Optimal Configuration of Wind–Solar–Thermal-Storage Power Energy Based on Dynamic Inertia Weight Chaotic Particle Swarm

Abstract

The proposed approach involves a method of joint optimization configuration for wind–solar–thermal-storage (WSTS) power energy bases utilizing a dynamic inertia weight chaotic particle swarm optimization (DIWCPSO) algorithm. The power generated from the combination of wind and solar energy is analyzed quantitatively by using the average complementarity index (ACI) to determine the optimal ratio of wind and solar installations. We constructed a multi-objective optimization configuration model for the WSTS power generation systems, considering the equivalent annual income and the optimal energy consumption level as objective functions of the system. We solved the model using the chaotic particle swarm optimization algorithm with linearly decreasing dynamic inertia weight. To validate the effectiveness of the proposed approach, we conducted a simulation using the 2030 power energy base planning data of a particular region in Inner Mongolia. The results demonstrate that the proposed method significantly improves the annual income, enhances the consumption of wind–solar energy, and boosts the power transmission capacity of the system.

1. Introduction

Considering the growing global concerns regarding energy security, environmental sustainability, and climate change, countries worldwide are prioritizing the large-scale development and utilization of renewable energy, such as wind and solar power, in their energy strategies [1,2,3]. The Three-North regions of China host the country’s main renewable energy bases. However, the energy consumption capacity of these regions’ local markets is limited, and their power grid infrastructure is relatively weak. Hence, the construction of supporting transmission projects involving high-voltage and long-distance transmission lines is necessary to transmit excess electricity to load centers for consumption [4,5]. To address the challenges posed by the volatility, intermittency, and uncontrollability of wind and solar power generation, a combined WSTS system for outbound transmission utilizing the complementary characteristics of wind and solar power in the time domain is used to smooth out the power delivery curve and alleviate peak load pressure at the receiving end. This system is expected to become a prevalent energy development approach in the Three-North regions.

Currently, the optimization of the capacity of WSTS joint outbound systems and its transmission channel capacity is of great importance in large-scale wind–solar remote consumption, attracting significant attention from researchers. In their study, reference [6] determined the optimal configuration of the power generation system’s capacity by integrating wind farms and photovoltaic power stations using a multi-stage stochastic planning method. The objective function consisted of the scheduling cost of conventional generators, the penalty cost for load shedding, and the penalty cost of non-compliance with the renewable energy quota. In a similar vein, reference [7] addressed the uncertainties in wind speed, sunlight, load, and energy market prices and conducted simulation verification on a grid-connected hybrid photovoltaic–wind distribution system in North Texas. This approach yielded an optimal system power configuration scheme that minimized the system’s annual cost. However, it is important to note that the aforementioned references primarily focused on optimizing the capacity of the supporting power supply while neglecting the significance of transmission channels. To address this gap, reference [8] established a capacity optimization model for WSTS hybrid power systems. Their objective was to level the electricity cost and maximize the utilization of transmission channels. The simulation results demonstrated the effectiveness of the proposed model in improving the utilization of transmission channels in wind power hybrid systems, thus exhibiting enhanced reliability and economic performance. Additionally, reference [9] conducted a comprehensive analysis of the complementarity of wind and fire power and constructed a multi-objective optimization model to optimize the dispatch power of wind and fire power in the day ahead. The resulting operating scheme achieved the maximum wind power outbound, the highest utilization of transmission channels, and a minimum operating cost for fire power. The models presented in the above references often involve multiple objective functions, resulting in a set of trade-off solutions known as the Pareto frontier. Multiple methods are currently employed to solve multi-objective optimization problems, including the multi-objective differential evolution algorithm and the multi-objective particle swarm optimization algorithm [10,11,12]. While these algorithms possess strong optimization capabilities and exhibit fast convergence, they also face challenges such as difficulty in balancing convergence and the diversity of the Pareto optimal solution set, as well as the uneven distribution of the optimal frontier. Therefore, further research in this area is imperative.

Based on the above, this paper presents an optimization approach for configuring a joint WSTS outbound system. Firstly, the complementary characteristics of wind–solar power output in a power energy base are quantitatively analyzed using the ACI. This analysis enables the determination of an optimal wind–solar capacity ratio that maximizes complementary benefits. Moreover, the objective functions of the system’s equivalent annual profit and optimal new energy consumption level are considered, leading to the establishment of a multi-objective optimization configuration model for the WSTS base. To solve this model, the DIWCPSO algorithm is employed. Finally, a simulation is conducted using the planning data of a power energy base in a specific region of Inner Mongolia in the year 2030 to verify the effectiveness of the proposed optimization configuration method.

