Simulation of Time-Sequence Operation Considering DC Utilization Hours of New Energy Base in Desert and Gobi Area

Abstract

Direct current power transmission is a crucial method for consuming new energy in desert and Gobi regions. Given the issue of the inefficient use of transmission channels, this study develops a simulation model for the operational time sequence of new energy bases in these areas. The model integrates factors such as hours of DC power transmission, environmental impacts, economic considerations, and operational flexibility. Initially, the model addresses the significant variability and unpredictability of wind and solar energy in these regions by introducing an analysis method combining Gaussian Kernel Density Estimation (GKDE) with a Gaussian Mixture Model (GMM). Subsequently, a flexible DC power transmission operational model is formulated, taking into account different DC transmission modes. The model’s efficiency is enhanced by employing the Dung Beetle Optimization algorithm with nondominated sorting to minimize variable ranges and expedite solution times. The model’s effectiveness is demonstrated through a simulation applied to a new energy base in Gansu Province, Northwest China, confirming its validity.

1. Introduction

To expedite the development of a clean, low-carbon, safe, and efficient energy system, China has prioritized the construction of extensive new energy bases in deserts, the Gobi, and wastelands [1]. Nonetheless, the variability of new energy output in these areas, particularly its seasonal characteristics, often exacerbates the peak load pressures on thermal power units and limits the full utilization of the transmission capacity within new energy corridors. The “14th Five-Year Plan” for a modern energy system emphasizes enhancing the construction of interprovincial and cross-regional power transmission channels, aiming for an average utilization exceeding 4500 h annually for these DC transmission channels. Employing power system timing operation simulations—a fundamental tool for both planning and operational processes [2]—to model the scheduling at new energy bases in desert and Gobi regions is crucial. This approach not only helps determine the power supply operational plan but also facilitates a quantitative assessment of the average utilization hours of the DC transmission channels. Such assessments are essential for improving the efficiency of new energy transmission channels and enhancing the consumption capacity at these new energy bases.

Timing operation simulation predominantly focuses on power production involving new energy sources. Extensive research has been conducted on the scheduling and planning of large-scale, multi-energy, multi-timescale new energy power systems. Serving as a crucial technical approach for studying large-scale multi-energy systems, mid/long-term time-series operation simulations are required to account for factors such as multi-energy complementarity, diverse power characteristics of different energy sources, and the uncertainty of new energy outputs [3,4,5,6]. A multi-timescale time-sequence operation simulation model for large-scale new energy power systems was introduced in [7]. This model differentiates between medium- and long-term operation simulations that address the seasonal variations in new energy output and short-term models that tackle the stochastic nature of these outputs, yielding comprehensive and accurate simulation results. Consequently, the simulation of new energy base time series operations in desert and Gobi areas should initially analyze the volatility and randomness of wind and photovoltaic power, in alignment with the specific characteristics of new energy outputs in these regions.

Numerous scholars have developed various index systems to quantify the fluctuation characteristics of wind power. These systems include metrics such as the wind power capacity factor, credible capacity factor, and peak and valley coefficients, which facilitate a detailed analysis of wind power fluctuation distribution across diverse spatial and temporal scales [8,9,10]. An improved scene reduction method, which integrates enhanced K-means clustering with the simultaneous backward generation elimination algorithm, was introduced in [11]. This method aims to represent complex scenarios with a minimal set of representative scenes effectively. Additionally, a renewable energy scene reduction technique that combines clustering and optimization algorithms was proposed in [12] to efficiently achieve scene reduction. However, expressing the volatility of wind PV is more suitably conducted probabilistically, and K-means clustering faces challenges with determining the optimal number of clusters.

In the realm of DC outgoing operation models, a high-voltage DC liaison line operation model was introduced in [13] to enhance the regulation of inter-regional wind power. Addressing the challenge of large-scale wind power aggregation within the sender power system, a two-stage optimal scheduling model was developed in [14]. This model facilitates day-ahead optimal scheduling for the sender power system. To fully leverage the flexible regulation capacity of the UHV DC liaison line, a multitemporal coordinated optimization method that considers the joint outflow of wind, photovoltaic, and photothermal energies was devised in [15], significantly improving the utilization of wind and solar resources. Additionally, a joint scheduling plan model integrating flexible direct, pumped storage, and thermal power was proposed in [16], aimed at optimizing the joint scheduling strategy to maximize new energy consumption. Lastly, a time-series simulation calculation method, performing week-by-week calculations across a full year of 8760 h, was proposed in [17] to achieve reasonable optimization of the medium- and long-term operation modes of the DC outgoing system. Furthermore, a multi-objective optimization methodology for enhancing the overall transmission capacity of AC-DC hybrid interfaces is put in [18]. This proposed methodology is designed to reduce the initial investment costs associated with the energy delivery system while simultaneously promoting the utilization of renewable energy sources.

Notwithstanding the comprehensive nature of the aforementioned studies, none of them investigated the influence of the DC transmission mode on the operational modeling of HVDC liaison lines. In the context of China’s market-based power trading, a singular transmission trading mode no longer reflects the actual production scenarios accurately. Additionally, while these studies primarily focus on maximizing new energy consumption, they do not necessarily ensure the efficient operation of the DC transmission channel. For instance, the Qishao UHV system, during its initial year and ten months of operation, transmitted a total of 9 billion kWh to Hunan, which is substantially lower than its designed annual capacity of 40 billion kWh. Consequently, the actual utilization rate fell below the design value.

