# Effects of Local Electricity Trading on Power Flows and Voltage Levels for Different Elasticities and Prices

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method for Local Electricity Trading and Estimation of Its Impacts on the Grid

#### 2.1. Auction-Based Method for LET

- -
- energy balance constraints for each time period $t$, in time horizon made of $T$ periods, as listed in Equation (2):$$\sum}_{b=1}^{B}{\displaystyle \sum}_{i=1}^{I}ACCEP{T}_{s,t,b,i}\xb7{q}_{s,t,b,i}\ge {\displaystyle \sum}_{b=1}^{B}{\displaystyle \sum}_{i=1}^{I}ACCEP{T}_{d,t,b,i}\xb7{q}_{d,t,b,i$$
- -
- technical constraints of maximal supply and demand capacities for each peer $i$ in period $t$ (${q}_{{MAX}_{s,t,i}}$ and ${q}_{{MAX}_{d,t,i}}$ respectively) have to be integrated into demand and supply offers, while individually can be written as in Equations (3) and (4):$$0\le {\displaystyle \sum}_{b=1}^{B}{q}_{s,t,b,i}\le {q}_{{MAX}_{s,t,i}}$$$$0\le {\displaystyle \sum}_{b=1}^{B}{q}_{d,t,b,i}\le {q}_{{MAX}_{d,t,i}}$$

#### 2.2. Method for Simulation of Effects of LET on LV Distribution Grid Power Flows and Voltage Levels

## 3. Case Study

#### 3.1. Scenarios and Input Data

#### 3.2. Outputs of the First Stage of the Simulation: Equilibrium Quantities and Prices

#### 3.3. Results: Power Flows

#### 3.4. Results: Voltage Levels

^{+}) and negative voltage deviations (dU

^{−}).

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Topology of the IEEE European LV Test Feeder where the simulation of the LET was implemented.

**Figure 2.**Illustration of the demand and supply offering curves of the peers for the cases: (1) for the demand curves ${p}_{{N}_{d,t,i}}$ = 0.100 EUR/kWh, $q{D}_{{N}_{t,i}}$ = 1 kWh and the differences relate to the slope of the curves which is defined by the factor $k$; (2) for the supply curves ${q}_{{MAX}_{s,t,i}}$ = 3 kWh and the differences relate to the nominal supply price are defined by the ${p}_{{N}_{s,t,i}}$.

**Figure 3.**Merit order supply and demand curves: (

**a**) Aggregated (merit order) supply offers for the “high price” and “low price” cases in the time interval 9:35–9:40 a.m. (

**b**) Aggregated demand offers for the “high elasticity” and “low elasticity” cases in the time interval 9:35–9:40 a.m.

**Figure 4.**Equilibrium prices and volumes (points of intersections of supply and demand curves) for the scenarios S1–S4 of the one 5-min time interval (9:35–9:40 a.m.) of market trading. The labels of the points mark scenario names, quantities, and prices, respectively.

**Figure 5.**The auction-based LET: (

**a**) The equilibrium prices in analyzed time horizon, (

**b**) The volume of LET energy traded in analyzed time horizon.

**Figure 6.**Energy balance in the microgrid: (

**a**) Energy balance in reference scenario SREF; (

**b**) Energy balance in the S1 scenario; (

**c**) Energy balance in the S2 scenario; (

**d**) Energy balance in the S3 scenario; (

**e**) Energy balance in the S4 scenario.

**Figure 7.**Voltage, U (p.u.) and voltage differences, dU (p.u.) over time (minutes) for different busses: (

**a**) Voltage in reference scenario SREF; (

**b**) Voltage difference between scenario S1 and SREF; (

**c**) Voltage difference between scenario S1 and S2; (

**d**) Voltage difference between scenario S1 and S3; (

**e**) Voltage difference between scenario S2 and S3.

**Figure 9.**MAE of the voltage deviations (for all deviations, positive deviations, and negative deviations) from the nominal voltage over all periods, busses, and phases. For the clarity of the results, MAE is divided by the nominal voltage and expressed as a percentage.

**Table 1.**Key differences of the analyzed scenarios and input data for individual peers, where “High” supply price is set at 0.075 EUR/kWh and “Low” supply price at 0.025 EUR/kWh.

Scenario | S1 | S2 | S3 | S4 | SREF |
---|---|---|---|---|---|

Maximal supply offering price | High | High | Low | Low | NA (feed-in-tariff) |

Price elasticity of demand | Increased | Decreased | Increased | Decreased | Perfectly inelastic (passive demand) |

**Table 2.**Energy balance (kWh) in the microgrid for the analyzed scenarios in the observed time horizon (from 8:00 a.m. until 10:00 a.m.).

Item | SREF | S1 | S2 | S3 | S4 |
---|---|---|---|---|---|

Total microgrid consumption | 1321 | 783.5 | 687 | 883 | 883 |

Total microgrid production | 896 | 778.5 | 682 | 896 | 896 |

Peers self-consumption | 282 | 205.5 | 172.5 | 235 | 235 |

Local electricity trading | 583 | 573 | 509.5 | 643 | 643 |

Import from upstream grid | 456 | 5 | 5 | 5 | 5 |

Export to upstream grid | −31 | 0 | 0 | −18 | −18 |

**Table 3.**Average voltage levels and difference of the average voltage level from the nominal in all scenarios.

Scenario | SREF | S1 | S2 | S3 | S4 |
---|---|---|---|---|---|

Average voltage level | 1.04490 | 1.04977 | 1.04983 | 1.05008 | 1.05008 |

Average voltage level difference from the nominal | −0.486% | −0.022% | −0.016% | 0.007% | 0.007% |

**Table 4.**MAE between grid voltage and nominal voltage (for all deviations, positive deviations, and negative deviations) over all periods, busses, and phases. For the clarity of the results, MAE is divided by the nominal voltage and expressed as a percentage.

Scenario | SREF | S1 | S2 | S3 | S4 |
---|---|---|---|---|---|

MAE (all voltage deviations) (%) | 1.300% | 0.700% | 0.650% | 0.730% | 0.730% |

MAE (positive voltage deviations) (%) | 1.072% | 0.707% | 0.676% | 0.751% | 0.751% |

MAE (negative voltage deviations) (%) | 1.432% | 0.697% | 0.626% | 0.718% | 0.718% |

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**MDPI and ACS Style**

Herenčić, L.; Ilak, P.; Rajšl, I.
Effects of Local Electricity Trading on Power Flows and Voltage Levels for Different Elasticities and Prices. *Energies* **2019**, *12*, 4708.
https://doi.org/10.3390/en12244708

**AMA Style**

Herenčić L, Ilak P, Rajšl I.
Effects of Local Electricity Trading on Power Flows and Voltage Levels for Different Elasticities and Prices. *Energies*. 2019; 12(24):4708.
https://doi.org/10.3390/en12244708

**Chicago/Turabian Style**

Herenčić, Lin, Perica Ilak, and Ivan Rajšl.
2019. "Effects of Local Electricity Trading on Power Flows and Voltage Levels for Different Elasticities and Prices" *Energies* 12, no. 24: 4708.
https://doi.org/10.3390/en12244708