2. Evaluation Indicators for Wind and Solar Power Output Characteristics

Wind power and solar power exhibit complementarity in terms of time and space. The degree of complementarity in their combined output is influenced by the varying proportions of installed capacities for different wind and solar power sources. This study introduces complementary indicators based on the rate and magnitude of output changes to evaluate the presence and strength of complementarity among various power sources in renewable energy installations [13]. Consequently, these indicators facilitate the identification of the most efficient allocation of wind and solar capacities.

(a)

Output change rate

$$r=\frac{P_{t+T}-P_t}{P_{\mathrm{rated}}}\times 100\%$$

(1)

where $P_t$ represents the power output of wind farms or photovoltaic power stations at time t, while $P_{\mathrm{rated}}$ represents the rated capacity of wind farms or photovoltaic power stations.

(b)

Output change magnitude

$$\gamma =\frac{P_{t+T}-P_t}{T}$$

(2)

(c)

Average complementarity index

Consistency index:

$$\alpha =\{\begin{array}{l}\left|r_{\mathrm{WT} }-r_{\mathrm{PV} }\right|\frac{r_{\mathrm{WT} }{r}_{\mathrm{PV} }}{\left|r_{\mathrm{WT} }{\delta }_{\mathrm{PV} }\right|},r_{\mathrm{WT} }\ne 0,r_{\mathrm{PV} }\ne 0\hfill \\ \left|r_{\mathrm{WT} }-r_{\mathrm{PV} }\right|, \mathrm{else}\hfill \end{array}$$

(3)

where $r_{\mathrm{WT}}$ and $r_{\mathrm{PV}}$ represent output change rate indicators for wind farms and photovoltaic power stations, respectively. When $\alpha$ = 0, the rates and directions of wind power and solar power are consistent. When $\alpha$ > 0, the rates are inconsistent, but the directions remain the same. Conversely, when $\alpha$ < 0, the rates and directions are opposite, indicating the presence of complementarity.

Complementarity measure index:

$$\beta =\left|{\gamma }_{\mathrm{WT} }+{\gamma }_{\mathrm{PV} }\right|$$

(4)

where ${\gamma }_{\mathrm{WT}}$ and ${\gamma }_{\mathrm{PV}}$ represent indicators for the magnitude of output changes in wind farms and photovoltaic power stations, respectively. When $\beta$ = 0, it indicates that the change in output direction for wind power and solar power is opposite, with equal magnitudes, achieving complete complementarity within the time period T. When $\beta$ > 0, it indicates that there is partial complementarity, and further analysis with the indicators can determine the degree of complementarity.

ACI:

$$\mu =\{\begin{array}{ll}{\displaystyle \sum _{i=1}^{n-1}\left|\frac{\alpha \beta }{\left|\alpha \right|(n-1)}\right|},\hfill & \alpha ⩽0\hfill \\ 0,\hfill & \alpha >0\hfill \end{array}$$

(5)

where $n$ represents the number of sampling periods, and the size of $\mu$ indicates the strength of complementarity.

3. Optimization Model for the Configuration of a WSTS Energy Base with a Coordinated Dispatch System

3.1. Structure of the Coordinated Dispatch System for the Power Energy Base

The structure of the coordinated dispatch system for the power energy base studied in this paper is illustrated in Figure 1. In the figure, $P_t^{\mathrm{line}}$ represents the power delivered from the power energy base, $P_t^{\mathrm{load}}$ denotes the local electricity demand, $P_t^{\mathrm{TH}}$ represents the output power of the thermal power units, $P_t^{\mathrm{PV}}$ indicates the output power of the photovoltaic power stations, and $P_t^{\mathrm{WT}}$ indicates the output power of the wind farms. Additionally, $P_t^{\mathrm{ESS}}$ represents the output power of the wind energy storage and solar energy storage. The power energy base encompasses multiple wind farms and photovoltaic power stations, complemented by corresponding wind energy storage and solar energy storage facilities. Energy storage is utilized for peak-shaving and valley filling, thereby mitigating the fluctuations in wind turbine and photovoltaic power outputs. The coordinated operation of large-capacity conventional thermal power units and energy storage devices (ESDs) enables substantial peak-shaving support for electricity delivery. Moreover, the ultra-high-voltage direct current transmission channel possesses favorable characteristics, such as high transmission capacity and long-distance transmission capability, making it suitable for transmitting renewable energy power.

