# Use of Energy Storage to Reduce Transmission Losses in Meshed Power Distribution Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Power System Components and Problem Formulation

#### 2.1. Power Flow

#### 2.2. Load Profiles

#### 2.3. Generation Profiles

#### 2.4. Energy Storage Model

#### 2.5. Multiobjective Problem Formulation

## 3. Multiobjective Optimization Methods

#### 3.1. Pareto and Box Domination

#### 3.2. NSGA-II

#### 3.3. BRKGA

#### 3.4. MPSO

## 4. Test Case and Results

#### 4.1. Cases Description

#### 4.1.1. System without RES—Test Case 1

#### 4.1.2. System with PV Generation at Bus 10—Test Case 2

#### 4.1.3. System with PV Generation at Bus 15—Test Case 3

#### 4.1.4. System with Two PV Generations—Test Case 4

#### 4.2. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Daily load profile for Spring ($\mathcal{S}1$), Summer ($\mathcal{S}2$), Autumn ($\mathcal{S}3$) and Winter ($\mathcal{S}4$).

**Figure 3.**Example of application of the peak shaving strategy for BESS. The energy returned during the day by BESS (orange field) is equal to the drawn energy (blue field) and corresponds to the useful capacity of the energy storage.

**Figure 4.**Example of assignment of a group of solutions of the bi-objective problem to corresponding Pareto fronts in accordance with the definition of $\u03f5$-dominance. Points ${x}_{5}$ oraz ${x}_{9}$ lie in the same square. Therefore, the fact that ${x}_{5}\succ {x}_{9}$ is determined by their distance from point d (${d}_{1}<{d}_{2}$) [40].

**Figure 5.**Example of division of the objective space of a bi-objective problem, with the Pareto front marked with a blue line, into: (

**a**) uniform areas in accordance with $\u03f5-$dominance; (

**b**) areas with variable dimensions determined according to $pa\u03f5$-dominance. The blue line marks the ideal Pareto front for a certain bi-objective problem. The red dots are points which belong to the front and are, at the same time, not dominated in accordance with the selected algorithm of division into areas [41].

**Figure 7.**Diagram of the 16-bus system used in tests. Node 1 is a slack bus. Generator G2 represents a PV installation.

**Figure 8.**Diagram of the 16-bus system used in tests. Node 1 is a slack bus. Generator G3 represents a PV installation.

**Figure 9.**Diagram of the 16-bus system used in tests. Node 1 is a slack bus. Generators G2 and G3 represent a PV installation.

**Figure 10.**Pareto Front determined by means of the NSGA-II, MPSO, BRKGA and $pa\u03f5-$BRKGA methods for: (

**a**) Test Case 1; (

**b**) Test Case 2; (

**c**) Test Case 3; (

**d**) Test Case 4.

**Table 1.**Example of a crossover of two parents a and b using the coin tossing method. Individuals have 4-gene chromosomes. After generating 4 random numbers (one per each gene), the obtained values are compared to ${\rho}_{a}$.

Item | Gene 1 | Gene 2 | Gene 3 | Gene 4 |
---|---|---|---|---|

Parent a | 0.52 | 0.8 | 0.43 | 0.3 |

Parent b | 0.74 | 0.34 | 0.54 | 0.26 |

Random | 0.62 | 0.45 | 0.81 | 0.35 |

${\rho}_{a}=0.75$ | < | < | > | < |

Offspring | 0.52 | 0.8 | 0.54 | 0.3 |

Bus No. | P [MW] | Q [MVar] | Bus No. | P [MW] | Q [MVar] |
---|---|---|---|---|---|

1 | 0 | 0 | 9 | 35 | 26.9 |

2 | 50 | 30.2 | 10 | 0 | 0 |

3 | 35 | 7.7 | 11 | 35 | 16.4 |

4 | 40 | 21.8 | 12 | 30 | 5.4 |

5 | 45 | 23.6 | 13 | 25 | 15 |

6 | 40 | 5.2 | 14 | 35 | 7.1 |

7 | 35 | 3.3 | 15 | 0 | 0 |

8 | 50 | 19.9 | 16 | 35 | 19.6 |

Overall | 490 | 202.1 |

Case | Method Efficiency $\mathit{\eta}$ (Founded Solutions ${\mathit{N}}_{\mathbf{all}}$) | |||
---|---|---|---|---|

