Optimal Configuration of Electric-Gas-Thermal Multi-Energy Storage System for Regional Integrated Energy System

Abstract

With the increasing attention of the clean and efficient use of energy, the regional integrated energy system (RIES), as an efficient measure to improve energy efficiency, is tending to play an important role in the field of energy supply. The configuration of multiple energy storage equipment in the RIES can greatly improve the economy of the system, which is an important research direction of RIES planning. However, at present the research on the configuration optimization of electric-gas-thermal multi-energy storage devices in RIES is insufficient. Under this background, a method for configuring the rated capacity and power of various energy storage devices in the RIES under both off-grid and grid-connected operating modes was proposed in this paper, and the configuration optimization model was also established. Firstly, the RIES was divided into four parts: Energy supply, energy conversion, energy storage and the load. Based on the energy hub concept, the four parts were modeled respectively. Secondly, considering the influence of electric energy substitution and operation strategy, the optimal configuration of multi-energy storage devices was modeled as a MILP formulation and solved with the Gurobi optimizer. Finally, a case study verified the effectiveness of the proposed model and the method. Furthermore, the sensitivity analysis was carried out to quantify the influence degree of each factor (such as price, etc.) on the energy storage configuration.

1. Introduction

In contemporary world, undergoing drastic development of the energy internet and increasing connection of energy sources such as electricity, gas and heat, the clean and efficient use of energy has gradually become the focus of attention [1,2]. The transformation and upgrading of traditional energy systems are imminent, therefore, the RIES has emerged as the times require [3]. The RIES is a typical energy internet based on a multi-energy complementary structure, which combines various ways of energy supply, such as electric power, photovoltaic energy, wind energy, nature gas and other types of energy to provide users with gas, heat and electricity at a higher overall system energy efficiency [4].

The electricity sectors and heat sectors are interconnected by technologies such as combined heat and power (CHP), the electric heat pump (HP), and electric boiler (EB), and they have been recently recognized as prominent examples for creating add-on values for both sectors [5,6]. CHP [7] and EB [8] were adopted to solve the problem of wind power consumption and environmental pollution, however, the varieties of energy contained in above studies were limited. The gradually mature power to gas (P2G) technology has enhanced the integration between power and gas networks, providing new ideas for the consumption of wind power and photovoltaic power in the RIES [9]. In [10], a joint scheduling model of P2G and thermal-electric decoupling CHP was proposed for the integrated energy microgrid system and the results show that P2G can greatly improve the wind abandonment phenomenon. The Implementation Opinions on Promoting the Construction of Multi-energy Complementary Integration Optimization Demonstration Project issued by the National Energy Administration [11] also pointed out that energy complementarity and coordinated supply should be realized through electric heating triple supply and distributed renewable energy. Therefore, the research on RIES has important practical significance, and the RIES planning is the basis for efficient, economical and reliable operation of the system.

The research of RIES planning is mainly divided into two categories [12]: (1) The structure of RIES is known to optimize the capacity or model of the system equipment; (2) optimizing the system structure and capacity or model of the RIES at the same time, that is the initial planning from scratch. The main difficulties in RIES planning are summarized as four parts [13]: Multi-energy coupling modeling, multiple load forecasting, technical economic assessment and planning optimization model solving. Optimal planning of RIES has been previously studied and some attention-grabbing planning models have been proposed. Shen, X. et al. [14] proposed the robust planning method for RIES considering multi-energy load uncertainties. Li, Z. et al. [15] proposed the expansion planning method for RIES considering the uncertainty of wind power. Song, Y. et al. [16] put forward a planning model incorporating demand response and thermo-electrical coupling. Those models are essentially a mixed-integer no-linear programming (MINLP) problem, and the classical convex optimization algorithm is difficult to solve directly. The current solutions are mainly divided into two categories: One is to approximate the optimization model to a linear problem by simplification, which can be solved with optimizer, such as CPLEX [17]; the other is to use intelligent algorithms, such as particle swarm optimization, and genetic algorithms [18]. The energy storage system has played an important role in improving the operation efficiency and economy of RIES, but the study on configuration of the energy storage system is ignored in these papers.

Moreover, most of the research on energy storage is based on battery models, while less research involves thermal storage and gas storage equipment [19]. Essentially, all energy (electricity, gas, heat) storage can be called energy storage systems, and the configuration of multiple energy storage equipment in the RIES can greatly improve the economy of the system and the phenomenon of wind abandonment [20]. Due to the relatively low cost of gas storage, it is possible to develop gas storage technology in the RIES [21]. Electric-thermal energy storage systems were used in [22] to increase the wind power consumption rate of the system. In [23], the impact of electric-thermal storage systems on the operation of Northern Communities’ microgrids was analyzed. P2G and gas energy storage were adopted in a multi-source microgrid to study their impact on the economy of the system and the ability to absorb wind power in [24]. The operational impact of P2G on electrical and gas transmission networks was studied in [25]. Further, the study in [26] optimized the configuration of energy storage equipment in the RIES by a bi-level planning approach, but the gas storage system was not involved in it. None of the research above proposed the configuration model of electro-gas-thermal energy systems. Mutual influence between electric-thermal-gas energy storages was studied in [27], and the conclusion that multi-energy storage systems have the optimal economics was obtained. However, the capacity of the energy storage equipment has a certain impact on the above conclusion, of which there is lack of in further discussions.

In general, there are many studies on the RIES planning with electric and thermal loads as terminal loads. However, the load demand in the RIES is diversified, and the gas load is gradually becoming an indispensable energy demand, but the research on the RIES planning with electric-thermal-gas loads as terminal loads is insufficient. In addition, a variety of energy storage equipment can improve the efficiency and economy of the RIES, but the research objects of related research are mostly concentrated in the source, network, and load. Therefore, the research on the electric-gas-heat integrated energy storage configuration method is insufficient. Moreover, the RIES operation mode is also divided into grid-connected and off-grid. At present, the planning for the RIES is mostly studied from grid-connected or off-grid mode, and the research on planning of RIES operating on both grid-connected and off-grid modes is less involved.

In this paper, the RIES was first modeled from the four parts of the supply side, energy conversion side, energy storage side and the load side. Then, a method for configuring the rated capacity and power of electric-thermal-gas energy storage devices in the RIES with electric, thermal, gas loads as terminal loads was proposed. The contributions of this paper are summarized as follows:

(1) In order to more clearly describe the functions of each link in RIES, this paper carried out extended modeling of the RIES, which can reduce repetitive modeling time and increase efficiency when the RIES structure is changed.

(2) The configuration optimization model of electric-thermal-gas energy storage systems for the RIES under both off-grid and grid-connected operating modes was proposed. In other words, the method to determine the optimal configuration scheme of electric-gas-thermal energy storage equipment of the RIES was carried out.

(3) The electric energy substitution and operation strategy were considered in the configuration optimization model.

(4) The sensitivity analysis was carried out to quantify the influence degree of each factor (such as price, etc.) on the result of the energy storage configuration.

The remaining sections of this paper are as follows: Section 2 describes the RIES mathematical model. The configuration optimization model of energy storage systems is introduced in Section 3. A case study and results analysis are given in Section 4. The discussion is given in Section 5. Finally, Section 6 draws the conclusion.

