*3.1. Regulation Characteristics of Energy-Intensive Load*

Energy-intensive load are divided into continuously adjustable load and discretely adjustable load. In this section, the regulation characteristics of two typical energy-intensive load of an electrolytic aluminum and titanium alloy are analyzed as examples [25].

(1) Electrolytic aluminum production load

Electrolytic aluminum production uses cryolite-alumina as raw materials, and direct current is applied to electrolysis in its molten salt until, finally, aluminum is obtained. Under normal circumstances, the load of electrolytic aluminum is stable, and adjustment within a certain range only affects the output and does not affect product quality and equipment safety. However, due to the limited impact tolerance of electrolytic aluminum equipment, stable production is required for a period of time after one adjustment, and frequent adjustments are not allowed. The schematic diagram of electrolytic aluminum load adjustment is shown in Figure 5.

**Figure 5.** Schematic diagram of electrolytic aluminum load regulation characteristics.

(2) Titanium alloy production load

Titanium alloy production uses alloy oxide charge as raw material to reduce to titanium alloy at high temperature. Titanium alloys generally adopt uninterrupted production methods, and their production load fluctuates slightly, basically stable, with continuous adjustment capabilities, and flexible adjustments, which are not affected by stable production time. The schematic diagram of titanium alloy load adjustment is shown in Figure 6.

Summarizing the above load regulation characteristics, energy-intensive load can be divided into continuously adjustable loads and discretely adjustable loads. Various types of energy-intensive load regulation characteristics are shown in Table 1.

**Table 1.** Various types of energy-intensive load regulation characteristics.


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

From the analysis in Section 3.1, it can be seen that the continuously adjustable load can be adjusted in real time according to the fluctuation of wind power, and the risk is relatively small. However, the discretely adjustable load cannot be adjusted continuously in a short period of time. After one adjustment, it needs to run stably for a period of time before the next adjustment can be carried out. The time period is longer. If the load regulation is large, the predicted output of wind power during this period is higher but the actual output is lower, which will cause the problem of a mismatch between the load increment and the power generation increment, resulting in a higher risk of load shedding. Conversely, if the load regulation amount is small, the flexibility of the energy-intensive load cannot be fully utilized, and a large wind curtailment may also occur. Therefore, the uncertainty of wind power and the regulation characteristics of the load should be fully considered when the discrete energy-intensive load participates in the wind power consumption.

In this paper, the discrete adjustable load is analyzed and studied [26]. Without losing generality, the mathematical model of a smelting furnace is used to represent the discrete adjustable load [27].

Other constraints of the electricity load and active power model of the smelting furnace are as follows:

$$\begin{cases} \begin{aligned} P\_{j,t}^{EF} &= P\_j^{EF, \text{int}} (1 - \mathbf{x}\_{j,t}^{EF}) + P\_j^{EF, \rho \text{in}} \mathbf{x}\_{j,t}^{EF} + P\_{j,t}^{EF, \text{adj}} \\ &- P\_j^{EF, \text{id}} \mathbf{x}\_{j,t}^{EF} \le P\_{j,t}^{EF, \text{adj}} \le P\_j^{EF, \mu} \mathbf{x}\_{j,t}^{EF} \\ &- M(\mathbf{u}\_{j,t}^{EF} + 1 - \mathbf{x}\_{j,t}^{EF}) \le P\_{j,t}^{EF, \text{adj}} - P\_{j,t-1}^{EF, \text{adj}} \le M \mathbf{u}\_{j,t}^{EF} \end{aligned} \end{cases} \tag{5}$$

Formula (5) is the active power constraints of the smelting furnace. Where *PEF <sup>j</sup>*,*<sup>t</sup>* , *<sup>P</sup>EF*,*adj <sup>j</sup>*,*<sup>t</sup>* , *xEF <sup>j</sup>*,*<sup>t</sup>* , *<sup>u</sup>EF <sup>j</sup>*,*<sup>t</sup>* are the total active power, continuous regulation, state variable and start flag of smelting furnace *j* at time *t*, respectively; *PEF*,int *<sup>j</sup>* , *<sup>P</sup>EF*,*on <sup>j</sup>* , *<sup>P</sup>EF*,*<sup>d</sup> <sup>j</sup>* and *<sup>P</sup>EF*,*<sup>u</sup> <sup>j</sup>* are the oven power, normal production power, maximum down-regulated power and maximum up-regulated power of smelting furnace *j*, respectively.

