# Multi-Objective Virtual Power Plant Construction Model Based on Decision Area Division

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## Abstract

**:**

## 1. Introduction

## 2. Decision Area Division and Decision Variable Determination of Virtual Power Plant

#### 2.1. Distributed Energy Resource Output Model

_{t}of a single fan is obtained according to the power characteristic curve of the wind turbine, the product of the sum of all the fan power and the coefficient representing the output power [13], and can be described as:

_{t}is the wind speed at the location of the fan, V

_{ci}is the threshold wind velocity of the fan, V

_{r}is the rated wind speed of the fan, V

_{co}is the resection wind speed of the fan, and P

_{r}is the rated power of the fan.

_{PV}is the actual output power of PV generation system, P

_{sn}is the rated power of the PV generation system, R

_{c}is the characteristic intensity of solar irradiance which is generally 150 W/m

^{2}, and R

_{r}is the solar radiation intensity when the PV power generation system just reaches the rated power (generally 1000 W/m

^{2}).

_{0}is the initial charging state, D is the actual mileage number, and L is the maximum mileage number.

_{shift}(k) is the response amount of the transferable load at period k, P

_{0}(k) is the base load at period k, Δp

_{shift}(k) is the power price difference between period k and other periods, k

_{shift}(k) is the mutual elasticity between period k and other periods, v

_{shift}(k) is the transfer rate, T is the time period.

_{re}(k) is the change in price of period k, l

_{re}(k) is the elastic coefficient of the period k, and v

_{re}(k) is cutting speed.

_{2}(t) is the initial power consumption curve, and Δk(Δp) is the load translation period caused by Δp.

#### 2.2. Division of Decision Area

_{j}(j = 1, 2, …, K). Then, each area is carefully divided. The division criterion is to minimize the number of divided areas under certain constraints, that is, the regional area cannot exceed S

_{maxj}, and the maximum power of the mixed resource in each area cannot exceed Q

_{maxj}. The area S

_{j}is divided according to the regional function, so the mixture resource density ρ

_{j}is different. There is a negative function relationship between S

_{maxj}and ρ

_{j}. The steps for dividing the decision area of VPP are as follows:

- (1)
- Determine the type and quantity of resources in different locations of the region.
- (2)
- Divide the region preliminary according to the regional function, and record the area as S
_{j}(j = 1, 2, …, K). - (3)
- Divide area S
_{j}particularity, initialize division block number N_{j}in each area, determine the parameters S_{maxj}and Q_{maxj}in the constraints. - (4)
- According to the number N
_{j}of areas, make S_{j}divided into equal areas. Determine whether to meet the constraints; if satisfied, turn (5), and vice versa (6). - (5)
- N
_{j}= N_{j}+ 1, return to (3). - (6)
- Obtain the final detailed division result of regional S
_{j}, which is the corresponding division result of N_{j}= N_{j}− 1.

_{1}is finally divided into 4 parts, which is shown in Figure 4.

_{j}can be divided into C

_{j}sub-areas, the region is divided into m areas after the detailed division, which is as follows:

_{i}which is made up of 0 and 1 elements and can be written as:

## 3. The Construction Model of Virtual Power Plant

#### 3.1. Objective Function

_{1}is the daily cost of VPP; C

^{DG}is the daily average generation cost of DR; C

^{ES}is the daily charging cost of ES device; C

^{SN}is the punishment cost for the VPP to pay the grid; ${P}_{ki}^{DG}$ is the DR output of area i at time period k; ${X}_{i}^{DG}$ represents whether there is a DR generation in area i, and if satisfied, the value is 1, and vice versa 0; n

_{i}is the daily average charging times of ES devices; ${P}_{ki}^{ES}$ is the charging power of ES device of area i at time period k; ${X}_{I}^{ES}$ represents whether there is a ES device in the area i, and if satisfied, the value is 1, and vice versa 0; ${P}_{ki}^{DR}$ is the controllable load power of area i at time period k; C

_{s}is the unit punishment cost; and P

_{k}

_{0}is the planned output at time period k.

_{2}is the volatility of the curve L; σ is the standard deviation; μ is the geometric mean; L

_{k}is the difference between the actual output and planned output of the VPP at time period k; and $\overline{L}$ is the arithmetic mean of output power.