2. The RIES Mathematical Model

Typical RIES generally contains various forms of energy (such as electricity, gas, heat, etc.), which can be divided into energy supply, energy conversion, energy storage and load. The RIES structure studied in this paper can be described by Figure 1, including 4 parts: 1) The supply side: power grid, photovoltaic (PV), wind turbine (WT), natural gas network; 2) the conversion side: micro turbine (MT), bromine cooler (BC), EB, P2G, gas boiler (GB); 3) the storage side: electrical energy storage(EES), thermal energy storage(TES), gas energy storage(GES); 4) the load side: electrical loads, heat loads, gas loads.

As there are many energy storage and conversion links in the RIES in this paper, the mathematical models of the main equipment involved in the RIES (such as CHP, P2G, EB, etc.) are referred to References [17,18,19,20,21,22]. It will not be repeated in this paper due to space limitations. For a better analysis of the energy conversion, energy storage and energy distribution in the RIES, the system is modeled by the energy hub concept [28]. The interaction and coupling characteristics of energy supply, energy conversion, energy storage, and load are expressed by Equation (1):

$$\mathit{L}=\mathit{C}\mathit{P}+\mathit{S}$$

(1)

$$\left[\begin{array}{l}{L}_a\\ L_b\\ ⋮\\ L_x\end{array}\right]=\left[\begin{array}{cccc}{C}_{aa}& C_{ba}& \cdots & C_{xa}\\ C_{ab}& C_{bb}& \cdots & C_{xb}\\ ⋮& ⋮& \ddots & ⋮\\ C_{ax}& C_{bx}& \cdots & C_{xx}\end{array}\right]\left[\begin{array}{l}{P}_a\\ P_b\\ ⋮\\ P_x\end{array}\right]+\left[\begin{array}{l}{S}_a\\ S_b\\ ⋮\\ S_x\end{array}\right]$$

(2)

where L, C, P, S represents the load matrix, energy conversion matrix, energy supply matrix and the energy storage matrix of the RIES respectively; $L_a$, $P_a$, $S_a$ are the output, input and storage of type a energy, respectively; $C_{ab}$ denotes the conversion factor between energy a and b.

Since there are many energy conversion and storage links in the RIES, and there are energy conversion links in series form, the direct description is more complicated. In order to more clearly describe the functions of each link in RIES, this study carried out extended modeling of the RIES. According to the position of the energy conversion device, the RIES was divided into the supply side, the conversion component and the load side, as shown in Figure 1, reflecting the series characteristics of energy distribution, conversion and stored process in the model. The model of each part described above is modeled as follows.

2.1. Load Model

With the improvement of the electrification level on the user side, the coupling between electrical, gas and thermal loads becomes closer. By using efficient electric heating equipment and other devices, part of the heat demand and gas demand of the users is replaced with electric energy. As shown in Figure 1, space heating and hot water are partly met by electric heating devices such as the air conditioner, heat pump, etc. At the same time, the differences in user behavior of the electric heating supply have certain impacts on the total demand in the RIES, so the differences between the individual and aggregate demand should be taken into account in the load model. The load side could be characterized as Equation (3):

$$\{\begin{array}{l}{L}_{\mathrm{e}}(t)={\displaystyle \sum _{n=1}^N{L}_n^{\mathrm{e}}(t)=E(t)+{\displaystyle \sum _{n=1}^N{E}_n^{\prime }(t)}}\\ L_{\mathrm{h}}(t)={\displaystyle \sum _{n=1}^N{L}_n^{\mathrm{h}}(t)=H(t)-{\displaystyle \sum _{n=1}^N{H}_n^{\prime }(t)}}\\ L_{\mathrm{g}}(t)={\displaystyle \sum _{n=1}^N{L}_n^{\mathrm{g}}(t)=G(t)}\end{array}$$

(3)

where $L_{\mathrm{e}}(t)$, $L_{\mathrm{h}}(t)$, $L_{\mathrm{g}}(t)$ are the aggregate electric, heat, gas load of users at time t, respectively; $L_n^{\mathrm{e}}(t)$, $L_n^{\mathrm{h}}(t)$, $L_n^{\mathrm{g}}(t)$ are the electric, heat, gas loads of user n at time t, respectively; N is the number of users; E(t), H(t), G(t) are the direct electric, heat, gas demand of users at time t respectively which can be predicted through top-down methods such as statistical method with historical data; $E_n^{\prime }(t)$, $H_n^{\prime }(t)$ are the electric demand, heat demand of user n produced from electric heating supply respectively, which is generally predicted through bottom-up methods that focus on the individual energy requirements of different users in the RIES.

The electric energy substitution strategy (replacing heat energy with electric energy, replacing gas energy with electric energy) is an effective means to improve the load structure and reduce pollution [29,30] since the load is the basis of energy storage configuration. The change of load structure mainly affects the choice of the RIES operation strategy and the optimization range of power and capacity during the energy storage system configuration. At present, the electric energy substitution has been rarely considered in existing methods of energy storage configuration. The use of EB in the supply side for district heating of the RIES can reduce the use of GB, while P2G devices can convert surplus electric energy into natural gas when the wind power is high and the electric load is low in the evening. The use of P2G and EB can be treated as the electric energy substitution. The P2G and EB devices are considered as loads to establish an equivalent load model:

$$\left[\begin{array}{l}\stackrel{\wedge }{L_{\mathrm{e}}}(t)\\ \stackrel{\wedge }{L_{\mathrm{h}}}(t)\\ \stackrel{\wedge }{L_{\mathrm{g}}}(t)\end{array}\right]=\left[\begin{array}{l}{L}_{\mathrm{e}}(t)\\ L_{\mathrm{h}}(t)\\ L_{\mathrm{g}}(t)\end{array}\right]+\left[\begin{array}{l}{P}_{\mathrm{P}2\mathrm{G}}(t)+P_{\mathrm{EB}}(t)\\ -{\eta }_{\mathrm{EB}}{P}_{\mathrm{EB}}(t)\\ -{\eta }_{\mathrm{P}2\mathrm{G}}{P}_{\mathrm{P}2\mathrm{G}}(t)\end{array}\right]$$

(4)

$$\stackrel{\wedge }{\mathit{L}}=\mathit{L}+{\mathit{P}}_{\mathrm{P}2\mathrm{G},\mathrm{EB}}$$

(5)

where $\stackrel{\wedge }{L_{\mathrm{e}}}(t)$, $\stackrel{\wedge }{L_{\mathrm{h}}}(t)$, $\stackrel{\wedge }{L_{\mathrm{g}}}(t)$ are the equivalent electric, heat, gas load at time t, respectively; $P_{\mathrm{P}2\mathrm{G}}(t)$, $P_{\mathrm{EB}}(t)$ are the P2G power, EB power at time t respectively; ${\eta }_{\mathrm{P}2\mathrm{G}}$, ${\eta }_{\mathrm{EB}}$ are the P2G efficiency, EB efficiency respectively; $\stackrel{\wedge }{\mathit{L}}$, $\mathit{L}$, ${\mathit{P}}_{\mathrm{P}2\mathrm{G},\mathrm{EB}}$ are the equivalent load matrix, load matrix, P2G and EB power matrix.

