*2.1. Optimization Model of Offshore Wind Energy Storage Capacity Planning*

#### 2.1.1. Objective Function

On the premise of satisfying the system demand and all kinds of constraint conditions, the system can minimize the total national economic expenditure in the whole planning period. The objective function of the model can be expressed as:

$$MinF\_{\Sigma} = \sum\_{t=1}^{N\_m} \mathbb{C}\_t (1+i)^{N\_m - t} + \sum\_{t=1}^{N\_T} \left( F\_{\mathcal{G}t} + F\_{kt} + O\_t - B\_t \right) \cdot (1+i)^{-N\_T} \tag{1}$$

where *Nm* is the construction cycle of the newly invested energy storage power station, *Ct* is the investment cost of the newly invested energy storage power station at the beginning of the year *t*, and *Fgt* and *Fkt* are the fixed operation and maintenance costs and fuel costs of the system in year *t*, respectively. *Ot* is the outage loss cost of the system in year *t*, and *Bt* is the benefit obtained by the system in year *t*, except for power generation. *NT* is the number of planning years and *i* is the discount rate.

Taking the first year as the base year, when the construction process of the newly invested energy storage power station is simplified, it can be considered that the power station generates investment costs at the beginning of the first year of the planning period, and the loss of power outage and other benefits are ignored. The total calculated cost of the planning period can be equivalent to the annual cost. It means that the investment cost of the new power station at the beginning of the first year can be evenly allocated to each year of the planning period, and then added to the annual operating cost. Then the objective function can be expressed as:

$$MinF = \frac{i(1+i)^{N\_T}}{(1+i)^{N\_T} - 1} \times C\_{\text{ess}} + \left(F\_{\text{\%}} + F\_k\right) \tag{2}$$

*Cess*, the investment cost of the energy storage power station, can be expressed as:

$$C\_{\rm ess} = \lambda\_p P\_{\rm ess} + \lambda\_e E\_{\rm ess} \tag{3}$$

$$E\_{\rm css} = P\_{\rm css} T\_{\rm css} \tag{4}$$

where *Pess* and *Eess* are the rated power capacity and energy capacity of the energy storage, respectively, *Tess* is the charging and discharging time of energy storage, and *λ<sup>p</sup>* and *λ<sup>e</sup>* are the cost per unit power capacity and the cost per unit energy capacity, respectively.

The annual fixed operation and maintenance cost *Fg* consists of a conventional thermal power station *Fg*<sup>1</sup> and an energy storage station *Fg*2, which can be expressed as:

$$F\_{\mathbb{S}^1} = \mathfrak{a}\_{\mathbb{S}^1} \cdot \mathbb{C}\_{\mathbb{S}^1} \tag{5}$$

$$F\_{\mathfrak{J}^2} = \mathfrak{a}\_{\mathfrak{J}^2} \cdot P\_{\text{ess}} \tag{6}$$

$$F\_{\mathfrak{F}} = F\_{\mathfrak{F}1} + F\_{\mathfrak{F}2} \tag{7}$$

where *Cg*<sup>1</sup> is the total investment cost of a conventional thermal power station, *αg*<sup>1</sup> is the annual fixed operation and maintenance cost rate of the power station, and *αg*<sup>2</sup> is the fixed operation and maintenance cost of energy storage per unit power.

The thermal power station's annual operating fuel cost *Fk* can be expressed as:

$$F\_k = \beta\_k \cdot E\_k \tag{8}$$

where *Ek* is the annual energy yield of a conventional thermal power station, and *β<sup>k</sup>* is the fuel cost of the unit energy yield of the power station.

#### 2.1.2. Constraint

In comprehensively considering a variety of power supply types, including wind power, photovoltaic, hydropower, thermal power, pumped storage and new energy storage units, the electricity transmitted by the inter-provincial tie lines and the transmission lines outside the province can be classified into the load demand, and the constraint conditions to be met are shown in the following equations.

<sup>1</sup> Constraints on system power balance:

$$Pess\_t + P\_{0t} = LD\_t(1 + \rho + \sigma) \tag{9}$$

where *Pesst* represents the output of the newly invested energy storage system at time *t*, *P*0*<sup>t</sup>* represents the output of the original power station of the system at time *t*, *LDt* is the load value of the system at time *t*, and *ρ* and *σ* are the power consumption rate and system line loss rate, respectively.

