Research on Industrial and Commercial User-Side Energy Storage Planning Considering Uncertainty and Multi-Market Joint Operation

Abstract

With the continuous development of the Energy Internet, the demand for distributed energy storage is increasing. However, industrial and commercial users consume a large amount of electricity and have high requirements for energy quality; therefore, it is necessary to configure distributed energy storage. Based on this, a planning model of industrial and commercial user-side energy storage considering uncertainty and multi-market joint operation is proposed. Firstly, the total cost of the user-side energy storage system in the whole life cycle is taken as the upper-layer objective function, including investment cost, operation, and maintenance cost. The lower layer takes the economy and environment of energy storage operation as the goal, and considers the ancillary service market revenue, demand response constraints, and operational constraints. Secondly, considering the uncertainty of the power market price, and based on the robust optimization theory, the robust transformation is carried out to effectively deal with the impact of uncertain variables on the system operation. Finally, the model is verified in a typical IEEE 30-node system. The results show that the uncertainty of renewable energy will affect the optimal location and capacity of energy storage. From the results of energy storage location, energy storage will be configured in the important transmission nodes and renewable energy power generation access nodes in the power system.

1. Introduction

In the 21st century, energy and environmental pollution have become the global focus. Building an environmentally friendly and sustainable human society has become a global consensus. Many countries have put forward requirements for the transformation and upgrading of the energy industry [1]. The Energy Internet is an effective way to increase the proportion of renewable energy generation on the premise of ensuring the possibility of services [2]. Energy Internet refers to a modern comprehensive energy system with the power system as the core and integrating natural gas, transportation, heat, and other networks [3]. Energy storage, as a “buffer” between the uncertainty of power generation and the disorder of load use in the Energy Internet, is its key supporting technology. Unlike the large-scale centralized energy storage on the power supply side and the grid side, distributed energy storage is usually installed on the user side or in the microgrid. It can be used to cope with the peak load regulation of new energy access, store excess renewable energy, or modify the user load curve to reduce electricity consumption [4]. Industrial and commercial users consume large amounts of electricity and have high requirements for a stable power supply. Therefore, it is necessary to encourage industrial and commercial users to arrange energy storage, and how to make reasonable planning is the main problem.

At present, scholars have conducted a lot of research on energy storage planning issues. The problem that only the profit or cost of the energy storage planning scheme is considered and other economic standards are not considered. Li N et al. [5] propose a new hybrid multi-criteria decision-making method, which combines the Bayesian best worst method, entropy weight method, and gray cumulative prospect theory to select the optimal energy storage planning scheme considering multiple economic criteria. Xu T et al. [6] propose a two-stage heuristic planning strategy, which considers the economic operation and life of the distributed energy storage system to determine the optimal location and scale of energy storage in the distribution system. Dang Q et al. [7] provide a planning strategy to use the electric vehicle (EV) fleet as energy storage equipment to reduce and save additional battery pack investment in the community microgrid. Wang C et al. [8] propose a two-level nested distributed energy storage planning model to solve the serious voltage quality problem caused by the mismatch between residential load and distributed photovoltaic output.

With the further development of energy storage technology, the energy storage configuration ratio on the user side gradually increases. For the planning of the energy storage system on the user side, the main problems are: Li D et al. [9] consider the annual comprehensive cost of installing the energy storage system and the daily electricity charge of users and establish a two-level optimization model. The external model optimizes the photovoltaic and energy storage capacity, and the internal model optimizes the operation strategy of energy storage. Chen S et al. [10] propose an expansion planning model of integrated power generation and user-end energy storage system, and the expansion and operation of the energy storage system are based on the goal of reducing the total cost of the power system. Based on the maximum demand control on the user side, Zhang H et al. [11] propose a two-level optimal allocation model of energy storage on the user side considering the synergy of load response resources and energy storage. Based on the user’s initiative in using energy, Ye P et al. [12] classify the user energy interconnection system and analyze the configuration of the user-side energy storage system from the perspective of planning according to the “source network load” structure. Wu Y et al. [13] establish a three-stage multi-criteria decision-making framework in an uncertain environment and focus on the optimal planning of various energy storage equipment considering 13 grid demand scenarios. The results show that the optimal planning changes with the change in the power grid demand scenario. Ma M et al. [14] propose a two-level model to optimize the capacity of shared energy storage on the user side in hybrid renewable power generation systems.

In the planning of an energy storage system, it is often necessary to deal with the uncertainties involved. Yu J et al. [15] describe the energy storage planning problem as a two-stage stochastic programming model and use five different scenario-generation methods to illustrate the applicability of this method. Hemmati R et al. [16] propose an optimal planning and scheduling method of energy storage systems for congestion management of power systems including renewable energy and use stochastic optimization to solve the uncertainty problems in the system. Alharbi H et al. [17] propose a new stochastic programming framework, which uses a new representation of the energy graph of the energy storage system to determine the best battery energy storage system capacity and installation year in the microgrid. Nazari A et al. [18] analyze the cost benefit of energy storage to evaluate and quantify the benefits of installing energy storage systems in a typical microgrid, and define a two-stage stochastic programming model to solve the probabilistic properties of parameters. Zhao X et al. [19] propose a two-stage stochastic planning model for energy storage systems, and consider the auxiliary service income of energy storage degradation and frequency regulation. The model considers the uncertainty of load demand and electricity price. The Gaussian mixture model is used to characterize these uncertainties, and a group of representative scenes is sampled. Flores-Quiroz A et al. [20] propose a comprehensive generation, transmission, and storage planning model considering short-term constraints and long-term uncertainty, and use scenario trees to represent long-term uncertainty.

According to the above literature analysis, the existing research deficiencies are mainly reflected in the following two aspects: Firstly, in the energy storage planning of the user side, only the charging and discharging conditions of participating in the energy market are considered, and other markets are not involved. However, with the development of energy storage technology, especially the application of electrochemical energy storage, it has the ability to further participate in ancillary services and other market operations. Secondly, in energy storage planning, stochastic optimization is often used to deal with uncertain factors. However, under the limited historical data, it is impossible to accurately obtain the true probability distribution of uncertainty factors. In addition, with the increase in scenes, the calculation difficulty of the model will increase, and even the model cannot be solved.

The main contributions of this paper are listed as follows:

(1)

A multi-market joint energy storage planning framework considering the energy market and ancillary service market is proposed. Considering the economic benefits of industrial and commercial user-side energy storage in the whole life cycle as the objective function, a double-layer programming decision-making model is constructed. Thus, different time scale problems can be solved in the upper and lower layers, respectively.

(2)

Considering the uncertainty of electricity market price, a robust optimization model is introduced. When constructing uncertain sets, the conservatism of the results of robust optimization is effectively reduced by adding budget parameters. Using dual theory, it is transformed into a mixed-integer linear programming problem that is easy to solve.