$$\begin{cases} \begin{aligned} \mathbf{x}\_{j,t}^{EF} - \mathbf{x}\_{j,t-1}^{EF} &\le \mathbf{u}\_{j,t}^{EF} \\ \mathbf{u}\_{j,t}^{EF} &\le \mathbf{x}\_{j,t}^{EF} \\ \mathbf{u}\_{j,t}^{EF} &\le 1 - \mathbf{x}\_{j,t-1}^{EF} \\ \mathbf{x}\_{j,t-1}^{EF} - \mathbf{x}\_{j,t}^{EF} &\le 1 - \mathbf{x}\_{j,\tau}^{EF} \; \forall \tau \in \left[t + 1, \min\left(t + T\_j^{EF,\rho\mathbf{u}} - 1, T\right)\right] \\ \mathbf{u}\_{j,t}^{EF} &\le 1 - \mathbf{x}\_{j,t+T\_j^{EF,\rho\mathbf{u}}}^{EF} \\ \mathbf{r} + T\_j^{EF,\text{int}} - 1 &\quad \forall \tau \in \left[1, T - T\_j^{EF,\text{int}} + 1\right] \end{aligned} \end{cases} \tag{6}$$

Formula (6) is the logical constraints of smelting furnace *j*, which are used to describe the discrete operating characteristics of smelting furnaces. Where *TEF*,*on <sup>j</sup>* and *<sup>T</sup>EF*,int *<sup>j</sup>* are the maximum smelting time and the maximum oven time of smelting furnace *j*, respectively.

#### *3.3. Risk Constraints of Energy-Intensive Load*

Energy-intensive load has a large load capacity. In order to make the energy be used efficiently, this paper introduces an energy-intensive load to participate in wind power consumption. When energy-intensive loads participate in wind power consumption, and considering that wind farms have obviously volatility, the risk constraint adjustment of energy-intensive load can modify the admissible range of wind power in Section 2.1 (so as to control the risk of wind curtailment).

When energy-intensive loads participate in wind power consumption, energy-intensive load enterprises can purchase electric energy from wind farms at a relatively low price. If the output of wind power is lower than expected after load adjustment, the interests of load enterprises may be harmed, thus dampening the enthusiasm of energy-intensive load to participate in wind power consumption. Therefore, in a dispatch cycle, the wind farm's curtailment expectations and load increase should meet certain risk constraints to ensure the abundance of wind power. This paper defines the conservative degree of load participating in coordinated dispatch as: the expected wind power curtailment before the load participates in the regulation can meet the minimum proportion of the load's increased power consumption after the load participates in the coordination. The concept of conservativeness can form the risk constraints when energy-intensive loads participate in the consumption of wind power.

$$\sum\_{i=1}^{\mathcal{W}} \sum\_{t=1}^{T} E\_{i,t}^{\mu} \left( w\_{i,t}^{\mu} \right) \ge \beta^{\text{adj}} \sum\_{j=1}^{E} \sum\_{t=1}^{T} \max \left( 0, P\_{j,t}^{EF\prime} - P\_{j,t}^{EF} \right) \tag{7}$$

where *β*adj represents the degree of conservation; *PEF j*,*t*  and *PEF <sup>j</sup>*,*<sup>t</sup>* represent the electricity consumption plan before the adjustment of the energy-intensive load *j* at time *t* and the electricity consumption plan after the adjustment, respectively; *W* represents the number of wind farms; and *E* represents the number of energy-intensive load. This formula shows that the total wind curtailment expectation of the wind farm before the energy-intensive load participates in the mediation is greater than *β*adj times the energy-intensive load adjustment.

