**1. Introduction**

By the end of 2020, Chinese-installed wind power capacity has continued to grow to 281 million kilowatts. However, wind power output is volatile and random [1]. When largescale wind power is integrated into the grid, the wind power consumption of the wind farm is hindered due to the insufficient peak shaving capacity of the system, which results in a large number of wind abandonment [2]. To improve the consumption level of wind power, the energy storage resources [3] and the load-side resources need to be fully utilized at the same time [4]. In recent years, due to the rapid development of energy storage technology, energy storage devices have gradually been deployed into new energy systems [5]. This strategy can effectively increase the rate of new energy consumption, which has attracted wide attention from many researchers and governments [6]. Besides, enterprises with energy-intensive load are usually built near large-scale wind power bases [7], so the load is highly concentrated and large in capacity, making the control of the load more flexible [8]. Therefore, to alleviate the problem of Chinese wind power consumption, it is feasible to use energy storage systems and load-side to consume congested wind power on-site.

**Citation:** Zhang, S.; Zhang, K.; Zhang, G.; Xie, T.; Wen, J.; Feng, C.; Ben, W. The Bi-Level Optimization Model Research for Energy-Intensive Load and Energy Storage System Considering Congested Wind Power Consumption. *Processes* **2022**, *10*, 51. https://doi.org/10.3390/pr10010051

Academic Editors: Alon Kuperman and Alessandro Lampasi

Received: 8 November 2021 Accepted: 23 December 2021 Published: 27 December 2021

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At present, the existing references have researched the load-side participation in wind power consumption. Reference [9] divides the energy-intensive load into interruptible and translatable loads according to the response mode, and comprehensively considers all available factors on the source side, grid side, and load side. On this basis, a source-gridload comprehensive planning model is established. However, this model does not consider the power consumption characteristics and adjustment methods of an energy-intensive load. Since improper adjustment of the energy-intensive load can cause serious losses, in order to make reasonable use of the adjustable performance of the energy-intensive load, it is necessary to carry out fine modeling of the electrical characteristics of load. Since demand response is playing an increasingly important role in balancing short-term supply and demand, researchers propose three different methods to integrate demand response into a unit combination optimization model that considers operating constraints [10]. However, this model is established when the wind power forecasting is accurate and does not consider the volatility of wind power. In order to alleviate the problems of grid integration and safe operation of the power system caused by the uncertainty of wind power, pumped storage and demand response participate in the process of grid operation as auxiliary services. In addition, the Lagrangian relaxation method is proposed to solve the unit combination problem [11]. However, the adjustment cost of an energy-intensive load is not considered in this process, which will lead to excessively high overall operating costs of the system. Aiming at the uncertainty of renewable energy output, reference [12] proposes a two-stage robust scheduling model. Due to the high flexibility of demand response, this model can meet electricity demand with minimal energy costs and maximize the use of clean energy potential. However, due to the complexity of the model, it is not suitable for grid dispatch calculation. Reference [13] uses the dynamic adjustment capabilities of hydropower and energy-intensive load to propose an optimal wind power-solar capacity allocation method to reduce the uncertainty of output. However, the risk constraints of energy-intensive load and wind power are not considered. When the discretely adjustable energy-intensive load participates in the consumption of wind power, since it cannot be continuously adjusted in a short time, the adjustment increment of the energy-intensive load does not match the output of wind power, which increases the risk of wind power curtailment or load shedding of the energy-intensive load.

On the other hand, the energy storage system can store the power during the low load period and release it during the peak load period [14]. Joint dispatch with wind power can effectively reduce the wind power curtailment rate [15]. Therefore, there are currently many studies that combine energy storage and wind power into a joint system for optimal dispatch [16]. By analyzing the negative impact of wind speed variability on the large-scale grid integration of wind power, the researcher proposes to use energy storage systems to mitigate it [17]. Based on the reliability analysis under the unit operation and technical constraints, the AC power flow model is used to determine the scale of the energy storage system. However, the operating cost of the energy storage system is not considered, which leads to excessively high system operating costs, and is not conducive to the economic operation of the system. Reference [18] is based on the complementary characteristics of solar and wind energy, and proposes a method to optimize the configuration of renewable energy by using battery energy storage technology so as to make the system more reliable. However, this research does not take into account the uncertainty of renewable energy output, which affects the planning and operation of the energy storage system, thereby reducing the applicability and reliability of the results. In view of the fact that wind power cannot be accurately predicted, reference [19] proposes an approach for planning and operating an energy storage system for a wind farm in the electricity market while using electrochemical batteries to compensate for changes in power generation. However, this method does not explain how to determine the capacity of the energy storage system and cannot guarantee that the capacity is the optimal value. The energy storage capacity should be optimally configured to improve the overall investment benefit. Reference [20] proposes a multi-objective optimal scheduling model based on the operating characteristics of the

battery energy storage system and the uncertainty of wind power output, which reduces the risk of the integrated power system with wind farms and batteries. Although the scheduling model considers the uncertainty of wind power, it does not quantify the risk of wind power curtailment. Besides, the existing references mostly focus on the exploration of the effect of energy-intensive load or energy storage system alone. Few references analyze the effective coordination between the energy-intensive load and energy storage system.