The rest of this paper is organized as follows: In Section 2 and Section 3, the planning model of energy storage on the industrial and commercial user side is constructed, and its robust transformation is carried out. A system simulation is performed in Section 4, and some main conclusions are presented in Section 5.

2. Construction of Energy Storage Planning Model on the Industrial and Commercial User Side

When planning the industrial and commercial user-side energy storage (ICUS-ES) system, it is necessary to comprehensively consider the economy and environment of the system. Thus, it can ensure that the planning results of industrial and commercial user-side energy storage are more in line with the actual situation. Based on this, this section will also synergistically optimize the configuration and operation of energy storage on the industrial and commercial user sides with the help of the double-layer optimization structure.

Among them, the upper-layer model mainly involves the fixed costs of the configuration of ICUS-ES. This layer takes the construction location and capacity of energy storage as decision variables. In the lower-layer model, the economic and environmental performance of ICUS-ES is the goal, and it participates in the electric power market and ancillary service market at the same time. This layer takes the charging and discharging strategy of energy storage and the upper-level interactive power as decision variables. That is, the upper-layer model provides the location and capacity configuration data of ICUS-ES for the operation of the lower-layer model, and the operation results of the lower layer will be fed back to the upper-layer model, such as the charging and discharging strategy of energy storage and the interactive power with the utility grid.

2.1. Objective Function of the ICUS-ES System

2.1.1. Objective Function of the Upper-Layer Model

The cost $C_{es}^{ic}$ of the ICUS-ES system mainly includes the initial investment cost $C_{inv}^{ic}$, annual operation and maintenance cost $C_{mo}^{ic}$, energy consumption cost $C_{em}^{ic}$, replacement cost $C_r^{ic}$, and decommissioning disposal cost $C_{de}^{ic}$. Therefore, the cost function of energy storage on the industrial and commercial user side is as follows.

$$C_{es}^{ic}=C_{inv}^{ic}+C_{mo}^{ic}+C_r^{ic}+C_{em}^{ic}+C_{de}^{ic}$$

(1)

According to the actual situation of the energy storage equipment, the life of the ICUS-ES is $L_{ic}$, the benchmark discount rate is i_0, and it is updated and replaced l times in the life cycle $L_{ic}$. Next, the specific costs of each stage within the ICUS-ES’s life cycle will be analyzed.

(1) The initial investment cost

The initial investment cost of the ICUS-ES is mainly directly related to the capacity and power of the energy storage equipment, and its expression is: According to the actual situation of the energy storage equipment, the life of the ICUS-ES is $L_{ic}$, the benchmark discount rate is $i_0$, and it is updated and replaced $l$ times in the life cycle $L_{ic}$. Next, the specific costs of each stage within the ICUS-ES’s life cycle will be analyzed.

$$C_{inv}^{ic}=\left(c_{e,ic}{E}_{ic}+c_{p,ic}{P}_{ic}\right)\frac{i_0{\left(1+i_0\right)}^{L_{ic}}}{{\left(1+i_0\right)}^{L_{ic}}-1}$$

(2)

where $c_{e,ic}$ represents the cost investment coefficient of electricity storage per unit capacity, and $c_{p,ic}$ represents the unit power storage cost investment coefficient of the ICUS-ES. $E_{ic}$ represents the capacity of the ICUS-ES. $P_{ic}$ represents the rated power of the ICUS-ES.

(2) Annual operation and maintenance cost

$$C_{mo}^{ic}=c_{p,ic}{E}_{ic}\frac{i_0{\left(1+i_0\right)}^{L_{ic}}}{{\left(1+i_0\right)}^{L_{ic}}-1}$$

(3)

(3) Replacement cost

When the actual operating time of the ICUS-ES is less than the estimated time in the initial construction period, the ICUS-ES needs to be replaced to ensure its operating efficiency. The replacement cost of energy storage can be expressed as follows.

$$C_r^{ic}={\alpha }_{ic}{C}_{inv}^{ic}=\alpha \left(c_{e}E+c_{p}P\right)\frac{i_0{\left(1+i_0\right)}^{L_{ic}}}{{\left(1+i_0\right)}^{L_{ic}}-1}$$

(4)

where ${\alpha }_{ic}$ represents the replacement coefficient of the ICUS-ES for equipment replacement.

(4) Energy consumption cost

Industrial and commercial users can directly participate in the electricity market according to the operating rules. Therefore, when the ICUS-ES is in operation, electricity can be purchased from the electricity market. At this time, the energy consumption cost is the charging cost of the ICUS-ES, which can be expressed as:

$$C_{em}^{ic}={\displaystyle \sum }_t^{8760}\left({\lambda }_D{P}_{em,t}\right)$$

(5)

where ${\lambda }_D$ represents the price of the unit electric power purchased by the ICUS-ES, that is, the real-time price of the electricity market. $P_{em,t}$ represents the electric power that the ICUS-ES participates in and purchases from the electricity market.

(5) Decommissioning and disposal cost

$$C_{de}^{ic}={\beta }_{ic}{C}_{inv}^{ic}$$

(6)

where ${\beta }_{ic}$ represents the decommissioning cost coefficient of the ICUS-ES. It can be seen from the formula that the decommissioning cost is only related to the initial investment cost of the ICUS-ES.

2.1.2. Objective Function of the Lower-Layer Model

The lower-layer model is mainly analyzed from the perspective of system operation. The ICUS-ES can participate in the electric energy market and auxiliary service market at the same time, and take the maximum benefit as the goal. These things considered, it is also necessary to comprehensively consider the economy and environment of the system. Based on this, the objective function of the lower-layer model can be expressed as:

$$B_{total}^{ic}=B_{ar}^{ic}+B_{sub}^{ic}+B_{re}^{ic}+B_{em}^{ic}$$

(7)

where $B_{total}^{ic}$ represents the total benefit of the ICUS-ES. $B_{ar}^{ic}$ represents the peak valley difference arbitrage income of the ICUS-ES, and $B_{sub}^{ic}$ represents the subsidy benefit of the ICUS-ES. $B_{re}^{ic}$ represents the benefit of the ICUS-ES participating in the auxiliary service market, and $B_{em}^{ic}$ represents the benefits of the ICUS-ES participating in the distribution network market.

(1) Peak valley difference arbitrage benefit

In the electricity market environment, the electricity price fluctuates in real time with the load. In the energy market, the ICUS-ES system can be charged when the electricity price is low and discharged when the electricity price is high to realize arbitrage.

$$B_{ar}^{ic}={\displaystyle \sum }_{t=1}^T\left(P_{dis,t}^{ic}{u}_{dis,t}^{ic}-P_{ch,t}^{ic}{u}_{ch,t}^{ic}\right)r_{ar}^{ic}{\lambda }_D$$

(8)

where $P_{dis,t}^{ic}$ represents the discharge power of the ICUS-ES system. $P_{ch,t}^{ic}$ represents the charge power of the ICUS-ES system. $u_{dis,t}^{ic}$ and $u_{ch,t}^{ic}$ are the 0–1 variable, which represents the discharging and charging state of the ICUS-ES, respectively. $r_{ar}^{ic}$ represents the proportion of the ICUS-ES charge and discharge capacity used to participate in market arbitrage.