NSGA-II | BRKGA | $\mathbf{pa}\mathit{\u03f5}$-BRKGA | MPSO | |

Test Case 1 | 29% (38) | 62% (37) | 100% (17) | 12% (41) |

Test Case 2 | 53% (38) | 37% (41) | 96% (24) | 32% (41) |

Test Case 3 | 27% (41) | 41% (41) | 94% (35) | 17%(41) |

Test Case 4 | 8% (37) | 34% (41) | 79% (39) | 20% (41) |

**Table 4.**Three solutions founded by $pa\u03f5$-BRKGA with ca. 100 MWh, 200 MWh and 500 MWh of overall BESS capacity for Test Case 1.

Bus No. | ca. 100 MWh [MWh] | ca. 200 MWh [MWh] | ca. 500 MWh [MWh] |
---|---|---|---|

1 | 0.0 | 0.0 | 0.0 |

2 | 0.2 | 0.2 | 42.4 |

3 | 0.2 | 0.2 | 36.6 |

4 | 0.2 | 0.2 | 74.4 |

5 | 0.3 | 85.1 | 85.1 |

6 | 0.0 | 0.0 | 80.2 |

7 | 1.5 | 1.5 | 0.0 |

8 | 0.0 | 0.0 | 0.0 |

9 | 0.0 | 0.0 | 0.0 |

10 | 0.0 | 0.0 | 0.0 |

11 | 0.0 | 0.0 | 40.3 |

12 | 38.9 | 38.9 | 38.9 |

13 | 49.1 | 49.1 | 49.1 |

14 | 0.2 | 45.3 | 70.8 |

15 | 0.0 | 0.2 | 0.0 |

16 | 0.9 | 0.9 | 0.9 |

${\mathbf{f}}_{\mathbf{1}}$[MWh] | 91.5 | 221.6 | 518.7 |

$\mathbf{\Delta}\mathbf{E}$[MWh] | 5855.2 | 11,856.7 | 19,405.6 |

$\mathsf{\Psi}$[MWh/MWh] | 64.0 | 53.5 | 37.4 |

**Table 5.**Three solutions founded by $pa\u03f5$-BRKGA with ca. 100 MWh, 200 MWh and 500 MWh of overall BESS capacity for Test Case 2.

Bus No. | ca. 100 MWh [MWh] | ca. 200 MWh [MWh] | ca. 500 MWh [MWh] |
---|---|---|---|

1 | 0.0 | 0.0 | 0.0 |

2 | 0.0 | 0.0 | 0.0 |

3 | 0.0 | 0.0 | 0.0 |

4 | 0.1 | 0.1 | 80.5 |

5 | 0.2 | 48.9 | 88.1 |

6 | 10.5 | 15.7 | 94.6 |

7 | 0.0 | 0.1 | 0.1 |

8 | 0.1 | 0.0 | 0.1 |

9 | 0.0 | 0.0 | 0.0 |

10 | 0.3 | 0.3 | 0.3 |

11 | 0.1 | 39.0 | 39.0 |

12 | 31.4 | 31.4 | 29.1 |

13 | 58.2 | 58.2 | 58.2 |

14 | 0.1 | 0.1 | 84.2 |

15 | 0.0 | 0.0 | 0.0 |

16 | 0.2 | 0.2 | 0.2 |

${\mathbf{f}}_{\mathbf{1}}$[MWh] | 101.2 | 194.0 | 474.4 |

$\mathbf{\Delta}\mathbf{E}$[MWh] | 6993.3 | 12,292.5 | 20,697.8 |

$\mathsf{\Psi}$[MWh/MWh] | 69.1 | 63.4 | 43.6 |

**Table 6.**Three solutions founded by $pa\u03f5$-BRKGA with ca. 100 MWh, 200 MWh and 500 MWh of overall BESS capacity for Test Case 3.