Addressing the challenges outlined previously, this study introduces a simulation model for the time-sequence operation of new energy bases in desert and Gobi areas, with a focus on DC utilization hours. Given the volatility of wind power output in these regions, the number of Gaussian functions in the Gaussian Mixture Model (GMM) is determined by analyzing wind power and photovoltaic output data using “Gaussian Kernel Density Estimation (GKDE) + GMM”. Concurrently, a flexible DC transmission model that incorporates DC transmission modes is developed. This model primarily employs mid/long-term DC transmission modes, with spot DC transmission serving as a supplementary mechanism for the consumption of wind power and photovoltaic energy. In solving the time-series operation model, the dung beetle optimization algorithm with non-dominated sorting is utilized to reduce variable counts and decrease the computational times required by commercial solvers. Ultimately, a simulation model for the time-sequence operation of the desert and Gobi area New Energy Base is proposed, taking into account DC utilization hours, environmental factors, economic considerations, and operational flexibility. The model’s efficacy is demonstrated using a case study from the New Energy Base in Gansu Province, Northwest China. Results indicate that the model facilitates efficient utilization of the DC transmission channel and high levels of new energy consumption while accounting for economic, flexibility, and environmental factors.

This paper is organized as follows. Section 2 analyzes the fluctuation characteristics of wind power and photovoltaic in desert, Gobi, and desert beach areas; Section 3 constructs an operation model for new energy bases in desert, Gobi, and desert beach areas; Section 4 describes the objective function and solution process of the operation simulation model for new energy bases in desert, Gobi, and desert beach areas; and in Section 5, the simulation results of the basic scenarios as well as the time-sequence operation simulation with the addition of pumped storage are given, respectively, and the results are analyzed. The simulation results are analyzed. Finally, Section 6 is the conclusion.

2. Analysis of the Volatility of Wind Power Output in the Gobi and Desert Area

The large volatility of wind power output in the desert and Gobi area is the main factor affecting DC transmission. At present, the k-means method is mostly adopted to analyze the clustering of wind power, but it is only able to strictly divide the data and cannot reflect the probability characteristics of the volatility. GMM could be an excellent solution to the above problems. Firstly, the Gaussian mixture model could fit all shapes theoretically. In addition, the clustering results of GMM are expressed through the form of probability, which does not force the data points to be divided into a certain class, and it is possible to better reflect the volatility and stochasticity of the scenic outflow of the desert and Gobi area. Therefore, it utilizes GKDE estimation in this paper for the initial processing of the scenery data. The kernel density estimation is the ability to analyze the extent to which the current dataset conforms to the Gaussian function, thus determining the number of Gaussian functions for the GMM.

The standard deviation is commonly employed to measure the fluctuation of new energy output, and to determine the fluctuation of two adjacent moments, the mean value in the standard deviation is replaced with the value of the scenery output at the previous moment. The formula is as follows Equation (1):

$$S=\sqrt{{\displaystyle \frac{1}{T_w}}\sum _{t=1}^{T_w}{\left(P_t-P_{t-1}\right)}^2}$$

(1)

where: $T_w$ is the time scale of the calculation, a total of 168 h for one week, $P_t$ and $P_{t-1}$ denote the wind power or PV output data under the moments of t and $t-1$, respectively.

In addition to the fluctuation timeshare as another indicator to describe the volatility of wind and light output, when the change in output from the previous moment to the next moment exceeds $\delta$, it is regarded as output fluctuation. The formula is as follows Equation (2):

$$T=T_{\mathrm{wave}}/T_w$$

(2)

where: $T_{\mathrm{wave}}$ is the time of the week when the wind or PV output fluctuates.

Calculate the level of fluctuation and the percentage of time of fluctuation for each week in the three desert regions of Tengger, Badanjilin and Kumutag. These data are analyzed with Gaussian kernel density estimation and the results are obtained as shown in Figure 1 and Figure 2.

According to the kernel density estimation results in the figures, the T-value of wind power and the S, T-value of PV output are bimodal in the volatility indicators of wind power and PV, indicating that they conform to two Gaussian distributions. The S-value of wind power output is single-peaked, indicating compliance with one Gaussian distribution. Therefore, the number of Gaussian functions of the Gaussian mixture model for wind power and PV is determined to be 2.

The results of the GMM analysis are shown in

Table 1. GMM analysis results.

Function	Mixing Factor	Center Coordinate	Covariance
Gaussian function 1 for wind power	0.4151	(0.0854, 0.1425)	[0.00076, 0.00144; 0.00144, 0.00376]
Gaussian function 2 for wind power	0.5849	(0.1347, 0.2845)	[0.00093, 0.00147; 0.00147, 0.00441]
Gaussian function 1 for PV	0.8822	(0.1164, 0.2705)	[0.00023, 0.00004; 0.00004, 0.00103]
Gaussian function 2 for PV	0.1178	(0.1078, 0.1875)	[0.00148, 0.00260; 0.00260, 0.00496]

. Based on the parameters in Table 1 it is sufficient to calculate the probability that the fluctuating data of the wind and light outputs for each week belong to each Gaussian function, which is calculated by the following (3) and (4):

$$g_w(k,S,T)={\displaystyle \frac{{\alpha }_w\left(k\right)\ast G_w\left(S,T\mid {\mu }_{wi},{\sigma }_{wi}^2\right)}{{\sum }_{i=1}^2{\alpha }_w\left(k\right)\ast G_w\left(S,T\mid {\mu }_{wi},{\sigma }_{wi}^2\right)}}$$

(3)

$${\mathit{g}}_s(k,S,T)={\displaystyle \frac{{\alpha }_s\left(k\right)\ast G_s\left(S,T\mid {\mu }_{si},{\sigma }_{si}^2\right)}{{\sum }_{i=1}^2{\alpha }_s\left(k\right)\ast G_s\left(S,T\mid {\mu }_{si},{\sigma }_{si}^2\right)}}$$

(4)

where: ${\mathit{g}}_w(k,S,T)$ and ${\mathit{g}}_s(k,S,T)$ denote the probability of wind power and PV output fluctuation characteristics belonging to Gaussian function i, respectively. ${\alpha }_w\left(k\right)$ and ${\alpha }_s\left(k\right)$ denote the mixing coefficients of wind power and PV Gaussian function i, ${\mu }_{wi}$ and ${\sigma }_{wi}^2$ denote the center coordinates and covariance of wind power Gaussian function i, ${\mu }_{si}$ and ${\sigma }_{si}^2$ denote the center coordinates and covariance of PV Gaussian function i, S and T denote the weekly fluctuation index of wind power, $G_w$ and $G_s$ denote the probability value of wind power and PV fluctuation index belonging to the probability value of the two-dimensional Gaussian function.