(2) Ancillary services market benefit

Similar to the benefit model of peak valley difference arbitrage, the benefit of the ICUS-ES in participating in the auxiliary service market mainly comes from the difference between the price of this service and the cost of energy supply. Based on this, the operating benefit of the ICUS-ES participating in auxiliary services is:

$$B_{re}^{ic}={\displaystyle \sum }_{t=1}^T\left(P_{dis,t}^{ic}{u}_{dis,t}^{ic}{p}_{as,t}-P_{ch,t}^{ic}{u}_{ch,t}^{ic}{\lambda }_D\right)r_{ar}^{ic}$$

(9)

where $B_{re}^{ic}$ represents the benefits of the ICUS-ES participating in the electric auxiliary service market. $p_{as,t}$ represents the market price of ancillary services. $r_{ar}^{ic}$ represents the proportion of the ICUS-ES charging and discharging capacity participating in ancillary service market transactions.

(3) Participating in distribution network market benefit

The benefits of the ICUS-ES in the distribution network market mainly refer to the benefits of reducing system congestion management after the participation of the ICUS-ES. Based on this, the benefits of the ICUS-ES in the distribution system operator market can be expressed as:

$$B_{em}^{ic}={\displaystyle \sum }_{t=1}^T\left(P_{dis,t}^{ic}{u}_{dis,t}^{ic}{C}_{CI,t}-P_{ch,t}^{ic}{u}_{ch,t}^{ic}{p}_{c,t}\right)r_{cc,t}^{ic}$$

(10)

where $C_{CI,t}$ represents the blocking cost of the branch, and $r_{cc,t}^{ic}$ represents the proportion of the ICUS-ES charge and discharge capacity applied to the distribution network system operator market.

Assuming that the network branch in the system is $N$, the blocking cost of branch $l$ is:

$$C_{CI,t}=\frac{T_{CI}}{P_{w,t}-P_{n,t}}$$

(11)

where $T_{CI}$ represents the change in the total cost of the system. $P_{w,t}$ represents the power value of the branch $l$ under the condition of no constraints, and $P_{n,t}$ represents the power value of branch $l$ under the condition of containing constraints.

(4) Subsidy benefit

There are also various forms of the ICUS-ES subsidy. The commonly used subsidy methods are: according to the charge and discharge capacity of the ICUS-ES and according to the investment cost of the ICUS-ES projects. Among them, the most widely used form is the subsidy based on the charge and discharge capacity of the ICUS-ES, and this subsidy form will also be selected in this paper. Based on this, the ICUS-ES subsidy benefits on the industrial and commercial user side are:

$$B_{sub}^{ic}={\displaystyle \sum }_{t=1}^T{P}_{dis,t}^{ic}{u}_{dis,t}^{ic}{p}_{sub,ic}+P_{ch,t}^{ic}{u}_{ch,t}^{ic}{p}_{sub,ic}$$

(12)

where $p_{sub,ic}$ represents the government’s additional subsidy price for the ICUS-ES.

2.2. Constraint Condition of the ICUS-ES System

The main constraints considered in the two-layer planning operation model of industrial and commercial user-side energy storage include: power flow constraints of power grid and operation constraints of energy storage equipment. These constraints reflect the interaction between various devices in the system.

2.2.1. Constraint Condition of the Upper-Layer Model

(1) Power balance constraint

$${\displaystyle \sum }_{t=1}^T\left(P_{em,t,i}+P_{dis,t,i}^{ic}-P_{ch,t,i}^{ic}\right)=P_{i,l,t}^{ic}$$

(13)

where $P_{em,t,i}$ refers to the electric energy purchased from the power market, that is, the active power injected into node $i$. $P_{i,l,t}^{ic}$ represents the load of industrial and commercial users.

(2) Total investment cost constraint

$$C_{inv}^{ic}\le C_{inv}^{ic,max}$$

(14)

where $C_{inv}^{ic,max}$ represents the total upper limit of the ICUS-ES investment cost.

(3) Grid power flow constraints

$${\displaystyle \sum }_{t=1}^T\left(P_{em,t,i}+P_{dis,t,i}^{ic}-P_{L,t,ic}-P_{ch,t,i}^{ic}\right)={\displaystyle \sum }_{i,j\in \mathsf{\Omega }}^{I,J}{\displaystyle \sum }_{t=1}^T{P}_{i-j,t,ic}$$

(15)

$${\displaystyle \sum }_{t=1}^T(Q_{i,t,ic}-Q_{L,t,ic})={\displaystyle \sum }_{i,j\in \mathsf{\Omega }}^{I,J}{\displaystyle \sum }_{t=1}^T{Q}_{i-j,t,ic}$$

(16)

$$P_{i-j,t,ic}=\frac{R_{i-j}\left[{\left(P_{em,t,i}\right)}^2+{\left(Q_{j,t,ic}\right)}^2\right]}{V_{j,t}^2}+P_{em,j,t}$$

(17)

$$Q_{i-j,t}=\frac{X_{i-j}\left[{\left(P_{em,t,i}\right)}^2+{\left(Q_{j,t,ic}\right)}^2\right]}{V_{j,t,ic}^2}+Q_{em,j,t}$$

(18)

$$V_{j,t,ic}=V_{i,t,ic}-\frac{P_{buy,j,t}-j{Q}_{j,t}}{V_{j,t,ic}^{*}}\left(R_{i-j,ic}+j{X}_{i-j,ic}\right)$$

(19)

$$V_{j,min}\le \left|V_{j,t,ic}\right|\le V_{j,max}$$

(20)

$$S_{i-j,t,ic}=P_{i-j,t,ic}+j{Q}_{i-j,t,ic}$$

(21)

$$\left|S_{i-j,t,ic}\right|\le S_{i-j,max}$$

(22)

where $\mathsf{\Omega }$ represents the set of distribution network nodes, and $i, j\in \Omega$. $Q_{i,t,ic}$ represents the reactive power injected for node $i$. $P_{L,t,ic}$ and $Q_{L,t,ic}$ represent the active load and reactive load of node $i$, respectively. $P_{i-j,t,ic}$ represents the active power at the head end of the branch $\left(i, j\right)$. $Q_{i-j,t,ic}$ represents the reactive power at the head end of the branch $\left(i, j\right)$. $R_{i-j,ic}+j{X}_{i-j,ic}$ represents the equivalent impedance of the branch $\left(i, j\right)$. $V_{j,t,ic}$ and $V_{i,t,ic}$ represent the voltage values of node $i$ and node $j$, respectively. $V_{j,max}$ represents the upper limit of the node $j$ voltage. $V_{j,min}$ represents the lower limit of the node $j$ voltage. $V_{j,t}^{*}$ represents the conjugate of the voltage value of node $j$. $S_{i-j,t,ic}$ represents the complex power at the head end of the branch $\left(i, j\right)$. $S_{i-j,max}$ represents the upper limit of the complex power.

(4) Maximum output constraint

$$0\le P_{em,t,i}\le P_{em}^{max}$$

(23)

where $P_{em}^{max}$ represents the maximum amount of electricity that can be purchased from the market.

2.2.2. Constraint Condition of the Lower-Layer Model

(1) Constraints on the charging and discharging power of the ICUS-ES

Considering the characteristics of the energy storage device, when the charging and discharging current is too large, the life of the energy storage device will be shortened. Based on this, the charging and discharging power of the ICUS-ES during operation should not be higher than the rated value, that is:

$$0\le P_{dis,t,i}^{ic}\le u_{dis,t,i}^{ic}{P}_{dis,t,i}^{ic,max}$$

(24)

$$0\le P_{ch,t,i}^{ic}\le u_{ch,t,i}^{ic}{P}_{ch,t,i}^{ic,max}$$

(25)

$$0\le u_{dis,t,i}^{ic}+u_{ch,t,i}^{ic}\le 1$$

(26)

where $P_{dis,t,i}^{ic,max}$ represents the maximum discharge power of the ICUS-ES, and $P_{dis,t,i}^{ic,max}$ represents the maximum charge power of the ICUS-ES. $u_{dis,t,i}^{ic}$ represents the discharge state of the ICUS-ES, which is a 0–1 variable. $u_{ch,t,i}^{ic}$ represents the charging state of the ICUS-ES, which is a 0–1 variable.

(2) Energy storage state of charge constraints

During the operation of the energy storage, its remaining capacity should meet certain constraints. That is, in any period of time, the state of charge of the energy storage must be smaller than the maximum state of charge and greater than the minimum state of charge. In addition, the energy stored by the energy storage at the beginning and end of each dispatch period should be consistent, which is beneficial to ensure the periodicity of the continuous operation of the energy storage.

$$SO{C}_{t,ic}=SO{C}_{t-1,ic}+\frac{\left({\eta }_{ch,ic}{P}_{ch,t,i}^{ic}-\frac{P_{dis,t,i}^{ic}}{{\eta }_{dis,ic}}\right)\Delta t}{E_{max,ic}}$$

(27)

$$SO{C}_{0,ic}=SO{C}_{T,ic}$$

(28)

$$SO{C}_{min,ic}\le SO{C}_{t,ic}\le SO{C}_{max,ic}$$

(29)

where $SO{C}_{t,ic}$ represents the state of charge of the ICUS-ES at time 𝑡. ${\eta }_{ch,ic}$ represents the charging efficiency of the ICUS-ES, and ${\eta }_{dis,ic}$ represents the discharging efficiency of the ICUS-ES. The $\Delta t$ is the time interval of the ICUS-ES, which is set to 1 h in this paper. $SO{C}_{0,ic}$ represents the state of charge at the initial moment of the ICUS-ES. $SO{C}_{T,ic}$ represents the state of charge of the ICUS-ES at the final moment. $SO{C}_{max,ic}$ represents the maximum state of charge of the ICUS-ES, and $SO{C}_{min,ic}$ represents the minimum state of charge of the ICUS-ES.

3. Robust Reconstruction of Planning Model

During market operation, industrial and commercial users can directly participate in the electricity market. However, the electricity market price has certain randomness and volatility due to the influence of the market environment. That is to say, the energy storage planning model constructed in the previous section contains uncertain factors, which brings difficulties to the model solution. In addition, wind power and photovoltaic output are also random and fluctuating.

This paper will use the robust optimization method to transform the ICUS-ES planning and operation model constructed in the previous section to deal with the impact of uncertain variables in the model on system operation.

3.1. Treatment of Uncertain Factors of Electricity Price

Combined with the power system dispatching problem with uncertain factors, the robust optimization theory can be introduced as follows:

$$\underset{y}{\min }{N}^{T}y$$

(30)

$$\{\begin{array}{c}Ax+By+C\omega \le D\\ Ex+Fy+G\omega =H\\ \omega \in \Re \end{array}$$

(31)

where $\omega$ is the uncertainty variable, and $y$ is the decision variable.

In robust optimization, an uncertain set $\Re$ is usually used to describe random variables. Robust optimization is defined as finding a solution, such that, for all scenarios where random variables may appear in $\Re$, the constraints are satisfied and the objective function in the worst scenario is optimal. The optimization of the worst scenario is reflected in the $\max -\min$ structure of the model objective function, which can be regarded as a Cournot game between the external environment and the system scheduling department in essence. The optimal solution of the model is essentially the Nash equilibrium solution of the game problem.

Through the introduction of the above robust optimization method, it can be seen that when dealing with problems containing uncertain variables, it is first necessary to construct an uncertain set $\Re$ about the uncertain variables. In robust optimization, uncertainty sets are often constructed in the form of box uncertainty sets. The uncertainty is represented by a confidence interval, within which there is a certain probability. However, it may lead to results that are too conservative, since robust optimization optimizes its operation under worst-case scenarios, which are less likely to occur. Therefore, in addition to the confidence interval, another constraint needs to be added so that conservatism can be reduced without sacrificing robustness. Based on this, an uncertain set about the day-ahead electricity market price ${\lambda }_D$ is constructed, namely:

$$\mathsf{\Phi }\left({\lambda }_m,{\lambda }_h,{\mathsf{\Gamma }}_{\lambda }\right)=\{{\lambda }_D\in {ℝ}^T:{\displaystyle \sum }_{t=1}^T\frac{\left|{\lambda }_{D,t}-{\lambda }_{m,t}\right|}{{\lambda }_{h,t}}\le {\mathsf{\Gamma }}_{\lambda },$$

(32)

$${\lambda }_{D,t}\in \left[{\lambda }_{m,t}-{\lambda }_{h,t},{\lambda }_{m,t}+{\lambda }_{h,t}\right],\forall t\}$$

(33)

where ${\lambda }_m$ represents the midpoint of the confidence interval of the electricity price in the day-ahead electricity market, ${\lambda }_h$ represents half the length of the confidence interval of the electricity price in the day-ahead electricity market, and ${\mathsf{\Gamma }}_{\lambda }$ represents the adjustable uncertainty budget parameter to control the size of the uncertainty set.

$${\mathsf{\Gamma }}_{\lambda }=\lceil \sqrt{-2T\ln \left(1-\alpha \right)}\rceil$$

(34)

where $\lceil$$\rceil$ is rounded up, $T$ is the number of time periods dispatched, and $\alpha$ is the confidence level.

Equation (33) can be characterized by predicting the range of the electricity market price before each time period. In practice, it is very unlikely that the day-ahead electricity market price is actually at the interval boundary at each time period. Therefore, the uncertainty budget parameter ${\mathsf{\Gamma }}_{\lambda }$ is introduced in Equation (34) to reduce the conservativeness of the robust optimization model.

3.2. Robust Transformation of Model

After using the uncertainty set to characterize the uncertainty variable of day-ahead electricity market price in the model, the original model is further transformed to be robust.

3.2.1. Objective Function Transformation

The planning and operation model of industrial and commercial user-side energy storage constructed in this paper includes two layers. Among them, the upper-layer model can be rewritten as:

$$\begin{gathered} \underset{x}{\min }{C}_{inv}^{ic}+C_{mo}^{ic}+C_r^{ic}+C_{em}^{ic}+C_{de}^{ic}=\left(c_{e,ic}{E}_{ic}+c_{p,ic}{P}_{ic}\right)\frac{i_0{\left(1+i_0\right)}^{L_{ic}}}{{\left(1+i_0\right)}^{L_{ic}}-1}+c_{p,ic}{E}_{ic}\frac{i_0{\left(1+i_0\right)}^{L_{ic}}}{{\left(1+i_0\right)}^{L_{ic}}-1} \\ +\alpha \left(c_{e}E+c_{p}P\right)\frac{i_0{\left(1+i_0\right)}^{L_{ic}}}{{\left(1+i_0\right)}^{L_{ic}}-1}+{\displaystyle \sum }_t^{8760}\left({\lambda }_D{P}_{em,t}\right)+{\beta }_{ic}{C}_{inv}^{ic} \end{gathered}$$

(35)

The final objective function of the lower-layer function of the energy storage planning operation model on the industrial and commercial user side can be expressed as the maximum sum of multiple benefits.

$$\begin{array}{cc}\hfill max{B}_{ar}^{ic}+B_{sub}^{ic}& +B_{re}^{ic}+B_{em}^{ic}\hfill \\ \hfill & =\sum _{t=1}^T\left(P_{dis,t}^{ic}{u}_{dis,t}^{ic}-P_{ch,t}^{ic}{u}_{ch,t}^{ic}\right)r_{ar}^{ic}{\lambda }_D+\sum _{t=1}^T\left(P_{dis,t}^{ic}{u}_{dis,t}^{ic}{p}_{as,t}-P_{ch,t}^{ic}{u}_{ch,t}^{ic}{\lambda }_D\right)r_{ar}^{ic}\hfill \\ \hfill & +\sum _{t=1}^T\left(P_{dis,t}^{ic}{u}_{dis,t}^{ic}{C}_{CI,t}-P_{ch,t}^{ic}{u}_{ch,t}^{ic}{p}_{c,t}\right)r_{cc,t}^{ic}+\sum _{t=1}^T{P}_{dis,t}^{ic}{u}_{dis,t}^{ic}{p}_{sub,ic}+P_{ch,t}^{ic}{u}_{ch,t}^{ic}{p}_{sub,ic}\hfill \end{array}$$

(36)

3.2.2. Constraint Condition Transformation

When the waste heat of MT is insufficient to supply the heat load demand of the cogeneration system, the gas-fired boiler complements the system by burning gas.

The uncertainty of the day-ahead electricity market price is not considered in the constraints of the third section. After the price of the day-ahead power market is represented by the uncertainty set, other related constraints and related variables in the constraints also need to be robustly transformed accordingly. Based on this, a robust transformation of the constraints is carried out.

$$H:=\{PU:$$

$$\forall {\tilde{\lambda }}_D\in \mathsf{\Phi }, \exists \Delta P=\left(P_{em,1},\dots ,P_{em,T}, P_{dis,1}^{ic},\dots ,P_{dis,T}^{ic},P_{ch,1}^{ic},\dots ,P_{ch,T}^{ic}\right), \mathit{such} \mathit{that}$$

$${\displaystyle \sum }_{t=1}^T\left({\tilde{P}}_{em,t,i}+{\tilde{P}}_{dis,t,i}^{ic}-{\tilde{P}}_{ch,t,i}^{ic}\right)=P_{i,l,t}^{ic}$$

(37)

$$0\le P_{dis,t,i}^{ic}+\Delta P_{dis,t,i}^{ic}\le u_{dis,t,i}^{ic}{P}_{dis,t,i}^{ic,max}$$

(38)

$$0\le P_{ch,t,i}^{ic}+\Delta P_{ch,t,i}^{ic}\le u_{ch,t,i}^{ic}{P}_{dis,t,i}^{ic,max}$$

(39)

$$0\le u_{dis,t,i}^{ic}+u_{ch,t,i}^{ic}\le 1$$

(40)

$$SO{C}_{t,ic}=SO{C}_{t-1,ic}+\frac{\left({\eta }_{ch,ic}\left(P_{ch,t,i}^{ic}+\Delta P_{ch,t,i}^{ic}\right)-\frac{\left(P_{dis,t,i}^{ic}+\Delta P_{dis,t,i}^{ic}\right)}{{\eta }_{dis,ic}}\right)\Delta t}{E_{max,ic}}$$

(41)

$${\tilde{C}}_{inv}^{ic}\le C_{inv}^{ic,max}$$

(42)

$${\displaystyle \sum }_{t=1}^T({\tilde{Q}}_{i,t,ic}-{\tilde{Q}}_{L,t,ic})={\displaystyle \sum }_{i,j\in \mathsf{\Omega }}^{I,J}{\displaystyle \sum }_{t=1}^T{\tilde{Q}}_{i-j,t,ic}$$

(43)

$${\tilde{P}}_{i-j,t,ic}=\frac{{\tilde{R}}_{i-j}\left[{\left({\tilde{P}}_{em,t,i}\right)}^2+{\left({\tilde{Q}}_{j,t,ic}\right)}^2\right]}{V_{j,t}^2}+{\tilde{P}}_{em,j,t}$$

(44)

$${\tilde{Q}}_{i-j,t}=\frac{{\tilde{X}}_{i-j}\left[{\left({\tilde{P}}_{em,t,i}\right)}^2+{\left({\tilde{Q}}_{j,t,ic}\right)}^2\right]}{{\tilde{V}}_{j,t,ic}^2}+{\tilde{Q}}_{em,j,t}$$

(45)

$${\tilde{V}}_{j,t,ic}={\tilde{V}}_{i,t,ic}-\frac{{\tilde{P}}_{buy,j,t}-j{\tilde{Q}}_{j,t}}{V_{j,t,ic}^{*}}\left({\tilde{R}}_{i-j,ic}+j{\tilde{X}}_{i-j,ic}\right)$$

(46)

$$V_{j,min}\le \left|{\tilde{V}}_{j,t,ic}\right|\le V_{j,max}$$

(47)

$${\tilde{S}}_{i-j,t,ic}={\tilde{P}}_{i-j,t,ic}+j{\tilde{Q}}_{i-j,t,ic}$$

(48)

$$\left|{\tilde{S}}_{i-j,t,ic}\right|\le S_{i-j,max}\}$$

(49)

where $\Delta$ represents the adjustment amount of the variable in the second stage. Equations (38)–(49) refer to the constraints that need to be satisfied after the second stage adjustment. Its meaning is the same as the first stage, so it will not be repeated here.

When constructing the modified robust optimization model, in addition to the modified robustness constraints above, the original conventional constraints are also included. That is to say, all decision-making results of the collaborative planning model of the industrial user-side energy storage system should at least meet the basic requirements of the original model for the feasible region. The robustness constraints of Equations (38)–(49) correspond to the robustness constraints of the model. That is, the industrial user-side energy storage system collaborative planning model is required to make the nominal decision results of the lower model meet all the basic constraints of the eco-industrial user-side energy storage system collaborative planning model again in the case of foreseeable day-ahead power market price uncertainty.

3.3. Robust Model Solving

In this paper, the multiple uncertainties of renewable energy output and load are characterized by a series of stochastic scenarios. In order to overcome the problem of balancing the number of stochastic scenes between “local optimization” and “dimensional disaster”, a stochastic hierarchical scene generation model integrating Latin hypercube sampling (LHS), Wasserstein metric, and 0–1 scene dimensionality reduction is proposed.

The above model is a non-convex programming problem, which is a non-deterministic polynomial problem in mathematics. In order to solve this problem, this paper decomposes the original problem into a main problem and a sub-problem. Among them, the main problem is a linear programming problem, and the sub-problem is a bilinear problem, which will be solved by the C&CG algorithm.

For the model proposed in this paper, combined with the C and CG method, the transformed two-layer optimization model can be expressed as (for simplicity, it will be expressed in matrix form):

(1) The original problem:

$$\min {\mathit{b}}^T\mathit{y}$$

(50)

s.t

$$\mathit{K}\mathit{y}\le \mathit{N}$$

(51)

$$\mathit{B}\mathit{y}+\mathit{C}\tilde{\lambda }\le \mathit{M}$$

(52)

$$\mathit{E}\mathit{y}+\mathit{F}\tilde{\lambda }=\mathit{G}$$

(53)

and

$$\mathit{H}=\{\mathit{P}\mathit{U}=\left({\mathit{y}}_{\mathbf{1}},{\mathit{y}}_{\mathbf{2}},\dots ,{\mathit{y}}_{\mathit{n}}\right):\forall \lambda \in \mathsf{\Phi } \exists \Delta \mathit{y} such that$$

(54)

$$\mathit{K}\left(\mathit{y}+\Delta \mathit{y}\right)\le \mathit{N}$$

(55)

$$\mathit{B}\left(\mathit{y}+\Delta \mathit{y}\right)+\mathit{C}\lambda \le \mathit{M}$$

(56)

$$\mathit{E}\left(\mathit{y}+\Delta \mathit{y}\right)+\mathit{F}\lambda =\mathit{G}$$

(57)

$$\left|\Delta \mathit{y}\right|\le \mathit{r}\}$$

(58)

where $\mathit{y}$ is decision variable, and $\tilde{\lambda }$ represents the base case of the uncertainty vector estimated in the first stage. Equation (54) means that no matter how $\lambda$ appears in $\mathsf{\Phi }$, $\Delta \mathit{y}$ must exist such that all constraints are still satisfied. $\mathit{B},\mathit{C},\mathit{E},\mathit{F},\mathit{K}$ stand for coefficient metrics in constraints, and $\mathit{M}$, $\mathit{G}, \mathit{N}$, $\mathit{r}$ represent parameter vectors in constraints. Obviously, the constraints of the second stage can guarantee adaptation to all uncertainties.

The uncertainty set $\mathsf{\Phi }$ contains an infinite number of scenarios $\lambda$, so the above model contains an infinite number of constraints. Based on the C and CG method, the original problem can be decomposed into the following two sub-problems:

(2) Bi-level optimization model

(1)

Mast-Problem:

$$\left(\mathit{MP}\right)\min {\mathit{b}}^{\mathit{T}}\mathit{y}$$

(59)

The constraints of Equations (51)–(53) need to be considered.

Iteratively expanded robust operational constraints:

$$\mathit{K}\left(\mathit{y}+\Delta {\mathit{y}}_k\right)\le \mathit{N}, \forall k\in \mathit{\kappa }$$

(60)

$$\mathit{B}\left(\mathit{y}+\Delta {\mathit{y}}_k\right)+\mathit{C}\tilde{\lambda }\le \mathit{M}, \forall k\in \mathit{\kappa }$$

(61)

$$\mathit{E}\left(\mathit{y}+\Delta {\mathit{y}}_k\right)+\mathit{F}\tilde{\lambda }=\mathit{G}, \forall k\in \mathit{\kappa }$$

(62)

(2)

Sub-Problem

$$(\mathit{SP}) Z=\underset{\lambda \in \mathsf{\Phi }}{\max }\underset{s^{+},s^{-},\Delta y}{\min }{\displaystyle \sum }\left({\mathit{s}}^{+}+{\mathit{s}}^{-}\right)$$

(63)

s.t.

$${\mathit{s}}^{+}\ge \mathbf{0}$$

(64)

$${\mathit{s}}^{-}\ge \mathbf{0}$$

(65)

$$\mathit{E}\left(\mathit{y}+\Delta \mathit{y}\right)+\mathit{F}\lambda +{\mathit{s}}^{+}+{\mathit{s}}^{-}=\mathit{G}$$

(66)

In addition, the constraints of Equations (55), (56), and (58) need to be considered.

In the above bi-level optimization model, $\mathit{\kappa }$ is the index set of worst-case price scenarios ${\lambda }_k$ $\left(\forall k\in \mathit{\kappa }\right)$, which gradually expands with the process of iterative solution of sub-problems. In the objective function of the sub-problem, ${\mathit{s}}^{+},{\mathit{s}}^{-}$ are non-negative relaxation variables. Therefore, solving the sub-problem is to find the worst point or worst scenario in the uncertainty set. The model-solving method of this bi-level optimization model can be summarized as the following Algorithm 1.

