# Green Power Trade Behavior in China’s Renewable Portfolio Standard: An Evolutionary Game-Based System Dynamics Approach

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

## 3. Behavioral Strategies of Green Power Plants and Power Sales Companies

- (1)
- $({\alpha}_{1},{\beta}_{1})$ signifies that both sides choose the transaction of green power, where ${\alpha}_{1}$ is the revenue for selling green power, and ${\beta}_{1}$ is the opposite of the payment for buying green power; namely, ${\beta}_{1}$ is the revenue of participating in the transaction for power sales companies.
- (2)
- $({\alpha}_{4},{\beta}_{4})$ signifies that both sides do not choose the transaction of green power, where ${\alpha}_{4}$ is the revenue for not selling green power, and ${\beta}_{4}$ is the revenue for not buying green power. Namely, green power plants do not gain incomes, and power sales companies pay fines.
- (3)
- $({\alpha}_{2},{\beta}_{2})$ signifies that one side chooses the transaction, and the other does not choose, where ${\alpha}_{2}$ is the revenue for selling green power, and ${\beta}_{2}$ is the revenue for not buying green power. This means that green power plants will convert green electricity into TGC to gain profits in the consumption market, and power sales companies will pay fines.
- (4)
- $({\alpha}_{3},{\beta}_{3})$ also signifies that one side chooses the transaction, and the other does not choose, where ${\alpha}_{3}$ is the revenue for not selling green power, and ${\beta}_{3}$ is the revenue for still buying green power. This means that green power plants will have no income, and power sales companies can only buy TGC from the consumption market.

## 4. Stability Analysis of Evolutionary Game

## 5. Discussion for General Equilibrium Conditions

- $A>0$, $P+\Delta b>C{\omega}_{1}$, the price for TGC is higher than the unit transaction cost for green power plants;
- $E>0$,$P-\Delta c>C{\omega}_{1}$, the real transaction price of RE is higher than the cost of unit transaction for green power plants;
- $D>0$, $f>P+C{\omega}_{2}$, the unit fine is higher than the sum of FIT and the unit transaction cost for power sales companies.

## 6. Example

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ESS | Evolutionary Stable Strategy |

LCOE | Levelized Cost of Electricity |

RE | Renewable Energy |

SD | System Dynamics |

FIT | Feed in Tariff |

NEA | National Energy Administration |

RPS | Renewable Portfolio Standard |

TGC | Trade of Green Certificate |

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**Figure 1.**Dynamics evolution schematic diagrams of Cases 1, 2, 3, 4 and 7. (

**a**) Case 1; (

**b**) Case 2; (

**c**) Case 3; (

**d**) Case 4; (

**e**) Case 7.

Types | Ref. | Players | Factors | Trading | |||||
---|---|---|---|---|---|---|---|---|---|

Quotas/Weighting | Fines | Subsidies | Prices | Costs | Government Supervision | ||||

Two sides | [21] | Thermal and renewable energy plants | √ | √ | - | √ | √ | - | TGC |

[22] | √ | √ | √ | √ | - | - | TGC | ||

[23] | √ | √ | - | √ | √ | - | TGC | ||

[24] | √ | √ | - | √ | √ | - | TGC | ||

Our work | Green power plants and power sales companies | √ | √ | √ | √ | √ | - | Green power | |

[25] | Local governments and power plants | √ | √ | √ | √ | - | √ | TGC | |

Three sides | [26] | Regulators, power plants and local governments | √ | √ | √ | √ | - | √ | TGC |

[27] | Conventional and renewable energy plants, power grid companies | - | - | - | - | - | √ | TGC | |

[28] | Central government, local governments and grid companies | √ | √ | √ | - | - | √ | TGC | |

[29] | combined heat and power plants, coal-fired plants, renewable energy plants | √ | - | - | √ | √ | - | TGC | |

[30] | The regulator and the two types of power sales companies | - | √ | √ | √ | √ | √ | TGC | |

[31] | Fossil energy power plants, provincial power grids and provincial governments | √ | √ | √ | √ | √ | √ | Green power | |