2.2. Supply Model

On the supply side, energy input includes the power grid, natural gas network, wind power and photovoltaic power. The wind turbines have anti-peaking characteristics. Wind power is high during the mid-night, but the electric load is low at that time, so the wind energy cannot be completely absorbed by the system, that is, part of the wind power is abandoned, and so does the PV. By introducing the wind and photovoltaic power utilization rate β_WT and β_PV to characterize the ability to absorb wind power and photovoltaic power of the system, the wind and photovoltaic output power is:

$$P_{\mathrm{WT}}(t)=P_{\mathrm{WT}}^{\mathrm{e}}(t){\beta }_{\mathrm{WT}}(t)$$

(6)

$$P_{\mathrm{PV}}(t)=P_{\mathrm{PV}}^{\mathrm{e}}(t){\beta }_{\mathrm{PV}}(t)$$

(7)

where $P_{\mathrm{WT}}(t)$, $P_{\mathrm{PV}}(t)$ are the wind and photovoltaic output power at time t; $P_{\mathrm{WT}}^{\mathrm{e}}(t)$, $P_{\mathrm{PV}}^{\mathrm{e}}(t)$ are the rated wind and photovoltaic output power without abandoning wind and photovoltaic power at time t, respectively. At this point, the abandoned wind and photovoltaic power can be expressed as:

$$P_{\mathrm{cut}}(t)=P_{\mathrm{WT}}^{\mathrm{e}}(t)(1-{\beta }_{\mathrm{WT}}(t))+P_{\mathrm{PV}}^{\mathrm{e}}(t)(1-{\beta }_{\mathrm{PV}}(t))$$

(8)

where $P_{\mathrm{cut}}(t)$ is the abandoned power at time t. ${\beta }_{\mathrm{WT}}(t)$, ${\beta }_{\mathrm{PV}}(t)$ are the wind and photovoltaic power utilization rate at time t, respectively.

The input power of the external power grid and natural gas is considered, and the energy loss is not considered because the transmission line/pipe is short. The supply model can be expressed as:

$$\left[\begin{array}{l}{P}_{\mathrm{e}}(t)\\ P_{\mathrm{g}}(t)\end{array}\right]=\left[\begin{array}{l}u{P}_{\mathrm{e}}^{\mathrm{net}}(t)\\ P_{\mathrm{g}}^{\mathrm{net}}(t)\end{array}\right]+\left[\begin{array}{l}{P}_{\mathrm{WT}}(t)+P_{\mathrm{PV}}(t)\\ 0\end{array}\right]$$

(9)

$$\mathit{P}={\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}}$$

(10)

where $P_{\mathrm{e}}(t)$, $P_{\mathrm{g}}(t)$ are the input electric and gas power at time t respectively; $P_{\mathrm{e}}^{\mathrm{net}}(t)$ is the interactive power between the RIES and the external power grid at time t; $P_{\mathrm{g}}^{\mathrm{net}}(t)$ is the interactive power between the RIES and natural gas network at time t; u represents a 0–1 variable. When u = 0, it means that the RIES is operating in the off-grid mode, while u = 1 means the grid-connected mode; $\mathit{P}$, ${\mathit{P}}^{\mathrm{net}}$, ${\mathit{P}}_{\mathrm{WT},\mathrm{PV}}$ is the supply matrix, interactive power matrix and wind and photovoltaic power matrix, respectively.

2.3. Storage Model

The mathematical model between the storage capacity and the input and output power of EES, TES and GES [27] can be expressed as:

$$\{\begin{array}{l}{E}_{\mathrm{EES}}(t)=(1-{\mu }_{\mathrm{e}})E_{\mathrm{EES}}(t-1)+[P_{\mathrm{ch}}^{\mathrm{e}}(t){\eta }_{\mathrm{ch}}^{\mathrm{e}}-\frac{P_{\mathrm{dis}}^{\mathrm{e}}(t)}{{\eta }_{\mathrm{dis}}^{\mathrm{e}}}]\Delta t\\ H_{\mathrm{TES}}(t)=(1-{\mu }_{\mathrm{h}})H_{\mathrm{TES}}(t-1)+[P_{\mathrm{ch}}^{\mathrm{h}}(t){\eta }_{\mathrm{ch}}^{\mathrm{h}}-\frac{P_{\mathrm{dis}}^{\mathrm{h}}(t)}{{\eta }_{\mathrm{dis}}^{\mathrm{h}}}]\Delta t\\ G_{\mathrm{GES}}(t)=(1-{\mu }_{\mathrm{g}})G_{\mathrm{GES}}(t-1)+[\frac{P_{\mathrm{ch}}^{\mathrm{g}}(t){\eta }_{\mathrm{ch}}^{\mathrm{g}}}{H_{\mathrm{CVNG}}}-\frac{P_{\mathrm{dis}}^{\mathrm{g}}(t)}{{\eta }_{\mathrm{dis}}^{\mathrm{g}}{H}_{\mathrm{CVNG}}}]\Delta t\end{array}$$

(11)

where $E_{\mathrm{EES}}(t)$, $H_{\mathrm{TES}}(t)$, $G_{\mathrm{GES}}(t)$ are the storage capacities of EES, TES and GES at time t respectively; ${\mu }_{\mathrm{e}}$, ${\mu }_{\mathrm{h}}$, ${\mu }_{\mathrm{g}}$ are the self-discharge rate, self-heat dissipation rate and self-deflating rate of EES, TES and GES, respectively; $P_{\mathrm{ch}}^{\mathrm{e}}(t)$, $P_{\mathrm{dis}}^{\mathrm{e}}(t)$ are the charging and discharging power of EES at time t; ${\eta }_{\mathrm{ch}}^{\mathrm{e}}$, ${\eta }_{\mathrm{dis}}^{\mathrm{e}}$ is the charging and discharging efficiency of EES; $P_{\mathrm{ch}}^{\mathrm{h}}(t)$, $P_{\mathrm{dis}}^{\mathrm{h}}(t)$ are the charging and discharging power of TES at time t; ${\eta }_{\mathrm{ch}}^{\mathrm{h}}$, ${\eta }_{\mathrm{dis}}^{\mathrm{h}}$ are the charging and discharging efficiency of TES; $P_{\mathrm{ch}}^{\mathrm{g}}(t)$, $P_{\mathrm{dis}}^{\mathrm{g}}(t)$ is the charging and discharging power of GES at time t; ${\eta }_{\mathrm{ch}}^{\mathrm{g}}$, ${\eta }_{\mathrm{dis}}^{\mathrm{g}}$ are the charging and discharging efficiency of GES; H_CVNG is the low calorific value of natural gas. The energy storage model can be expressed as:

$$\left[\begin{array}{l}{S}_{\mathrm{e}}(t)\\ S_{\mathrm{h}}(t)\\ S_{\mathrm{g}}(t)\end{array}\right]=-\left[\begin{array}{l}{P}_{\mathrm{ch}}^{\mathrm{e}}(t)\\ P_{\mathrm{ch}}^{\mathrm{h}}(t)\\ P_{\mathrm{ch}}^{\mathrm{g}}(t)\end{array}\right]+\left[\begin{array}{l}{P}_{\mathrm{dis}}^{\mathrm{e}}(t)\\ P_{\mathrm{dis}}^{\mathrm{h}}(t)\\ P_{\mathrm{dis}}^{\mathrm{g}}(t)\end{array}\right]$$

(12)

$$\mathit{S}=-{\mathit{P}}_{\mathrm{ch}}+{\mathit{P}}_{\mathrm{dis}}$$

(13)

where $S_{\mathrm{e}}(t)$, $S_{\mathrm{h}}(t)$, $S_{\mathrm{g}}(t)$ are the power of EES, TES and GES at time t, respectively; $\mathit{S}$, ${\mathit{P}}_{\mathrm{ch}}$, ${\mathit{P}}_{\mathrm{dis}}$ is the storage matrix, charging matrix and discharging matrix, respectively.