Algorithm 1. Solution of above optimization model

(1) $\mathit{\kappa }\leftarrow \varnothing ,k\leftarrow 1,\mathsf{{\rm Z}}\leftarrow \infty$, the error tolerance of the Mast-Problem is defined as δ; (2) Solve Mast-Problem, and obtain its optimal solution ($\mathit{P}\mathit{U}$); (3) Based on $\mathit{P}\mathit{U}$, Sub-Problem is solved to obtain worst-case $\lambda$ and adjustments solution $\Delta \mathit{y}$; (4) Expand the robust operational constraints in Mast-Problem based on $\lambda$, $\mathit{\kappa }\leftarrow \mathit{\kappa }{\displaystyle \cup }k, k\leftarrow k+1$; (5) If $\mathsf{{\rm Z}}\ge \mathsf{\delta }$, return (2), otherwise enter (6); (6) The iteration terminates and the optimal solution obtained by solving Mast-Problem for the last time is the output.

4. Simulation Analysis

4.1. Example Description

In the industrial and commercial user-side energy storage planning and operation simulation, the analysis will be based on the IEEE 30-node system, as shown in Figure 1. The electrical load on the industrial and commercial user side will also change with time. User load can be divided according to seasonal changes. Select typical days in each season to build four typical day scenes in the spring, summer, autumn, and winter. The industrial and commercial power load under each typical daily scenario is shown in Figure 2.

Industrial and commercial users purchase electric energy from the utility grid according to the power market price. The day-ahead electricity market price is an uncertain variable, and its uncertainty set is shown in Figure 3.

The operating parameters of various energy storage devices are shown in

Table 1. Parameters of energy storage equipment.

Parameters	Li-Ion Battery	Lead-Acid Battery	Lead-Carbon Battery
System cost (CNY/kWh)	1600	1000	974.53
Operation and maintenance cost (CNY/kWh)	0.008	0.003	1274.87
Efficiency (%)	95	85	90
Depth of discharge (%)	90	65	90
Life cycle (year)	10	7	8

.

4.2. Analysis of Energy Storage Planning Results on ICUS

The service life of energy storage is about 20 years, and the benchmark discount rate is 5%. Based on this, the energy storage on the industrial and commercial user side is optimized.

4.2.1. ICUS-ES Planning Result Analysis

(1) Operation cost analysis

According to the ICUS-ES planning and operation model constructed in this paper, the energy storage on the industrial and commercial user side is optimized. The results are shown in

Table 2. Configuration results of energy storage on ICUS.

	Location	Planned Capacity (kW)	Operation Cost (CNY)	Operation Benefit (CNY)
Li-ion battery	10, 19	923	9,745,373	2,482,475
Lead-acid battery	10, 19	1240	12,743,487	1,943,497
Lead-carbon battery	10, 19	1056	11,429,408	3,291,978

.

Due to the different specifications and technical parameters of different battery energy storage, the economy may also be different in the whole life cycle. From the results of various types of energy storage configuration, the configuration cost of lithium-ion battery energy storage is the lowest, while the configuration cost of lead-acid battery energy storage is the highest. Therefore, from an economical point of view, lithium-ion batteries are a more suitable type of electrochemical energy storage configuration. In addition, in recent years, the technology of the lithium-ion battery is also gradually maturing, so the space for cost reduction in the future will gradually become larger. On the industrial and commercial user side, it will also have more advantages to use lithium-ion batteries to obtain revenue.

From the perspective of energy storage revenue, the lithium-ion battery has the largest revenue and the lead-acid battery has the smallest revenue. The possible reason is that the charging and discharging efficiency and discharge depth of the lead-acid battery are low, which affects its low operation efficiency. Different types of energy storage will not affect the location of energy storage configuration, so the location of three types of energy storage configuration is the same.

(2) Analysis of the impact of energy storage characteristics on cost

From the above analysis, it can be seen that the characteristics of energy storage will have a certain impact on the configuration cost of the system. To further explore this relationship, the following analysis is conducted. Assume that the cost of lithium-ion batteries, lead-acid batteries, and lead-carbon batteries is reduced by 10%, 15%, and 20%, respectively. Based on this, its impact on operating income is analyzed, and the results are shown in

Table 3. Revenue values under different cost reduction rates.

Cost Reduction Rate	10%	15%	20%
Li-ion battery configuration benefits	CNY 2,953,484	CNY 23,492,543	CNY 4,973,445
Lead-acid battery configuration benefits	CNY 2,153,536	CNY 2,528,708	CNY 2,580,115
Lead-carbon battery configuration benefits	CNY 4,290,334	CNY 5,451,183	CNY 6,127,809

.

As can be seen from Table 3, under different cost reduction rates, the configuration benefits of lithium-ion batteries have increased by 18.73%, 40.47%, and 99.98%, respectively. The revenue of lead-acid batteries increased by 10.46%, 29.29%, and 83.69%, respectively. The benefits of lead-carbon batteries increased by 30.19%, 65.51%, and 85.61%, respectively. It can be seen that an important way to improve system revenue is still to seek to reduce the cost of energy storage.

In order to further analyze the impact of the charging and discharging efficiency of different types of energy storage on the revenue of the energy storage system, the analysis will be based on different charging and discharging efficiencies. The result is shown in Figure 4.

Figure 4 shows the impact of changes in conversion efficiency of three different types of energy storage on the benefit of the ICUS-ES system. The configuration benefit of the lithium-ion battery, lead-acid battery, and lead-carbon battery increases in positive proportion with the change in conversion efficiency. If the conversion efficiency of the lithium-ion battery, lead-acid battery, and lead-carbon battery increases by 1%, respectively, on the basis of Table 1, the net income of the three will be CNY 2.6312 million, CNY 1.9998 million, and CNY 3.5783 million, respectively. Compared with before, it increased by CNY 143,700, CNY 50,100, and CNY 280,500, respectively. Overall, under the specific load curve and energy storage configuration results, the net income of the lead-carbon energy storage system is greater than that of lithium-ion and lead-acid energy storage systems.

4.2.2. ICUS-ES System Operation Analysis

(1) Effect analysis of ICUS-ES operation in the summer

Through the above two-level optimization model, we can obtain the operation state of ICUS-ES in the summer, as shown in Figure 5.

According to Figure 5 and electricity price, 1:00–6:00 is the valley period of electricity price, 7:00–10:00 is the first peak period of electricity price, 11:00–16:00 is the first parity period of electricity price, 17:00–20:00 is the second peak period of electricity price, and 21:00–24:00 is the second valley period of electricity price. The ICUS-ES is charged during the low electricity price period, and the charging amount is relatively large, which is close to the upper limit of energy. During the first peak period of the electricity price, the ICUS-ES is discharged and then charged during the first parity period to supplement the electricity consumed during the peak period. The energy stored in the ICUS-ES is released during the second peak period. Therefore, the energy storage in the ICUS obtains benefits through peak discharge and valley charging. At the other time when electricity prices are low, the electricity load is mainly met by purchasing electricity from the grid.

Through the above analysis, it can be seen that the ICUS-ES is in the form of two charging and two discharging in the summer, that is charging in the peak period of electricity price and discharging in the valley period, and charging in the parity period and discharging in the peak period.

