# Research on Capacity Allocation Optimization of Commercial Virtual Power Plant (CVPP)

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. CVPP Capacity Allocation Modeling

#### 2.1.1. Base Load Type

_{1}denotes the standard deviation of P

_{t}; P

_{t}denotes the total out power of CVPP, the F

_{1}value and the total output fluctuation are in the direct ratio; P

_{p}(t), P

_{w}(t), and P

_{h}(t) denote the photovoltaic power, wind power, and hydropower generation, respectively, the calculation formulas will be introduced in Section 2.2; α and β denote the weight—α is the proportion of photovoltaic power in total CVPP output, (1−α)β is the wind power proportion in total CVPP output, (1−α)(1−β) is the hydropower proportion in total CVPP output. Then, when α = 1, it is combined into 100% photovoltaic; when α = 0 and β = 1, means 100% wind power generation; when α = 0 and β = 0, means 100% hydropower generation.

#### 2.1.2. Peak Shaving Type

_{2}denotes the mean square deviation of R

_{t}; R

_{t}denotes the residual load after deducting wind power, photovoltaic, and hydropower, the larger the F

_{2}value, the greater the residual load fluctuation, and the smaller the F

_{2}value, the smaller the residual load fluctuation; P

_{p}(t), P

_{w}(t), and P

_{h}(t) denote the photovoltaic power, wind power, and hydropower generation, respectively; the remaining variables are the same as shown in Section 2.1.1.

#### 2.2. Power Modeling

- (1)
- Wind power model

_{w}is the power generation of wind turbines under different wind speed conditions, and will be calculated as follows [30]

_{r}denotes the rated wind output under the rated conditions; v denotes the real-time wind speed; v

_{i}denotes the cut-in wind speed; v

_{o}denotes the cut-out wind speed; v

_{r}denotes the rated wind speed.

- (2)
- Photovoltaic model

_{p}is linearly related to the solar light intensity, and is calculated as follows [31]

_{r}denotes the rated photovoltaic output under the rated conditions; G denotes the actual solar irradiance (W/m

^{2}); G

_{r}denotes the rated solar irradiance (1000 W/m

^{2}); a

_{T}denotes the temperature coefficient; T denotes the actual surface temperature of the photovoltaic cells (°C); T

_{r}denotes the rated surface temperature of the photovoltaic cells (25 °C) [32].

- (3)
- Hydropower model

_{h}will be calculated as follows [33]

^{2}); η

_{h}denotes the efficiency of the generator; ρ denotes the density of the water (1000 kg/m

^{3}); Q denotes the water flow (m

^{3}/s); h denotes the height of the water drop (m).

_{W,max}denotes the wind power rated output (MW);

_{P,max}denotes the photovoltaic rated output (MW);

_{t+}

_{1}and V

_{t}denotes the reservoir storage (m

^{3}) at the end and the beginning, respectively; I

_{t}denotes the reservoir inflow (m

^{3}/s);

_{t}

^{l}and V

_{t}

^{u}denote the lower and upper limits for reservoir storage (m

^{3}), respectively;

_{t}

^{l}and Q

_{t}

^{u}denote the lower and upper limits for river discharge flow (m

^{3}/s), respectively;

_{t}

^{l}denotes the lower limits for hydropower output (MW) (The output of the reservoir must be discharged for meeting the downstream irrigation, water supply, navigation, etc.); N

_{t}

^{u}denotes the upper limits for hydropower output (MW);

_{s}denotes the schedulable output (MW), which refers to the output that the hydropower can offer in CVPP on the satisfying water dispatching premise.

#### 2.3. Hybrid Algorithm Based on ReliefF and APSO

#### 2.3.1. APSO Algorithm

_{n}denotes the individual optimal position of the nth particle; P

_{g}denotes the best position of the group obtained from all particles in the previous iteration.