In view of the above problems, this paper takes the energy-intensive load and energy storage system together as an important means to consume wind power and jointly participate in the optimal dispatch of the power grid. Firstly, the regulation characteristics of the energy-intensive load are analyzed, and the energy-intensive load dispatching model is established. On the basis of fully considering the uncertainty of wind power, the risk constraints of the energy-intensive load and wind power have been established. At the same time, taking into account the adjustment cost and adjustment constraints of the energy-intensive load and energy storage system, a bi-level optimization model considering the congested wind power consumption is established. The upper level determines the configured capacity of the energy storage system with the goal of minimizing the total economic investment of the energy storage system, and the lower level coordinates the dispatching with the goal of maximizing wind power consumption and minimizing system operating costs. The simulation results show that the above method can effectively improve the consumption capacity of wind power and reduce the operating cost of the system.

#### **2. Uncertainty Analysis of Wind Power**

Wind power output has strong randomness and volatility. When large-scale wind farms are integrated into the grid, the safe and stable operation of the system will be affected. Therefore, the uncertainty of wind power output needs to be analyzed. This chapter firstly proposes the concept of wind power admissible interval to represent the power grid's ability to integrate wind power. Then, the characteristics of wind power output are analyzed, considering the uncertainty of wind speed changes, and a probability distribution model is usually used to describe it. On this basis, analysis and research are carried out according to the wind curtailment situation outside of the capacity of the grid, and the curtailment risk is characterized by the wind curtailment expected value.

#### *2.1. The Admissible Region of Wind Power*

Energy-intensive load and energy storage system are mainly used to consume wind curtailment. Therefore, the acceptance level of power grid to wind power should be calculated to evaluate the wind curtailment situation in the future [21].

The calculation of the wind curtailment index is closely related to the grid's acceptance level to wind power. This paper uses the admissible region of wind power (ARWP) to indicate the acceptance level of wind power in power grid [22]. The acceptance region of the power grid for the output of a wind farm is shown in Figure 1. The blue solid line in the figure is the planned output of the wind farm, and the red dotted line is the admissible wind power output range of the power grid without curtailed wind or reduced load.

According to the concept of ARWP, the wind power output satisfies the following relationship:

$$\begin{cases} \left. w^l\_{i,t} \le w\_{i,t} \le w^u\_{i,t} \right. \\ \left. w\_{i,t} = w^p\_{i,t} + \Delta v \partial\_{i,t}^p \right. \end{cases} \tag{1}$$

where *w<sup>p</sup> i*,*t* , Δ*w*ˆ*i*,*t*, *wi*,*t*, *w<sup>u</sup> i*,*t* , and *w<sup>l</sup> <sup>i</sup>*,*<sup>t</sup>* represent planned output, wind power output fluctuation, actual output, the upper boundary before coordinated dispatching, and the lower boundary before coordinated dispatching of the *i*-th wind farm at time *t*, respectively.

**Figure 1.** ARWP of a wind farm.

#### *2.2. Distribution of Wind Power Output*

Wind power output is highly uncertain. In this paper, the uncertainty of wind power output is described as a probability function that obeys a normal distribution near the predicted point [23]. As shown in Figure 2.

The distribution of wind farm output is:

$$\mathcal{N}(w\_{i,t}^p + \Delta v\_{i,t}^p) \sim \mathcal{N}(w\_{i,t'}^f (\sigma\_i + t\Delta \sigma\_i)^2) \tag{2}$$

where *N*(*w<sup>f</sup> i*,*t* ,(*σ<sup>i</sup>* + *t*Δ*σi*) 2 ) represents the normal distribution with expectation *w<sup>f</sup> <sup>i</sup>*,*<sup>t</sup>* and variance (*σ<sup>i</sup>* + *t*Δ*σi*) 2 ; *w<sup>f</sup> <sup>i</sup>*,*<sup>t</sup>* is the predicted output of wind farm *i* at time *t*; *σ<sup>i</sup>* is the initial standard deviation of wind farm *i* load forecasting; and Δ*σ<sup>i</sup>* is the standard deviation increment of wind farm *i* load forecasting process with time scale.