2.4. Conversion Model

In the conversion side, there is energy conversion equipment such as, MT and GB, which play the role of connecting supply and demand sides. In summary, combining the supply model, the conversion model, the storage model and the load model, the energy relationship in the RIES can be expressed by a matrix:

$$\mathit{L}+{\mathit{P}}_{\mathrm{P}2\mathrm{G},\mathrm{EB}}=\mathit{C}({\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}})-{\mathit{P}}_{\mathrm{ch}}+{\mathit{P}}_{\mathrm{dis}}$$

(14)

$$where\mathit{C}=\left[\begin{array}{cc}1& {\lambda }_1(t){\eta }_{\mathrm{MT}}\\ 0& {\lambda }_2(t){\eta }_{\mathrm{GB}}+{\lambda }_1(t)(1-{\eta }_{\mathrm{MT}}-{\eta }_{\mathrm{L}}){\eta }_{\mathrm{r}}{C}_{\mathrm{O}}\\ 0& {\lambda }_3(t)\end{array}\right]$$

(15)

where λ₁(t), λ₂(t), λ₃(t) are the distribution coefficient that the input gas power assigned to MT, GB and gas loads, respectively, satisfying λ₁(t) + λ₂(t) + λ₃(t) = 1; ${\eta }_{\mathrm{MT}}$, ${\eta }_{\mathrm{L}}$ are the efficiency and heat loss rates of MT; $C_{\mathrm{O}}$, ${\eta }_{\mathrm{r}}$ is the heating coefficient and smoke recovery rate of BC; ${\eta }_{\mathrm{GB}}$ is the efficiency of GB; $\mathit{C}$ is the conversion matrix.

For different types of RIES, the equipment contained inside may be different. The above matrix can be modified according to the type of RIES. For example, if the RIES contains no energy storage systems, then the matrix is:

$$\mathit{L}+{\mathit{P}}_{\mathrm{P}2\mathrm{G},\mathrm{EB}}=\mathit{C}({\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}})$$

(16)

If there are no P2G, EB and no energy storage systems, the model can be expressed as:

$$\mathit{L}=\mathit{C}({\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}})$$

(17)

To summarize, the RIES is represented through a linear model in this paper, which can reduce repetitive modeling time and increase efficiency when the RIES structure is changed.

3. The Configuration Optimization Model of Energy Storage Systems

Energy storage systems are divided into EES, TES and GES. The configuration of energy storage systems includes power and capacity configuration. EES includes storage batteries, converters and other equipment, so the investment cost is settled in two forms—power and capacity. TES includes a heat storage tank and thermal conductive material, therefore the investment cost is also settled in the form of power and capacity, and so is GES.

The allocation of energy storage systems affects the investment cost of energy storage systems, the operation cost and the new energy (wind power, photovoltaic power) consumption rate of the RIES. The configuration of energy storage systems with lower capacity cannot achieve the expected economy and stability of the system, and cannot effectively reduce operating costs, while may cause part of a new energy abandoned at the same time. The configuration of energy storage systems with higher capacity has higher investment costs, and the overall maintenance costs are relatively high. Therefore, the optimal configuration of energy storage system can achieve a balance among investment costs, operation costs and new energy consumption rates, which means the choice of the energy storage system configuration that makes the total cost of the system reach the minimum.

3.1. The Objective Function

As the energy storage system planning problem interacts with its operating problem, the operational strategy should be considered in the configuration optimization model to guide the planning of the RIES. For this reason, the energy storage system planning and operation optimization are combined in this paper, and the model that aims at the optimal economics of the RIES is also established. The objective function is the minimum of the sum of energy storage configuration costs and daily operating costs of the RIES. The configuration costs contain the capacity configuration cost and power configuration cost. The operating costs include unit start-stop costs, maintenance costs, penalty costs and so forth.

$$\begin{array}{ll}\min f& =C_{\mathrm{inv}}(E_{\mathrm{s}}^i,P_{\mathrm{s}}^i)+C_{\mathrm{op}}(P_y,P_{\mathrm{s}},P_l)\\ & =C_{\mathrm{inv}}+{\displaystyle \sum _{t=1}^T[C_{\mathrm{buy}}(t)+C_{\mathrm{st}}(t)+}{C}_{\mathrm{mt}}(t)+C_{\mathrm{cut}}(t)]\Delta t\end{array}$$

(18)

$$C_{\mathrm{inv}}={\displaystyle \sum _i^{}\{(C_{\mathrm{E}}^i}{E}_{\mathrm{s}}^i+C_{\mathrm{P}}^i{P}_{\mathrm{s}}^i)\frac{r_0{(1+r_0)}^{Y_i}}{365[{(1+r_0)}^{Y_i}-1]}\}$$

(19)

$$C_{\mathrm{buy}}(t)=u{C}_{\mathrm{e}}{P}_{\mathrm{e}}^{\mathrm{net}}(t)+C_{\mathrm{g}}{P}_{\mathrm{g}}^{\mathrm{net}}(t)+\epsilon C_{{\mathrm{CO}}_2}{P}_{\mathrm{P}2\mathrm{G}}(t){\eta }_{\mathrm{P}2\mathrm{G}}$$

(20)

$$\begin{array}{ll}{C}_{\mathrm{st}}(t)=& \max \{0,U_{\mathrm{EB}}(t)-U_{\mathrm{EB}}(t-1)\}{C}_{\mathrm{st},\mathrm{EB}}+\max \{0,U_{\mathrm{MT}}(t)-U_{\mathrm{MT}}(t-1)\}{C}_{\mathrm{st},\mathrm{MT}}\\ & +\max \{0,U_{\mathrm{GB}}(t)-U_{\mathrm{GB}}(t-1)\}{C}_{\mathrm{st},\mathrm{GB}}\end{array}$$

(21)

$$\begin{array}{l}{C}_{\mathrm{mt}}(t)=C_{\mathrm{PV}}{P}_{\mathrm{PV}}(t)+C_{\mathrm{WT}}{P}_{\mathrm{WT}}(t)+C_{\mathrm{MT}}{P}_{\mathrm{MT}}(t)+C_{GB}{P}_{GB}(t)\\ +C_{\mathrm{EB}}{P}_{\mathrm{EB}}(t)+C_{\mathrm{P}2\mathrm{G}}{P}_{\mathrm{P}2\mathrm{G}}(t)+{\displaystyle \sum _i{C}_S^i}\left|P_{\mathrm{ch}}^i(t)-P_{\mathrm{dis}}^i(t)\right|\end{array}$$

(22)

$$C_{\mathrm{cut}}(t)=C_{\mathrm{cut}}{P}_{\mathrm{cut}}(t)$$

(23)

where the subscript y, s, l represents the source, storage and load, respectively; the subscript i represents the type of energy storage system (EES, TES, GES); $C_{\mathrm{inv}}$ is the daily average allocation cost over the life cycle; $C_{\mathrm{buy}}(t)$ is the purchase cost including the interaction cost with the grid and natural gas network, CO₂ material costs; $C_{\mathrm{st}}(t)$, $C_{\mathrm{mt}}(t)$, $C_{\mathrm{cut}}(t)$ are the start-stop cost, maintenance cost and abandonment cost, respectively; T is the total number of daily scheduling periods, and Δt is the unit scheduling time; $C_{\mathrm{e}}$, $C_{\mathrm{g}}$ are the electricity and natural gas prices; ε, $C_{{\mathrm{CO}}_2}$ is the CO₂ coefficient required to generate unit natural gas and the CO₂ price; $C_{\mathrm{st},\mathrm{EB}}$, $C_{\mathrm{st},\mathrm{MT}}$, $C_{\mathrm{st},\mathrm{GB}}$ is the EB, MT, GB start-up costs respectively; U_EB(t), U_MT(t), U_GB(t) are the EB, MT, GB start and stop status at time t respectively; $C_{\mathrm{MT}}$, $C_{\mathrm{PV}}$, $C_{\mathrm{WT}}$, $C_{GB}$, $C_{\mathrm{EB}}$, $C_{\mathrm{P}2\mathrm{G}}$, $C_S^i$ are the unit power maintenance costs of MT, PV, WT, GB, EB, P2G, energy storage systems respectively; $C_{\mathrm{cut}}$ is the unit abandonment cost of PV and WT.

