# Mixed Linear Model of a Safety Dispatch Model in an Active Distribution Network for Source–Grid–Load Interactions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Independent Grid Nodes Safety Control Model

#### 2.1. System Safety Dispatch Control Target Model

_{br}is the number of nodes, $\pi (n)$ is the node running state quantity, ${V}_{i}^{n}$ is the actual value of the node voltage, and ${V}_{r,i}$ is the standard voltage value of the node.

_{EX}/${Q}_{EX}$ are active/reactive variables for contact line exchange.

_{br}is the total number of branch nodes of the distribution network in the system, and R

_{i}

_{(m,n)}and G

_{i}

_{(m,n)}are the tightness value and conductance of the m and n branch of node i, respectively.

#### 2.2. Combination Optimization Model of Safety Control of Power Generation Nodes

#### 2.3. Virtual Power Generation Safety Dispatching Model of Load Nodes

## 3. Optimization Model of Mixed Linear Multi-Node Combination

_{i}, i =1,2…,n, the problem of combinatorial optimization is the global optimal solution that satisfies the H constraints. For any of s* ∈ S, if f(s*) ≤ f(s), then s* is a value more approximating the global optimal solution and provides at least one global optimal solution for F.

- (1)
- Set up multiple ants according to the specific optimization goals, and at the same time make three initial groups for the three sides of the source network load, and search separately;
- (2)
- Initialize an equal amount of pheromones on each path, as:$${\tau}_{ij}(0)=C\hspace{1em}\hspace{1em}\hspace{1em}\Delta {\tau}_{ij}(0)=0$$
- (3)
- Take an ant, calculate the transition probability, select the next optimized calculation node according to the roulette method, and update the taboo table [16]. After each ant completes an optimized output, it releases pheromone on the path of the optimized combination. The amount of pheromone is proportional to the quality of the solution. Considering the correlation between nodes, a random local search strategy is adopted. It can optimize the operation of two adjacent nodes to the best one, and the amount of pheromone on the better node is also the largest. Later, the probability of ant selection increases;
- (4)
- Each ant takes the legal system node optimization path and retains the pheromone amount $\Delta {\tau}_{ij}^{k}$ that the ant did not release between the nodes, and the ant dies;
- (5)
- Repeat steps 3–4 until all ants complete the optimization process;
- (6)
- Compute pheromone increments $\Delta {\tau}_{ij}^{k}$ and pheromones for all optimization modes ${\tau}_{ij}(t+n)$;
- (7)
- Record this iteration path and update the current optimum combination to empty the taboo table;
- (8)
- Reach a predetermined number of iteration steps or stagnation (all ants choose the same path and the solution no longer changes) [17]; the algorithm ends with the current optimal solution as the optimal solution of the problem, otherwise the iteration continues.

- (1)
- Transfer probabilistic calculation formula:

- (2)
- Pheromone calculation formula:

_{k}is all of the ants in this traversal.

- (3)
- Pheromone update method

_{1},…,x

_{n})

^{T}, each sample is obtained independently from the Gaussian distribution using a maximum likelihood estimation method with its likelihood function of:

_{i}samples the solution through the Gaussian function, according to its covariance matrix.

## 4. Solving the Calculation Example

#### 4.1. Basic Scenario

#### 4.2. Distribution Network Operation Scenario

#### 4.3. Model Calculation Results

#### 4.3.1. Grid Voltage Control Target Value

#### 4.3.2. Optimization Result of Safety Control of Power Generation Nodes

#### 4.3.3. Optimization Result of Load Node Safety Control

#### 4.3.4. Combined Optimization

## 5. Conclusions

- (1)
- For power generation nodes, the mode of source-source interaction is adopted, the unit combination mode of the output node is considered, the safety control model of the power generation node is constructed, and the operating boundary conditions of the generator set are used as constraints to obtain the operating safety combination of the units in the network.
- (2)
- For the load node, this paper uses a flexible control model to calculate and analyze the safety scheduling strategy of the load; the model of node voltage deviation in one day is used as the ultimate objective function to solve the safety scheduling of the distribution network. After calculating the independent safety scheduling model, a joint optimization model is established according to a heuristic algorithm model to analyze the overall network security characteristics of the active distribution network, and a Lagrangian relaxation calculation is introduced to ensure that the optimization target is obtained in the active distribution network.
- (3)
- The model availability and accuracy of this section are verified through the actual grid calculation examples, and it is found via the actual comparison that the power quality in the network can be effectively optimized and adapted to the optimization analysis of the active distribution grid of various new energy scenarios.
- (4)
- The overall safety requirements of the source–network–load interaction, especially voltage stability, are the basis for ensuring that the source–network–load interaction can be implemented. Good distribution network planning and internal family division of the distribution network can maximize the internal reliability indicators of the distribution network. Therefore, in the design and planning of the new ADNs, a good family analysis is required. Some current grid plans can already meet this demand to a great extent.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**The 96 data points for a day’s optimization. Each color in the figure represents the predicted terminal load of different branches.

**Figure 7.**Targets of voltage control for the grid. Each color in the figure represents the voltage of a different node.

**Figure 8.**Generator combinations of the network. Each color in the figure represents the output power of different units.

**Figure 11.**Original combination safety check results. Each color in the figure represents different branches.

Node Number | Node Type | Response Characteristics | Main Properties | Elastic Index |
---|---|---|---|---|

1 | Load | Rigid | Commercial electricity consumption | 15.21% |

2 | Load | Rigid | Residential areas | 4.36% |

3 | Power generation | Elasticity | Cascading hydropower | 40.93% |

4 | Power generation | Rigid | Basin runoff is a small hydropower group | 12.67% |

5 | