# Integration of Intelligent Neighbourhood Grids to the German Distribution Grid: A Perspective

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## Abstract

**:**

## 1. Introduction

- Modelling of the neighbourhood grid according to the scenario.
- Modelling of the distribution grid according to the scenario.
- Combination of the neighbourhood grid and the distribution grid as a bi-level multi-objective optimisation problem.
- Proposing two methods to solve this problem using centralised and decentralised approach.
- Assessing the policy implications and design of experiments to test the approach experimentally.

## 2. Related Works

## 3. Problem Formulation

#### 3.1. Scenario Description

#### 3.2. Distribution Grid

#### 3.2.1. Model Parameters

- (i)
- t∈$\mathbb{N}$: is defined as the time step. The time step is usually 15 min. This parameter is the same also for the neighbourhood grid.
- (ii)
- (iii)
- ${N}_{grid,t}$∈$\mathbb{N}$: is defined as the number of generators that have to comply with a redispatch measurement at time t for every $t=1,\dots ,T$.
- (iv)
- ${N}_{Lines}$∈$\mathbb{N}$: represents the number of lines.
- (v)
- ${R}_{i}$∈$\mathbb{R}$: is a parameter that represents the resistance of the line.
- (vi)
- ${N}_{NR}$∈$\mathbb{N}$: represents the number of non-renewable generators.
- (vii)
- ${C}_{{\mathrm{CO}}_{2}}$∈$\mathbb{R}$: is the cost of $\mathrm{C}{\mathrm{O}}_{2}$.
- (viii)
- ${C}_{Redispatch}^{i}$∈$\mathbb{R}$: is the Redispatch cost for the ith generator.

#### 3.2.2. Decision Variables

- (i)
- ${P}_{G}^{i}$∈$\mathbb{R}$: is defined as the power generated by the ith generator that could be subject to redispatch measures at time t for $i=1,\dots ,{N}_{grid}$, where ${N}_{grid}$ represents the number of generators as defined in Section 3.2.1.
- (ii)
- ${P}_{Loss}^{i}$∈$\mathbb{R}$: represents the power loss in the ith line, for every time t. This is a calculation based on the results of the power flow.
- (iii)
- ${E}_{NR}^{i}$∈$\mathbb{R}$: represents the energy generated by the ith non-renewable energy source.

#### 3.2.3. Objectives

- (i)
- Minimise real power losses.$$\begin{array}{c}\hfill minOb{j}_{1}^{U}=\sum _{i=1}^{{N}_{Lines}}{P}_{Loss}^{i}\end{array}$$$$\begin{array}{c}\hfill {P}_{Loss}^{i}={I}_{i}^{2}\left(t\right)\times {R}_{i}\end{array}$$
- (ii)
- Minimise CO${}_{2}$ cost.$$\begin{array}{c}\hfill minOb{j}_{2}^{U}=\sum _{i=1}^{{N}_{NR}}\mathrm{C}{\mathrm{O}}_{2}^{i}\times {E}_{NR}^{i}\end{array}$$
- (iii)
- Minimise Redispatch costs.$$\begin{array}{c}\hfill minOb{j}_{3}^{U}=\sum _{i=1}^{{N}_{grid}}{C}_{Redispatch}^{i}\times {P}_{G-redispatch}^{i}\end{array}$$$$\begin{array}{c}\hfill \sum _{i=1}^{{N}_{grid}}{P}_{G-redispatch}^{i}={P}_{G-offered}^{i}-{P}_{G}^{i}\end{array}$$

#### 3.2.4. Constraints

- (i)
- Equality constraints$$\begin{array}{cc}\hfill \sum _{i=1}^{{N}_{G}}{P}_{G}^{i}+\sum _{j=1}^{{N}_{L}}{P}_{L}^{j}+{P}_{S}& =0\hfill \end{array}$$$$\begin{array}{cc}\hfill \sum _{i=1}^{{N}_{G}}{Q}_{G}^{i}+\sum _{j=1}^{{N}_{L}}{Q}_{L}^{j}+{Q}_{S}& =0\hfill \end{array}$$
- (ii)
- Inequality constraints$$\begin{array}{cc}\hfill {P}_{G,Min}^{i}& \le {P}_{G}^{i}\le {P}_{G,Max}^{i}\hfill \end{array}$$$$\begin{array}{cc}\hfill {Q}_{G,Min}^{i}& \le {Q}_{G}^{i}\le {Q}_{G,Max}^{i}\hfill \end{array}$$$$\begin{array}{cc}\hfill {V}_{Min}^{i}& \le {V}^{i}\le {V}_{Max}^{i}\hfill \end{array}$$$$\begin{array}{cc}\hfill {T}_{j}^{Min}& \le {T}_{j}\le {T}_{j}^{Max}\hfill \end{array}$$$$\begin{array}{cc}\hfill \left|L{F}_{k}\right|& \le L{F}_{k}^{Max}\hfill \end{array}$$

#### 3.3. Neighbourhood Grid

#### 3.3.1. Model Parameters

- (i)
- ${n}_{L}$∈$\mathbb{N}$: number of household loads.
- (ii)
- ${n}_{PV}$∈$\mathbb{N}$: number of photovoltaic generators.
- (iii)
- ${n}_{Wind}$∈$\mathbb{N}$: number of wind generators.
- (iv)
- ${p}_{L,t}^{i}$∈$\mathbb{R}$, ${p}_{L,t}^{i}\le 0$ power of the ith load at time t on households.
- (v)
- ${p}_{PV,t}^{i}$∈$\mathbb{R}$, ${p}_{PV,t}^{i}\ge 0$ PV power of ith PV at time t.
- (vi)
- ${p}_{Wind,t}^{i}$∈$\mathbb{R}$, ${p}_{Wind,t}^{i}\ge 0:$ power of the wind generator at time t.
- (vii)
- ${C}_{\mathrm{C}{\mathrm{O}}_{2}}$∈$\mathbb{R}$ is the cost of $\mathrm{C}{\mathrm{O}}_{2}$ emission to generate unit energy.
- (viii)
- $\alpha \in (0,1):$ minimum state of charge allowed.
- (ix)
- $\beta \in (0,1):$ maximum state of charge allowed ($\alpha <\beta $).
- (x)
- ${M}_{CHP}$∈$\mathbb{R}$: maximum energy generated by the CHP unit.
- (xi)
- $\Delta >0:$ sampling time (or time step).
- (xii)
- $Forecas{t}_{Emob,t}$∈$\mathbb{R}$, $Forecas{t}_{Emob,t}\le 0:$ Forecast of the energy for the electric vehicles needed at time t.
- (xiii)
- $SoC\left(t\right)$∈$\mathbb{R}$: state of charge of the battery at time t.
- (xiv)
- ${E}_{Chp}\left(t\right)$∈$\mathbb{R}$: energy produced by the CHP unit at time t.

#### 3.3.2. Decision Variables

- (i)
- ${F}_{Chp,t}$∈$\mathbb{R}$: flexibility power offer from CHP at time t.
- (ii)
- ${F}_{Bat,t}$∈$\mathbb{R}$: flexibility power offer from Battery at time t.
- (iii)
- ${F}_{Emob,t}$∈$\mathbb{R}$: flexibility power offer from e-mobility at time t.

#### 3.3.3. Objectives

- (i)
- Maximise self-consumption/minimise energy supply from the distribution grid.$$\begin{array}{cc}\hfill Ob{j}_{1}^{L}& =min\underset{t=1,\dots ,T}{max}\left\{\sum _{i=0}^{{n}_{L}}{p}_{L,t}^{i}-\sum _{i=0}^{{n}_{PV}}{p}_{PV,t}^{i}-\sum _{j=0}^{{n}_{Wind}}{p}_{Wind,t}^{j}-({F}_{Chp,t}+{F}_{Bat,t}+{F}_{Emob,t})\right\}\hfill \end{array}$$
- (ii)
- Maximise flexibility offers for Redispatch 2.0.$$\begin{array}{c}\hfill Ob{j}_{2}^{L}=max\sum _{t=1}^{T}({F}_{Chp,t}+{F}_{Bat,t}+{F}_{Emob,t})\end{array}$$
- (iii)
- Minimise $\mathrm{C}{\mathrm{O}}_{2}$ emissions.$$\begin{array}{c}\hfill Ob{j}_{3}^{L}=min{C}_{\mathrm{C}{\mathrm{O}}_{2}}\sum _{t=1}^{T}{F}_{Chp,t}\end{array}$$

#### 3.3.4. Constraints

- (i)
- Energy produced by the CHP unit is fed into the neighbourhood grid.$$\begin{array}{c}\hfill 0\le {F}_{Chp,t}\le {M}_{CHP}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}t=1,\dots ,T.\end{array}$$$$\begin{array}{c}\hfill {E}_{Chp}(t+1)=\mathcal{F}({E}_{Chp}\left(t\right),{F}_{Chp,t})\end{array}$$
- (ii)
- The e-mobility flexibilities are considered as load shifting, therefore the aggregated flexibility offered over the entire period is 0 so that the load equals the forecast by the end of the period T.$$\begin{array}{c}\hfill \sum _{t=1}^{T}{F}_{Emob,t}=0\end{array}$$
- (iii)
- Energy supplied/consumed by battery storage.$$\begin{array}{cc}\hfill \forall \phantom{\rule{0.277778em}{0ex}}t=1,\dots ,T:\alpha M& \le SoC\left(t\right)\times M-t\times {F}_{Bat,t}\le \beta M\phantom{\rule{1.em}{0ex}}\&\phantom{\rule{1.em}{0ex}}\alpha \le SoC\left(t\right)\le \beta \hfill \end{array}$$$$\begin{array}{cc}\hfill SoC(t+1)& =SoC\left(t\right)-\frac{{F}_{Bat,t}}{M}\Delta \hfill \end{array}$$

## 4. Solution Approach

#### 4.1. Centralised Approach

#### 4.2. Decentralised Approach

#### 4.3. Evaluation

## 5. Policy Implications

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Abbreviation | Meaning |

COHDA | Combinatorial Optimisation Heuristic for Distributed Agents |

CHP | Combined Heat and Power |

DERs | Distributed Energy Resources |

DG | Distribution Grid |

DSO | Distributed System Operator |

F | Flexibility |

G | Generators |

KPIs | Key Performance Indicators |

NG | Neighbourhood Grid |

OCP | Optimal Control Problem |

PV | Photovoltaic |

SQP | Sequential Quadratic Programming |

SoC | State of Charge |

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**Figure 2.**Representation of a distribution grid, with loads, generators (G) and DERs and neighbourhood grids.

Key Performance Indicator | Meaning | Source |
---|---|---|

Activation rate of Redispatch to avoid grid congestions from the DGs perspective | Amount of activations needed to avoid grid congestions | Present Paper |

Congestion solving capability | Performance in using distributed system operator (DSO) assets, DER’s and neighbourhood grids to execute congestion solving and percentage reduction of overloaded lines using the flexibility | [49] |

Community self-sufficiency | Percentage of electricity demanded by the local community agents that is produced within the community | [50] |

Demand flexibility | The amount of load that can be shifted temporally at each time step | [51] |

Degree of curtailment | Percentage of curtailment from the generation | [52] |

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## Share and Cite

**MDPI and ACS Style**

Acosta, R.R.; Wanigasekara, C.; Frost, E.; Brandt, T.; Lehnhoff, S.; Büskens, C.
Integration of Intelligent Neighbourhood Grids to the German Distribution Grid: A Perspective. *Energies* **2023**, *16*, 4319.
https://doi.org/10.3390/en16114319

**AMA Style**

Acosta RR, Wanigasekara C, Frost E, Brandt T, Lehnhoff S, Büskens C.
Integration of Intelligent Neighbourhood Grids to the German Distribution Grid: A Perspective. *Energies*. 2023; 16(11):4319.
https://doi.org/10.3390/en16114319

**Chicago/Turabian Style**

Acosta, Rebeca Ramirez, Chathura Wanigasekara, Emilie Frost, Tobias Brandt, Sebastian Lehnhoff, and Christof Büskens.
2023. "Integration of Intelligent Neighbourhood Grids to the German Distribution Grid: A Perspective" *Energies* 16, no. 11: 4319.
https://doi.org/10.3390/en16114319