Dynamic Robust Optimization Method Based on Two-Stage Evaluation and Its Application in Optimal Scheduling of Integrated Energy System

Abstract

As an emerging energy allocation method, shared energy storage devices play an important role in modern power systems. At the same time, with the continuous improvement in renewable energy penetration, modern power systems are facing more uncertainties from the source side. Therefore, a robust optimization algorithm that considers both shared energy storage devices and source-side uncertainty is needed. Responding to the above issues, this paper first establishes an optimal model of a regional integrated energy system with shared energy storage. Secondly, the uncertainty problem is transformed into a dynamic optimization problem with time-varying parameters, and a modified robust optimization over time algorithm combined with scenario analysis is proposed to solve such optimization problems. Finally, an optimal scheduling objective function with the lowest operating cost of the system as the optimization objective is established. In the experimental part, this paper first establishes a dynamic benchmark test function to verify the validity of proposed method. Secondly, the multi-mode actual verification of the proposed algorithm is carried out through a regional integrated energy system. The simulation results show that the modified robust optimization over time (ROOT) algorithm could find solutions with better robustness in the same dynamic environment based on the two-stage evaluation strategy. Compared with the existing algorithms, the average fitness and survival time of the robust solution obtained by the modified ROOT algorithm are increased by 94.41% and 179.78%. At the same time, the operating cost of the system is reduced by 11.65% by using the combined optimization scheduling method proposed in this paper.

1. Introduction

In-depth development of an RES is a considerable way to reduce carbon emissions in power systems [1]. An RIES based on the CCHP is a crucial way to improve energy efficiency and promote the consumption of the RES. Vigorously developing a CCHP-based RIES is a momentous means for China to achieve “carbon peak and carbon neutrality” [2]. On the other hand, an RIES contains an RES, which makes the overall power generation output curve intermittent, random and volatile. An ESS is considered an important method to suppress the internal uncertainty of the new power system due to its generation–use electrolytic coupling effect [3]. Although energy storage has great potential, it still faces problems such as a high investment cost and long return period, which limits the development of ESSs [4].

Based on the above background, SESSs proposed by the combination of sharing economy and ESS technology have become the focus of attention of experts and scholars [5]. References [6,7] introduce the basic principle, operation mechanism, pricing strategy and evaluation method of SESSs in detail and put forward suggestions for the next research direction of SESSs. Zhao et al. [8] proved that the rational allocation of SESSs can effectively reduce the storage–use bilateral operation cost by establishing a double level optimal configuration model. Based on the problem of energy community configuration sharing energy storage, Chang et al. [9] proposed a community configuration framework and set up three energy storage device allocation methods. The test results show that the reasonable arrangement of SESSs in the community can save configuration access and use costs. Liu et al. [10] studied the role of SESSs in new energy consumption trends and low-carbon operation. Huang et al. [11] applied SESSs to multi-microgrid grid-connected systems, and an optimal scheduling strategy was proposed to improve the local consumption of RESs. Reference [12] reduced the total energy cost and peak–valley difference rate of the entire power grid through the virtualized SESS scheduling strategy. Currently, the academic community generally believes that the participation of SESSs in the optimal scheduling of RIESs is crucial for the stability and efficiency of system operation, which needs to be further studied and discussed. However, due to the access of the RES, the RIES has great uncertainty, which has a certain risk impact on the participation of the SESS in operation of the RIES. Therefore, it is necessary to consider the uncertainty of RIESs when studying SESSs, which is the focus of this paper.

From the perspective of control theory, the optimization problem considering RES uncertainty can be regarded as a kind of dynamic optimization problem with time-varying parameters. And ROOT can provide dynamic solutions according to specific time-varying fitness functions [13]. Yu et al. [14] proposed the dynamic optimization algorithm concept of ROOT for the first time. The main idea is to search for a set of dynamic robust solutions which can be used by multiple continuous dynamic environments. Jin et al. [15] proposed a framework of ROOT and introduced the implementation method of each module in the framework. Fu et al. [16] proposed a method for characterizing and analyzing environmental changes in ROOT. Based on the concept of robustness, Fu et al. [17] proposed two new robustness metrics. A new semi-ROOT was introduced by Yazdani et al. [18], which can find a better solution when the current solution is acceptable. Novoa-Hernández et al. [19] proposed the idea of using an approximate model to analyze ROOT. Fox et al. [20] studied different prediction methods of the ROOT algorithm. Zhang et al. [21] studied the prediction model under the ROOT framework. Guzmán-Gaspar et al. [22] made an empirical comparison between the DE algorithm and random sampling method and analyzed the feasibility and effectiveness of the differential evolution algorithm to solve the modified ROOT problem in dynamic environments by using the survival time method. Yazdani et al. [23] proposed a multi-population ROOT and introduce two metrics, one of which is to estimate the robust estimation component of the promising region, and the other is the dual-mode computing resource allocation component considering various factors such as robustness. Chen et al. [24] proposed a new dynamic optimization method based on the environment-driven method and ROOT and selected different algorithms to solve different problems. The current research of ROOT is generally based on the AF or ST concept to find a solution with better robustness. Therefore, the accuracy of the predicted solution needs to be improved, and how to improve the accuracy is the focus of this paper.