The probability calculation of the wind power $\mathrm{PV}$ volatility data of the example scenario is shown in Figure 3, where $\mathrm{W}\_\mathrm{g}1$ and $\mathrm{W}\_\mathrm{g}2$ denote the wind power Gaussian function 1 and the wind power Gaussian function 2, respectively, and $\mathrm{S}\_\mathrm{g}1$ and $\mathrm{S}\_\mathrm{g}2$ denote the PV Gaussian function 1 and the PV Gaussian function 2, respectively. As shown in Figure 3, the lighter the color denotes the higher the probability of being affiliated with the current Gaussian function, and the darker the color denotes the lower the probability of being affiliated with the current Gaussian function. In this paper, the wind PV output is reconstructed based on the calculated probability values.

3. New Energy Base Operational Model for the Desert and Gobi Area

3.1. Power Operation Constraints

3.1.1. Wind and Solar Power Output Range Constraints

The value of wind and solar power output is greater than zero and less than the theoretical value. As shown in (5) and (6):

$$0\le p_t^w\le p^w$$

(5)

$$0\le p_t^s\le p^s$$

(6)

where: $p_t^w$ and $p_t^s$ denote the wind power and PV output at the moment t, respectively, $p^w$ and $p^s$ denote the theoretical upper limit of wind power and PV output at the time period t, respectively.

3.1.2. Thermal Power Unit Operational Constraints

Aggregate modeling is applied to thermal power units [17]. The constraints include (7)–(10):

$$x_t^g{p}_{min}^g\le p_t^g\le x_t^g{p}_{max}^g$$

(7)

$$x_{min}^g\le x_t^g\le x_{max}^g$$

(8)

$$p_t^g-p_{t-1}^g-p_{min}^g\left(x_t^g-x_{t-1}^g\right)\le \Delta p_{up}^g{x}_{t-1}^g\Delta t$$

(9)

$$p_{t-1}^g-p_t^g-p_{min}^g\left(x_{t-1}^g-x_t^g\right)\le \Delta p_{\mathrm{down}}^g{x}_t^g\Delta t$$

(10)

where: t is the sequence of time periods, $\Delta t$ is the time spanned by a single time period, $p_t^g$ denotes the output power of a thermal power unit, $p_{\min }^g$ expresses the minimum technical output of a thermal power unit, $p_{max}^g$ denotes the maximum output power, of a thermal power unit during a state of stable operation, $x_t^g$ is the number of thermal power units commissioned, $x_{\max }^g$ is the maximum number of thermal power units commissioned, $x_{min}^g$ is the minimum number of thermal power units commissioned, $\Delta p_{up}^g$ denotes the maximum creeping power of a single thermal power unit, $\Delta p_{\mathrm{down}}^g$ denotes the maximum climbdown power of a single thermal power unit.

3.1.3. Photothermal Power Station Operational Constraints

The same photovoltaic power plant adopted the aggregation model [19,20]. The constraints include (11)–(18):

$$\begin{array}{c}\hfill E_t^{TES}=E_{t-1}^{TES}+\left[{\eta }_{in}^{TES}{p}_t^{TE\mathrm{S}-in}-p_t^{TES-out}/{\eta }_{out}^{TES}\right]\Delta t\end{array}$$

(11)

$$0\le p_t^{IES-in}\le p_{max,t}^{TES-in}$$

(12)

$$p_{max,t}^{TES-in}=\left(p_t^{\mathrm{solar}}-p_t^{\mathrm{solarw}}\right){\eta }^{SF}$$

(13)

$$p_t^{\mathrm{solar}}=S·E_t^{\mathrm{solar}}$$

(14)

$$0\le p_t^{TES-\mathrm{out}}\le p_{max}^{TES-\mathrm{out}}$$

(15)

$$E_{min}^{TES}\le E_t^{TES}\le X_t^{csp}{E}_{max}^{TES}$$

(16)

$$x_t^{csp}{p}_{min}^{csp}\le p_t^{csp}={\eta }^{csp}{p}_t^{TES-out}\le x_t^{csp}{p}_{max}^{csp}$$

(17)

$$0\le x_t^{csp}\le X_t^{csp}$$

(18)

where: $E_t^{TES}$ indicates the heat storage capacity of the heat storage tank in time period t, ${\eta }_{\mathrm{in}}^{TES}$, ${\eta }_{\mathrm{out}}^{TES}$ is the storage and release heat efficiency of the heat storage tank, $p_t^{TES-in}$, $p_t^{\mathrm{TES}-\mathrm{out}}$ indicate the heat storage power of the heat storage tank and the heat release power of the heat storage tank in time period t, respectively. $p_{maxt}^{TES-in},p_{max}^{TES-out}$ indicate the upper and lower limits of the heat storage capacity of the heat storage tank and the heat release power of the heat storage tank, respectively. $E_{max}^{TES},E_{min}^{TES}$ indicate the upper and lower limits of the heat storage capacity of the individual photovoltaic power plant, $p_t^{csp}$ indicates the generator set output power, $p_{max}^{csp},p_{min}^{csp}$ indicate the generator set output power upper and lower limits, $X_t^{csp}$ is the number of photovoltaic power plants put into operation, $X_t^{csp}$ is the maximum number of photovoltaic power plants put into operation, ${\eta }^{csp}$ is the thermoelectric conversion efficiency, $p_t^{\mathrm{solar}}$ is the total irradiated power, $p_t^{\mathrm{solanw}}$ is the discarded power, ${\eta }^{SF}$ is the photothermal conversion efficiency, S is the area of the mirror field, and $E_t^{\mathrm{solar}}$ is the irradiance.

3.1.4. Electrochemical Energy Storage Operational Constraints

The electrochemical energy storage power plants are the main means of realizing the new energy time shift, and the operation model includes (19)–(25):

$$Q_{soc}=E_t^b/E_N^b$$

(19)

$$p_{t,c}^{bat}=\left\{\begin{array}{c}-u_t^{ch}{p}^{bat}{Q}_{soc}\in (0,0.5)\hfill \\ -u_t^{ch}{p}^{bat}{\displaystyle \frac{0.9-Q_{soc}}{0.4}}{Q}_{soc}\in (0.5,0.9)\hfill \\ 0Q_{soc}\in (0.9,1)\hfill \end{array}\right.$$

(20)

$$p_{t,d}^{bat}=\left\{\begin{array}{c}{u}_t^{dc}{p}^{bat}{Q}_{soc}\in (0.5,1)\hfill \\ u_t^{dc}{p}^{bat}{\displaystyle \frac{Q_{soc}-0.1}{0.4}}{Q}_{soc}\in (0.1,0.5)\hfill \\ 0Q_{soc}\in (0,0.1)\hfill \end{array}\right.$$

(21)

$$p_t^{bat}=u_t^{dc}{p}_{t,d}^{bat}-u_t^{ch}{p}_{t,c}^{bat}$$

(22)

$$u_t^{ch}+u_t^{dc}\le 1$$

(23)

$$E_t^b=E_{t-1}^b-\left[{\eta }^{ch}{u}_t^{ch}{p}_t^{ch}-u_t^{dc}{p}_t^{dc}/{\eta }^{dc}\right]\Delta t$$

(24)

$$E_{min}^b\le E_t^b\le E_{max}^b$$

(25)

where: $Q_{soc}$ denotes the energy storage battery SOC at time t, $E_t^b$ indicates the storage power of the storage power station in time t, $E_N^b$ indicates the rated capacity of the energy storage, $p_{t,c}^{bat}$ indicates the charging power of the storage battery, $p_{t,d}^{bat}$ indicates the discharge power of the energy storage, $p_t^{\mathrm{bat}}$ is the charge/discharge power of the storage power station in time period t, $p^{\mathrm{bat}}$ indicates the maximum charge/discharge power of the storage power station, $u_t^{ch}$, $u_t^{dc}$ is the charge/discharge state of the storage power station in time period t, all of them are 0–1 integer variables, the storage power station is charged in time period t with $u_t^{ch}=1$, the storage power station is discharged in time period t with $u_t^{dc}=1$, the charging/discharging state of the storage power station at the same time is mutually exclusive, $E_t^b$ indicates the storage power of the storage power station in time period t, ${\eta }^{ch},{\eta }^{dc}$ is the charging/discharging efficiency of the storage power station, $E_{max}^b,E_{min}^b$ indicate the maximum and minimum power storage capacity of the storage power station.

3.1.5. Pumped Storage Plant Operational Constraints

The pumped storage power plant selects a variable-speed constant-frequency unit to enable continuous adjustability of the pumping power of the plant under pumping conditions. The constraints include (26)–(31):

$$C_t^{\mathrm{Resup}}=C_{t-1}^{\mathrm{Resup}}+p_t^{cx}{u}_t^{wp}{\eta }^{wp}-p_t^{cx}{u}_t^{wt}{\eta }^{wt}$$

(26)

$$C_t^{\mathrm{Res}\mathrm{down}}=C_{t-1}^{\mathrm{Res}\mathrm{down}}-p_t^{cx}{u}_t^{wp}{\eta }^{wp}+p_t^{cx}{u}_t^{wt}{\eta }^{wt}$$

(27)

$$C_{min}^{\mathrm{Resup}}\le C_t^{\mathrm{Resup}}\le C_{max}^{\mathrm{Resup}}$$

(28)

$$C_{min}^{\mathrm{Resdown}}\le C_t^{\mathrm{Resdown}}\le C_{max}^{\mathrm{Res}\mathrm{down}}$$

(29)

$$-u_t^{wp}{p}^{wp}\le p_t^{cx}\le u_t^{wt}{p}^{wt}$$

(30)

$$u_t^{wt}+u_t^{wp}\le 1$$

(31)

where: $C_t^{\mathrm{Resup}}$, $C_t^{\mathrm{Res}\mathrm{down}}$ indicates the storage capacity of the upper and lower reservoirs of the pumping-storage power station, $C_{min}^{\mathrm{Resup}}$, $C_{max}^{\mathrm{Resup}}$, $C_{min}^{\mathrm{Res}\mathrm{down}}$, $C_{max}^{\mathrm{Res}\mathrm{down}}$ are the maximum and minimum storage capacity of the upper and lower reservoirs, $p_t^{cx}$ indicates the operating power of the pumping-storage power station, $p^{wp}$, $p^{wt}$ indicates the maximum pumping power and the maximum generating power of the pumping-storage power station, ${\eta }^{wt}$, ${\eta }^{wp}$ are the conversion coefficients of the water/electricity quantity for the electricity generation and the pumping, $u_t^{wt}$, $u_t^{wp}$ are the power generation/pumping state variables, all of which are 0–1 variables, so when the pumping-storage unit is in the generating state, $u_t^{wt}=1$, when the pumping-storage unit is in the pumping state, $u_t^{wp}=1$, the power generating and pumping states are mutually exclusive.

3.2. Flexible DC Transmission Operational Model

To be close to the actual production situation, the flexible DC transmission model established in this paper takes the DC transmission mode into consideration. Currently, the DC transmission modes are mainly: mid/long-term transmission mode and spot transmission mode. The mid/long-term transmission mode needs to determine the DC transmission power curve in the transaction period with rigid implementation requirements. Spot transmission mode does not require a power curve, but only wind power PV trading, requiring no new thermal power output [21]. The transmission mode is based on the mid/long-term transmission mode, the spot transmission mode is mainly for the wind power PV not covered by the mid/long-term transmission mode for trading, to enhance the level of consumption and utilization of DC transmission channel and economic benefits.

This paper studied enhancing the stable delivery capability of AC and DC systems through the utilization of flexible DC transmission technology [22]. This methodology circumvents the inherent limitations of conventional DC transmission, namely phase change faults and reactive power compensation. In addition, benefiting from the excellent performance of flexible DC technology, this paper no longer limits the number of DC daily regulations, the shortest 1h power regulation can be carried out once, and the maximum number of DC daily regulations is 24 times. The constraints include (32)–(40):

$$PDC{L}_{min}\le PDC{L}_t^k\le PDC{L}_{max}$$

(32)

$$PDC{X}_{min}\le PDC{X}_t^k\le PDC{X}_{max}$$

(33)

$$-▵PDCL\le PDC{L}_t^k-PDC{L}_{t-1}^k\le ▵PDCL$$

(34)

$$-▵PDCX\le PDC{X}_t^k-PDC{X}_{t-1}^k\le ▵PDCX$$

(35)

$$PDC{L}_t^k=p_t^w+p_t^s+p_t^g+p_t^{csp}+p_t^{bat}+p_t^{cx}$$

(36)

$$\begin{array}{c}\hfill PDC{L}_t^k+PDC{X}_t^k=p_t^w+p_t^s+p_{t-1}^g+p_t^{csp}+p_t^{bat}+p_t^{cx}\end{array}$$

(37)

$$E_{DCL}=\sum _k\sum _{t}PDC{L}_t^k\Delta t$$

(38)

$$E_{DCX}=\sum _k\sum _{t}PDC{X}_t^k\Delta t$$

(39)

$$\left(E_{DCL}+E_{DCX}\right)/P_{DCN}\ge T_{min}^{DC}$$

(40)

where: $PDC{L}_t^k,PDC{L}_{min},PDC{L}_{max}$ indicates the $\mathrm{DC}$ mid/long-term transmission power at hour t, week k, the minimum and maximum DC mid/long-term transmission power, $PDC{X}_t^k$, $PDC{X}_{min}$, $PDC{X}_{max}$ indicates the DC spot transmission power at hour t, week k, the minimum and maximum DC spot transmission power, $▵PDCL$, $▵PDCX$ indicates the DC mid/long-term transmission power and the upper limit of the DC spot transmission power climb, $E_{DCL}$, $E_{DCX}$ indicates the DC mid/long-term transmission power and the DC spot transmission power, $P_{DCN}$ is the rated power of the transmission, $T_{min}^{DC}$ is the minimum number of hours of DC utilization.

4. Simulation Model of Time-Sequence Operation of New Energy Base in Desert and Gobi Area

4.1. Objective Function

The objective function considers the economic benefits, environmental factors, and flexibility of the desert and Gobi area New Energy Base while considering the DC utilization hours. The net profit, carbon emission, and peak shaving and valley filling power are used to quantify the economic benefits, environmental factors, and flexibility of the Desert and Gobi Area New Energy Base. The objective function is as follows (41)–(45):

$$f_h=max\sum _{k=1}^{52}{T}_k^{DC}$$

(41)

$$f_c=max\sum _{k=1}^{52}\left[C_{in}^k-C_{cost}^k\right]$$

(42)

$$f_{ce}=min\sum _{k=1}^{52}{C}_{gce}^k$$

(43)

$$f_d=max\sum _{k=1}^{52}\left(E_{bat}^k+E_{cx}^k\right)$$

(44)

$$C_{cost}^k=C_w^k+C_s^k+C_g^k+C_{csp}^k+C_{bat}^k+C_{cx}^k+C_{DC}^k+C_q^k$$

(45)

where: $f_h$, $f_c$, $f_{ce}$, $f_d$ are DC utilization hours, net profit, carbon emission, and peak shaving and valley filling power, respectively. $T_k^{DC}$ represents the DC utilization hours in the k week, $C_{in}^k$ is the revenue from electricity sales in week k, calculated as the product of annual electricity sales and cross-provincial electricity price, and cross-provincial electricity price is shown in

Table 2. Electricity sales price.

Type of Transmission	Electricity Sales Price (CNY/kWh)
Thermal power landed price	0.41072
New energy landed price	0.49872

. $C_{cost}^k$ is the cost of the base in week k, where $C_w^k$, $C_s^k$, $C_{csp}^k$, $C_{bat}^k$, $C_g^k$, $C_{cx}^k$ are the cost of wind power generation, photovoltaic power generation, solar thermal power, energy storage, thermal power, and pumped storage in week k. The base cost is calculated as the product of kWh cost and generation capacity. The cost of kWh refers to the comprehensive cost incurred by the project unit of on-grid electricity, which mainly includes the investment cost, operation and maintenance cost and financial cost of the project and the specific cost of kWh is shown in

Table 3. Unit cost of electricity.

Power Type	Cost of kWh (CNY/kWh)
Thermal power	0.32
Wind power	0.24
PV	0.35
Electrochemical energy storage	0.66
Solar thermal power generation	0.70
Pumped storage	0.25
Wind and light reductions	0.60

and

Table 4. DC outgoing cost and thermal power carbon emission factor.

DC Outgoing Costs	Carbon Emission Factors for Thermal Power
644 CNY/(km·MW/a)	832 (g/kWh)

. $C_{DC}^k$ is the transmission cost of ±800 kV DC in week k, calculated as the product of transmission power and unit distance transmission cost and transmission distance, $C_q^k$ is the penalty cost of wind and light abandonment in week k, $C_{gce}^k$ is the carbon emission of thermal power in week k, $E_{bat}^k$, $E_{cx}^k$ is the amount of peak-shaving and valley-filling power of energy storage and pumped storage in week k.