#### *2.3. Risk Analysis of Wind Curtailment*

Due to the randomness and volatility of wind power output, prediction errors are prone to occur when predicting wind power output, which will increase the uncertainty of large-scale wind power integrated into the grid. It will have a great impact on the peak shaving capacity of the power grid, which will lead to the obstruction of wind power consumption and a large amount of wind curtailment [24]. Figure 3 is the schematic diagram of congested wind power consumption.

**Figure 3.** Schematic diagram of congested wind power consumption.

Based on the above analysis, the risk of wind curtailment of wind farm *i* can be expressed as:

$$\mathbb{C}\_{i}^{u,VaR}(w\_{i,t}^{u}) = \rho^{u} \sum\_{t=1}^{T} \mathbb{E}\_{i,t}^{u}(w\_{i,t}^{u}) = \rho^{u} \sum\_{t=1}^{T} \int\_{w\_{i,t}^{u}}^{w\_{i,t}^{\max}} (\mathbf{x} - w\_{i,t}^{u}) f\_{i,t}(\mathbf{x}) d\mathbf{x} \tag{3}$$

where *ρ<sup>u</sup>* is the penalty for wind curtailment; *E<sup>u</sup> i*,*t* (·) is the wind curtailment expectation of wind farm *i* at time *t*; *T* is the time scale of dispatching control; *w*max *<sup>i</sup>*,*<sup>t</sup>* is the upper limit of output of wind farm *i* at time *t*, taking the installed capacity of wind farm; *fi*,*t*(*x*) is the probability density function of wind farm *i* output at time *t*.

According to Formula (3), *Cu*,*VaR <sup>i</sup>* is a complex nonlinear nonconvex function. It will not only increase the difficulty of finding the global optimal solution, but also increase the computational complexity and time. Therefore, this paper linearizes *E<sup>u</sup> i*,*t* (*w<sup>u</sup> i*,*t* ) piecewise, and the piecewise linearization models with different values are shown in Formula (4).

$$\begin{cases} E\_{i,t}^u(w\_{i,t}^u) = \sum\_{s=1}^n a\_{i,t}^{u,s} w\_{i,t}^{u,s} + b\_{i,t}^{u,s} z\_{i,t}^{u,s} \\ 0 \le w\_{i,t}^{u,s} \le M z\_{i,t}^{u,s} \\ \sum\_{s=1}^n w\_{i,t}^{u,s} = w\_{i,t}^u \\ \sum\_{s=1}^n z\_{i,t}^{u,s} = 1 \end{cases} \tag{4}$$

where *n* is the total number of sections; *wu*,*<sup>s</sup> <sup>i</sup>*,*<sup>t</sup>* and *<sup>z</sup>u*,*<sup>s</sup> <sup>i</sup>*,*<sup>t</sup>* are respectively the continuous and discrete auxiliary variables of the *s*-th segment of the upper boundary of the ARWP of wind farm *i* at time *t* before the load participates in the coordination; *au*,*<sup>s</sup> <sup>i</sup>*,*<sup>t</sup>* and *<sup>b</sup>u*,*<sup>s</sup> <sup>i</sup>*,*<sup>t</sup>* are respectively the slope and intercept of the *s*-th segment of the ARWP upper boundary of wind farm *i* at time *t*, which can be obtained in advance from the distribution of wind farm *i*. Here, *M* is a preset large number constant.

From Formula (4), it can be seen that *Cu*,*VaR <sup>i</sup>* (·) can be changed from a complex function to a series of mixed integer linear constraints, which is easy to solve.

#### **3. Model of Energy-Intensive Load Dispatching**

The uncertainty of wind power output imposes a burden on the regulation of the power grid. When the regulation capacity of conventional power sources is insufficient, the energy-intensive load can be adjusted to ensure the balance between supply and demand of the power system. The premise for using energy-intensive load to consume congested wind power is to have an accurate understanding of load power characteristics. Therefore, it is necessary to analyze the characteristics of different types of energy-intensive load regulation and establish a mathematical model of energy-intensive load regulation. On this basis, combined with the wind curtailment situation outside the capacity of the grid analyzed in Section 2.3, the risk constraints related to load consumption increment and wind curtailment volume are constructed. The flow chart of this process is shown in Figure 4.

**Figure 4.** Schematic diagram of risk constraints of energy-intensive load and wind power.