Since the purpose of energy-intensive load is to consume wind power, after energyintensive load participates in wind power consumption, the change of electric energy caused by the adjustment of the upper boundary of wind power curtailment shall be greater than or equal to *β*adj times of the energy-extensive adjustment. This process meets the following requirements:

$$\begin{cases} \begin{aligned} w\_{i,t}^{\mu, \text{add}} & \geq w\_{i,t}^{p} \\ \sum\_{t=1}^{T} \sum\_{i=1}^{W} (w\_{i,t}^{\mu, \text{add}} - w\_{i,t}^{\mu}) & \geq \mathcal{J}^{\text{adj}} \sum\_{j=1}^{E} \sum\_{t=1}^{T} \max(0, P\_{j,t}^{EF\prime} - P\_{j,t}^{EF}) \end{aligned} \tag{8}$$

where *wu*,*add <sup>i</sup>*,*<sup>t</sup>* represents the adjusted upper boundary of ARWP. It can be seen from the above calculation formula that when the upper boundary of wind power admissible interval is adjusted and changed, the risk of wind curtailment of the wind farm will be reduced, and the risk constraint of wind curtailment of the wind farm is further realized.

#### **4. Bi-Level Optimization Model Considering Congested Wind Power Consumption**

Based on the above analysis of the wind power uncertainty and energy-intensive load dispatching model, the upper model aims at the lowest investment cost of the energy storage system, and establishes an energy storage capacity optimization configuration model on the basis of ensuring the system power balance. The lower model aims at the maximum wind power consumption and the lowest operation cost of the system. Combined with the capacity configuration's results of the energy storage system obtained from the upper optimization model, a coordinated dispatching model of energy-intensive load and energy storage system is constructed. The bi-level optimization model considering congested wind power consumption is shown in Figure 7.


**Figure 7.** Flowchart of bi-level optimization model considering congested wind power consumption.

#### *4.1. Model of Energy Storage Capacity Configuration*

In order to improve the level of wind power consumption, this paper establishes the model by means of effective cooperation between the energy-intensive load and energy storage system. Wind farms are equipped with energy storage systems [28], relying on the peak-load shifting of the energy storage systems to improve system flexibility and reduce wind curtailment rate.

#### 4.1.1. Objective Function

Configuring energy storage capacity with the goal of minimizing energy storage system investment, operation and maintenance costs, the expression is shown in (9):

$$\begin{cases} \min \mathbf{C} = \frac{1}{365} [a \mathbf{C}\_{inv} + \mathbf{C}\_{on}] \\\ a = \frac{\mathbf{r} (1 + \mathbf{r})^{\mathsf{T}}}{(1 + \mathbf{r})^{\mathsf{T}} - 1} \\\ \mathbf{C}\_{inv} = (k\_S P\_b + k\_E E\_b) \\\ \mathbf{C}\_{\mathsf{off}} = k\_S k\_M P\_b \end{cases} \tag{9}$$

where *a* is the equal-year system coefficient; *τ* is the annual interest rate; *γ* is the service life of the energy storage system; *Cinv* and *Con* are the investment and construction cost and operation and maintenance cost of the energy storage system respectively; *kS* and *kE* are the unit power cost and unit capacity cost of the energy storage system respectively; *kM* is the operation and maintenance cost rate of the energy storage system; and *Pb* and *Eb* are the investment power and investment capacity of the energy storage system, respectively.

4.1.2. Constraints

$$\begin{cases} \begin{array}{l} E\_b^{\min} \le E\_b \le E\_b^{\max} \\ P\_b^{\min} \le P\_b \le P\_b^{\max} \end{array} \end{cases} \tag{10}$$

where *E*max *<sup>b</sup>* and *<sup>E</sup>*min *<sup>b</sup>* are the upper and lower limits of the investment capacity of the energy storage system; *P*max *<sup>b</sup>* and *<sup>P</sup>*min *<sup>b</sup>* are the upper and lower limits of the investment power of the energy storage system, respectively.