In order to supplement the shortcomings of the current research, this paper establishes the model of multi-district RIESs considering SESS access and establishes an objective function with the optimal RIES daily operating cost. Aiming to address the uncertainty of RESs, a modified ROOT algorithm combined with scenario analysis is proposed from the perspective of optimal control. The contribution and novelty of this study are as follows:

• Aiming to resolve the dynamic optimization problem, the ROOT-TSE-PCCG is proposed. FD, SD and SFV are introduced as new evaluation metrics to improve the prediction accuracy of ROOT, and the above three new evaluation metrics are used as the first-stage evaluation index of the robust solution set. On this basis, the ST and AF are introduced as the second-stage evaluation index. Finally, through the two-stage evaluation method, the optimal robust solutions of the dynamic optimization problem are obtained.
• To address the problem of uncertainty in RESs, this paper proposes an algorithm that integrates the modified ROOT based on a two-stage evaluation with scenario analysis methods. By using LHS to generate the scene of the RES output power curve, then using BR to reduce the scene of the generated multiple scenes, and fitting the final power curve conversion, the RES uncertainty problem is transformed into a dynamic optimization problem with time-varying parameters. The modified ROOT method based on two-stage evaluation and scene analysis is used to solve the above optimization model, and the dynamic environment robust solution of RES output power is obtained.

The rest of this paper is structured as follows: Section 2 introduces the structure of the RIES with an SESS. In Section 3, the modified ROOT algorithm combined with scenario analysis is proposed. Section 4 establishes the system optimization objective and discusses the constraints. Section 5 analyzes the methodology of this paper through an arithmetic example and Section 6 gives the conclusions obtained.

2. Structure Modeling of RIES Considering SESS

2.1. Structure of Multi-District RIES

The structure of the whole system is shown in Figure 1. This paper stipulates that the bidirectional energy interaction objects of the CCHP in the region are the EPG and SESS, and the purpose of energy interaction is to build an interconnected power network in the region.

The internal structure diagram of the CCHP contained in Figure 1 is shown in Figure 2. It can be seen from Figure 2 that the CCHP can be divided into source side, converter module and load side. The source side consists of a WT, PV cell, GT and GB. The converter modules consist of a WHB, ES, EB, EC, AC and HE. The load side consist of electrical, cooling and heating loads. Due to the limited space, and because the mathematical modeling work of various types of equipment contained in the CCHP is very mature, the modeling work of this paper is no longer discussed, and the mathematical model of each equipment can be found in [25,26].

2.2. Modeling of SESS

The operator establishes an SESS among user groups for unified operation and management and provides energy storage services for multiple users in the same distribution network area [6,27]. At the same time, operators make use of the differences in the electricity consumption behavior of users at different moments and of different users at the same time to allocate energy storage resources, thus further improving the utilization rate of energy storage equipment and achieving the purpose of increasing the system’s operating income [28,29]. In summary, the mathematical model of the SESS runtime should meet the following conditions.

2.2.1. Constraint of State of Charge of SESS [30]

During the normal operation of the SESS, the electric energy contained in it should not mutate.

$$E_t^{SESS}=\left(1-{\eta }_{SESS}^{loss}\right)E_{t-1}^{SESS}+({\eta }_{SESS}^{abs}{P}_t^{SESS,abs}-\frac{1}{{\eta }_{SESS}^{relea}}{P}_t^{SESS,relea})\Delta t,$$

(1)

2.2.2. Capacity Constraints of SESS

The normal operation of the SESS should conform to the physical parameters of its equipment.

$$\{\begin{array}{l}{\sigma }_{SESS}^{\min }{E}_{max}^{SESS}\le E_t^{SESS}\le {\sigma }_{SESS}^{\max }{E}_{\max }^{SESS}\\ E_{start}^{SESS}={\sigma }_{SESS}^{init}{E}_{\max }^{SESS}=E_{end}^{SESS}\end{array},$$

(2)

2.2.3. Charge and Discharge Power Constraints of SESS

When the SESS is in normal operation, it cannot have both charging behavior and discharging behavior at the same time with any single user.

$$\{\begin{array}{l}0\le P_t^{SESS,abs}\le P_{\max }^{SESS}{U}_{abs}^{SESS}\\ 0\le P_t^{SESS,relea}\le P_{\max }^{SESS}{U}_{relea}^{SESS}\\ U_{abs}^{SESS}+U_{relea}^{SESS}\le 1\\ U_{abs}^{SESS}\in \left\{0,1\right\}{U}_{relea}^{SESS}\in \left\{0,1\right\}\end{array},$$

(3)

3. Uncertainty Analysis Method of RES

3.1. Problem Description

The robustness of the RIES optimal operation requires that the system can maintain stable operation in the case of large fluctuations. At the same time, the robust RIES optimal scheduling results have practical engineering application significance. Therefore, considering the actual engineering situation, when the external RES available energy is the smallest, the stability of the system is the worst. Therefore, based on the theoretical requirements of robustness requirements, this paper sets the optimization goal as the minimum output of the RES. It is assumed that the output of the WT is $P_{i,t}^{WT}$ and the output of the PV cell is $P_{i,t}^{PV}$. Obviously, both $P_{i,t}^{WT}$ and $P_{i,t}^{PV}$ are time-varying parameters [31]. Therefore, the expression of the optimization problem with $P_{i,t}^{WT}$ and $P_{i,t}^{PV}$ parameters is as follows:

$$P_{i,t}^{RG}=\min f\left(P_{i,t}^{WT}+P_{i,t}^{PV}\right),$$

(4)

where f is the objective function. It is assumed that $P_{i,t}^{WT}$ and $P_{i,t}^{PV}$ change only at the specified time point of the specified scheduling conversion. In other words, within a fixed time period [0, T], the minimization problem described in (4) can be expressed by the changing behavior of definitions $P_{i,t}^{WT}$ and $P_{i,t}^{PV}$ as follows: the function sequence consisting of a set of static functions consisting of multiple subintervals $P_{i,t}^{WT}$ and $P_{i,t}^{PV}$ represents the optimization problem (4), which is described as follows:

$$\langle f\left(P_{i,1}^{WT},P_{i,1}^{PV}\right),\dots ,f\left(P_{i,t}^{WT},P_{i,t}^{PV}\right),\dots ,f\left(P_{i,T}^{WT},P_{i,T}^{PV}\right)\rangle ,$$

(5)

For the optimization problem defined by (5), ROOT is a novel algorithm used to solve this problem due to its ability to provide dynamic solutions according to specific time-varying fitness functions [15]. In order to better apply ROOT to obtain a more robust solution, this paper first uses the scenario method to obtain the typical output curve of renewable energy, fits the output curve and then substitutes the fitted result into the ROOT algorithm for calculation. At the same time, the existing ROOT algorithm finds a new robust solution according to its future predicted fitness value. However, the error of predicting the future fitness value is often too large, which makes it difficult to find a better robust solution. Aiming to solve the problems existing in the ROOT algorithm, this paper proposes a modified ROOT algorithm.

3.2. Scenario Analysis Method

In order to make the time-varying parameters of the WT and PV cell contained in the established dynamic optimization problem closer to the model reality, this paper chooses the LHS and BR scenario method as the pre-method to modify the ROOT calculation method, so as to ensure that the dynamic optimization algorithm can obtain a more robust solution in the time domain. The scenario generation method is a way to analyze the uncertainty of power systems by constructing deterministic scenarios, including scene generation and scene restoration. Scene generation refers to the generation of a large number of scenes with uncertain features based on the PDF of the research object, which is represented by the set S = {S₁, S₂, …, S_N}. Here, LHS is used to generate typical scenarios. Through the analysis of the generated scene data set $S$, BR is used here to filter the scenes with high similarity, and finally, the scene of set K = {K₁, K₂, …, K_M} with the highest expected value is obtained. Set _K can replace the large-scale low-probability scene of the original production with a small-scale high-probability scene. The process of scene analysis is shown in Figure 3.

3.3. Modified Robust Optimization over Time

The accuracy of the existing algorithm depends on the amount of statistical data, that is, the statistical data required to cover the past and current fitness values of the search space. However, in the problem of high dimension or large search space, as much data as possible are needed to obtain a more accurate approximation, which is difficult to achieve in practical engineering. Therefore, based on the spatial characteristics of the solution of the dynamic robust optimization problem, this paper finds three important metrics that affect the search robust optimal prediction: the sum of feasible direction, stability degree and floating value. Based on the three new metrics, ROOT-TSE-PCCG is proposed.

3.3.1. Feasible Direction

The FD is used to describe the change trend of the objective function, which is as follows:

$$R^{fd}\left(x,t,u,v\right)=\frac{1}{u+v+1}{\displaystyle \sum _{i=t-u}^{i=t+v}\left|f\left(x,{\phi }_{i+1}\right)-f\left(x,\phi \right)\right|},$$

(6)

where _u and _v are the number of historical and future environments, respectively; _t is the current moment; R^fd determines the FD of the objective function value (OFV) by calculating the sum of the objective function change value under _p historical environments, _q future environments and current _t and then taking the average value.

In the process of evolutionary optimization of the algorithm, the change trajectory of the corresponding solution can be obtained according to the change in the OFV of each solution in the whole dynamic environment. Taking the single-objective maximization problem as an example, 2 solutions are selected in 100 continuous dynamic environments based on whether the FD is considered. The trajectory of the OFV obtained is shown in Figure 4; both solutions are higher than the set threshold ${ }_{\delta }$. From Figure 1, it can be seen that in the A, B and C regions, the prediction error between the OFV and the actual value of the two is the same, but the solution considering the FD can judge the change trend of the optimal robust solution through the existing robust solution and the predictive robust solution, and better track the change direction of the optimal solution, so the overall error is small. Without considering the solution of the FD, the change trend of the optimal robust solution cannot be judged in time; so, the tracking effect of the optimal robust solution is general, and the overall error is large. Based on the above analysis, it can be seen that the introduction of the FD into the prediction solution helps to obtain a robust solution with better robustness.

3.3.2. Stability Degree

The SD is used to describe the stability of the predicted value, which is as follows:

$$\begin{array}{l}{R}^{SD}\left(x,t,u,v\right)=\left|\frac{f\left(x,{\phi }_j\right)-\left[\max f\left(x,{\phi }_i\right)+\min f\left(x,{\phi }_i\right)\right]}{\eta }\right|\\ s.t.i\in [1,u],j\in [t+1,v],\eta \in \left[1,+\infty \right)\end{array},$$

(7)

where ${ }_{\delta }$ is the fluctuation threshold.

The trajectory of the OFV obtained is shown in Figure 5; both solutions are higher than the set threshold $\delta$. As shown in Figure 5, it can be seen that the candidate robust solution considering the SD can judge its change range and offset the degree by the size of the value of the SD that is constantly updated. If the SD of the OFV is large, the prediction accuracy is poor at this time, and the robust solution obtained may not be accurate enough. If the SD of the OFV is small, the prediction accuracy is good at this time, and the accuracy of the robust solution obtained is high. From the above analysis, it can be seen that the value of the SD is also an important metric to guide the algorithm to find a solution with better robustness.

3.3.3. Sum of Floating Value

The SFV of the objective function in the adjacent environment can represent the change state of the OFV corresponding to the solution, which is as follows:

$$R^{SFV}\left(x,t,u,v\right)={\displaystyle \sum _{i=t-u}^{i=t+v}\left(f\left(x,{\phi }_{i+1}\right)-f\left(x,{\phi }_i\right)\right)},$$

(8)

The trajectory of the OFV obtained is shown in Figure 6; both solutions are higher than the set threshold ${ }_{\delta }$. As can be seen from Figure 6, the candidate robust solution considering the SFV can continuously predict the change state of the optimal robust solution at the next moment by updating the positive and negative values of the SFV, so as to better track the function value at a future moment so that the error of the robust solution is kept in a small interval. From the tracking curves of the A and B regions in Figure 3, it can be seen that the optimal robust solution cannot be effectively tracked without considering the candidate robust solution of the SFV when the optimization problem is in a state of fluctuation in a dynamic environment, thus increasing the prediction error of the algorithm. From the above analysis, it can be seen that the SFV is also an important metric in selecting the optimal robust solution.

3.4. Analysis Method of Renewable Energy Uncertainty Problem

Based on the above analysis, this paper introduces three new metrics on the basis of the existing ROOT algorithm and proposes the ROOT-TSE- PCCG algorithm. The algorithm flow chart is shown in Figure 7. The algorithm design idea of this paper can be reflected by the algorithm flow chart shown in Figure 7. Firstly, the typical output curve of the RES is calculated by using the pre-scene analysis method. On the basis of the output curve fitting results, $P_{i,t}^{WT}$ and $P_{i,t}^{PV}$ are rewritten as time-varying parameters and brought into the dynamic optimization problem shown in (4). Secondly, the proposed ROOT-TSE- PCCG algorithm is used to solve the dynamic optimization problem. Finally, the robust solution set is evaluated by using the two-stage evaluation method to obtain the optimal robust solution to the dynamic optimization problem.

4. Optimal Scheduling Model

4.1. Optimization Objective

The objective function is shown below.

$$\min C_{IES}=C_{grid}+C_{gas}+C_{om}+C_{sess},$$

(9)

where C_grid and C_gas are the electrical energy transaction expenditure and gas energy transaction expenditure of the EPG, respectively; C_om is the operation and maintenance expenditure of the RIES; C_sess is the energy transaction expenditure of the SESS.

$$C_{grid}={\displaystyle \sum _{n=1}^N{\displaystyle \sum _{t=1}^T\left(c_{b,t}^{gird}{P}_{n,t}^{Grid,buy}-c_{s,t}^{gird}{P}_{n,t}^{Grid,sell}\right)\Delta t}},$$

(10)

$$C_{gas}={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^T{c}_{gas}\left[P_{i,t}^{GT}/\left({\eta }_i^{GT}{H}_{ng}\right)+H_{i,t}^{GB}/\left({\eta }_i^{GB}{H}_{ng}\right)\right]\Delta t}},$$

(11)

$$C_{om}={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^T\left(K_{om}^{Elec}{P}_{i,t}^{Elec}+K_{om}^{Heat}{H}_{i,t}^{Heat}+K_{om}^{Cold}{C}_{i,t}^{Cold}\right)\Delta t}},$$

(12)

$$C_{sess}={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^T\left(c_{b,t}^{sess}{P}_{i,t}^{SESS,cha}-c_{s,t}^{sess}{P}_{i,t}^{SESS,dis}\right)\Delta t}},$$

(13)

4.2. Optimization Constraints

For the multi-district RIES shown in Figure 1, the constraints can be categorized into CCHP constraints, SESS constraints and coupling constraints between the CCHP and SESS, as shown in

Table 1. Optimization constraints of multi-district RIES.

Constraint Type	CCHP	SESS	Coupling Relationship
Equality constraints	1. Power bus energy balance constraints	1. Energy continuity constraint	1. CCHP-SESS energy coupling constraint
	2. Electric storage energy relationship constraints
Inequality constraints	1. Equipment operating power constraints	1. Charging/discharging power constraints	/
	2. Electric storage charging/discharging power constraints	2. Capacity constraints

.