3.2. The Constraints

3.2.1. Power Balance Constraint

The energy relationship in the RIES is expressed in Equation (15), including electric power balance, thermal power balance and gas power balance. The specific power balance constraint is:

$$P_{\mathrm{g}}^{\mathrm{net}}(t)+{\eta }_{\mathrm{P}2\mathrm{G}}{P}_{\mathrm{P}2\mathrm{G}}(t)+P_{\mathrm{dis}}^{\mathrm{g}}(t)-P_{\mathrm{MT}}(t)/{\eta }_{\mathrm{MT}}-P_{\mathrm{GB}}(t)/{\eta }_{\mathrm{GB}}-P_{\mathrm{ch}}^{\mathrm{g}}(t)-L_{\mathrm{g}}(t)=0$$

(24)

$$u{P}_{\mathrm{e}}^{\mathrm{net}}(t)+P_{\mathrm{PV}}(t)+P_{\mathrm{WT}}(t)+P_{\mathrm{MT}}(t)+P_{\mathrm{dis}}^{\mathrm{e}}(t)-P_{\mathrm{ch}}^{\mathrm{e}}(t)-P_{\mathrm{P}2\mathrm{G}}(t)-P_{\mathrm{EB}}(t)-L_{\mathrm{e}}(t)=0$$

(25)

$$P_{\mathrm{MT}}(t)(1-{\eta }_{\mathrm{MT}}-{\eta }_{\mathrm{L}}){\eta }_{\mathrm{r}}{C}_{\mathrm{O}}/{\eta }_{\mathrm{MT}}+P_{\mathrm{EB}}(t){\eta }_{\mathrm{EB}}+P_{\mathrm{GB}}(t){\eta }_{\mathrm{GB}}+P_{\mathrm{dis}}^{\mathrm{h}}(t)-P_{\mathrm{ch}}^{\mathrm{h}}(t)-L_{\mathrm{h}}(t)=0$$

(26)

where $P_{\mathrm{MT}}(t)$, $P_{\mathrm{GB}}(t)$ are the output powers of MT and GB at time t, respectively.

3.2.2. Interactive Power Constraint

Considering the requirements of the energy coupling system (gas distribution-distribution network) for the RIES, the exchange power of the RIES and the energy coupling system needs to be maintained within a certain range:

$$P_{\mathrm{emin}}^{\mathrm{net}}\le P_{\mathrm{e}}^{\mathrm{net}}(t)\le P_{\mathrm{emax}}^{\mathrm{net}}$$

(27)

$$P_{\mathrm{gmin}}^{\mathrm{net}}\le P_{\mathrm{g}}^{\mathrm{net}}(t)\le P_{\mathrm{gmax}}^{\mathrm{net}}$$

(28)

where $P_{\mathrm{emax}}^{\mathrm{net}}$, $P_{\mathrm{emin}}^{\mathrm{net}}$ are the upper and lower limits of the interaction power between the RIES and the distribution network; $P_{\mathrm{gmax}}^{\mathrm{net}}$, $P_{\mathrm{gmin}}^{\mathrm{net}}$ are the upper and lower limits of the interaction power between the RIES and the natural gas network.

3.2.3. Controllable Unit Constraint

The controllable unit including MT, GB, EB and P2G needs to meet the output constraint, which means that the output of these components must be limited to the upper and lower limits. In addition, MT, GB and EB should also meet the unit climbing constraint:

$$a=\{\begin{array}{l}{P}_{\mathrm{MT}\min }\le P_{\mathrm{MT}}(t)\le P_{\mathrm{MT}\max }\\ P_{\mathrm{GB}\min }\le P_{\mathrm{GB}}(t)\le P_{\mathrm{GB}\max }\\ P_{\mathrm{EB}\min }\le P_{\mathrm{EB}}(t)\le P_{\mathrm{EB}\max }\\ P_{\mathrm{P}2\mathrm{G}\min }\le P_{\mathrm{P}2\mathrm{G}}(t)\le P_{\mathrm{P}2\mathrm{G}\max }\end{array}$$

(29)

$$b=\{\begin{array}{l}\Delta P_{\mathrm{MT},\mathrm{down}}\le \Delta P_{\mathrm{MT}}(t)\le \Delta P_{\mathrm{MT},\mathrm{up}}\\ \Delta P_{\mathrm{GB},\mathrm{down}}\le \Delta P_{\mathrm{GB}}(t)\le \Delta P_{\mathrm{GB},\mathrm{up}}\\ \Delta P_{\mathrm{EB},\mathrm{down}}\le P_{\mathrm{EB}}(t)\le \Delta P_{\mathrm{EB},\mathrm{up}}\end{array}$$

(30)

where category a constraint is the output power constraint, $P_{\mathrm{MT}\max }$, $P_{\mathrm{GB}\max }$, $P_{\mathrm{EB}\max }$, $P_{\mathrm{P}2\mathrm{G}\max }$ are the upper limits of MT, GB, EB, P2G power, respectively; $P_{\mathrm{MT}\min }$, $P_{\mathrm{GB}\min }$, $P_{\mathrm{EB}\min }$, $P_{\mathrm{P}2\mathrm{G}\min }$ are the lower limits of MT, GB, EB, P2G power, respectively; category b constraint is a climbing constraint, $\Delta P_{\mathrm{MT},\mathrm{up}}$, $\Delta P_{\mathrm{GB},\mathrm{up}}$, $\Delta P_{\mathrm{EB},\mathrm{up}}$ are the up climbing rates of the MT, GB, EB, respectively; $\Delta P_{\mathrm{MT},\mathrm{down}}$, $\Delta P_{\mathrm{GB},\mathrm{down}}$, $\Delta P_{\mathrm{EB},\mathrm{down}}$ are the down climbing rates of the MT, GB, EB, respectively.

3.2.4. Energy Storage System Constraint

The energy storage installation capacity constraint is:

$$\{\begin{array}{l}{E}_{\mathrm{smin}}^i\le E_{\mathrm{s}}^i\le E_{\mathrm{smax}}^i\\ P_{\mathrm{smin}}^i\le P_{\mathrm{s}}^i\le P_{\mathrm{smax}}^i\end{array}$$

(31)

where $E_{\mathrm{s}}^i$, $P_{\mathrm{s}}^i$ is the rated capacity and rated power of electric, heat and gas energy storage equipment; $E_{\mathrm{smax}}^i$, $E_{\mathrm{smin}}^i$ are the upper and lower limits of installation capacity of electric, heat and gas energy storage equipment; $P_{\mathrm{smax}}^i$, $P_{\mathrm{smin}}^i$ are the upper and lower limits of installation power of electric, heat and gas energy storage equipment. It is mainly limited by technology, cost, etc.