4.2. Solution Method

The problem of computational efficiency is particularly prominent in the mid/long-term time-series operation simulation, where the solution needs to be repeatedly invoked to realize full-cycle multi-scenario simulation. The current solution includes three main aspects [2]:

• Decompose the original problem into subproblems that can be processed in parallel.
• Variable reduction and constraint reduction.
• Application of larger scale computational resources.

It adopts the method of reducing some variables to solve the problem of low computational efficiency and long solution time of the time series operation model in this paper. The detailed method is to simplify the constraints, then adopt the dung beetle optimization algorithm with non-dominated ordering to solve the model preliminarily; the solution result of the algorithm can be regarded as the boundary value of DC power in the scenario to reduce the range of solving for the timing operation simulation model and reduce the solving time. The solution schematic is shown in Figure 4.

The process is shown in Figure 5. Simulation of the Time-Sequence Operation model is solved by calling the GUROBI solver through YALMIP for multi-objective solving in the MATLAB platform. The first choice is to reconstruct the scenery data based on the results of the scenery volatility analysis and simplify some of the constraints, and use the dung-beetle optimization algorithm with non-dominated ordering to make preliminary calculations of the example scenarios to obtain the boundary values of the DC power. The boundary value is passed to the time series operation simulation model, which is called several times for solving to finally arrive at the multi-objective optimal solution for the whole year.

5. Case Analysis

Calculations simulate the Tengger Desert’s new energy base power supply configuration: wind power 4 million kilowatts, photovoltaic 7 million kilowatts, peaking coal power 4 million kilowatts, photothermal 0.2 million kilowatts, electrochemical storage of 2 million kilowatts (2 h), and the planning of pumped storage power station 1 million kilowatts, considered in the comparison scenarios. The total installed capacity of the base is 18.2 million kilowatts, of which wind power, photovoltaic power and photothermal power generation have an installed capacity of 11.2 million kilowatts, representing 61.54% of the total installed capacity. When pumped storage is taken into account, the installed capacity of renewable energy accounts for 67.07% of the total installed capacity. The base scenario indicators are shown in

Table 5. Base scenario run simulation metrics.

Parametric Indicators	Numerical Value
DC utilization hours (h)	≥4500
Mid/long-term DC transmission cycle (week)	1
Mid/long-term DC outgoing power shortest stabilization time (h)	4
Spot outgoing power duration (h)	8 (9:00∼17:00)
Percentage of minimum technical output of thermal power (%)	40
Whether to consider pumped storage	No
The rate of utilization of wind and photovoltaic power	≥95%

.

5.1. Comparison of Solution Methods

With the addition of the dung beetle optimization algorithm with non-dominated ordering, the DC power solution range is reduced from a matrix of 8760 × 8000 (number of variables × range of variables) to a matrix of 8760 × R, with R being the boundary value result of the algorithm’s solution, and the number of variables is reduced from 70,080,000 to 50,494,000, with a range reduction of 27.95%, as compared to the direct invocation of the solver for the time-slot solution. The solution time is shown in

Table 6. Solution time.

Solution Methods	Algorithm Solving Time	GUROBI Solving Time	Total
Optimization algorithm with adding dung beetles	58.4 min	113.7 min	172.1 min
Optimization algorithm without adding dung beetles	-	194.6 min	194.6 min

.

5.2. Analysis of Base Scenario Results

Table 7. Solution time.

Parametric Indicators	Numerical Value
DC utilization hours (h)	5150.5
Mid/long-term DC hours (h)	4914.8
Spot DC hours (h)	235.7
Total cost of base (CNY billion)	13.15
Total revenue of base (CNY billion)	16.48
Base net profit (CNY billion)	3.33
Carbon emission (ten thousand tons)	1650.3
Total peak shaving and valley filling power (billion kWh)	1.41
The utilization rate of wind and PV power (%)	98.82

,

Table 8. Base scenario various types of power outlets.

Parametric Indicators	Power Generation (Billion kWh)	Transmission Share (%)
Wind power and PV sent out	20.13	48.85
Thermal power sent out	20.62	50.04
Solar thermal power sent out	0.18	0.43
Electrochemical energy storage sent out	0.28	0.68
Total	41.21	100

and

Table 9. Basic scenario energy storage charge and discharge.

Electrochemical Energy Storage Charge (Billion kWh)	Electrochemical Energy Storage Discharge (Billion kWh)	Electrochemical Energy Storage Sent out (Billion kWh)
0.84	0.56	0.28

show the annual simulation operation results of the base scenario.

The calculation results show that the base scenario ensures that the DC utilization hours meet the minimum requirements, the base achieves positive profitability, and the utilization rate of wind PV is 98.82%. Figure 6 shows the simulation results of a weekly time series operation. The results show that the proposed DC transmission power operation model ensures the rigid execution of the mid/long-term transmission curve, and at the same time, in the period when the spot transmission is turned on, spot trading is carried out to supplement the mid/long-term transmission curve.

5.3. Analysis of Results for Scenarios with Different DC Operational Parameters

In this section, the simulation results are studied for the two parameters of mid/long-term DC outgoing period and the shortest stabilization time of mid/long-term DC outgoing power as shown in

Table 10. Simulation results for different mid/long-term DC power stabilization durations.