[32] | Power plants, power grid companies and central government | √ | √ | √ | √ | - | √ | TGC |

Items | Power Sales Companies | ||
---|---|---|---|

Buy (y) | Not Buy (1 − y) | ||

Green power plants | Sale (x) | $({\alpha}_{1},{\beta}_{1})$ | $({\alpha}_{2},{\beta}_{2})$ |

Not sale (1 − x) | $({\alpha}_{3},{\beta}_{3})$ | $({\alpha}_{4},{\beta}_{4})$ |

Parameters | Meanings/(Units) |
---|---|

${q}_{i}$ | The tradable amount between green power plants and power sales companies, i = 1, 2, 3, 4 (kWh) |

$P$ | The price for green power, usually take FIT as benchmark price (yuan/kWh) |

$-\Delta c$ | The marginal cost difference between thermal power and green power usually equals to RE subsidies, ∆c < 0 (yuan/kWh) |

$C$ | The cost of unit green power (yuan/kWh) |

${\omega}_{1}$ | The cost coefficient of green power plants |

${\omega}_{2}$ | The cost coefficient of power sales companies, ${\omega}_{1}+{\omega}_{2}=1$ |

$\Delta b$ | The price difference between green power and TGC (yuan/kWh) |

$f$ | Fines for unit green power (yuan/kWh) |

$P-\Delta c-{\omega}_{1}C$ | The unit revenue of selling green power for green power plants (yuan/kWh) |

$P+{\omega}_{2}C$ | The unit cost of buying green power for power sales companies (yuan/kWh) |

$P+\Delta b-{\omega}_{2}C$ | The cost of buying one unit TGC for power sales companies (yuan/kWh) |

Parameters | Meaning for Green Power Plants | Parameters | Meaning for Power Sales Companies |
---|---|---|---|

${U}_{A1}$ | Revenue for selling green power | ${U}_{B1}$ | Revenue for buying green power |

${U}_{A2}$ | Revenue for not selling green power | ${U}_{B2}$ | Revenue for not buying green power |

${U}_{A}$ | Expected revenue | ${U}_{B}$ | Expected revenue |

Equilibrium Point | Eigenvalues | det (J) | tr (J) |
---|---|---|---|

${E}_{1}(0,0)$ | ${\lambda}_{11}={q}_{i}A,{\lambda}_{12}={q}_{i}B$ | ${\lambda}_{11}\cdot {\lambda}_{12}$ | ${\lambda}_{11}+{\lambda}_{12}$ |

${E}_{2}(0,1)$ | ${\lambda}_{21}={q}_{i}E,{\lambda}_{22}=-{q}_{i}B$ | ${\lambda}_{21}\cdot {\lambda}_{22}$ | ${\lambda}_{21}+{\lambda}_{22}$ |

${E}_{3}(1,0)$ | ${\lambda}_{31}=-{q}_{i}A,{\lambda}_{32}={q}_{i}D$ | ${\lambda}_{31}\cdot {\lambda}_{32}$ | ${\lambda}_{31}+{\lambda}_{32}$ |

${E}_{4}(1,1)$ | ${\lambda}_{41}=-{q}_{i}A,{\lambda}_{42}=-{q}_{i}D$ | ${\lambda}_{41}\cdot {\lambda}_{42}$ | ${\lambda}_{41}+{\lambda}_{42}$ |

Case | Classification | ESS | Unstable Points | Saddle Points |
---|---|---|---|---|