3.2. Mathematical Model of a Joint Dispatch System for a Power Energy Base

In this section, we address the optimization configuration problem of a joint dispatch system used for power energy bases. Our objective is to maximize the system’s equivalent annual revenue and optimize the level of new energy absorption. To achieve this, we need to configure the output power of its thermal power units, the capacity of its wind and solar energy storage, and the power export capacity of the system. This configuration should not only ensure good economic performance but also facilitate the integration of new energy sources.

3.2.1. Objective Function

(a)

Equivalent Annual Revenue $E$

The equivalent annual revenue of the system includes annual electricity sales income, $E_{\mathrm{sell}}$; unit investment and operation costs, $C_{Yw}$; and assessment fees, $C_{Kh}$.

$$\max E=E_{\mathrm{sell}}-C_{Yw}-C_{Kh}$$

(6)

The annual electricity sales income, $E_{\mathrm{sell}}$, of the system comes from the equivalent annual electricity sales income of wind farms, photovoltaic power stations, and thermal power plants. The specific form is as follows:

$$E_{\mathrm{sell}}={\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{t=1}^{24}\left\{{\gamma }_{sell,WT}{\displaystyle \sum _{i=1}^{N_{\mathrm{WT}}}\left(P_{i,t}^{\mathrm{WT}}+P_{i,t}^{\mathrm{ESS},\mathrm{WT}}\right)}+{\gamma }_{sell,PV}{\displaystyle \sum _{i=1}^{N_{PV}}\left(P_{i,t}^{\mathrm{PV}}+P_{i,t}^{\mathrm{ESS},\mathrm{PV}}\right)}+{\gamma }_{sell,TH}{P}_t^{\mathrm{TH}}\right\}}}$$

(7)

where $N_{\mathrm{WT}}$ and $N_{PV}$ represent the number of wind farms and photovoltaic power stations, respectively. ${\gamma }_{sell}$ represents the selling price of electricity for different power plants. $P_{i,t}^{\mathrm{WT}}$ and $P_{i,t}^{\mathrm{PV}}$ represent the output power of the i-th wind farm and photovoltaic power station at time t. $P_t^{\mathrm{TH}}$ represents the power generation of the thermal power plant at time t. $P_{i,t}^{\mathrm{ESS},\mathrm{WT}}$ and $P_{i,t}^{\mathrm{ESS},\mathrm{PV}}$ represent the power generation of the self-storage energy of the i-th wind farm and solar power plant at time t.

The cost, $C_{Yw}$, involved in unit investment and operation comprises the investment cost, $C_{inv}$; operation cost, $C_{om}$; and fuel expenses of the unit, $C_{fuel}$.

$$\{\begin{array}{l}{C}_{Yw}=C_{inv}+C_{om}+C_{fuel}\\ C_{\mathrm{inv} }=I_{\mathrm{ESS}}{C}_{\mathrm{ESS}}+I_{TH}{C}_{TH}+I_{\mathrm{line} }{C}_{\mathrm{line} }\\ I=\frac{r{(r+1)}^L}{{(r+1)}^L-1}\\ C_{\mathrm{ESS}}={\displaystyle \sum _{i=1}^{N_{\mathrm{w}}+N_{\mathrm{pv}}}\left({\gamma }_{\mathrm{P}}{P}_{N,i}^{ESS}+{\gamma }_{\mathrm{S}}{S}_i^{ESS}\right)}\\ C_{\mathrm{line} }={\gamma }_{\mathrm{line} }{l}_{\mathrm{line} }{P}_{\max }^{line},C_{TH}={\gamma }_{TH}{S}_N^{TH}\\ C_{\mathrm{om}}={\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{l=1}^{24}\left[{\displaystyle \sum _{i=1}^{N_{\mathrm{WT}}}\left({\pi }_{WT}{P}_{i,t}^{\mathrm{WT}}+{\pi }_{ESS}{P}_{i,t}^{\mathrm{ESS},\mathrm{WT}}\right)}+{\displaystyle \sum _{i=1}^{N_{PV}}\left({\pi }_{PV}{P}_{i,t}^{\mathrm{PV}}+{\pi }_{ESS}{P}_{i,t}^{\mathrm{ESS},\mathrm{PV}}\right)}\right]}}\\ C_{\mathrm{fuel}}={\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{t=1}^{24}\left(a{\left(P_t^{TH}\right)}^2+b{P}_t^{\mathrm{TH}}+c\right)}}\end{array}$$

