-{\lambda }_{m,t}\right),$$

(12)

where ${\nu }_m\ge 0$ and ${\eta }_{m,t}\ge 0$ are the Lagrangian multipliers. The applied Karush–Kuhn–Tucker (KKT) conditions [29] are:

$$\begin{array}{cc}& {\nu }_m\left({\displaystyle \sum }_{t\in \mathcal{T}}{e}_{m,t}-{\gamma }_m{\displaystyle \sum }_{t\in \mathcal{T}}{g}_t\right)=0,\hfill \\ & {\eta }_{m,t}\left(e_{m,t}-{\lambda }_{m,t}\right)=0,||\forall |t\in \mathcal{T},\hfill \\ & \hfill \frac{\partial \mathcal{L}\left(e_{m,t},{\nu }_m,{\eta }_{m,t}\right)}{\partial e_{m,t}}& =& \frac{\partial B_m\left(e_{m,t}\right)}{\partial e_{m,t}}+{\nu }_m+{\eta }_{m,t}=0\hfill \end{array}$$

(13)

.

The KKT conditions are the conditions that must be satisfied for the solution of a relaxed problem to be an optimal value. In Equation (13), the first and second equations are the complementary slackness conditions, and the third equation expresses the stationarity.

In the last condition in Equation (13), the Lagrangian multiplier ${\eta }_{m,t}$ acts as a slack variable. Thus, the last condition is expressed as

$${\nu }_m\ge -\frac{\partial B_m\left(e_{m,t}\right)}{\partial e_{m,t}},$$

(14)

and the solution $e_{m,t}$ is directly calculated as

$$e_{m,t}=\left\{\begin{array}{ll}0,\hfill & B_m\left(\cdot \right)\le {\nu }_m,\hfill \\ d_{m,t}-\frac{1}{p_d+p_{e,t}}{\nu }_m,\hfill & B_m\left(\cdot \right)\ge {\nu }_m|\mathrm{and} \mathrm{Peak} \mathrm{time},\hfill \\ d_{m,t}-\frac{1}{p_{e,t}}{\nu }_m,\hfill & B_m\left(\cdot \right)\ge {\nu }_m|\mathrm{and} \mathrm{Off}-\mathrm{peak} \mathrm{time}.\hfill \end{array}\right.$$

(15)

By substituting Equation (15) into the first condition in Equation (13), $e_{m,t}$ and ${\nu }_m$ can be obtained. Moreover, using the second equation, $e_{m,t}^{*}$ is solved as follows:

$$e_{m,t}^{*}=\min \left(e_{m,t},{\lambda }_{m,t}\right).$$

(16)

This solution represents one application of the water-filling algorithm [31]. In general, water-filling algorithms increase the objective by adding resources to elements below the water level. However, this study reduces the objective by adding resources to elements above the water level, as shown in Equation (15). This can be expressed as shown in Figure 4 using the negative function. In the figure, the Lagrangian multiplier ${\nu }_m$ decides water level. The region is flooded to the level which uses a total quantity of water equal to ${\gamma }_m{\displaystyle \sum }_{t\in \mathcal{T}}{g}_t$. The height of the water (shown shaded) above each decision time presents the electricity bill saving by the allocation $e_{m,t}^{*}$ as $B_m\left(\cdot \right)-B_m\left(e_{m,t}^{*}\right)$. Considering the basement that is the original electricity bill $B_m\left(\cdot \right)$ and the total quantity of water that is the community solar generation, the water level is decided. Based on the water level, the solution is calculated, which is the community solar generation allocated to the member at each decision time.