Bus No. | ca. 100 MWh [MWh] | ca. 200 MWh [MWh] | ca. 500 MWh [MWh] |
---|---|---|---|

1 | 0.1 | 0.1 | 0.1 |

2 | 0.0 | 0.1 | 0.3 |

3 | 0.0 | 0.0 | 0.0 |

4 | 0.0 | 0.0 | 65.5 |

5 | 59.0 | 59.0 | 78.4 |

6 | 0.2 | 0.0 | 94.5 |

7 | 0.1 | 9.8 | 0.1 |

8 | 0.2 | 0.2 | 0.2 |

9 | 0.0 | 0.2 | 0.2 |

10 | 0.0 | 0.0 | 0.0 |

11 | 0.2 | 34.1 | 49.7 |

12 | 40.3 | 40.3 | 40.3 |

13 | 0.2 | 58.8 | 58.8 |

14 | 0.3 | 0.1 | 86.7 |

15 | 0.0 | 0.2 | 0.0 |

16 | 0.0 | 0.2 | 0.2 |

${\mathbf{f}}_{\mathbf{1}}$[MWh] | 100.6 | 203.1 | 475.0 |

$\mathbf{\Delta}\mathbf{E}$[MWh] | 6614.9 | 11,601.8 | 19,910.1 |

$\mathsf{\Psi}$[MWh/MWh] | 65.8 | 57.1 | 41.9 |

**Table 7.**Three solutions founded by $pa\u03f5$-BRKGA with ca. 100 MWh, 200 MWh and 500 MWh of overall BESS capacity for Test Case 4.

Bus No. | ca. 100 MWh [MWh] | ca. 200 MWh [MWh] | ca. 500 MWh [MWh] |
---|---|---|---|

1 | 0.0 | 0.0 | 0.0 |

2 | 0.1 | 0.1 | 0.1 |

3 | 0.0 | 0.0 | 36.7 |

4 | 0.1 | 0.2 | 72.0 |

5 | 0.0 | 87.3 | 87.3 |

6 | 0.1 | 0.1 | 66.0 |

7 | 0.1 | 0.1 | 22.0 |

8 | 0.1 | 0.1 | 40.9 |

9 | 0.0 | 0.1 | 0.0 |

10 | 0.1 | 0.1 | 0.0 |

11 | 33.0 | 42.9 | 42.9 |

12 | 0.1 | 0.1 | 45.6 |

13 | 45.9 | 45.9 | 45.9 |

14 | 15.3 | 15.3 | 15.3 |

15 | 0.0 | 0.1 | 0.0 |

16 | 0.1 | 0.2 | 0.0 |

${\mathbf{f}}_{\mathbf{1}}$[MWh] | 95.0 | 192.6 | 474.7 |

$\mathbf{\Delta}\mathbf{E}$[MWh] | 6800.1 | 11,772.0 | 20,497.6 |

$\mathsf{\Psi}$[MWh/MWh] | 71.6 | 61.1 | 43.2 |

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**MDPI and ACS Style**

Mikulski, S.; Tomczewski, A.
Use of Energy Storage to Reduce Transmission Losses in Meshed Power Distribution Networks. *Energies* **2021**, *14*, 7304.
https://doi.org/10.3390/en14217304

**AMA Style**

Mikulski S, Tomczewski A.
Use of Energy Storage to Reduce Transmission Losses in Meshed Power Distribution Networks. *Energies*. 2021; 14(21):7304.
https://doi.org/10.3390/en14217304

**Chicago/Turabian Style**

Mikulski, Stanisław, and Andrzej Tomczewski.
2021. "Use of Energy Storage to Reduce Transmission Losses in Meshed Power Distribution Networks" *Energies* 14, no. 21: 7304.
https://doi.org/10.3390/en14217304