*4.2. Coordinated Dispatching Model of Energy-Intensive Load and Energy Storage System* 4.2.1. Objective Function

The coordinated operation of energy-intensive load and energy storage system can enable the system to consume more wind power within the existing regulation capacity. However, using this method will increase the operation cost of the system. Therefore, how to maximize wind power consumption with the lowest operating cost is the key to cooperative operation. In this paper, a multi-objective optimization model is established with the goal of maximizing wind power consumption and minimizing system operating cost, and the expression is as follows:

$$\text{minim}F = \sum\_{t=1}^{T} \left( \mathbb{C}\_{t}^{Con} + \mathbb{C}\_{t}^{B} + \mathbb{C}\_{t}^{G} + \mathbb{C}\_{t}^{W} \right) \tag{11}$$

where *CCon <sup>t</sup>* , *C<sup>B</sup> <sup>t</sup>* , *C<sup>G</sup> <sup>t</sup>* and *C<sup>W</sup> <sup>t</sup>* are the operating cost of conventional units, the charge and discharge management cost of energy storage system, the dispatching cost of energy-intensive load, and the penalty cost of curtailment wind, respectively. The specific calculation formula for each cost is as follows:

(3) The operating cost of conventional units *CCon t*

$$\mathbf{C}\_{t}^{Con} = \sum\_{k=1}^{N} \left( a\_{k} p\_{k,t}^{2} + b\_{k} p\_{k,t} + c\_{k} d\_{k,t} + d\_{on,k,t} \mathbf{C}\_{u,k,t} \right) \tag{12}$$

where *N* is the number of thermal power units; *ak*, *bk* and *ck* are the cost coefficient of thermal power units; *pk*,*<sup>t</sup>* is the output of the *k*-th thermal power unit at time *t*; *Cu*,*k*,*<sup>t</sup>* is the start-up cost of the thermal power unit; *dk*,*<sup>t</sup>* is a 0–1 variable, which is used to indicate the current on/off state of the unit; *don*,*k*,*<sup>t</sup>* is a 0–1 variable, which is used to indicate the starting state.

(4) The charge and discharge management cost of energy storage system *C<sup>B</sup> t*

$$\mathbf{C}\_t^B = \lambda\_{\mathbf{b}, \text{dis}} \mathbf{P}\_{\text{dis}, \text{t}} + \lambda\_{\mathbf{b}, \text{ch}} \mathbf{P}\_{\text{ch}, \text{t}} \tag{13}$$

where *λb*,*dis* is the discharging cost coefficient of the energy storage system; *λb*,*ch* is the charging cost coefficient of the energy storage system; *Pdis*,*<sup>t</sup>* is the discharge power of the energy storage system at time *t*; P*ch*,*<sup>t</sup>* is the charging power of the energy storage system at time *t*.

(5) The dispatching cost of energy-intensive load *C<sup>G</sup> t*

$$\mathbf{C}\_{t}^{G} = (\beta\_{MI} + \beta\_{Wr})E\_{i,t}^{u}(w\_{i,t}^{u}) + \pi N\_{f} + \varepsilon (E\_{i,t}^{u}(w\_{i,t}^{u}))c\_{Lr} \tag{14}$$

where *Nf* is the number of power changes of energy-intensive load; π is the corresponding equipment loss cost in case of single power change; *βMI* is the raw material cost coefficient per unit energy consumption; *βWr* is the equipment loss cost coefficient of unit regulated power; *E<sup>u</sup> i*,*t* (*wu*,*add <sup>i</sup>*,*<sup>t</sup>* ) is the expected curtailment of wind during the dispatching period; *cLr* is the increased labor cost of participating in the consumption of congested wind power during the control period; *ε*(*E<sup>u</sup> i*,*t* (*w<sup>u</sup> i*,*t* )) is shown in Formula (15).

$$\varepsilon(E\_{i,t}^{\mu}(w\_{i,t}^{\mu})) = \begin{cases} 0 & E\_{i,t}^{\mu}(w\_{i,t}^{\mu}) = 0\\ 1 & E\_{i,t}^{\mu}(w\_{i,t}^{\mu}) > 0 \end{cases} \tag{15}$$

(6) The penalty cost of curtailment wind *C<sup>W</sup> t*

$$\mathbf{C}\_{t}^{G} = (\beta\_{MI} + \beta\_{Wr})E\_{i,t}^{u}(w\_{i,t}^{u}) + \pi N\_{f} + \varepsilon (E\_{i,t}^{u}(w\_{i,t}^{u}))c\_{Lr} \tag{16}$$

#### 4.2.2. Constraints

Constraints include conventional unit constraints, system power balance constraints, energy storage system charging and discharging constraints, energy-intensive load constraints, etc.

