# Profit Allocation Strategy of Virtual Power Plant Based on Multi-Objective Optimization in Electricity Market

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## Abstract

**:**

## 1. Introduction

- (1)
- This paper designs the measurement index of a VPP’s attractiveness to participants. The ratio of the loss caused to the cooperative alliance when a participant leaves VPP to the loss suffered by the participant itself is recorded as the attraction index of VPP to the participant. It can quantitatively assess the risk of participants leaving the existing VPP and participating in other VPP cooperation.
- (2)
- This paper establishes a multi-objective-based profit allocation model for a VPP based on bidding optimization including fairness of profit allocation, stability of cooperative alliance, and attraction of participating entities. This model can be applied to both a single VPP market environment and to a multi-VPPs competition environment.
- (3)
- In this paper, a multi-objective evolutionary optimization algorithm based on reference points is introduced to effectively solve the Pareto solution set of VPP profit allocation. The algorithm can adaptively generate a series of reference points with superior performance based on the current population, and greatly improve the individual selection pressure by calculating the distance between the reference point and the individual.

## 2. Problem Statement

#### 2.1. VPP Cooperative Game Problem

#### 2.1.1. Interest Relationship between VPP’s Internal Subjects

#### 2.1.2. Establishment of VPP Cooperative Game Model

#### 2.2. Determination Process of VPP Cost Allocation Strategy

- (1)
- In the equation stage of day-ahead bidding strategy, transaction cost of VPP market is optimized through VPP market bidding strategy model.
- (2)
- Before submitting the bidding curve of day-ahead bidding market, the paper determines the expected cost proportion of each participant in VPP through VPP cost allocation model, which is regarded as the basis of the final cost allocation. Based on the optimization results of transaction costs in the expected market of VPP, this paper takes the fairness of cost allocation, the stability of cooperative alliances, and the attractiveness of participating members as objectives.
- (3)
- After the settlement of the real-time market, this paper calculates the cost borne by each participant according to the cost allocation proportion of VPP determined in the bidding stage and the final transaction cost of VPP market.

## 3. Bidding Optimization Model of VPP Based on CVaR

#### 3.1. Model Building of Uncertain Characteristics

- (1)
- Distributed wind power

- (2)
- Distributed photometry

- (3)
- Load demand

- (4)
- Market transaction price

#### 3.2. VPP Bidding Model

## 4. Cost Allocation Model of VPP Based on Multi-Objective Optimization

#### 4.1. Model Building

- (1)
- Stability objective

- (2)
- Fairness objective

- (3)
- Attraction objective

#### 4.2. Model Simplification

## 5. Multi-Objective Evolutionary Optimization Based on Reference Points

#### 5.1. Generation of Reference Points and Selection Strategy for Individuals

#### 5.1.1. Generation of Reference Points

- (1)
- Set the initial parameter: the population to be selected $G\left(k\right)$, the step size for generating reference points $\phi $ ($\phi \in \left(0,1\right)$), the sampling rate of reference points $\alpha $ ($\alpha \in \left[1/M,1\right]$), and the number of reference points $NR$ ($NR\le N$);
- (2)
- Select the nondominated solutions of $G\left(k\right)$ to form ${G}^{\prime}\left(k\right)$;
- (3)
- Sort ${G}^{\prime}\left(k\right)$ according to the crowding distance of the m dimensional target space;
- (4)
- Based on the $\alpha N$ individuals with the largest crowding distance, reference points are generated according to Equations (42) and (43) which form the set of reference points ${R}_{m}$ in the m dimensional target space;$$r=\left({f}_{1}\left(x\right),\dots ,{f}_{m}\left(x\right)-{\upsilon}_{m},\dots ,{f}_{M}\left(x\right)\right)$$$${\upsilon}_{m}=\phi \left({f}_{m}^{\mathrm{max}}-{f}_{m}^{\mathrm{min}}\right)$$
- (5)
- Reference point set $R=R\cup {R}_{m}$, judge the size of $m$, if $m<M$, then $m$ increase by 1, then return to step 3 and repeat the above process, otherwise go to step 6;
- (6)
- Delete the dominated points in $R$ and judge the number of reference points in $R$, if it is greater than $NR$, delete the $\left|R\right|-NR$ points with the largest congestion distance in $R$, otherwise go to step 7;
- (7)
- Output the set of reference points $R$.