Using the solution in Equation (16), each member can then decide how to minimize their own electricity bill in a distributed manner; however, future time information is still required. Information on the future time can be obtained based on the demand [32] and solar generation forecasting [33]. However, the forecasted value has an uncertainty, which represents the error between the actual and forecasted values. Therefore, Equation (13) should be updated at each decision time $t$ as follows:

$$\begin{array}{c}{\nu }_m\left({\displaystyle {\displaystyle \sum }_{t\in {\mathcal{T}}^{+}}}{e}_{m,t}-{\gamma }_m{\displaystyle {\displaystyle \sum }_{t\in {\mathcal{T}}^{+}}}{\widehat{g}}_t+R_{m,t}\right)=0,\\ {\eta }_{m,t}\left(e_{m,t}-{\lambda }_{m,t}\right)=0,||\forall |t\in \mathcal{T},\\ \frac{\partial \mathcal{L}\left(e_{m,t},{\nu }_m,{\eta }_{m,t}\right)}{\partial e_{m,t}}=\frac{\partial B_m^{+}\left(e_{m,t}\right)}{\partial e_{m,t}}+{\nu }_m+{\eta }_{m,t}=0\end{array}$$

(17)

. where ${\widehat{g}}_t$ is the forecasted generation solar energy at time $t$, $R_{m,t}$ is the residual allocation at the previous decision time calculated as $R_t={\displaystyle {\displaystyle \sum }_{t\in {\mathcal{T}}^{-}}}{e}_{m,t}-\gamma {\displaystyle {\displaystyle \sum }_{t\in {\mathcal{T}}^{-}}}{g}_t$, and

$$B_m^{+}\left(e_{m,t}\right)=p_d\underset{t\in {\mathcal{T}}^{+}}{\max }\left({\widehat{d}}_{m,t}-e_{m,t}\right)+{\displaystyle {\displaystyle \sum }_{t\in {\mathcal{T}}^{+}}}{p}_{e,t}\left({\widehat{d}}_{m,t}-e_{m,t}\right),$$

(18)

where ${\widehat{d}}_{m,t}$ is the forecasted demand at time $t$, and the residual allocation $R_{m,t}$ is the priority of member $m$ at time $t$ in the allocation.

Similar to Equation (15), the solution is calculated as:

$$e_{m,t}=\left\{\begin{array}{ll}0,\hfill & B_m^{+}\left(\cdot \right)\le {\nu }_m,\hfill \\ d_{m,t}-\frac{1}{p_d+p_{e,t}}{\nu }_m,\hfill & B_m^{+}\left(\cdot \right)\ge {\nu }_m|\mathrm{and} \mathrm{Peak} \mathrm{time},\hfill \\ d_{m,t}-\frac{1}{p_{e,t}}{\nu }_m,\hfill & B_m^{+}\left(\cdot \right)\ge {\nu }_m|\mathrm{and} \mathrm{Off}-\mathrm{peak} \mathrm{time},\hfill \end{array}\right.$$

(19)

and

$$e_{m,t}^{*}=\min \left(e_{m,t},{\lambda }_{m,t}\right).$$

(20)

This study has not covered the system implementation issue. However, the solutions in Equations (19) and (20) are linear equations according to cases, thus it can be implemented using the microcontroller with a light computing power such as a raspberry PI or an equivalent device.

The proposed operation strategy can be expressed as

Proposed community solar operation strategy

Initialization   Demand and generation forecasting, ${\widehat{d}}_t$ and ${\widehat{g}}_t$   Set the maximum iteration. At each decision time $t\in \mathcal{T}$ ,   Each member calculates $e_{m,t}$ using Equation (20) and sends it to the SESP.   The SESP calculates ${\lambda }_{m,t}$ using Equation (11) and sends it back to each member.   The process is repeated until convergence or the maximum iteration is reached.

4. Results

4.1. Experimental Environment

The SEC was considered to have 126 members, which were used in the evaluation of the performance of the proposed strategy. The demand was recorded with a 1-h resolution as part of the Korea Micro Grid Energy Project (K-MEG) [34]. Figure 5 shows the average daily demand distribution of SEC members. The community solar system was considered to be a solar generation system with a 100 kW solar module, a 20 kW $\times$ 6EA inverter, and a 17° installation angle. Moreover, generation data were recorded with a 1-h resolution similar to the demand. Figure 6 shows an example of community solar generation over three days. The ToU tariff for the medium general demand-metered service of the Pacific Gas and Electric Company was used to calculate the electricity bill, as shown in

Table 1. Time-of-use tariff of Pacific Gas and Electric Company.