(2) Effect analysis of ICUS-ES operation in the winter

Through the above two-layer optimization model, the operation state of the ICUS-ES in the winter can be obtained as shown in Figure 6.

Combining Figure 6 and the electricity price, it can be seen that the ICUS-ES is mainly charged and discharged according to the change in electricity price in the winter, so as to achieve the purpose of arbitrage. Specifically, it can be seen from the charging and discharging curve in the winter that charging is performed at 3:00–5:00, 23:00–24:00, etc., because the electricity price is relatively low at those times. The energy storage is discharged at the time of 9:00–11:00 and 13:00. At this time, the electricity price is relatively high, so as to achieve the purpose of “charging at a low price and discharging at a high price”, making the total cost of the system lower.

From the overall view of Figure 5, the ICUS-ES still maintains the working state of two charging and two discharging in the winter. That is to say, charging is performed at the end of the valley period of the electricity price and discharging is performed during the peak period, and charging is performed at the end of the parity period and discharging is performed during the peak period.

(3) Effect analysis of ICUS-ES operation in the autumn

The user load curves in the spring and autumn are similar, so autumn is used as the representative for analysis. Its specific operating status is shown in Figure 7.

It can be seen from Figure 7 that during the valley period, the system mainly purchases electrical energy from the external power grid to meet the load. At the end of the valley period, the electric energy storage is charged with the maximum power, and the energy storage is fully charged at the end of the valley period. The first peak period of electricity price is 7:00–10:00, and the electricity storage and discharge meet the electricity load. After entering the parity period of the electricity price, the system mainly purchases electric energy from the external power grid to meet the electricity load of the user and charges the electric energy storage in the later period of the parity period. In the second peak period of electricity price, similar to the first peak period, the electric energy storage and discharge meet the full electric load.

4.3. Sensitivity Analysis

(1) Sensitivity analysis of electricity price

In the above analysis, the electricity market price has certain volatility. Based on this, Figure 8 examines and compares three different levels of price scenarios, including worst-case, normal-case, and best-case scenarios. Among them, the normal-case is the base case used in the analysis in Section 4.2.

Under different electricity price cases, the results of commercial user-side energy storage planning and operation are shown in

Table 4. Energy storage planning results in different cases.

	Energy Storage Configuration Cost	Energy Storage Allocation Benefit
Worst-case	CNY 12,045,687	CNY 3,128,303
Normal-case	CNY 11,420,803	CNY 3,297,899
Best-case	CNY 9,833,494	CNY 3,529,232

.

It can be seen from Table 4 that the planning costs and planning benefits of energy storage on the industrial and commercial user side are different under different electricity price cases. In general, under the best-case, the planning cost of industrial and commercial user-side energy storage is the lowest and the planning benefit is the largest. In terms of energy storage in the industrial and commercial user-side planning cost, compared with the worst-case, which decreased by 5.47%, the benefits increased by 5.14%. This phenomenon shows that the electricity price will have a significant impact on the operation of energy storage planning on the industrial and commercial user side, so the price factor needs to be taken into account when planning energy storage.

(2) Robustness test of results

This section compares the optimization results ignoring uncertainty ($\mathsf{\Gamma }=0$) with the robust optimization results considering uncertainty ($\mathsf{\Gamma }=6$) on the basis of different degrees of actual electricity price and deviation $\mathsf{\Delta }$. In order to verify whether the planning results of the robust model output can resist the interference of uncertain factors in the system, this section introduces the Equation (67) for calculating the deviation $\Delta$, as follows:

$$\Delta ={\displaystyle \sum }_{t\in T}\frac{\left|{\tilde{\lambda }}_{D,t}-{\lambda }_{D,t}\right|}{{\lambda }_{D,t}}$$

(67)

As shown in

Table 5. Deviation cost of system under different deviation degrees.

Deviation ∆	The Cost of Ignoring Uncertainty	Cost Variance	The Cost of Considering Uncertainty	Cost Variance
0	CNY 11,029,313	-	CNY 11,420,877	-
0.1	CNY 10,936,956	CNY 92,407	CNY 11,397,734	CNY 23,174
0.2	CNY 10,824,221	CNY 205,197	CNY 11,372,527	CNY 48,302
0.3	CNY 10,774,915	CNY 254,404	CNY 11,351,221	CNY 69,604
0.4	CNY 10,728,797	CNY 300,728	CNY 11,339,603	CNY 81,293
0.5	CNY 10,668,517	CNY 360,974	CNY 11,288,974	CNY 131,974

, when there is no deviation between the predicted value and the actual value, the system operation cost under the energy storage planning result that ignores the influence of random interference is less than the system operation cost under the robust optimal location and volume determination result considering uncertainty. This considered, the deviation of operation cost increases with the increase in deviation degree ∆, but the deviation under the robust method considering uncertainty is significantly lower. Therefore, if the influence of uncertain factors in energy storage planning is ignored, once the actual electricity price deviates from the predicted value, the original optimal operation state of the system will be disturbed. Thus, the system cost will be increased, and even the optimal planning result of the original industrial and commercial user-side energy storage will be affected. In the planning process of the energy storage system, the deviation of power market price cannot be avoided, so there will always be deviation values in the operation status of system resources and system operation costs.

The robust planning method considering random interference can effectively reduce the impact of uncertainty factors on the planning results, so as to improve the ability of planning results to resist random interference. This method can significantly reduce its impact on the system operation cost, and the greater the deviation, the more obvious the effect.

5. Conclusions

In this paper, an industrial and commercial user-side energy storage planning model with uncertainty and multi-market joint operation is constructed, and a robust optimization method is introduced to deal with the influence of uncertain factors in the system. The model comprehensively considers the investment cost, operation and maintenance cost, peak valley arbitrage income, and participation in ancillary service market income of industrial users’ energy storage in the whole life cycle. The result of the simulation analysis shows that:

(1) The uncertainty of electricity price and the topology of the power system will affect the optimal location and capacity of energy storage. From the results of energy storage location, energy storage will be configured in the important transmission nodes and renewable energy power generation access nodes in the power system.

(2) The effectiveness of this method to resist stochastic uncertainty in the system is verified by the change in system operation cost under the scenarios of different degrees of deviation ∆. The results show that the proposed two-layer optimization model for energy storage system planning considering uncertainty can effectively reduce the influence of uncertainty factor deviation on the results of energy storage location selection and capacity determination, and improve the anti-interference ability of planning results. In addition, it also significantly reduces its impact on system operating costs, and the larger the deviation, the more obvious the effect.

(3) Energy storage system configuration is a decision-making problem under a long-term framework. This paper compares the economics of typical user-side energy storage of lithium-ion batteries, lead-acid batteries, and lead-carbon batteries. In addition, in terms of energy storage characteristics, the cost of energy storage and energy conversion efficiency are the key factors affecting the economy.