The energy storage equipment capacity constraint is:

$$\{\begin{array}{l}{\xi }_{\min }^{\mathrm{e}}{E}_{\mathrm{s}}^{\mathrm{e}}\le E_{\mathrm{EES}}(t)\le {\xi }_{\max }^{\mathrm{e}}{E}_{\mathrm{s}}^{\mathrm{e}}\\ {\xi }_{\min }^{\mathrm{h}}{E}_{\mathrm{s}}^{\mathrm{h}}\le H_{\mathrm{TES}}(t)\le {\xi }_{\max }^{\mathrm{h}}{E}_{\mathrm{s}}^{\mathrm{h}}\\ {\xi }_{\min }^{\mathrm{g}}{E}_{\mathrm{s}}^{\mathrm{g}}\le G_{\mathrm{GES}}(t)\le {\xi }_{\max }^{\mathrm{g}}{E}_{\mathrm{s}}^{\mathrm{g}}\end{array}$$

(32)

where ${\xi }_{\max }^{\mathrm{e}}$, ${\xi }_{\min }^{\mathrm{e}}$ are the upper and lower limits of the electric storage equipment remaining energy, for the purpose of extending the life of energy storage equipment; ${\xi }_{\max }^{\mathrm{h}}$, ${\xi }_{\min }^{\mathrm{h}}$ are the upper and lower limits of the thermal storage equipment remaining energy; ${\xi }_{\max }^{\mathrm{g}}$, ${\xi }_{\min }^{\mathrm{g}}$ are the upper and lower limits of the gas storage equipment remaining energy. $E_{\mathrm{s}}^{\mathrm{e}}$, $E_{\mathrm{s}}^{\mathrm{h}}$, $E_{\mathrm{s}}^{\mathrm{g}}$ are the rated capacities of EES, TES and GES, respectively.

The energy storage equipment also has charging and discharging power constraints. Considering that the energy storage equipment cannot be charged and discharged at the same time, the constraint is:

$$\{\begin{array}{l}{u}_{\mathrm{ch}}^i(t)P_{\mathrm{s}\min }^i\le P_{\mathrm{ch}}^i(t)\le u_{\mathrm{ch}}^i(t)P_{\mathrm{s}}^i\\ u_{dis}^i(t)P_{\mathrm{s}\min }^i\le P_{\mathrm{dis}}^i(t)\le u_{dis}^i(t)P_{\mathrm{s}}^i\\ u_{\mathrm{ch}}^i(t)+u_{dis}^i(t)\le 1\end{array}$$

(33)

where $P_{\mathrm{s}\min }^i$ is the lower limits of charging and discharging power of electric, heat and gas energy storage equipment; $u_{\mathrm{ch}}^i(t)$, $u_{dis}^i(t)$ are the 0–1 variables, 1 represents that the storage equipment is working at time t, while 0 means that it is not working.

In addition, in order to reserve a certain adjustment margin for the next scheduling period, the energy storage device needs to return to the initial state after a cycle. The constraint is:

$$\{\begin{array}{l}{E}_{\mathrm{EES}}(T)=E_{\mathrm{EES}}(0)\\ H_{\mathrm{TES}}(T)=H_{\mathrm{TES}}(0)\\ G_{\mathrm{GES}}(T)=G_{\mathrm{GES}}(0)\end{array}$$

(34)

where T and 0 indicate the beginning and end of a scheduling period.

3.2.5. Abandoned Wind and Photovoltaic Power Constraint

In order to improve the wind and photovoltaic power consumption rate of the RIES, the abandoned power needs to be maintained within a certain range:

$${\displaystyle \sum _{t=1}^T(2-{\beta }_{\mathrm{WT}}(t)-{\beta }_{\mathrm{PV}}(t))}\le {\beta }_{\mathrm{n}}$$

(35)

where ${\beta }_{\mathrm{n}}$ is the lowest abandonment rate that can be accepted by the RIES.

3.3. The Sensitivity Analysis

The sensitivity of the RIES configuration optimization refers to the sensitivity of the objective function to parameter changes [31]. This paper focuses on the impact of key factors, such as price, etc. Let the parameter matrix be X, then the sensitivity of the objective function f to X is:

$$\mathit{M}=\frac{\frac{\partial f(\mathit{X})}{f}}{\frac{\partial \mathit{X}}{\mathit{X}}}$$

(36)

where,

$$\mathit{X}=[C_{\mathrm{E}}^{\mathrm{e}},C_{\mathrm{P}}^{\mathrm{e}},C_{\mathrm{E}}^{\mathrm{h}},C_{\mathrm{P}}^{\mathrm{h}},C_{\mathrm{E}}^{\mathrm{g}},C_{\mathrm{P}}^{\mathrm{g}},C_{\mathrm{e}},C_{\mathrm{g}},C_{{\mathrm{CO}}_2},P_{\mathrm{P}2\mathrm{G}\max },P_{\mathrm{EB}\max },P_{\mathrm{MT}\max }]$$

(37)

Then there is:

$$\frac{\partial f(\mathit{X})}{f}={\displaystyle \sum _{i=1}^m{m}_i\frac{\partial x_i}{x_i}}$$

(38)

where $x_i$ is the parameter i in X; $m_i$ indicates the sensitivity of the objective function f to $x_i$, its value indicates the influence degree of the $x_i$ on the f.

4. Case Study

4.1. Basic Data

In this paper, the case system in Reference [27] is appropriately modified. The typical winter day was selected for analysis to verify the correctness of the configuration method. The operating parameters of the equipment in the RIES can be found in Reference [27], as shown in

Table 1. The operating parameters of the equipment in the RIES.

Type	Power Lower Limit/(kW)	Power Upper Limit/(kW)	Lower Climbing Rate/(kW·h)	Upper Climbing Rate/(kW·h)	Unit Maintenance Cost/(yuan/kW)
MT	40	180	5	15	0.025
EB	0	120	12	12	0.016
GB	0	120	11	11	0.012
P2G	0	120	-	-	0.021
WT	0	400	-	-	0.0196
PV	0	250	-	-	0.0235

. The decision vector parameters of the energy storage systems can be found in Reference [25] and [27], as shown in

Table 2. The decision vector parameters.

Type	Efficiency	Self-Release Rate	Unit Capacity Cost/(yuan/kW·h)	Unit Power Cost/(yuan/kW)	Unit Maintenance Cost/(yuan/kW)	Life/(year)
EES	0.9	0.001	1000	200	0.0018	10
TES	0.88	0.01	150	30	0.0017	10
GES	0.9	0.1	130	300	0.0015	20

. Other parameters for the case study are shown in

Table 3. The parameters for the case study.

Parameter	Value	Remarks	Parameter	Value	Remarks
${\eta }_{\mathrm{MT}}$	0.35	[27]	${\eta }_{\mathrm{P}2\mathrm{G}}$	0.7	[10]
${\eta }_{\mathrm{L}}$	15%	-	$C_{\mathrm{st},\mathrm{EB}}$	2.7 (yuan/kW)	[27]
${\eta }_{\mathrm{r}}$	0.9	-	$C_{\mathrm{st},\mathrm{MT}}$	1.94 (yuan/kW)	-
$C_{\mathrm{O}}$	1.2	[21]	$C_{\mathrm{st},\mathrm{GB}}$	2.1 (yuan/kW)	-
${\eta }_{\mathrm{GB}}$	0.9	[10]	${\eta }_{EB}$	0.95	-

.