_{p}and ω

_{ρ}are the weights of spatial location and load density attributes, respectively, and the sum of them is 1; p

_{i}and p

_{j}are the position coordinates of area i and area j; ρ

_{i}and ρ

_{j}are the load densities of area i and area j, respectively.

_{i}and X

_{h}indicate whether there is any resources involved in the construction of the VPP in areas i and h, respectively, and if satisfied, the value is 1, and vice versa 0; d(i, h) represents the fusion space distance between areas i and h.

#### 3.2. Constraint Condition

_{min}is the minimum number of resources; and Q

_{min}is the minimum power consumption in time period k.

_{max}is the maximum fusion space distance.

_{k}

_{min}and P

_{k}

_{max}are the minimum and maximum values of VPP output at time period k, respectively.

_{max}is the upper limit of the volatility.

_{x}is the standard deviation of the resource sequence x(k); and σ

_{y}is the standard deviation of the resource sequence y(k).

_{VPP}.

_{min}is the lower limit of complementarity.

## 4. The Improved Bat Algorithm Based on Priority Selection

#### 4.1. Basic Bat Algorithm

_{i}, the current best position of bat population is x*, and the update formulas of ${x}_{i}^{t}$ and ${v}_{i}^{t}$ are as follows:

_{old}is selected from the known optimal solution set, and then a new location is generated near that location, which is obtained by:

^{t}is the average loudness of all bats.

_{i}and rate R

_{i}. In general, the loudness will gradually decrease with the number of updates, and the rate will gradually increase with the number of updates, which are shown as:

#### 4.2. Improved Bat Algorithm Based on Priority Selection

_{or}and or refer to logical “xor operation” and “or operation”, respectively; x* is the best location for the bat population; and t is the algebra of bats.

_{i}(x(i)), and then determine the current pareto optimal solution.

_{new}and update the bat’s speed and location according to Equations (34)–(36):

_{old}randomly from the current pareto solution set and get a local solution x

_{new}through Equation (37).

_{i}(x

_{new})

_{new}.

_{i}(x

_{new})

_{new}> f

_{i}(x(i)), x(i) = x

_{new}; use Equation (38) to reduce A(i), and use Equation (39) to increase R(i), shown as following:

_{new}dominates some solutions of the solution set, the solutions that are dominated by x

_{new}should be removed from the current pareto solution set. If there is no dominance relation between x

_{new}and the solution set, x

_{new}should be directly moved to the current pareto solution set.

_{ab}is the bth objective function value of the ath solution for the pareto solution set; ${f}_{b}^{\mathrm{max}}$ and ${f}_{b}^{\mathrm{min}}$ are the maximum and minimum values of the bth objective function, respectively; ω

_{b}is the weight of the bth objective function; M is the number of objective functions; and N is the number of solutions for the pareto solution.

## 5. Example Analysis

#### 5.1. Division of Decision Areas and Determination of Regional Resources

#### 5.2. Result Analysis of Virtual Power Plant Construction

## 6. Conclusions

- (1)
- The decision variables are used to represent all kinds of DER in each area; therefore, the final construction results of VPP are more intuitive.
- (2)
- The compromise selection of the multiple optimal solutions is achieved through the priority selection, and a compromise optimal solution can be obtained which provides an effective reference for planners.
- (3)
- The actual VPP output curve obtained by this example is generally determined by the output curve of DG, ES and DR, which play an auxiliary regulatory role.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

VPP | Virtual power plant |

DER | Distributed energy resources |

DG | Distributed generation |

ES | Energy storage |

DR | Demand response |

WPP | Wind power plant |

PV | Photovoltaic generator |

WP | Wind power |

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Resources | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

DG | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |

ES | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |

DR | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |

Serial Number | Objective Function Set | Area Resources Not Involved in the Construction |
---|---|---|

1 | (2.5, 8.7, 3.3, 1.8) | ${X}_{1}^{ES},{X}_{1}^{DR},{X}_{2}^{DG},{X}_{5}^{ES},{X}_{5}^{DR},{X}_{9}^{DR},{X}_{11}^{ES}$ |

2 | (2.5, 7.3, 3.3, 1.8) | ${X}_{1}^{ES},{X}_{4}^{DR},{X}_{9}^{DR},{X}_{10}^{DR},{X}_{10}^{ES},{X}_{11}^{ES},{X}_{12}^{DG}$ |