Demand Price (USD/kW)	Energy Price (USD/kWh)
	Off-Peak	Mid-Peak	On-Peak
18.45	0.22	0.25	0.25

[35]. Under the ToU tariff, the energy prices for the mid-peak and on-peak times are equal.

To verify the efficiency, the performance of the proposed strategy is compared with the solution of P0 in Equation (6), and the fixed proportional operation (PP) is calculated as:

$$e_{m,t}=\gamma g_t,||\forall |t\in \mathcal{T},\forall |m\in \mathcal{M}.$$

(21)

4.2. Electricity Bill Saving

The objective of this community solar operation strategy is to minimize the electricity bills of the members.

Table 2. Overall monthly electricity bill savings for the members ($/month).

Method	Community Solar Capacity
	50 kWp	100 kWp	200 kWp	300 kWp	400 kWp	500 kWp
P0	3100	4915	8158	11,316	14,419	17,450
Proposed strategy	2720	4518	7734	10,819	13,832	16,822
PP	1777	3498	6843	10,087	13,251	16,389

presents the monthly electricity bill savings for all the members under varying community solar capacities. The results show that the maximum electricity bill savings is obtained in the solution of P0, which is optimally operated using information on the future time. Moreover, the solution of the proposed strategy has the second-best electricity bill saving and outperforms PP, which is a fixed proportional operation. Figure 7 shows the optimal gap compared with the results of P0. The blue line with circles and red line with diamonds represent the performance gaps of the proposed strategy and PP, respectively. It can be seen that the optimal gap of the proposed strategy is 12.2% at a community solar capacity of 50 kWp and reduces with increasing community solar capacity. Moreover, it is generally less than 10% in the case without the 50 kWp community solar capacity. It is also noteworthy that the results of the PP have an optimal gap that is on average 2.7 times larger than that of the proposed method.

As shown in Table 2, the community solar capacity increases with an increase in the electricity bill savings because the community solar capacity determines the capacity of solar generation. However, the electricity bill savings per community solar capacity is reduced with increasing community solar capacity, as shown in Figure 8. The black line with squares, blue line with circles, and red line with diamonds represent the results of P0, the proposed strategy, and PP, respectively. It can be seen that the efficiency of the community solar power generation is reduced with increasing capacity. Moreover, the results of P0 and the proposed strategy show a similar decreasing slope, but the slope of the PP results decreases more slowly than that of the other results.

4.3. Fairness

Resource fairness was the main constraint considered in this study. The resource fairness constraint was satisfied in all cases (the P0, the proposed strategy, and PP). To determine the effect of resource fairness, Jain’s fairness index [36], which is used to determine the fairness of a set of values in sharing systems, was calculated based on the electricity bill savings per allocated capacity of each member as follows:

$$\mathrm{Jain}\text{’}\mathrm{s} \mathrm{fairness} \mathrm{index}=\frac{1}{M}\frac{{\left({{\displaystyle \sum }}_{m\in \mathcal{M}}{\chi }_m\right)}^2}{{{\displaystyle \sum }}_{m\in \mathcal{M}}{\chi }_m^2},$$

(22)

where ${\chi }_m=\frac{B_m\left(\cdot \right)-B_m\left(e_{m,t}\right)}{{\gamma }_m{{\displaystyle \sum }}_{t\in \mathcal{T}}{g}_t}$ is the electricity bill saving per allocated capacity of member $m$.

Figure 9 shows the variation in the Jain’s fairness index with the community solar capacity, where the optimal case for the Jain’s fairness index is when the value is 1. The results show that the PP case has the optimal fairness index, and the proposed strategy case has a higher fairness index than that of P0.

Figure 10 shows the distribution of the electricity bill savings per allocated capacity of each member when the community solar capacity is 100 kWp. As shown in Figure 10c, the PP case has the distribution with the highest sharpness, and the distribution of the P0 case in Figure 10a has a heavier tail compared to that of the proposed strategy case in Figure 10b, which reduces the fairness index.

5. Discussion

From Section 4, it is evident that the proposed community solar operation strategy achieves near-optimal electricity bill savings and distributes the benefits of electricity bill savings to the members in relation to the optimal operation of P0 using the information on the future time. Based on these results, the following key points were derived for community solar operation in SECs.

• The central objective of the community solar operation strategy in P0 is to maximize the overall electricity bill savings of the members; however, the strategy requires information on the future time. The proposed distributed strategy with partial information has a slightly less electricity bill savings compared to P0, as shown in Table 2. However, the optimal gap was less than 10% without the consideration of a small community solar capacity of 50 kWp, as shown in Figure 7. Moreover, the proposed strategy distributes the electricity bill savings of the members more fairly than the strategy in P0. This verified the effectiveness of the proposed community solar operation strategy.
• The electricity bill savings per community solar capacity in Figure 8 and Jain’s fairness index in Figure 9 exhibit completely opposite shapes. This implies that there is a trade-off between the electricity bill savings and guarantee of fairness.
• The savings on the electricity bill were directly proportional to the community solar capacity, as shown in Table 2. However, the efficiency, measured as the electricity bill savings per capacity, was reduced with increasing community solar capacity, as shown in Figure 8. Moreover, increasing the community solar capacity requires additional investment from the SEC members; thus, an appropriate community solar capacity implementation is required when configuring a community solar system for the SEC.
• The fixed proportional operation strategy presented as PP has a large optimal performance gap compared to the centralized and proposed operation strategies, as shown in Figure 7. However, the electricity bill savings per community solar capacity in the PP strategy were decreased with increasing community solar capacity, as shown in Figure 8. Particularly, the Jain’s fairness index of PP was closest to the optimal value (c.f., the optimal Jain’s fairness index is 1), as shown in Figure 9. This implies that the PP strategy can be used as a baseline community solar operation strategy for SECs.

This study also presents a distributed fair community solar operation for SECs, and the following future research directions are suggested.

• In this study, the implementation cost of community solar power was neglected. As discussed above, by increasing the community solar capacity, the benefits of electricity bill savings and cost of generation are also increased. Therefore, the community solar implementation issue can be investigated in future research considering the trade-off between the benefits and costs.
• This study assumed a case in which the SESP implemented and operated community solar generation and distribution. This can be extended to a case where third-party service providers such as a community solar service providers (CSSP) are used to implement community solar generation and the SESP rents the community solar capacity. In the extended case, the benefit distribution between the CSSP and members of the SEC can be formulated as a new problem.
• This study did not consider the energy transaction constraints such as transmission and distribution congestion and cost because the SEC consists of members in close proximity to each other. Therefore, this study can be extended to large-scale grid connection systems by considering the energy transaction constraints.

6. Conclusions

This study proposes a distributed community solar operation strategy for SEC that considers resource fairness. The system was considered for an SEC model, which comprised the SEC, community solar, and utility grid as the main components. The community solar operation problem was formulated as a mixed-integer linear problem and decomposed into an individual electricity bill minimization problem for each member. Each member then selfishly decides on how the community solar operation can be conducted in a distributed manner, and the SESP manages it. The simulation results using a real dataset in Korea showed that the members who applied the proposed community solar operation achieved a fairer electricity bill savings benefit distribution. Moreover, the total electricity bill savings were marginal (less than 10%) compared to that of the centralized community solar operation that employs the information on the future time, except for the 50 kWp community solar capacity case. In addition, there is a trade-off between the benefits of electricity bill savings and the guarantee of fairness.

Moreover, the basic environments for SEC, community solar, and utility grids were considered and can be extended to more complex environments. For the community solar model, problems related to ownership and the cost-effective implementation of the community solar capacity can be further considered. For the utility grid model, a problem with more realistic environments can be extended, including the energy transaction constraints.