The constraints of the CCHP and SESS can be found in references [26,31] and Section 2.2, respectively. At the same time, according to Table 1, the direct energy coupling constraints of the CCHP and SESS should be considered. That is to say, from the perspective of the coupling system and engineering practice, the cumulative value of the energy interaction of all users using the SESS for charging and discharging behavior at a certain scheduling moment should be equal to the energy input/output of the SESS itself at this moment, and the energy source of each charging and discharging behavior of the SESS should be the cumulative value of user charging/discharging behavior.

$${\displaystyle \sum _{i=1}^N\left(P_{i,t}^{SESS,dis}-P_{i,t}^{SESS,cha}\right)}=P_t^{SESS,relea}-P_t^{SESS,abs},$$

(14)

For the CCHP established in this paper, as shown in Figure 2, it is also necessary to meet the waste heat balance constraints of the waste heat boiler, as shown below.

$$H_{i,t}^{HE}/{\eta }_{he}+C_{i,t}^{AC}/{\eta }_{ac}=H_{i,t}^{GT}{\gamma }_{gt}{\eta }_{whb},$$

(15)

4.3. Optimization Method

After substituting the RES power data obtained based on the scenario analysis method, the model is transformed into an MILP model. In this paper, the commercial solver CPLEX12.8 and YALMIP toolbox are used to solve the model in Matlab R2021a [32].

5. Case Study

5.1. Simulation System

We take a more common comprehensive area as an example, as shown in Figure 8. As shown in Figure 8, the RIES established in this paper consists of four sub-districts: RA, CA, IA and OA [33,34]. Each sub-district has a self-built CCHP, and each sub-district is connected to the energy transmission line between the EPG and SESS.

Table A1. Capacity parameters (kWh).

Equipment	RA	CA	IA	OA
PV	2500	4500	8500	2500
WT	/	/	6500	3500
GT	2500	5500	8500	3500
GB	5500	5500	8500	5500
WHB	5500	5500	8500	5500
ES	/	1500	2500	/
EH	5500	5500	8500	5500
EC	5500	5500	8500	5500
HE	4500	4500	8500	4500
AC	5500	5500	8500	5500

and

Table A2. Efficiency parameters.

Equipment	RA	CA	IA	OA
Efficiency of GT	0.35	0.35	0.35	0.35
Heat-to-electricity ratio of GT	2.3	2.3	2.3	2.3
Efficiency of WHB	0.74	0.74	0.74	0.74
Efficiency of GB	0.86	0.86	0.86	0.86
Efficiency of EH	0.98	0.98	0.98	0.98
Efficiency of EC	4	4	4	4
Efficiency of AC	1.2	1.2	1.2	1.2
Efficiency of HE	0.9	0.9	0.9	0.9
Maximum charge power of ES	/	250 kW	500 kW	/
Maximum discharge power of ES	/	250 kW	500 kW	/
Capacity of ES	/	1000 kWh	2000 kWh	/

in Appendix A describe the parameters of the energy equipment contained in each region.

Table A3. Equipment parameters of SESS.

Parameter	Value	Parameter	Value
Charging efficiency	0.95	Initial state of SOC	0.50
Discharging efficiency	0.95	Maximum state of SOC	0.90
Self-discharging efficiency	0.04	Minimum state of SOC	0.20
Maximum discharge power	1000 kW	Maximum charge power	1000 kW

in Appendix A describes the operating parameters of the SESS equipment in this paper.

Table A4. Time-of-use electricity price of EPG (CNY/kWh).

Price Types	Time Interval	Purchase Price	Sale Price
Peak time	06:00–08:00 17:00–23:00	0.763	0.420
Usual time	04:00–06:00 10:00–16:00	0.521	0.420
Valley time	23:00–00:00 0:00–03:00	0.253	0.420

and

Table A5. Time-of-use electricity price of SESS (CNY/kWh).

Price Types	Time Interval	Purchase Price	Sale Price
Peak time	08:00–09:00 19:00–24:00	0.725	0.435
Usual time	00:00–02:00 05:00–07:00 10:00–11:00 18:00–18:00	0.475	0.435
Valley time	03:00–04:00 12:00–17:00	0.271	0.435

in Appendix A describe the time-of-use electricity prices of the EPG and SESS, respectively. The equipment efficiency parameters of the ES installed in the CA and IA are the same as those of the SESS equipment. At the same time, the price and calorific value of natural gas are 2.46 CNY/m³ and 9.78 kWh/m³, respectively. For security considerations in real life, the RA and CA are not equipped with a WT. Figure 9 shows the typical RES output curve and typical electrical, heat and cold load curves in each region.

From Figure 9, the OA is a multi-power-type district; the RD and ID are a flat-power-type district; the CA is a power-shortage-type district. And the scheduling time T of each typical day is 24 h.