3 | (2.3, 6.4, 3.2, 1.7) | ${X}_{1}^{DR},{X}_{2}^{DG},{X}_{4}^{DG},{X}_{4}^{DR},{X}_{5}^{DR},{X}_{14}^{DG},{X}_{15}^{DG}$ |

4 | (2.3, 6.3, 3.2, 1.8) | ${X}_{1}^{DR},{X}_{4}^{DG},{X}_{4}^{DR},{X}_{5}^{DR},{X}_{11}^{DG},{X}_{12}^{DG},{X}_{14}^{DG}$ |

5 | (2.2, 6.8, 3.2, 1.8) | ${X}_{1}^{DG},{X}_{1}^{ES},{X}_{4}^{DG},{X}_{9}^{DG},{X}_{12}^{DG},{X}_{12}^{ES},{X}_{15}^{ES}$ |

6 | (2.2, 5.8, 3.1, 1.7) | ${X}_{1}^{DR},{X}_{2}^{DG},{X}_{2}^{DR},{X}_{11}^{DG},{X}_{12}^{DG},{X}_{14}^{DG},{X}_{15}^{DG}$ |

7 | (2, 4.1, 2.2, 1.5) | ${X}_{1}^{ES},{X}_{1}^{DR},{X}_{5}^{ES},{X}_{5}^{DR},{X}_{10}^{DR},{X}_{12}^{DG},{X}_{13}^{DG}$ |

8 | (1.9, 3.4, 2, 1.1) | ${X}_{2}^{DG},{X}_{2}^{DR},{X}_{3}^{DG},{X}_{9}^{ES},{X}_{11}^{DR},{X}_{12}^{DG},{X}_{14}^{DG}$ |

9 | (1.9, 3.5, 2.1, 1.1) | ${X}_{1}^{DG},{X}_{1}^{ES},{X}_{3}^{DG},{X}_{4}^{DR},{X}_{8}^{DG},{X}_{11}^{ES},{X}_{12}^{DG}$ |

10 | (2.1, 4.2, 2.2, 1.1) | ${X}_{1}^{DR},{X}_{2}^{DG},{X}_{3}^{DG},{X}_{4}^{DR},{X}_{9}^{ES},{X}_{14}^{DR}$ |

11 | (2.3, 6.7, 3.2, 1.9) | ${X}_{1}^{DG},{X}_{1}^{ES},{X}_{4}^{DG},{X}_{12}^{DG},{X}_{12}^{ES},{X}_{15}^{ES}$ |

Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

DG | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||

ES | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||||||

DR | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Resource Type | Complementary Coefficient |
---|---|

WP, PV | 0.2375 |

WP, ES | 0.3100 |

WP, DR | 0.3341 |

PV, ES | 0.3116 |

PV, DR | 0.2534 |

ES, DR | 0.3167 |

Number | ① | ② | ③ | ④ | ⑤ | ⑥ | ⑦ | ⑧ | ⑨ | ⑩ |
---|---|---|---|---|---|---|---|---|---|---|

DG | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||

ES | ✓ | ✓ | ✓ | |||||||

DR | ✓ | ✓ |

Number | F1 | F2 | F3 | F4 |
---|---|---|---|---|

Detailed division | 19,044 | 3.52% | 20,505 | 1,133,120 |

Preliminary division | 19,121 | 5.89% | 20,406 | 1,487,020 |

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## Share and Cite

**MDPI and ACS Style**

Duan, J.; Wang, X.; Gao, Y.; Yang, Y.; Yang, W.; Li, H.; Ehsan, A. Multi-Objective Virtual Power Plant Construction Model Based on Decision Area Division. *Appl. Sci.* **2018**, *8*, 1484.
https://doi.org/10.3390/app8091484

**AMA Style**

Duan J, Wang X, Gao Y, Yang Y, Yang W, Li H, Ehsan A. Multi-Objective Virtual Power Plant Construction Model Based on Decision Area Division. *Applied Sciences*. 2018; 8(9):1484.
https://doi.org/10.3390/app8091484

**Chicago/Turabian Style**

Duan, Jie, Xiaodan Wang, Yajing Gao, Yongchun Yang, Wenhai Yang, Hong Li, and Ali Ehsan. 2018. "Multi-Objective Virtual Power Plant Construction Model Based on Decision Area Division" *Applied Sciences* 8, no. 9: 1484.
https://doi.org/10.3390/app8091484