#### 5.1.2. Individual Selection Strategy Based on Reference Points

#### 5.2. Algorithm Flow

## 6. Case Study

#### 6.1. Simulation Data

#### 6.2. Cost Allocation Results and Analysis

#### 6.2.1. Cost Allocation Result

#### 6.2.2. Cost Allocation Scheme under Situations of Different Risk Factors

#### 6.2.3. Cooperative Benefits of VPP

#### 6.3. Algorithm Performance Analysis

## 7. Conclusions

- (1)
- VPP cooperation can save the cost of 10.76% of overall market transaction, and the cost-saving ratio of each member is between 7.82% and 18.66%, which can ensure the sustainable stability of VPP cooperation alliance.
- (2)
- The cooperation benefit and profit allocation effect of VPP are affected by its risk response and tolerance. Prosumers will be more willing to participate in VPP cooperation when bidding risk is high in electricity market.
- (3)
- Individual members with low bidding cost have advantages in VPP cooperation, which can get a higher proportion of cost savings. It indicates that the profit allocation framework proposed in this paper is helpful to encourage prosumers of small size to participate in VPP cooperation.
- (4)
- Compared with other members, a VPP is less attractive to individual members with higher bidding cost, and such members are more likely to participate in other VPP cooperative alliances. This indicates that in the multi-VPP competition environment, VPP cooperative alliances with a smaller gap between internal participating members’ size are more solid.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Indices (Sets) | |

I | Set of prosumers |

S | Cooperation alliance between VPPs |

a^{S} | Indicated vector |

v(I) | Market trading cost of cooperation game H(I;v) |

v({i}) | Transaction cost of individual participating members in the market |

core(H) | Core set of cooperation game H(I;v) |

t | Time indicator |

s | Situation indicator |

o | Stepwise bidding indicator |

Parameters | |

L^{R} | Flexible load scale (MW) |

${P}_{t,s,in}^{DA}$ | Electricity purchasing price in the day-ahead market (¥/MW) |

${P}_{t,s,out}^{DA}$ | Electricity selling price in the day-ahead market (¥/MW) |

${P}_{t,s,in}^{RT}$ | Electricity purchasing price in the real-time market (¥/MW) |

${P}_{t,s,out}^{RT}$ | Electricity selling price in the real-time market (¥/MW) |

P^{DP} | Penalty power price of unbalanced power (¥/MW) |

${P}_{i}^{R}$ | Compensation offer of flexible load adjustment (¥/MW) |

${Q}_{i,t,s}^{G,\mathrm{min}}$ | DRE’s minimum output (MW) |

${Q}_{i,t,s}^{G,\mathrm{max}}$ | DRE’s maximum output (MW) |

${Q}_{i,t,s}^{G}$ | DRE’s true output (MW) |

${D}_{i}^{\mathrm{max}}$ | Participating member i’s maximum load (MW) |

R_{i,t,s} | Participating member i’s load reduction capability in the situation s during t period (%) |

${R}_{i}^{up}/{R}_{i}^{down}$ | The upper/lower limit of ramping up and down of participating member i’s flexible load regulation |

${D}_{i,o,t}^{R,\mathrm{max}}$ | Participating member i’s maximum reduction load of bid section o |

δ | Standard of deviating power assessment in the electricity market (%) |

λ | Period length, 1 h |

β | Risk parameter |

α | Confidence coefficient |

ρ_{s} | Probability of scene s |

N | Population size |

M | Number of objective functions |

Variables | |

${Q}_{t}^{DA}$ | Expected interaction power between VPP and grid in the day-ahead market (MW) |