5.2. Analysis of the Validity of Modified ROOT

To test the performance of ROOT-TSE-PCCG, all experiments in this paper are conducted on mMPB [16], which can be described as follows:

$$F_t\left(\overrightarrow{X}\right)=\stackrel{i=m}{\underset{i=1}{\max }}\left\{H_t^i-W_t^i\times {\Vert \overrightarrow{X}-{\overrightarrow{C}}_t^i\Vert }_2\right\},$$

(16)

where $F_t\left(\overrightarrow{X}\right)$ is the objective function; $H_t^i$, $W_t^i$ and ${\overrightarrow{C}}_t^i$ are the height, width and central position of the i-th peak function, respectively; $\overrightarrow{X}$ is the decision variable; _m is the total number of peaks. In order to remain dynamic, t is added to 1 after Δe in a certain period of time, and Δe is measured by the number of fitness evaluations. The dynamic changes in $H_t^i$, $W_t^i$ and ${\overrightarrow{C}}_t^i$ are as follows:

$$H_{t+1}^i=H_t^i+height\_severit{y}^i\times N\left(0,1\right),$$

(17)

$$W_{t+1}^i=W_t^i+width\_severit{y}^i\times N\left(0,1\right),$$

(18)

$${\overrightarrow{C}}_{t+1}^i={\overrightarrow{C}}_t^i+{\overrightarrow{v}}_{t+1}^i,$$

(19)

$${\overrightarrow{v}}_{t+1}^i=\frac{s\times ((1-\lambda )\times \overrightarrow{r}+\lambda \times {\overrightarrow{v}}_t^i)}{\Vert (1-\lambda )\times \overrightarrow{r}+\lambda \times {\overrightarrow{v}}_t^i\Vert },$$

(20)

where N (0, 1) is a random number of Gaussian distributions with a mean of zero and a variance of one. The height and width of each peak are initialized according to its own set of height_severityⁱ and width_severityⁱ, and the above two parameters are randomly selected in height_severity_range and width_severity_range. The parameter setting of mMPB is shown in reference [18]. The comparison algorithms are proposed in reference [16] and reference [18]. The experiment is tested under the condition that mMPB changes randomly 150 times, and each comparison algorithm runs independently 30 times to take the average value. The experimental results are shown in Figure 10.

It can be seen from Figure 10a,b that as the fitness threshold set by the dynamic optimization problem increases, the ST obtained by each dynamic optimization problem decreases. The larger the fitness threshold set, the higher the robustness of the robust solution obtained by the dynamic optimization problem in dealing with time-varying parameters. It can be seen that when the fitness threshold is set to 40, the robust solution obtained by the dynamic optimization algorithm has high robustness in the current external environment. However, when the fitness threshold is set to 50, some solutions with low robustness cannot adapt to the changing environment, resulting in a continuous decrease in the ST of the robust solutions obtained by each ROOT algorithm.

Similarly, from Figure 10c,d, it can be seen that the average robustness of the robust solution obtained by the dynamic optimization problem is also reduced with the increase in the set threshold. The larger the threshold setting of the time window, the higher the robustness of the robust solution obtained by the dynamic optimization problem when dealing with time-varying parameters. When time window value is set to 2, the robust solution obtained by dynamic optimization problem can adapt to the two minimum dynamic environments. When the time window value is set to 6, the robust solution obtained by requiring the previous time window to be 2 can satisfy more changing environments. At this time, some robust solutions cannot adapt to the changing environment of the outside world, resulting in a decrease in the average robustness of the robust solutions obtained by each ROOT algorithm.

In the case of mMPB, the robustness results of the average ST and the average AF of different algorithms are shown in

Table 2. Comparison of average ST and AF of different ROOT algorithms under mMPB.

Algorithm	Fitness Threshold		Time Window
	40	50	2	6
Jin’s ROOT	1.54	0.69	25.95	18.64
Fu’s ROOT	3.03	1.72	53.58	9.17
ROOT-TSE-PCCG	3.97	2.39	68.71	44.63

. The robustness of the proposed algorithm in terms of the average ST and the average AF is significantly improved compared with the comparison algorithm. From Table 2 and Figure 10, it can be seen that in general, with the increase in the threshold set by the decision maker, the average robust performance of each dynamic optimization algorithm shows a downward trend. At the same time, from the experimental results in the mMPB environment, it can be seen that the average robustness of the proposed algorithm has achieved good robustness results in any case.

5.3. Analysis of SESS Capacity Configuration and RIES Operation Cost

In order to study the influence of different RES uncertainty calculation methods on SESS capacity configuration and the role of the SESS in RIES optimal scheduling, SO is introduced as a comparison algorithm for solving RES uncertainty, and the following four modes are set up.

Mode 1: Calculation of RES output power using SO without considering the participation of the SESS in the optimized scheduling.

Mode 2: Calculation of RES output power using SO, and the SESS is considered to participate in optimal scheduling.

Mode 3: Calculation of RES output power using ROOT-TSE-PCCG without considering the participation of the SESS in the optimized scheduling.

Mode 4: Calculation of RES output power using ROOT-TSE-PCCG, and the SESS is considered to participate in optimal scheduling.

In the subsequent analysis, it is stipulated that the power is positive when the electric energy is charged into the SESS. At this time, it means that each sub-region charges its own electric energy into the SESS, and the power is negative when the electric energy is released by the SESS. At this time, it means that the electric energy in each region is recovering from the energy storage system. The results of SESS capacity configuration and RIES operation cost under different conditions are shown in

Table 3. The details of SESS capacity configuration and RIES operating cost under different modes.