Parametric Indicators	Scenario 1 a	Scenario 2 b	Scenario 3 c	Scenario 4 d
DC utilization hours (h)	5100.0	5176.3	5203.8	5223.8
Mid/long-term DC hours (h)	4795.9	4971.3	5021.6	5046.3
Spot DC hours (h)	304.1	205.0	182.2	177.5
Total sent out (billion kWh)	40.80	41.41	41.63	41.79
Wind power and PV sent out (billion kWh)	20.07	20.21	20.14	20.16
Thermal power sent out (billion kWh)	20.28	20.74	21.03	21.17
Solar thermal power sent out (billion kWh)	0.17	0.18	0.18	0.19
Electrochemical energy storage sent out (billion kWh)	0.28	0.28	0.28	0.27
The proportion of renewable energy transmitted (%)	49.61	49.24	48.81	48.67

^a Scenario 1: Outbound delivery cycle of 1 week with a minimum stabilization duration of 6 h. ^b Scenario 2: Outbound delivery cycle of 1 week with a minimum stabilization duration of 3 h. ^c Scenario 3: Outbound delivery cycle of 1 week with a minimum stabilization duration of 2 h. ^d Scenario 4: Outbound delivery cycle of 1 week with a minimum stabilization duration of 1 h.

and

Table 11. Simulation results for different mid/long-term DC outgoing cycles.

Parametric Indicators	Scenario 5 e	Scenario 6 f	Scenario 7 g
DC utilization hours (h)	5058.8	4946.3	4791.3
Mid/long-term DC hours (h)	4753.6	4549.1	4216.0
Spot DC hours (h)	305.2	397.2	575.3
Total sent out (billion kWh)	40.47	39.57	38.33
Wind power and PV sent out (billion kWh)	20.10	19.87	19.72
Thermal power sent out (billion kWh)	19.92	19.38	18.38
Solar thermal power sent out (billion kWh)	0.18	0.13	0.07
Electrochemical energy storage sent out (billion kWh)	0.27	0.19	0.16
The proportion of renewable energy transmitted (%)	50.11	50.54	51.63

^e Scenario 5: The outbound delivery cycle is 2 weeks (half a month). ^f Scenario 6: The outbound delivery cycle is 4 weeks (full month). ^g Scenario 7: The outbound delivery cycle is 13 weeks (quarterly).

.

As shown in Figure 7, the highest wind PV utilization is in Scenario 2, but there is not much of a gap between Scenario 2 and the other scenarios, and there is not much of a gap between the wind PV outbound power. Among them, Scenario 1 has the highest spot DC utilization hours, which is because the DC power of Scenario 1 is not flexible enough, and the medium- and long-term outgoing curves covering the scenarios are not as comprehensive as those of the other scenarios. Scenario 5, Scenario 6, and Scenario 7, however, are due to the period considered to be too long, resulting in a lower peak value of the outgoing curve, which has a great impact on PV consumption, especially in the middle of the day resulting in many PV not being able to be sent out. Meanwhile, as the time cycle increases, the spot DC transmission mode plays a complementary role and the number of spot DC transmission hours increases.

The mean and maximum values of daily DC transmission power for the aforementioned seven scenarios are presented in

Table 12. Average and maximum values of daily DC transmission power.

Scenario	Numeric Value 1 (Week) h	Numeric Value 2 (h) i	Numeric Value 3 (MW) j	Numeric Value 4 (MW) k
Base scenario	1	4	5184.7	8000.0
Scenario 1	1	6	5043.1	7358.7
Scenario 2	1	3	5214.0	8000.0
Scenario 3	1	2	5301.3	8000.0
Scenario 4	1	1	5326.8	8000.0
Scenario 5	2	4	4858.3	6450.6
Scenario 6	3	4	4826.2	6328.7
Scenario 7	13	4	4447.3	5573.7

^h Numeric value 1: Mid/long-term DC transmission cycle (week). ⁱ Numeric value 2: Mid/long-term DC outgoing power shortest stabilization time (h). ^j Numeric value 3: Average values of daily DC transmission power (MW). ^k Numeric value 4: Maximum values of daily DC transmission power (MW).

. Figure 8 illustrates the trend of daily DC transmission power. From the analysis of the results presented in Table 12, it can be observed that when the DC shortest stabilization period is less than 4 h, the maximum value of the DC outgoing power can be maintained at 8000 MW. Furthermore, with the enhancement of the DC regulation capability, the average value of the DC outgoing power will also increase slightly. When the DC outgoing cycle exceeds one week, it is necessary to consider the impact of long-term generation fluctuations on DC transmission power. This results in a decline in both the average daily DC transmission power and the maximum daily DC transmission power.

Furthermore, Figure 8 illustrates that an increase in DC regulation capability is associated with a concomitant rise in DC transmission power fluctuation. This is exemplified by the DC transmission curve in Scenario 4.

5.4. Analysis of the Results of Different Technical Indicator Scenarios

This section examines two parameters, minimum technical output of thermal power and spot trading hours. The simulation results are shown in

Table 13. Simulation results for different thermal power technology outputs.

Parametric Indicators	Scenario 8 h	Scenario 9 i	Scenario 10 j	Scenario 11 k
DC utilization hours (h)	5095.0	5066.3	5038.8	5007.5
Mid/long-term DC hours (h)	4907.2	4894.7	4882.4	4865.5
Spot DC hours (h)	187.8	171.6	156.4	142.0
Total sent out (billion kWh)	40.76	40.53	40.31	40.06
Wind power and PV sent out (billion kWh)	20.13	20.14	20.18	20.19
Thermal power sent out (billion kWh)	20.17	19.94	19.69	19.45
Solar thermal power sent out (billion kWh)	0.18	0.18	0.19	0.19
Electrochemical energy storage sent out (billion kWh)	0.28	0.27	0.25	0.23
The proportion of renewable energy transmitted (%)	49.83	50.14	50.53	50.87

^h Scenario 8: The minimum technical output of thermal power is 35% of the rated power. ⁱ Scenario 9: The minimum technical output of thermal power is 30% of the rated power. ^j Scenario 10: The minimum technical output of thermal power is 25% of the rated power. ^k Scenario 11: The minimum technical output of thermal power is 20% of the rated power.

and

Table 14. Simulation results for different thermal power technology outputs.