(8)

where $I_{\mathrm{ESS}}$ and $I_{\mathrm{line} }$ represent the annual value coefficients of energy storage and transmission lines, respectively. r represents the discount rate. L represents the lifespan of each unit, with ESS being 10 years, TH being 25 years, and line being 30 years. $C_{\mathrm{ESS}}$, $C_{TH}$, and $C_{\mathrm{line} }$ represent the investment costs for ESS, TH, and line, respectively. ${\gamma }_{\mathrm{P}}$ and ${\gamma }_{\mathrm{S}}$ represent the power cost and unit cost of energy storage, respectively. ${\gamma }_{TH}$ represents the construction cost per unit capacity of the thermal power plant. $S_N^{TH}$ represents the capacity of the thermal power plant. $P_{N,i}^{ESS}$ and $S_i^{ESS}$ represent the rated power and installed capacity of the i-th energy storage unit. ${\gamma }_{\mathrm{line} }$ represents the investment cost for the transmission line per unit length. $l_{\mathrm{line} }$ represents the length of the transmission line. $P_{\max }^{line}$ represents the capacity of the transmission line. ${\pi }_{WT}$, ${\pi }_{PV}$, and ${\pi }_{ESS}$ represent the unit operational costs of wind power plants, photovoltaic power stations, and energy storage, respectively. a, b, and c represent the coal consumption coefficients of the thermal power units.

The assessment of system costs, $C_{Kh}$, primarily takes into account the penalties for curtailed solar power and curtailed electricity in a combined power generation system. It can be represented as follows:

$$C_{kh}={\gamma }_{WT,PV}{\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{t=1}^{24}\left[{\displaystyle \sum _{i=1}^{N_{\mathrm{WT}}}\left(P_{i,t}^{\mathrm{WT}}+P_{i,t}^{\mathrm{ESS},\mathrm{WT}}\right)}+{\displaystyle \sum _{i=1}^{N_{PV}}\left(P_{i,t}^{\mathrm{PV}}+P_{i,t}^{\mathrm{ESS},\mathrm{PV}}\right)}+P_t^{\mathrm{TH}}-P_t^{\mathrm{line}}-P_t^{\mathrm{load}}\right]}}$$

(9)

where ${\gamma }_{WT,PV}$ represents the penalty cost per unit of power for curtailed wind and solar energy. $P_t^{\mathrm{line}}$ and $P_t^{\mathrm{load}}$ represent the exported power from the renewable energy base and the local load, respectively.

(b)

Level of renewable energy consumption, $\pi$

$$\max \pi =\frac{{\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{t=1}^T\left(P_t^{\mathrm{load}}+P_t^{line}-P_t^{\mathrm{TH}}\right)}}}{{\displaystyle \sum _{d=1}^{365}{\displaystyle \sum _{t=1}^{24}\left({\displaystyle \sum _{i=1}^{N_{\mathrm{WT}}}{P}_{\mathrm{N},i}^{\mathrm{WT}}}+{\displaystyle \sum _{i=1}^{N_{\mathrm{PV}}}{P}_{\mathrm{N},i}^{\mathrm{PV}}}\right)}}}$$

(10)

where $\pi$ represents the level of renewable energy consumption. $P_{\mathrm{N},i}^{\mathrm{WT}}$ and $P_{\mathrm{N},i}^{\mathrm{PV}}$ represent the rated power of the i-th wind farm and solar power plant.

3.2.2. Constraint Conditions

(a)

Constraint on Thermal Power Units

$$\{\begin{array}{l}{P}_{t,\min }^{\mathrm{TH}}<P_t^{\mathrm{TH}}⩽P_{t,\max }^{\mathrm{TH}}\\ -r_{THD}⩽P_t^{\mathrm{TH}}-P_{t-1}^{\mathrm{TH}}⩽r_{THU}\end{array}$$

(11)

where $P_{t,\max }^{\mathrm{TH}}$ and $P_{t,\min }^{\mathrm{TH}}$, respectively, represent the maximum and minimum output power of the thermal power unit. $r_{THU}$ and $r_{THD}$, respectively, represent the maximum upward ramp rate and maximum downward ramp rate of the thermal power unit.