(1) Conventional unit constraints

$$\mathcal{P}\_{\text{min},k} \stackrel{\prec}{\leq} \mathcal{P}\_{k,t} \stackrel{\prec}{\leq} \mathcal{P}\_{\text{max},k} \tag{17}$$

$$-p\_{dn,k} \le p\_{k,t} - p\_{k,t-1} \le p\_{up,k} \tag{18}$$

$$d\_{on,k,t} \ge d\_{k,t} - d\_{k-1,t-1} \tag{19}$$

$$\begin{cases} \left(d\_{k,t-1} - d\_{k,t}\right) (S\_{on,k,t} - S\_{on,\min,k}) \ge 0\\ \left(d\_{k,t} - d\_{k,t-1}\right) (S\_{off,k,t} - S\_{off,\min,k}) \ge 0 \end{cases} \tag{20}$$

$$\begin{cases} S\_{on,k,t} = S\_{on,k,t-1} d\_{k,t} + d\_{k,t} \\ S\_{off,k,t} = S\_{off,k,t-1} (1 - d\_{k,t}) + (1 - d\_{k,t}) \end{cases} \tag{21}$$

Formula (17) is the output constraint of the conventional unit, *p*max,*<sup>k</sup>* and *p*min,*<sup>k</sup>* are the upper and lower limits of the output of the *k*-th conventional unit respectively; Formula (18) is the ramp rate constraint of the conventional unit, *pdn*,*<sup>k</sup>* and *Pup*,*<sup>k</sup>* are the maximum descent rate and maximum ascent rate of the active power output of the *k*-th conventional unit, respectively; Formula (19) is the 0–1 constraint for unit startup; Formula (20) is the minimum start-stop time constraint of the *k*-th conventional unit, which *Son*,*k*,*<sup>t</sup>* is the continuous start-up time of the *k*-th conventional unit, *Son*,min,*<sup>k</sup>* is the minimum startup time of the *k*-th conventional unit, *Soff* ,*k*,*<sup>t</sup>* is the continuous shutdown time of the *k*-th conventional unit, and *Soff* ,min,*<sup>k</sup>* is the minimum shutdown time of the *k*-th conventional unit; Formula (21) is the constraint of the continuous operation time and continuous shutdown time of the unit.

(7) System power balance constraints

$$\sum\_{i=1}^{W} w\_{i,t}^{p} + \sum\_{k=1}^{G} p\_{k,t}^{g} + P\_{b,d}(t) = P\_{load}(t) + \sum\_{j=1}^{E} \left( P\_{j,t}^{EF} + \Delta P\_{j,t}^{EF} \right) + P\_{b,c}(t) \tag{22}$$

where *Pb*,*d*(*t*) and *Pb*,*c*(*t*) represent the discharge and charging power of the battery at time *t*, respectively; *Pload*(*t*) represents the conventional load power at time *t*; Δ*PEF j*,*t* represents the active power of the energy-intensive load *j* at time *t*.

(8) Energy storage system charging and discharging constraints are as follows:

$$\begin{cases} \ 0 \le p\_{ch,t} \le (1 - ESS\_t)p\_{ch,\text{max}}\\ \ 0 \le p\_{dis,t} \le ESS\_t p\_{dis,\text{max}} \end{cases} \tag{23}$$

$$\begin{cases} \text{SOC}\_{t-1} + \eta\_{\text{ESS},h} p\_{ch,t}/E\_{\text{ESS}} + ESS\_{l}D \le \text{SOC}\_{t} \le \text{SOC}\_{t-1} + \eta\_{\text{ESS},h} p\_{ch,t}/E\_{\text{ESS}} + ESS\_{l}D\\\text{SOC}\_{t-1} - p\_{\text{dis},t}/(\eta\_{\text{ESS},\text{dis}} E\_{\text{ESS}}) - ESS\_{l}D \le \text{SOC}\_{t} \le \text{SOC}\_{t-1} - p\_{\text{dis},t}/(\eta\_{\text{ESS},\text{dis}} E\_{\text{ESS}}) - ESS\_{l}D \end{cases} \tag{24}$$

$$0.1 \le SOC\_t \le 0.9\tag{25}$$

Formula (23) is the constraint equation for the charge and discharge power of the energy storage system, *pch*,*<sup>t</sup>* and *pdis*,*<sup>t</sup>* are the charge and discharge power of the energy storage system; *pch*,max and *pdis*,max are the upper limit of the charge and discharge power of the energy storage device; *ESSt* is a 0–1 variable indicating the state of energy storage: when *ESSt* = 0 is in the charging state, when *ESSt* = 1 is in the discharging state; Formula (24) is the energy storage state of charge constraint, *ηESS*,*ch* and *ηESS*,*dis* represent the charging and discharging efficiency of the energy storage system; *SOCt* is the energy storage state of charge; and *EESS* is the upper limit of the capacity of the energy storage device; Formula (25) is the range constraint of the state of charge of energy storage. The *D* appearing in the model is a sufficiently large parameter introduced.

(9) Constraints of energy-intensive load are shown in Formulas (5) and (6).