<sup>2</sup> Maximum and minimum output constraints of power station:

$$P\_{\text{kmin}} \le P\_{\text{k}} \le P\_{\text{kmax}} \tag{10}$$

where *P*kmin and *P*kmax are the minimum and maximum technical outputs of unit k. <sup>3</sup> Thermal power fuel consumption constraints:

$$\sum\_{t=1}^{\tau} E\_{it} \beta\_i \le A\_{i\tau} \tag{11}$$

where *Eit* is the generating capacity of the thermal power plant *i* at time *t*, *Ai<sup>τ</sup>* is the fuel consumption limit of power plant *i* in the period *τ*, and *β<sup>i</sup>* is the average fuel consumption per unit of power plant *i*.

<sup>4</sup> Climbing constraints of thermal power units:

$$
\delta L l\_i^t D \mathcal{R}\_i \le P\_i(t) - P\_i(t-1) \le \mathcal{U}\_i^t \mathcal{U} \mathcal{R}\_i \tag{12}
$$

where *URi* and *DRi* are the loading and unloading rate of unit *i*, respectively, and *Ui t* represents the start-stop state of thermal power unit *i* at time *t*, which is 0–1. The start-up is 1, and others are 0.

<sup>5</sup> Constraints on the start and stop of thermal power units:

$$\sum\_{k=t}^{t+T\_S-1} \left(1 - \mathcal{U}\_i^k \right) \ge T\_S(\mathcal{U}\_i^{t-1} - \mathcal{U}\_i^t) \tag{13}$$

$$\sum\_{k=t}^{t+T\_O-1} \mathcal{U}\_i^k \ge T\_O(\mathcal{U}\_i^t - \mathcal{U}\_i^{t-1}) \tag{14}$$

where *TS* and *TO* are the minimum shutdown and start-up time of the thermal power unit, respectively.

<sup>6</sup> Constraints on the generating capacity of hydropower units:

$$\sum\_{t=1}^{\tau} E\_{jt} \beta\_j \le \mathcal{W}\_{j\tau} \tag{15}$$

where *Ejt* is the generating capacity of the hydropower plant *j* at time *t*, *Wj<sup>τ</sup>* is the available water limit of power plant *j* in the period *τ*, and *β<sup>j</sup>* is the average water consumption per unit of power plant *j*.

<sup>7</sup> Constraints on pumped storage units:

$$E\_{j\mathbf{G}} = \eta\_j E\_{j\mathbf{P}} \tag{16}$$

$$C\_{P.t} = mP\_{PS.P.N} \tag{17}$$

where *η<sup>j</sup>* is the pumping-power generation conversion efficiency of pumped storage power station *j*, and *EjG* and *EjP* are the generating capacity and pumping load capacity of the pumped storage power station *j*, respectively, within its dispatching period *τ*. The pumped power of a pumped storage power station at a certain period of time must be an integer multiple of its single capacity. *CP.t* is the pumping capacity of the pumped storage power station at time *t*, and *PPS*.*P*.*<sup>N</sup>* is the rated pumping capacity of the pumped storage unit. <sup>8</sup> Energy storage operation constraints:

$$-P\_{\text{cmax\\_ESS}} \le P\_{\text{out\\_ESS}} \le P\_{\text{dmax\\_ESS}}\tag{18}$$

$$E\_{\rm min} \le E\_t \le E\_{\rm max} \tag{19}$$

$$E\_{\rm ess}(0) = E\_{\rm ess}(T) \tag{20}$$

where *Pcmax\_ESS* and *Pdmax\_ESS* are the maximum charge and discharge power, respectively. *Pout\_ESS* is the real-time output power, and *Et* is the real-time energy capacity.

<sup>9</sup> Standby constraints:

$$\sum\_{i=1}^{N} \mathcal{U}\_{i}^{\dagger} (P\_{i, \text{max}} - P\_{i}(t)) \ge \iota r\_{N}(t) \tag{21}$$

$$\sum\_{i=1}^{N} P\_{i, \text{max}} \ge \kappa L D\_{\text{max}} \tag{22}$$

where *N* units are providing a certain reserve capacity, *urN*(*t*) represents the spinning reserve of *N* units at time *t*, *α* is the total reserve rate, and *LD*max is the maximum load.

<sup>ᬎ</sup> Offshore wind power transmission channel constraints:

$$P\_{\text{pass}} \preceq^{\prime} \eta P\_{\text{WN}} \tag{23}$$

where *Ppass* is the maximum transmission capacity of the offshore wind power transmission channel. *PWN* is the rated installed capacity of the offshore wind farm, and *η* is the transmission channel ratio.