${Q}_{t,s,in}^{DA}$ | Electricity purchased by VPP in the day-ahead market (MW) |

${Q}_{t,s,out}^{DA}$ | Surplus renewable energy sold by VPP in day-ahead market (MW) |

${Q}_{t,s,in}^{RT}$ | VPP’s expected purchasing power in real-time market (MW) |

${Q}_{t,s,out}^{RT}$ | Electricity sold by VPP in the real-time market (MW) |

${Q}_{t,s}^{A}$ | Actual interaction power between VPP and grid (MW) |

${Q}_{t,s}^{RT}$ | Expected interaction power between VPP and grid in the real-time market during t period (MW) |

${D}_{t,s}^{Ri,}/{D}_{o,t,s}^{Ri,}$ | Flexible load reduction (MW) |

${D}_{i,t,}$ | Member i’s load demand during t period (MW) |

η_{s} | Risk deviation |

μ | VaR |

${C}_{t,s}^{DA}$ | VPP’s trading cost in the day-ahead market (¥) |

${C}_{t,s}^{RT}$ | VPP’s trading cost in the real-time market (¥) |

${C}_{t,s}^{DP}$ | Penalty cost of deviating power in VPP (¥) |

${C}_{t,s}^{DR}$ | Adjustment cost of flexible load in VPP (¥) |

${\epsilon}_{t,s}$ | VPP’s deviating power assessing rate (%) |

${\phi}_{t,s}$ | VPP’s deviating power ratio (%) |

ω | Minimum cost savings in all alliance s (¥) |

π | The largest difference of trading saving-cost ratio in VPP (%) |

$\overline{\theta}$/θ | The maximum/minimum proportion of members’ market transaction cost savings in VPP (%) |

γ | VPP’s attraction indicator to participants |

x | Cost allocation vector of cooperative game in VPP |

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**Figure 2.**Strategy determination process of VPP bidding and cost allocation in the electricity market.

Risk Scenario | The Effect of Cost Allocation | |||
---|---|---|---|---|

Stability | Fairness | Attraction | ||

1 | L^{R} = 10%, P^{D}^{P}= 700 | 1005.84 | 9.85% | 1.92 |

2 | L^{R} = 15%, P^{DP} = 700 | 1020.68 | 9.82% | 1.99 |

3 | L^{R} = 20%, P^{DP} = 700 | 1030.75 | 9.80% | 2.03 |

4 | L^{R} = 15%, P^{DP} = 300 | 324.62 | 5.56% | 3.54 |

5 | L^{R} = 15%, P^{DP} = 500 | 792.85 | 7.66% | 2.96 |

Performance Index | Improved NSGA-III | NSGA-III |
---|---|---|

GD | 0.0132 | 0.2124 |

SP | 0.0436 | 0.6423 |

Computation time (s) | 663 | 645 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Zhang, M.; Ao, J.; Wang, Z.; Dong, H.; Zeng, M.
Profit Allocation Strategy of Virtual Power Plant Based on Multi-Objective Optimization in Electricity Market. *Sustainability* **2022**, *14*, 6229.
https://doi.org/10.3390/su14106229

**AMA Style**

Wang Y, Zhang M, Ao J, Wang Z, Dong H, Zeng M.
Profit Allocation Strategy of Virtual Power Plant Based on Multi-Objective Optimization in Electricity Market. *Sustainability*. 2022; 14(10):6229.
https://doi.org/10.3390/su14106229

**Chicago/Turabian Style**

Wang, Yuqing, Min Zhang, Jindi Ao, Zhaozhen Wang, Houqi Dong, and Ming Zeng.
2022. "Profit Allocation Strategy of Virtual Power Plant Based on Multi-Objective Optimization in Electricity Market" *Sustainability* 14, no. 10: 6229.
https://doi.org/10.3390/su14106229