(b)

Constraint on Energy Storage device

$$\{\begin{array}{l}\begin{array}{l}{P}_t^{ESD}=(P_t^{ESD,ch}{\eta }^{ESD,ch}-P_t^{ESD,dc}/{\eta }^{ESD,dc})\Delta t\\ S_t^{ESD}=S_{t-1}^{ESD}+P_t^{ESD},S^{ESD,\min }\le S_t^{ESD}\le S^{ESD,\max }\end{array}\hfill \\ 0\le P_t^{ESD,ch}\le {\beta }_t^{ESDch}{P}_t^{ESD,ch,\max }\hfill \\ 0\le P_t^{ESD,dc}\le {\beta }_t^{ESD,dc}{P}_t^{ESD,dc,\max }\hfill \\ {\beta }_t^{ESD,ch}+{\beta }_t^{ESD,dc}=1,S_1^{ESD}=S_{24}^{ESD}\hfill \end{array}$$

(12)

where $S_t^{ESD}$ is the capacity of the ESD in period $t$; ${\beta }_t^{ESD,ch}$ and ${\beta }_t^{ESD,ch}$ are the charge–discharge state binary variable; $P_t^{ESD,ch}$ and $P_t^{ESD,dc}$ are the maximum charging and discharge electric power of the ESD; $S_t^{ESD,\max }$ and $S_t^{ESD,\min }$ are the maximum and minimum capacities of the ESD, respectively; ${\eta }^{ESD,ch}$ and ${\eta }^{ESD,dc}$ are the charging and discharging efficiencies of the ESD; and $\Delta t$ is the length of each time period (1 h).

(c)

Constraint on System’s Operating Power

The output of electricity from the combined transmission system of the renewable energy base at any given moment must meet the essential demand of the local load. This can be described as

$${\displaystyle \sum _{i=1}^{N_{\mathrm{WT}}}\left(P_{i,t}^{\mathrm{WT}}+P_{i,t}^{\mathrm{ESS},\mathrm{WT}}\right)}+{\displaystyle \sum _{i=1}^{N_{PV}}\left(P_{i,t}^{\mathrm{PV}}+P_{i,t}^{\mathrm{ESS},\mathrm{PV}}\right)}+P_t^{\mathrm{TH}}-P_t^{line}-P_t^{\mathrm{load}}⩾0$$

(13)

(d)

Constraint on System Export Power

The description of the combined transmission system of the renewable energy base can be defined as maximizing the export of electricity while ensuring sufficient power supply to the local grid and the secure and stable operation of the transmission channels.

$$\{\begin{array}{l}0⩽P_t^{line}⩽P_{\max }^{line}\hfill \\ {\displaystyle \sum _{t=1}^{24}{P}_t^{line}}⩾{\eta }_{line}{\displaystyle \sum _{t=1}^{24}{P}_{\max }^{line}}\hfill \\ -r_{line}{P}_{\max }^{line}⩽P_t^{line}-P_{t-1}^{line}⩽r_{line}{P}_{\max }^{line}\hfill \end{array}$$

(14)

where $P_{\max }^{line}$ represents the maximum value of the export power from the renewable energy base. ${\eta }_{line}$ represents the lower bound of the utilization rate for the export power channels of the renewable energy base. $r_{line}$ represents the limit for the rate of change of the export power from the renewable energy base.

3.3. The Solving Process of the Model Based on a DIWCPSO

The objective function of the developed model for the integrated outbound system of the power energy base considers both the equivalent annual income of the system and the level of new energy consumption, thus addressing a multi-objective decision problem. Solving multi-objective decision problems is inherently complex, and there is no dominant relationship between the objective values in different dimensions. In this study, the multi-objective particle swarm optimization (MOPSO) algorithm [14], known for its low number of parameters, fast search speed, and strong optimization capabilities, is employed for the solution. The formulas for updating the velocity and position of individual particles during the optimization iteration process are represented by Equations (15) and (16):

$$v_{i,k}^{\sigma +1}=w{v}_{i,k}^{\sigma }+c_1{r}_1\left(p_{i,k}-x_{i,k}^{\sigma }\right)+c_2{r}_2\left(g_k^{\sigma }-x_{i,k}^{\sigma }\right)$$

(15)

$$x_{i,k}^{\sigma +1}=x_{i,k}^{\sigma }+v_{i,k}^{\sigma +1}$$

(16)

where k represents the number of parameters in the optimization problem. $\sigma$ denotes the iteration count. $x_{i,k}^{\sigma }$ and $v_{i,k}^{\sigma }$ represent the position and velocity, respectively, of the kth dimension of the i-th particle at the $\sigma$-th iteration. $c_1$ and $c_2$ are the acceleration factors of the algorithm. $r_1$ and $r_2$ are random numbers between 0 and 1. $p_{i,k}$ represents the best historical position of the k-th dimension for the i-th particle. $g_k^{\sigma }$ represents the best position of the kth dimension in the population at the $\sigma$-th iteration. $w$ represents the inertia weight.

3.3.1. Dynamic Inertia Weight Chaotic Particle Swarm

(a)

Chaotic Initialization

Chaotic phenomena are widely recognized as nonlinear, exhibiting complex and random behavior with intricate underlying patterns. Considering the poor uniformity of the initial population in the standard multi-objective particle swarm optimization algorithm, this study employs Tent mapping to generate chaotic sequences for population initialization. The Tent mapping traversal demonstrates both uniformity and randomness, allowing for the preservation of population diversity and enhancing global search capabilities [15]. The specific mathematical model is presented as follows:

$$Z_{p+1}=\{\begin{array}{c}\frac{Z_p}{\lambda }\\ \frac{1-Z_p}{1-\lambda }\end{array}p=0,1,2,\cdots$$

(17)

where $Z_p$ represents the p-th chaotic vector, and $\lambda$ represents the control parameter. The specific process is as follows: generating an initial chaotic variable, $Z_0$; iterating multiple times using Equation (17) to generate multiple chaotic vectors; and then mapping each vector back to the range of the independent variables to generate the initial population of particles.

(b)

Adjustment of Inertia Weight

The inertia weight, $w$, plays a crucial role in the overall performance of the algorithm. When the inertia weight, $w$, is small, it may adversely affect the local search capability of the particle swarm algorithm. Conversely, when the inertia weight is large, it tends to enhance the algorithm’s global search ability. In order to improve the initial global optimization speed and post-optimal local search capability, the weight in this study is set to linearly decrease with the iteration count within a certain range, as expressed below.

$$w=w_{\max }-\left(w_{\max }-w_{\min }\right)t/t_{\max }$$

(18)

where $w_{\max }$ and $w_{\min }$ represent the maximum and minimum values of the inertia weight, respectively. $t_{\max }$ represents the upper limit of the iteration count.

3.3.2. Solution Steps

In this paper, a DIWCPSO algorithm is proposed. The key improvement steps of the algorithm are described in detail above. The specific solution process of the algorithm is illustrated in Figure 2.

4. Case Study

This case study is based on the planning data of a large-scale power energy base in a region of Inner Mongolia, China, for the year 2030. The wind and solar installation ratio is determined based on an optimal ratio of 1:0.5, obtained in Section 3.1. The photovoltaic capacity is set to 15 GW, and the wind power capacity is set to 7.5 GW. It is necessary to allocate a certain capacity of wind storage and solar storage for each wind and photovoltaic unit, with the supporting storage capacity being no less than 20% of its own installed capacity. The initial charging state is set at 0.5, with upper and lower limits of 0.9 and 0.1 respectively. The maximum charging and discharging power is equal to the rated power, which is 1,584,000 CNY/MW, and the maximum energy capacity is 3,390,000 CNY/MWh. Additionally, taking into account the current development and policy requirements of thermal power, this case study chooses 6 GW of supportive coal-fired power as complementary power for aggregated outward transmission. The unit investment cost for coal-fired power is 3800 CNY/kW, and the local coal price is 400 CNY/t. The model does not consider the grid structure and assumes that the new energy from the base is transmitted through a 600 km long-distance high-voltage direct current transmission line at a cost of 1800 CNY/km·MW.

4.1. A Comparison of the Complementary Characteristics of Wind and Solar Energy Bases

This study analyzes the average complementary index, $\mu$, of different wind–solar installation ratios, $\theta$, in a specific area of Inner Mongolia based on wind speed data from a wind turbine tower and solar radiation data from a meteorological station recorded hourly throughout the year 2022. The data are transformed into a theoretical output for wind turbines and photovoltaic arrays. The results, depicted in

Table 1. Comparison of complementary rates under different wind and solar installation ratios.

$\mathit{\theta }$	$\mathit{\mu }$
1:1.2	0.1986
1:1.1	0.2391
1:1.0	0.2515
1:0.9	0.2751
1:0.8	0.2896
1:0.7	0.3047
1:0.6	0.3202
1:0.5	0.3459
1:0.4	0.3184
1:0.3	0.2868
1:0.2	0.2208

, illustrate the comparison of average complementary indices under different wind–solar installation ratios.

According to Table 1, as $\theta$ decreases, $\mu$ exhibits an increasing-then-decreasing trend. The point of inflection, representing the maximum value, is observed at a wind–solar installation ratio of 1:0.5. Opting for a wind–solar installation configuration that corresponds to the maximum value of $\mu$ enables the full utilization of the natural complementary characteristics of wind and solar energy in both space and time, thereby preventing the wastage of resources.