#### *2.2. Principal Block Diagram of Planning and Optimization Process*

A typical case of a coastal power grid is taken to verify the effectiveness of the energy storage capacity planning method. First, the methods of cluster analysis and probabilistic modeling are adopted to consider the uncertainty of offshore wind power, and the annual output characteristic curves are shown in Figure 1.

**Figure 1.** Offshore wind power output curve clustering scenario set.

The principal block diagram of offshore wind power storage capacity planning and optimization is shown in Figure 2. The long-term operation data of the combined wind– storage system can be obtained through operation simulation, and the consumption index of offshore wind power can be calculated. After a comprehensive optimization comparison and sensitivity analysis, the optimal planning results can be outputted.

**Figure 2.** Principal block diagram of offshore wind energy storage capacity planning and optimization.

#### **3. Results and Discussion**

#### *3.1. Description of the Basic Conditions of the Example*

It is expected that by 2025, the annual maximum load of the power grid in this coastal area will be 0.0111 billion kW, with a total power consumption of 59.2 billion kWh, and the total installed offshore wind power will reach 9176.5 MW. The transmission channel ratio *η* = 0.8, and this means that the maximum capacity of the transmission channel will be 7341.2 MW.

The multi-type power supply and line structure in this coastal area are shown in Figure 3. The installed capacity of the multi-type power supply corresponding to Figure 3 is shown in Table 2. The installed capacity of offshore energy storage needs to be planned and then configured. Load characteristics are described by an annual maximum load curve, typical weekly maximum load curve and typical daily load curve. Load data are shown in Figure 4.

**Figure 3.** Power supply and line structure in this coastal area.

**Table 2.** The installed capacity of various power sources of the coastal power grid.


**Figure 4.** Annual load characteristic curves.

We used the Gurobi solver to solve the model in the MATLAB programming environment. The simulation was carried out with the year as the cycle and the day as the unit. Inputs should be the load curves and offshore wind power output curves of the coastal area based on historical data, combined with the power installation structure and the grid structure inside and outside of the province. The monthly statistics of offshore wind power and abandoned wind power in this coastal area can be obtained without new energy storage, as shown in Figure 5.

**Figure 5.** Annual utilization of offshore wind power in this coastal area.

All of the offshore wind farms in this coastal area can generate 25,441.25 GWh of electricity in a year. The practical electricity is 24,085.76 GWh, and the abandoned wind power is 1355.49 GWh. The abandoned wind rate is 5.33%, and the utilization hours of offshore wind power are 2625 h. Further, the utilization hours of the transmission channels are 3281 h. It can be seen from Figure 5 that the abandoned wind power of offshore wind power is mainly concentrated from January to April, with the most serious abandoned wind in February and a little abandoned wind in November and December.

For lead–acid battery and lithium-ion battery energy storage systems, the cost coefficients per unit of energy capacity, per unit power capacity, the operation and maintenance costs and engineering life obtained, are shown in Table 3.

**Table 3.** Related parameters of energy storage.


According to relevant parameters, the planning period is selected as 20 years, and the comprehensive discount rate for the whole society is 10%. According to the offshore wind energy storage capacity planning optimization model, the next step is to set up the energy storage configuration. The offshore wind farms are configured with an energy storage capacity of 10% to 40% of their rated installed capacity. Therefore, the rated power capacity of the energy storage system is described as 0.1~0.4 in the following. The installed capacity of energy storage under different configuration schemes is shown in Table 4. With daily cycle adjustments of energy storage devices, the charging and discharging time is set from 1 to 6 h, respectively, and the 24 energy storage configuration schemes are combined with different power P and charging and discharging time T.

**Table 4.** Storage capacity configuration of offshore wind farms.


#### *3.2. Example Analysis of Simulation Results*

Based on the energy storage configuration scheme, the annual electricity balance of operation simulation from the planning level is conducted to obtain the operation simulation results of the coastal area. The relationship between the abandoned wind rate of the offshore wind power and the energy storage configuration scheme is shown in Table 5. Thus, with the further increase in new energy storage power capacity and energy capacity, the abandoned wind rate of offshore wind power gradually decreases.

**Table 5.** Relationship between the abandoned wind rate of offshore wind power and the energy storage configuration scheme in this region.


Here, when the lithium-ion battery energy storage system with a scale of 917.65 MW/ 917.65 MWh is configured in the offshore wind farm of this coastal area, the annual cost is analyzed, as shown in Table 6.