The time of use (TOU) power price [16] and nature gas price [10] are shown in Figure 2a. The wind and photovoltaic forecasted power [27] are shown in Figure 2b, and the wind turbine has anti-peak characteristics. As shown in Figure 1, the heat demand for users was met by the supply side and the load side (electric heating equipment). The total air conditioning heat pump power for users was 100 kW and the total water heater power was 50 kW. The load forecasting curve [27] is shown in Figure 3. It can be seen from Figure 3 that the peak of the aggregated demand (after-diversity maximum demand) was much lower than the sum of individual load peaks.

The Gurobi Optimizer [32] is a state-of-the-art solver for mathematical programming. The solvers in the Gurobi Optimizer were designed from the ground up to exploit modern architectures and multi-core processors, using the most advanced implementations of the latest algorithms. It includes the following solvers: Linear programming solver (LP); mixed-integer linear programming solver (MILP); mixed-integer quadratic programming solver (MIQP); etc. The configuration optimization model proposed in this paper belongs to the MILP problem. In the Matlab software, the Yalmip toolbox was used to model the model, and the Gurobi solver was called to solve the model. The test platform solved by this model was: Intel Core i7-4710HQ 2.5 GHz CPU (Intel, Santa Clara, CA, USA); 16 GB memory (DDR3, Kingston, CA, USA); software version: Matlab R2016b (The MathWorks, Inc, Natick, MA, USA); Yalmip R20180926; Gurobi 8.1 (Gurobi Optimization, Beaverton, OR, USA).

4.2. Results and Analysis

4.2.1. Impact of Energy Storage Equipment and Electric Energy Substitution on RIES

In order to compare and analyze the effect of the energy storage equipment on the RIES and the impact of electric energy substitution on energy storage system configuration, the following three scenarios are set.

Scenario 1: The RIES contains no energy storage systems;

Scenario 2: The RIES contains no P2G and EB (no electric energy substitution strategy);

Scenario 3: The RIES contains energy storage systems, P2G and EB.

As can be seen from the above analysis in Section 2, the power balance equation in each scenario can be described as:

Scenario 1: $\mathit{L}+{\mathit{P}}_{\mathrm{P}2\mathrm{G},\mathrm{EB}}=\mathit{C}({\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}})$;

Scenario 2: $\mathit{L}=\mathit{C}({\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}})-{\mathit{P}}_{\mathrm{ch}}+{\mathit{P}}_{\mathrm{dis}}$;

Scenario 3: $\mathit{L}+{\mathit{P}}_{\mathrm{P}2\mathrm{G},\mathrm{EB}}=\mathit{C}({\mathit{P}}^{\mathrm{net}}+{\mathit{P}}_{\mathrm{WT},\mathrm{PV}})-{\mathit{P}}_{\mathrm{ch}}+{\mathit{P}}_{\mathrm{dis}}$.

In this paper, the Yalmip toolbox was used to model the model, and the Gurobi solver was called to solve the model. Before Gurobi starts to solve the problem, there is a pre-solve process for the model This process is a branch and bound process in which the solution search space of this model is greatly reduced. Solution results were as follows: Yalmip modeling time was 1.7064s, iteration number was 25, and solution time was 0.2006s. The configuration results solved by Gurobi in both off-grid mode and grid-connected mode are shown in

Table 4. The configuration results.

		EES		TES		GES
		C1/kW·h	P2/kW	C/kW·h	P/kW	C/kW·h	P/kW
Off-grid	Scen.31	-	-	-	-	-	-
	Scen.2	363.58	125.84	484.77	86.85	121.45	53.56
	Scen.3	284.70	96.49	145.98	37.8	80.1	33.96
Grid-connected	Scen.1	-	-	-	-	-	-
	Scen.2	109.04	47.14	189.47	76.25	63.1	21.2
	Scen.3	68.07	37.01	86.17	35.98	30.5	12.6

¹ Capacity; ² Power; ³ Scenario.

. The costs of the RIES in different scenarios are shown in

Table 5. The costs of the RIES in different scenarios.

		Cinv/yuan	Cop/yuan	Total Costs/yuan	Power Costs1/yuan	Gas Costs2/yuan	β/%
Off-grid	Scen.31	0	2902.48	2902.48	0	2062.15	4.02
	Scen.2	193.53	4291.84	4485.38	0	2840.41	32.39
	Scen.3	98.20	2356.04	2454.24	0	1976.16	0
Grid-connected	Scen.1	0	2379.06	2379.06	−524.6	2469.4	0
	Scen.2	59.77	2625.06	2711	−600.4	2830.08	5.2
	Scen.3	41.29	2129.42	2170.71	−516.6	2427.7	0

¹ Interaction costs with the grid; ² Interaction costs with the gas network; ³ Scenario.

.

As shown in Table 4 and Table 5, in the off-grid mode, the electric-gas-thermal energy storage systems were added in scenario 3 compared with scenario 1. Although the energy storage configuration cost was added, the system operation cost was greatly reduced. The total costs were reduced from 2902 yuan in scenario 1 to 2454 yuan in scenario 3, down 15.4%, while the cost of purchasing natural gas decreased by 4%, and the rate of abandoned wind power reduced from 4.02% to 0. A similar conclusion can be drawn in the grid-connected mode. The results of comparing scene 2 with scene 1 illustrates the conclusion that the energy storage systems can improve the economic benefits of the RIES.

As shown in Table 4 and Table 5, in the off-grid mode, there were no P2G or EB devices in scenario 2 compared with scenario 3, where lot of wind power was abandoned. Due to the electric energy substitution strategy in scenario 3, where the surplus electricity was converted into natural gas and heat by P2G and EB equipment during the period of abandoning wind power, the costs of abandoned wind power was thus reduced. Moreover, the total costs were reduced by 45.3% compared with scenario 2, with a 30.4% reduction in the cost of purchasing natural gas, and the cost of energy storage configuration was also reduced. The conclusion that the P2G and EB equipment can reduce energy storage systems configuration costs and significantly improve the economics of the RIES has been obviously drawn according to the results of comparing scene 3 with scene 2. Similar results can be obtained in the grid-connected mode, therefore, it will not be repeated again. It is noted that the interaction power with the grid plays a key role in energy storage configuration in the grid-connected mode, the conclusion obtained above may be different in the grid-connected mode, which has been analyzed in detail below. For further discussion, the electricity, gas and heat output of each device in scene 3 under both off-grid and grid-connected modes are shown in the Figure 4.

As shown in Figure 3 and Figure 4, the wind power was high but the electric load demand was low during 1–7 h in the evening. During this period, the space for the system to accept wind power could not be improved even though the MT was working with minimum power, causing lot of wind power to be abandoned in scenario 2. P2G and EB equipment were added in scenario 3. During the abandonment period, P2G and EB works were equivalent to increasing the electric load. At the same time, the surplus electric energy was converted into natural gas and heat energy respectively, and the remaining electric energy was stored by the battery for discharging when the electric demand was high. P2G only works when the wind power is high, and P2G turns off when the electric load demand is high in the day, while EB works all day because of the heat load demand, and its output force follows the change of heat load value. As the abandoned wind power was consumed by P2G and EB, the system abandonment rate reduced from 32% to 0. At the same time, the cost of purchasing natural gas from the external gas network reduced because part of the natural gas needed by the RIES was produced by the P2G, while EB heat production reduced the output of CHP and optimized the operation of the system. The cost was significantly reduced, and the storage system configuration capacity was also significantly reduced.