4.2. Validation of the Superiority of the DIWCPSO Algorithm

In order to validate the effectiveness of the proposed algorithm, the DIWCPSO algorithm presented in this paper is compared with the standard MOPSO algorithm and the NSGA-II [16] algorithm. The Pareto optimal front obtained after the iterative execution of these three algorithms is depicted in Figure 3.

According to Figure 3, the Pareto frontiers of the three algorithms exhibit the same trend, indicating a positive correlation between the system’s equivalent annual income and the level of renewable energy consumption. This is because, as the amount of renewable energy generation increases, although there is a gradual increase in the investment and operation costs of the units, there is also an improvement in the utilization rate of renewable energy, as well as the revenue from selling the electricity. Additionally, the reduction in wind and solar energy curtailment also lowers the assessment costs. When comparing the three algorithms, the Pareto graph coverage range of the DIWCPSO algorithm is larger. To some extent, this leads to an improvement in continuity and evenness, which verifies the superiority of chaotic initialization. Furthermore, the Pareto graph of the DIWCPSO algorithm tends toward a better direction (higher equivalent annual income under the same wind and solar energy consumption rate). The results of the optimal solution search for the DIWCPSO algorithm, the MOPSO algorithm, and the NSGA-II algorithm are presented in

Table 2. The results of optimal solution search under different algorithms.

Solution Method	Wind Energy Storage Capacity/GW	Solar Energy Storage Capacity/GW	Outgoing Capacity/GW	$\mathbf{Equivalent} \mathbf{Annual} \mathbf{Income}/{10}^{10}$ CNY
DIWCPSO	1.6	3.2	8.0	2.08
MOPSO	1.6	3.2	7.8	1.89
NSGA-II	1.6	3.2	7.7	1.83

. From this table, it can be seen that the DIWCPSO algorithm achieves a 10.05% increase in the system’s equivalent annual income compared with the MOPSO algorithm and a 13.66% increase compared with the NSGA-II algorithm. This confirms that setting the linearly decreasing inertia weight is advantageous for improving the algorithm’s ability to find local optima. It is worth noting that there is little difference in the wind energy storage capacity and solar energy storage capacity between the different algorithms. This is because the investment cost of battery energy storage is currently high, and decision-makers aim to maximize the system’s equivalent annual income, so they try to reduce the capacity of the energy storage configuration as much as possible. Therefore, the results of the energy storage configuration are close to the lower limit specified for the storage configuration.

4.3. A Comparison to Determine Whether to Implement an ESD in the Wind–Solar-Thermal Power Energy Base

The main function of energy storage in a combined wind, solar, and fire power energy base with an interconnection system is to mitigate power output fluctuations and adjust the supply cycle to effectively improve the utilization of transmission channels. In order to verify the economic and reliable performance of the model proposed in this paper, a comparison is made between a wind–solar–thermal (WST) system (Case 1) and a WSTS system with the same wind and solar capacity (Case 2). The results of comparing the equivalent annual income, various cost components, and wind and solar energy consumption levels in different scenarios are presented in

Table 3. Comparisons between Case1 and Case2.

Case	$\mathbf{Equivalent} \mathbf{Annual} \mathbf{Income}/{10}^{10}$ CNY	Energy Consumption Level Rate	$\mathbf{Electricity} \mathbf{Sales} \mathbf{Income}/{10}^{10}$ CNY	$\mathbf{Unit} \mathbf{Investment} \mathbf{and} \mathbf{Operation} \mathbf{Cos}\mathbf{ts} \mathbf{Cos}\mathbf{ts}/{10}^{10}$ CNY	$\mathbf{Assessment} \mathbf{Fees}/{10}^{10}$ CNY	Dynamic Recycling Cycle/a
Case1	1.84	85.36%	6.19	1.28	1.02	5.52
Case2	2.08	93.64%	6.92	2.35	0.87	4.73

.