#### 2.3.2. ReliefF Algorithm

- (1)
- Calculate S
_{A}^{Hit}, the distance between R and NearHit on each feature A. - (2)
- Calculate S
_{A}^{Miss}, the distance between R and NearMiss on each feature A. - (3)
- Compare the two distances S
_{A}^{Hit}and S_{A}^{Miss}. If S_{A}^{Hit}is greater than S_{A}^{Miss}, each feature of the A is helpful to distinguish the same kind and different kinds. If S_{A}^{Hit}is less than S_{A}^{Miss}, each feature of the A hurts, distinguishing the same class and different classes and reduces the weight of the feature. - (4)
- Repeat the above process m times to gain the average weight of each feature, as is shown in Formula (19)

_{j}) denotes the difference between sample R and H

_{j}in feature A, as is shown in Formula (20); M

_{j}(C) denotes the j-th nearest sample in category C; p(C) denotes the target probability of class C, given by Formula (21). When the number of samples is approximately the same, there are p(C) = 1/C.

#### 2.3.3. ReliefF–APSO Hybrid Algorithm

- (1)
- The given data set is normalized by Z-score before training;
- (2)
- Using the Formula (19) to extract the features of the ReliefF algorithm and take the first d features with relatively large weight as the training set and test set of APSO, d = 100;
- (3)
- Generate population, set the number of particles N, set each particle as a random number vector within (−1, 1), and set the number of neurons and hidden layer nodes. In the experiment, N takes 20;
- (4)
- Initialize the speed and position variables of APSO, and set the individual optimal position and group optimal position of the population;
- (5)
- Calculate the fitness value of each particle;
- (6)
- Update the position and velocity of the adaptive particle swarm according to Formulas (17) and (18);
- (7)
- Judge whether the maximum number of iterations is reached. If so, stop the iteration. Otherwise, turn to step (5) and continue the iteration.

## 3. Case Study

## 4. Results and Discussion

#### 4.1. Comparative Analysis of ReliefF–APSO Hybrid Algorithm, APSO, and PSO

_{1}= c

_{2}= 2. In the ReliefF–APSO hybrid algorithm and APSO algorithm, w

_{max}= 0.9, w

_{min}= 0.4, and learning factor c

_{1a}= c

_{2a}= 2. The number of particles is 20 and the maximum number of iterations is 100. The results of the algorithm comparison are shown in Figure 6.

#### 4.2. Base load Type Operation Model

_{1}is 5.65 on sunny days and 4.83 on rainy days, which means the CVPP output on rainy days is more stable. That is because on rainy days, the proportion of photovoltaic is small, and the proportion of hydropower is high, which is more conducive to maintaining the stability of the overall output. The largest F

_{1}is 10.63 on sunny days and 13.09 on rainy days, which means compared to the single energy mode, the CVPP could reduce the base load fluctuation by 46.8% on sunny days and 63.1% on rainy days. The operation results of the base load type in different weather are shown in Figure 8.

#### 4.3. Peak shaving Type Operation Model

_{2}on sunny days is larger than on rainy days, which means the residual load on rainy days is more stable than on sunny days. That is because, on sunny days, the proportion of photovoltaic is large. However, it cannot provide the peak shaving power at the evening peak, so more thermal power and other energy are needed to help hydropower and wind power for peak shaving. The largest F

_{2}is 13.09 on sunny days and 11.34 on rainy days, which means compared to the single energy mode, the CVPP could reduce the residual load fluctuation by 54.3% on sunny days and 58.8% on rainy days. The operation results of the peak shaving type in different weather are shown in Figure 11.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**The energy proportion of the peak shaving type operation. (

**a**) Sunny days; (

**b**) rainy days.

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**MDPI and ACS Style**

Wang, S.; Jia, R.; Shi, X.; Luo, C.; An, Y.; Huang, Q.; Guo, P.; Wang, X.; Lei, X.
Research on Capacity Allocation Optimization of Commercial Virtual Power Plant (CVPP). *Energies* **2022**, *15*, 1303.
https://doi.org/10.3390/en15041303

**AMA Style**

Wang S, Jia R, Shi X, Luo C, An Y, Huang Q, Guo P, Wang X, Lei X.
Research on Capacity Allocation Optimization of Commercial Virtual Power Plant (CVPP). *Energies*. 2022; 15(4):1303.
https://doi.org/10.3390/en15041303

**Chicago/Turabian Style**

Wang, Songkai, Rong Jia, Xiaoyu Shi, Chang Luo, Yuan An, Qiang Huang, Pengcheng Guo, Xueyan Wang, and Xuewen Lei.
2022. "Research on Capacity Allocation Optimization of Commercial Virtual Power Plant (CVPP)" *Energies* 15, no. 4: 1303.
https://doi.org/10.3390/en15041303