Details of Operating Cost	Mode 1	Mode 2	Mode 3	Mode 4
Electrical energy transaction expenditure	18,410.47 CNY	15,122.97 CNY	17,410.43 CNY	14,225.04 CNY
Gas energy transaction expenditure	78,229.09 CNY	71,094.58 CNY	74,161.40 CNY	66,716.22 CNY
Operation and maintenance expenditure	6055.71 CNY	6117.08 CNY	5963.88 CNY	6120.32 CNY
Energy transaction expenditure with SESS	/	3571.85 CNY	/	3666.71 CNY
Capacity configuration of SESS	/	15,352.76 kWh	/	15,761.51 kWh
Total cost	102,695.27 CNY	95,906.49 CNY	97,535.71 CNY	90,728.29 CNY

.

By comparing mode 1 and mode 3, it can be seen that compared with SO, ROOT-TSE-PCCG can obtain a more robust solution due to the introduction of three metrics R^fd, R^SD and R^SFV. Therefore, when solving the dynamic optimization problem considering RES uncertainty, the total cost of the system can be reduced. Compared with mode 1, the total operating cost of mode 3 decreased by 5.02%. By comparing mode 2 and mode 4, it can be seen that the RES robust solutions obtained by different algorithms also have an impact on the capacity configuration of the SESS. Since the solution obtained by ROOT-TSE-PCCG is more robust, the required SESS capacity configuration is higher in this case, and the capacity configuration of the SESS under mode 4 is 2.66% higher than that under mode 2. In summary, ROOT-TSE-PCCG can better solve the RES uncertainty problem and obtain a more robust solution so that the RIES can operate under more economical and stable conditions. By comparing mode 3 and mode 4, it can be seen that when the RIES configures the SESS, the total operating cost of the system is further reduced. Although the cost of interaction between the RIES and SESS is increased, due to the complementary effect of the SESS by coordinating the power load curve of each region, the energy that cannot be absorbed by the rich areas of RESs can be reasonably stored and allocated to the areas in need. Therefore, the electricity and gas purchase costs of the whole RIES are reduced, of which the electricity purchase cost is reduced by 18.30% and the gas purchase cost is reduced by 10.04%. In summary, the rational allocation of SESSs is also an important means to enhance the stability of RIES operation and reduce operating costs.

5.4. Analysis of SESS-Optimized Operation Results

Taking the established mode 2 and mode 4 as an example, the optimal scheduling operation results of the SESS are calculated, and the optimal energy interaction results between each region and the SESS in each scheduling day are shown in Figure 11. In Figure 11, when the value represented by a vertical column is positive (the vertical column is above the left horizontal axis y = 0 kW), it means that the sub-region corresponding to the vertical column is charging electricity power into the SESS. Otherwise, it means that the sub-region corresponding to the vertical column retrieves electricity power from the SESS. The red curve represents the change curve of the state of charge at each scheduling moment of the SESS, and the value of the state of charge corresponds to the value of the right y axis.

It can be seen from Figure 11 that the SOC curves of the SESS under mode 2 and mode 4 are similar, because whether it is SO or ROOT-TSE-PCCG, the above algorithms calculate the robust output based on the uncertainty of historical data of RESs and do not produce large offset changes. At the same time, due to the different robust solutions obtained by different algorithms, the interaction strategy between each region and the SESS in the 15:00–20:00 time period is different. Combined with Figure 9, it can be seen that the OA mainly charges power into the SESS because it contains abundant RESs, and its own load is small. The RA, IA and CA are mainly powered from the SESS. It is worth noting that due to the large power load demand of the CA in the evening peak period, the CA purchases a large amount of power from the SESS during the 18:00–23:00 period. While meeting its own power load, it reduces the interaction with the EPG to achieve the purpose of reducing operating costs.

5.5. Analysis of Optimal Scheduling Results of RIES Considering SESS

We take mode 4 as an example to analyze the optimal scheduling result for each region in the RIES.

The optimal scheduling results of power load in each region of the RIES are shown in Figure 12. On the whole, RESs in all regions can participate in the actual power load supply; so, the optimal scheduling strategy can complete the consumption of RESs well. At the same time, the area with abundant RESs sells a large amount of electric energy to the EPG to reduce the operation cost of the whole system. Similarly, abundant electric energy can also be stored in the SESS to ensure the rational utilization of renewable energy in the RIES. Specifically, it can be seen from Figure 12a that the RA and CA only contain a PV cell, which belongs to the RES-deficient area. Therefore, when the RA has no PV output during 03:00–04:00 and 18:00–24:00, it is necessary to purchase electricity from the EPG to meet its own demand for power load. When the output power of the PV cell is large at 09:00–11:00, most of the users of the RA have moved to other areas to consolidate their lives. At this time, their own power load is small, so they can be charged to the SESS to improve their own electricity sales revenue and complete the consumption of RESs. For the CA, since the power load and heat load are at the peak stage during the period of 10:00–17:00, and during this period, the CA’s own photovoltaic power generation cannot meet the load’s demand for electricity, the CA mainly purchases electricity from the EPG during this period. In the rest of the time period, due to the comprehensive consideration of the coupling supply of cold and heat energy, some of the electricity is supplied through a GT. From Figure 12b, it can be seen that the IA has abundant RESs and its own power load is low; so, the IA can sell rich power resources to the EPG to earn profits. Similarly, while the OA region is rich in RESs, its own power load is lower than that of the IA, so it can sell a large amount of power to the EPG.

The optimal scheduling results of the RIES heat load are shown in Figure 13. On the whole, the thermal energy generated by the GB is the main source used to meet the thermal load in the region, accounting for 86.58% of the total cooling load supply, and the remaining thermal energy supply is completed by the HE and EB. The following is a detailed analysis of the thermal energy supply model for each region from Figure 14. Figure 13a shows the electric energy purchased from the EPG in the RA and CA areas. The RA and CA areas are mainly used to supply power to the EB, and the EB converts electric energy into heat energy to heat the area. In particular, because the electric load and heat load in the CA area are at their peak during 10:00–17:00 and the external electricity price is at the valley stage, the CA is mainly provided for by the EB during this period. It can be seen from Figure 13b that the IA and OA use the GB as the only device that provides more than 80% of thermal energy in a day. In particular, the IA only uses the EB and HE to provide a small amount of heat energy during the morning and evening due to electricity prices. The reason for the above results is that gasoline prices remain unchanged for a day. At the same time, in the process of the GB directly providing heat to the load, the energy from the conversion steps involved is less and the energy loss is lower.

Figure 14 shows the optimal scheduling results of the multi-region RIES cooling load. On the whole, the cold energy generated by the EC is the main source used to meet the cooling load in the region, accounting for 84.38% of the total cooling load supply, and the remaining cold energy supply is completed by the AC. The following is a detailed analysis of the cold energy supply mode in each region from Figure 14. From diagram (a), it can be seen that since there is no PV power supply in the RA area during 19:00–24:00, the EPG is in the peak stage of electricity prices, so the RA will use the GT to produce the required electricity, and the GT will produce high-temperature waste heat when running. In order to give full play to the advantages of the CCHP, improve energy utilization and reduce operating costs while ensuring the cascading utilization of energy, at this time, high-temperature waste heat passes through the heat pipe. Part of the heat energy is transmitted to the HE to continue to generate heat energy with a controllable success rate, and the other part of the heat energy is transmitted to the AC to convert high-temperature waste heat into cold power to the user. Thus, this is more economical to meet the user’s demand for cold power. Similarly, the optimal operation result of the CA is similar to that of the RA, that is, when there is no RES available, the AC is used to absorb high-temperature waste heat to provide the cooling load. It can be seen from Figure 14b combined with Figure 9b above that both the IA and OA are RES-rich areas. On the one hand, in order to consume their own RESs and reduce the rate of wind and light abandonment, and on the other hand, in order to reduce the expenditure of purchasing natural gas from the EPG and reduce the operating cost, the cooling load generated by the EC is mainly used to meet the needs of their users for the cooling load.

6. Conclusions

In this paper, the following work is carried out for the multi-area RIES optimal scheduling problem with an SESS, considering RES uncertainty. Firstly, a multi-area RIES system model considering SESS access is established. At the same time, the working state of SESS access of the RIES is considered from three aspects and the corresponding constraints are proposed. Secondly, PV cells and a WT are regarded as time-varying parameters, and a dynamic optimization problem model considering time-varying parameters is established. For such problems, this paper also proposes a ROOT-TES-PCPG algorithm combined with a scene analysis method to solve them. Finally, the proposed method is verified by establishing a practical example model. Based on the proposed different models, the following conclusions can be obtained through the results.

• For the dynamic robust optimization problem considering time-varying parameters, the improved ROOT algorithm based on the two-stage evaluation proposed in this paper has a better judgment effect on the predicted solution in the future, so that the robustness of the solution obtained by the overall algorithm is better. In the mMPB test environment, compared with the results of the existing ROOT algorithm, the solution AF index and ST index obtained by ROOT-TSE-PCPG are increased by 94.41% and 179.78, respectively. Therefore, the algorithm proposed in this paper provides a new method for calculating the optimal robust solution of dynamic optimization problems in practical engineering and has certain practical application value.
• When there are uncertainties such as a WT and PV cells in the RIES system, the ROOT-TSE-PCPG based on the scenario analysis method proposed in this paper can be used to analyze the uncertainty of RESs through the robust control method. At the same time, the method proposed in this paper can effectively reduce the operating cost of the RIES. The application of the proposed method in the optimal scheduling problem can reduce the operating cost of the whole system by 5.32% on average. Similarly, when there are multiple sub-energy regions in the system, the rational allocation of SESSs can make the energy consumption of the whole system more stable and the energy interaction more scientific, so as to achieve the purpose of reducing the operating cost of the system. The rational allocation of SESSs can reduce the operating cost of the whole system by an average of 6.81%, while considering the above two factors in the optimal scheduling problem can reduce the operating cost of the system by 11.65%. At the same time, the SESS also acts as an energy transmission line, which can transmit electricity from RES-rich areas to RES-deficient areas.

At present, although several SESS demonstration parks have been put into operation in China, they are still in the development stage. As China continues to move toward the goal of ‘carbon peak carbon neutrality’, the method proposed in this paper will provide a reference for the operation of SESSs in the future. At the same time, with the increasing uncertainty factors on the source-load side of the RIES, the operation cost and economy requirements of RIES optimal scheduling will be higher in the future, and the operation optimization objectives will be more diversified. Therefore, how to model and solve the dynamic robust optimization problem with multiple optimization objectives and uncertain time-varying parameters is an issue that needs to be studied in the future.