As shown in Table 3, the incorporation of energy storage into the WST system leads to an increase in investment and operational costs for the storage power station. The unit investment and operation costs of the system increase from 1.28 × 10¹⁰ CNY to 2.35 × 10¹⁰ CNY, representing an increase of 83.59%. However, this increase is offset by the rise in revenue from selling electricity and a reduction in assessment costs. Consequently, the equivalent annual income of the system significantly rises from $1.84\times {10}^{10}$ CNY to $2.08\times {10}^{10}$ CNY, marking a 13.04% increase. The dynamic recycling cycle decreases from the original 5.52 a to 4.73 a. Additionally, the renewable energy consumption rate improves by 8.28%. Therefore, adding an energy storage power station to the WST interconnection system enables the utilization of the storage system’s temporal energy characteristics and efficient regulation capabilities, ultimately enhancing the system’s renewable energy consumption level and economic benefits. Furthermore, to analyze the regulating advantages of energy storage in more detail, Figure 4 exhibits the power export curve for different scheduling schemes on typical days in each season.

As shown in Figure 4b, during the period from 1:00 to 9:00 and 20:00 to 24:00 on a typical summer day, the net load power output is lower than the transmission power of the transmission channel in the WSTS system. The energy storage system in the WSTS system compensates for the power supply shortage through discharge. However, because of the lack of energy storage in the WST system, the transmission channel cannot be fully utilized. During the period from 10:00 to 19:00, the net load power output is higher than the transmission channel power, and the WSTS system can store the excess electricity through energy storage, while the WST system can only achieve power balance through the abandonment of wind and solar power after the thermal power units are operating at full load. Similar situations also occur on other typical days, as shown in Figure 4a,c,d. It is worth mentioning that, in some extreme scenarios—such as prolonged intermittent wind and solar power outputs or a significant deviation of the net load curve from the transmission power of the transmission channel—the WST system will generate a large amount of wind and solar power abandonment, which seriously threatens the stability of the power transmission and the economic viability of the system. As described above, compared with the WST system without energy storage, the introduction of energy storage into the WST system effectively reduces the fluctuation range of the system’s power transmission, improves the utilization rate of the transmission channels, and enhances the stability of power transmission.

4.4. Sensitivity Analysis of ESD Cost

The cost of ESDs is an important factor affecting the benefits of renewable-energy-based power exports. With the development of technology and policy support, the cost of ESDs has significant potential for reduction. By using the model introduced in this paper, calculations were performed for different multiples of unit power and capacity costs for ESDs. The results are shown in Figure 5.

According to Figure 5, it can be observed that, with the decrease in the cost of ESD, the equivalent annual return and energy consumption level rate of the WSTS system gradually increase. This is because the reduction in ESD costs allows for a larger proportion of ESD allocation in the system. With the increase in ESD capacity, more electricity can be released and stored to adjust the local load and power export, resulting in higher and more stable power export through the transmission channel, reduced wind and solar power abandonment, increased revenue from power sales, and lower assessment costs. At the same time, with the ESD accounting for a significant proportion of the investment costs, the fast reduction in its cost multiplier leads to a rapid decrease in unit investment and operation costs, which, together, contribute to a significant increase in the system’s annual equivalent return. Additionally, it is worth noting that, after the decrease in the cost multiplier of energy storage exceeds 0.6, the growth rate of the energy accommodation rate slows down significantly. This is because, as the ESD capacity further increases, the ESD’s power charge and discharge can smooth out most of the power fluctuations in the transmission channel, resulting in deceleration in the growth of the energy accommodation rate.

5. Conclusions

To improve the energy consumption level of new energy in Inner Mongolia and address the issues of wind and solar power curtailment and insufficient power supply, this study proposes an optimized configuration method for a combination of WSTS systems. Based on the ACI, the optimal ratio of wind and solar installation is determined, and a multi-objective optimization model is established for the combination system. Simulation and verification are conducted using data from a power energy base in Inner Mongolia, leading to the following conclusions:

(1)

Because of the inherent differences in wind and solar resources, wind power and solar power exhibit complementary benefits in terms of temporal and spatial distribution. By calculating the ACI, this study determines the optimal ratio of wind and solar installation, effectively reducing the fluctuation level of their power output.

(2)

By incorporating chaotic initialization and linearly decreasing inertial weights into the MOPSO algorithm, the continuity and uniformity of the Pareto frontier are improved, enhancing the algorithm’s optimization capability.

(3)

Introducing an ESD into the WST system not only improves the equivalent annual revenue and the integration capacity of new energy but also effectively reduces the fluctuation range of power output in the combined system. This is beneficial for optimizing the utilization of transmission channels and ensuring the stability of power delivery. The optimized annual equivalent revenue increased by 13.04%, and the consumption rate of renewable energy increased by 8.28%. Additionally, the cost of energy storage significantly constrains its application. As the cost of the ESD decreases, the system’s new energy integration capacity and economic benefits will further improve.