Comparing Figure 4a with Figure 4b, it can be seen that interaction power with the grid played a key role in the grid-connected mode. In the abandonment period, the system sells surplus wind power to the grid more since selling electricity is obviously more economic than opening P2G. Therefore, P2G does not work, and the output of EB has also decreased, which is different from the off-grid mode. There was no significant difference between the heat output and the gas output of equipment in the grid-connected mode compared with the off-grid mode. Due to the existence of interactive power with the power grid, the overall benefit of the system in the grid-connected mode was better than the off-grid mode, and the energy storage configuration capacity was also reduced.

4.2.2. Economic Analysis in Different Energy Storage Modes

In order to compare and analyze the economics of the RIES under different energy storage modes, this paper divides the energy storage mode into the following three types:

Type 1: Single energy storage mode (EES, TES, GES);

Type 2: Dual energy storage mode (EES-TES, EES-GES, TES-GES);

Type 3: Integrated energy storage mode (EES-TES-GES).

The costs of the RIES in different types under the grid-connected mode are shown in

Table 6. The costs of the RIES in different types under the grid-connected mode.

Type	Cinv/yuan	Gas Costs1/yuan	Power Costs2/yuan	Cop/yuan	Total Costs/yuan
EES	35.48	2428.6	−501	2195.06	2230.5
TES	4.44	2449.2	−490.2	2254.10	2258.5
GES	3.15	2428.1	−468	2310.54	2313.6
EES-TES	37.25	2428.0	−510.4	2150.03	2187.2
EES-GES	31.2	2428.9	−503	2185.42	2216.6
TES-GES	7.45	2428.3	−485	2236.21	2243.6
EES-TES-GES	41.29	2427.7	−516.6	2129.42	2170.71

¹ Interaction costs with the gas network; ² Interaction costs with the grid.

.

As shown in Table 6, for the single energy storage mode, although configuration cost was higher for the EES mode, the system operating cost was the lowest at this time, and the interaction profit with the grid was the largest, so the total cost was the lowest compared with the TES and the GES mode. It shows that the electric energy is stored directly in the power storage system and is transferred to the peak of power consumption, which has better economics than converting into heat and gas energy. The total costs of configuring the dual energy storage were lower than the single energy storage mode. Furthermore, the configuration of EES-TES was the most economical solution. The configuration scheme that the system adopts, the EES-TES-GES integrated energy storage, has the optimal economy compared with the other two types of schemes. However, the energy storage configuration cost increased, and the operating cost was the lowest, and the interaction benefit with the grid was the highest. To further illustrate, the output of each energy storage device in the EES-TES-GES integrated energy storage mode is shown in Figure 5.

It can be seen from Figure 5, when the wind power was high, the system preferentially sells electricity to the grid, and the remaining electric energy was stored by the electric energy storage. The EES can release the electric energy stored to reduce the power generation costs and gas purchase costs of the MT during the peak of the electric load consumption. The EES plays a role in peak shaving. At 19–24 h and 1–5 h, the TES output increased due to the high heat load. During the daytime, the heat load is relatively stable and the electric load demand increases, the TES can store the heat energy produced by MT and other equipment. The GES mainly supplies/stores gas according to the value of the gas load. During the 1–5 h abandonment period, P2G consumed electric energy to generate natural gas. At this time, the gas load is small, the GES can store natural gas, so the purchased natural gas is reduced. GES supply gas during the peak of gas consumption in the daytime. In summary, under the integrated energy storage mode, each storage energy worked mostly in the peak period of the corresponding load demand, indicating that the energy storage was optimized according to the load change under the premise of satisfying the system load, so that the system economy was optimal.

4.3. Sensitivity Analysis

According to the Equation (36) and the parameter matrix X, the sensitivity analysis of the main factors of the energy storage configuration in the off-grid and the grid-connected mode was analyzed. The quantified sensitivity factor results are shown in Figure 6.

Where the positive value of the sensitivity factor was a positive factor, indicating that the total cost of the system configuration decreased with the increase of the factor, and the negative value of the sensitivity was negative. The magnitude of its absolute value indicates the degree of influence on the objective function. The larger the absolute value, the greater the influence on the objective function. As shown in Figure 6, in both off-grid and grid-connected mode, the energy storage configuration unit capacity and power price are all important factors affecting the total cost. Among them, the EES price had the greatest impact, so it is of great practical significance to optimize the energy storage system. In the off-grid mode, the capacity of P2G and EB is an important positive factor. Since the interaction power with the grid plays a key role in the system operation, the upper limit of the interactive power with the grid is an important positive factor in the grid-connected mode. It can be seen that planning of the RIES and optimizing the capacity of each device play an important role in improving the economics of the system.

5. Discussion

The configuration model of electric-gas-thermal energy storage system proposed in this paper can be used to determine the optimal configuration scheme of electric-gas-thermal energy storage equipment of the RIES and the optimal operating strategy of the system. Compared with the configuration model proposed in Reference [16,20,26], the configuration model proposed in this paper can deal with the allocation of gas energy storage systems, and not only the allocation of electric and thermal energy storage systems. Moreover, the configuration model can also determine the optimal configuration scheme of the RIES operating both on off-grid mode and grid-connected mode, compared with the model and method proposed in Reference [27]. In addition, the RIES was firstly divided into the energy supply, conversion, storage and output side, and was thus better modeled because the method reduced repetitive modeling time and increased efficiency when the RIES structure was changed. In the above References, the gas load was ignored while the model proposed in this paper made the electric, heat and gas load be the terminal load in the demand side, better considering the coupling relationship among electric, heat and gas. The load model proposed in this paper considered the differences between the individual and aggregate demand. This is more realistic. However, the model is relatively simple, while the thermal and gas systems are dynamic with pressure, temperature and other technical parameters that were entirely neglected in the paper. The theory of how gas demand is affected by the electric heating supply was also neglected in this paper.

6. Conclusions

The structure of the RIES with electrical thermal load as the terminal load was first established in this paper, and the system was modeled from four parts: Energy supply, conversion, storage and load. Then, by combining the configuration and operation, an electric-gas-thermal multi-energy storage optimization configuration mixed integer model was established, which was solved by Gurobi. Finally, an example was given to analyze the effects of different energy storage modes and electric energy substitution on the energy storage configuration of the RIES in both off-grid and grid-connected modes, and the sensitivity analysis was carried out. The conclusions were drawn as follows:

(1) The energy storage system can reduce the cost of the RIES, in which the electricity-gas-heat integrated energy storage has the optimal economy;

(2) P2G and EB equipment (that is, electric energy substitution), can greatly reduce the abandon rate of wind and operating costs of the RIES in the off-grid mode. Among them, since the interaction power with the grid plays a key role in the grid-connected mode, the result of electric energy substitution is second to the off-grid mode.

(3) The energy storage installation cost is a key negative factor that limits energy storage configuration. Equipment capacity, such as P2G and EB, is a positive factor in improving the economics of energy storage configuration.

Proper planning of integrated energy systems and optimization of the capacity of important equipment in the system are the next research directions.