Parametric Indicators	Scenario 12 l	Scenario 13 m	Scenario 14 n
DC utilization hours (h)	5158.8	5166.3	5170.0
Spot DC hours (h)	244.0	234.1	250.8
Total sent out (billion kWh)	41.27	41.33	41.36
Wind power and PV sent out (billion kWh)	20.19	20.25	20.28
The proportion of renewable energy transmitted (%)	49.36	49.43	49.47

^l Scenario 12: Spot trading duration 10 h (8:00∼16:00). ^m Scenario 13: Spot trading duration 12 h (7:00∼17:00). ⁿ Scenario 14: Spot trading duration 14 h (6:00∼18:00).

.

As evidenced by the data presented in Table 13, the reduction in the minimum technical output of thermal power allows for a limited opportunity for wind PV to contribute. In instances where this is not feasible during the spot trading hours, the consumption interval previously provided by thermal power is filled by wind PV. At the same time, the wind and PV power from spot trading is further reduced, and the DC utilization hours of spot outbound are reduced, leading to a decrease in the total DC utilization hours. From the results in Table 14 and Figure 9, with the increase in spot trading hours and the increase in spot trading DC utilization hours, the outgoing power of wind power and PV are both improved, but still, the increase in wind power is larger. Because the original spot trading hours have already covered the generation period of PV power generation, the extension of the spot trading hours will not significantly increase the outgoing power of PV, but it is able to dissipate the power generation of wind power in other time periods. Wind power consumption is the main reason for the increase in the utilization rate of wind power PV and the DC utilization hours of spot trading.

5.5. Impact of Pumped Storage on Operational Simulation Results

Considering the effect of adding pumped storage on the operational simulation results, the results are shown in

Table 15. Consider simulation results of pumped storage scenario operation.

Parametric Indicators	Numerical Value
DC utilization hours (h)	5243.2
Mid/long-term DC hours (h)	5145.5
Spot DC hours (h)	97.7
Total cost of base (billion yuan)	13.35
Total revenue of base (billion yuan)	16.78
Base net profit (billion yuan)	3.43
Carbon emission (million tons)	1621.4
Total peak shaving and valley filling power (billion kWh)	2.18

,

Table 16. Consideration of pumped storage scenarios for all types of power outflows.

Parametric Indicators	Power Generation (Billion kWh)	Transmission Share (%)
Wind power and PV sent out	20.29	48.38
Thermal power sent out	20.70	49.36
Solar thermal power sent out	0.18	0.41
Electrochemical energy storage sent out	0.28	0.68
Pumped storage sent out	0.50	1.11
Total	41.95	100

and

Table 17. Pumped storage charging and discharging.

Pumped Storage Charge (Billion kWh)	Pumped Storage Discharge (Billion kWh)	Pumped Storage Sent out (Billion kWh)
0.71	0.21	0.50

. The DC utilization hours for the scenario considering pumped storage is 5243.2 h, which is an increase of 1.8% compared to the base scenario, in which the mid/long-term DC hours increase and the spot DC hours decrease. In addition, the wind PV utilization is 99.61%, which is 0.79% higher compared to the base scenario. Thermal power outgoing power increases by 0.08 billion kWh, solar thermal outgoing power and electrochemical storage outgoing power remain unchanged, and pumped storage outgoing power is added by 0.5 billion kWh. The total outgoing power was 41.95 billion kWh, an increase of 1.8% compared to the base scenario. In addition, base net profit increased by CNY 0.1 billion and the total peak shaving and valley filling power increased by 0.74 billion kWh.

The results show that pumped storage energy will further increase wind PV utilization and DC utilization hours, improve economic efficiency, and increase system flexibility. The role of pumped storage is not only reflected in the regulation of resources, but also can provide more consumption zones for the wind power PV, and enhance the utilization rate of wind power PV, as can be seen from Figure 10 and Figure 11. At the same time, pumped storage can also be a power generation source to increase the total DC outgoing power and enhance the DC utilization hours. Meanwhile, pumped storage has a higher boost to wind utilization in fall and winter, and a smaller boost to wind utilization in spring and summer. Although pumped-storage improves DC utilization hours for all weeks, it improves more for weeks with abundant wind resources and less for weeks with poor wind resources.

6. Conclusions

This paper presents a time-series operation simulation model for the Desert and Gobi area New Energy Base, accounting for DC utilization hours, environmental factors, economic considerations, and operational flexibility. The model uses the dung beetle optimization algorithm with non-dominated sorting to reduce variables, significantly enhancing computational efficiency. The model is executed on a weekly time scale over a full year to determine optimal operational solutions. The following key findings are reported:

• The integration of the dung beetle optimization algorithm with non-dominated sorting enhances the heuristic algorithm’s computational efficiency and successfully narrows the range of variables, reducing the solution time by 22.5 min compared to direct time-series approaches.
• When employing a weekly mid/long-term DC transmission cycle, the DC operational parameters have a minimal impact on DC utilization hours and the utilization rates of wind and PV power. The main constraints on the utilization rates are the minimum technical output of thermal power and the duration of spot trading. As the DC outbound cycle lengthens, there is a notable decrease in mid/long-term DC power peaks, a reduction in PV outbound power, and an increase in spot outbound power.
• The minimum technical output of thermal power is negatively correlated with the utilization of wind and photovoltaic power. However, excessively low thermal power outputs can compromise the outgoing power capacity of thermal units, subsequently diminishing DC utilization hours. Moreover, spot trading hours are directly proportional to the utilization rate of wind and PV power; longer spot trading durations facilitate greater compensation for consumption through wind and solar energy.
• Pumped storage not only plays a crucial role in regulating resources and compensating for the lack of energy storage capacity, thereby enhancing the utilization rate of wind and PV power and improving DC utilization hours, but it also acts as a supplementary power source. This increases the total outgoing power and enhances the economic performance of the base, representing an effective strategy to boost base indicators.