**Table 6.** Composition of annual expenses (104 Yuan).

Based on this, the relationship between different energy storage configuration schemes and the annual costs can be obtained, as shown in Table 7. It can be seen that with the further increase in new energy storage power capacity and energy capacity, the annual system costs gradually increase. Therefore, the decrease in the abandoned wind rate of offshore wind power is accompanied by an increase in the annual system cost. This paper studies the method to achieve the lowest annual cost while meeting the strict constraints below a certain curtailment level.

**Table 7.** Annual total cost under different schemes.


Based on Tables 5 and 7, contour lines of wind curtailment rate and annual cost can be drawn on a two-dimensional plane, as shown in Figures 6 and 7, respectively. The curve of wind curtailment rate indicates that different energy storage configurations can bring the same consumption effect of offshore wind power.

**Figure 6.** Contour lines of abandoned wind rates of offshore wind power.

**Figure 7.** Contour lines of the annual cost of the planning scheme.

In order to find the optimal economic scheme combined with the annual cost contour line, it can be known that when the abandoned wind rate is at a certain standard level, different annual cost contour lines are used to be tangent to the determined abandoned wind rate contour line, and the tangent point (power P, charge and discharge time T) is the best scheme.

In practical application, 5% of new energy is allowed to abandon power, which is scientifically reasonable. Therefore, the alternative energy storage configuration schemes are (0.3, 1), (0.2, 2), (0.1, 6), etc. According to this method, the best energy storage configuration scheme is (0.3, 1). It means that the scale of the lithium-ion battery energy storage system configured for the offshore wind farm with a total installed capacity of 9176.5 MW in the coastal area is 2752.95 MW/2752.95 MWh.

At this time, the practical electrical output of the offshore wind farm is 24,225.85 GWh. The abandoned wind power quantity is 1215.4 GWh, and the abandoned wind rate is 4.78%. The utilization hours of offshore wind power are 2640 h, and the utilization hours of the transmission channel are 3300 h. Further, the annual cost is 75.978 billion yuan.

For this study, only 24 scenarios, based on the optimization model to present the energy storage capacity allocation method, were used. By using fast computer calculation, the step size of the configuration scheme is further reduced. Based on the energy storage capacity planning method proposed in this paper, the configuration scheme with the best economy and applicability can be obtained more quickly and accurately.

#### *3.3. Sensitivity Analysis*

According to the above scheme, the configuration of a 2752.95 MW/2752.95 MWh lithium-ion battery energy storage system is relatively large in terms of the annual cost from 73.434 billion yuan to 75.978 billion yuan. This section studies the factors influencing the abandoned wind rate of offshore wind power from other perspectives, exploring feasible schemes to reduce the abandoned wind rate, and further allocating the source-side energy storage, paving the way to reduce the power capacity and energy capacity of the energy storage system configuration, thus reducing the investment costs and operation and maintenance costs, and improving the economic performance.

As shown in Figure 3, the consumption and utilization of offshore wind power in this coastal area are not only related to the installed scale of the power structure, including offshore wind power and energy storage but it is also affected by the transmission agreement signed with other provinces and the exchange of electricity in contact lines with other regions in the province. Therefore, a sensitivity analysis is carried out from the transmission agreement of the transmission lines outside of the province and the capacity allocation of the link line within the province.

#### 3.3.1. Influence of Transmission Line Agreement

Out-of-province transmission line refers to a power transmission line from another province to the coastal area, with a maximum transmission capacity of 760 MW, which is sent to the coastal area in accordance with the transmission agreement signed with another province and given priority to use. Taking the daily transmission curve as an example, the transmission agreement can be adjusted to 1.1 times the original transmission agreement, the original transmission agreement, 0.9 times the original transmission agreement, and 0.8 times the original transmission agreement, as shown in Figure 8.

**Figure 8.** Schematic diagram of different transmission protocols.

The original transmission agreement refers to the existing transmission agreement between the grid in the coastal area and another province. Under the existing transmission agreement, this paper adjusts it to 1.1 times, 0.9 times and 0.8 times, and then obtains the utilization of offshore wind power according to the optimization model, and analyzes the reasons for this situation. After the operation simulation, the changes in the offshore abandoned wind power rate under different transmission agreements can be compared and analyzed, and the results are shown in Table 8.


**Table 8.** Utilization of offshore wind power under different transmission agreements.

Therefore, it can be seen that the electricity sent by the out-of-province transmission lines in this coastal area is too much, which affects the consumption and utilization of internal offshore wind power. Therefore, the transmission agreement can be optimized in the direction of reduction without additional cost.