0 | $A>0,B<0,E<0,D<0$ | ${E}_{3}(1,0)$ | ${E}_{4}(1,1)$${E}_{4}(1,1)$ | ${E}_{1}(0,0)$${E}_{2}(0,1)$ |

1 | $A>0,B<0,E<0,D>0$ | \ | \ | ${E}_{1}(0,0)$${E}_{2}(0,1)$${E}_{3}(1,0)$${E}_{4}(1,1)$ |

2 | $A>0,B<0,E>0,D<0$ | ${E}_{3}(1,0)$ | ${E}_{2}(0,1)$ | ${E}_{1}(0,0)$${E}_{4}(1,1)$ |

3 | $A>0,B<0,E>0,D>0$ | ${E}_{4}(1,1)$ | ${E}_{2}(0,1)$ | ${E}_{1}(0,0)$${E}_{3}(1,0)$ |

4 | $A>0,B>0,E<0,D<0$ | ${E}_{2}(0,1)$${E}_{3}(1,0)$ | ${E}_{1}(0,0)$${E}_{4}(1,1)$ | \ |

5 | $A>0,B>0,E<0,D>0$ | ${E}_{2}(0,1)$ | ${E}_{1}(0,0)$ | ${E}_{3}(1,0)$${E}_{4}(1,1)$ |

6 | $A>0,B>0,E>0,D<0$ | ${E}_{3}(1,0)$ | ${E}_{1}(0,0)$ | ${E}_{2}(0,1)$${E}_{4}(1,1)$ |

7 | $A>0,B>0,E>0,D>0$ | ${E}_{4}(1,1)$ | ${E}_{1}(0,0)$ | ${E}_{2}(0,1)$${E}_{3}(1,0)$ |

Study | Method | Players | Parameter | ||
---|---|---|---|---|---|

Fine $\left(\mathit{f}\right)$ | Price for RE | Price for TGC | |||

Ref. [24] | Subjective game | Green power plants and thermal power plants | $f=2{P}_{\mathrm{TGC}}$ | \ | \ |

Ref. [23] | Evolution game | $f=2{P}_{\mathrm{TGC}}-\Delta c$ | \ | \ | |

Ref. [22] | $f>{P}_{\mathrm{TGC}}{q}_{TGC}/q$ | \ | \ | ||

The present study | Green power plants and power sales companies | $f>P+C{\omega}_{2}$ | $P-\Delta c>C{\omega}_{1}$ | $P+\Delta b>C{\omega}_{1}$ |

Parameter Type | Initial Stage | Intermediate Stage | Mature Stage |
---|---|---|---|

Generation share of wind power | 0.55 | 0.57 | 0.58 |

Generation share of photovoltaic | 0.38 | 0.40 | 0.41 |

FIT of wind power (yuan/kWh) | 0.38 | 0.33 | 0.26 |

FIT of photovoltaic (yuan/kWh) | 0.35 | 0.30 | 0.26 |

FIT of green power (yuan/kWh) | 0.34 | 0.31 | 0.26 |

LCOE of wind power (yuan/kWh) | 0.50 | 0.45 | 0.44 |

LCOE of photovoltaic (yuan/kWh) | 0.77 | 0.66 | 0.62 |

Cost C of unit green power | 0.63 | 0.51 | 0.29 |

Price of TGC (yuan/kWh) | 0.28 | 0.27 | 0.25 |

$f$ (yuan/kWh) in the present study | 0.63 | 0.57 | 0.51 |

$f$ (yuan/kWh) in Refs. [23,24] | 0.56 | 0.54 | 0.50 |

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## Share and Cite

**MDPI and ACS Style**

Na, C.; Jin, C.; Pan, H.; Ding, L.
Green Power Trade Behavior in China’s Renewable Portfolio Standard: An Evolutionary Game-Based System Dynamics Approach. *Sustainability* **2022**, *14*, 5155.
https://doi.org/10.3390/su14095155

**AMA Style**

Na C, Jin C, Pan H, Ding L.
Green Power Trade Behavior in China’s Renewable Portfolio Standard: An Evolutionary Game-Based System Dynamics Approach. *Sustainability*. 2022; 14(9):5155.
https://doi.org/10.3390/su14095155

**Chicago/Turabian Style**

Na, Chunning, Can Jin, Huan Pan, and Lixia Ding.
2022. "Green Power Trade Behavior in China’s Renewable Portfolio Standard: An Evolutionary Game-Based System Dynamics Approach" *Sustainability* 14, no. 9: 5155.
https://doi.org/10.3390/su14095155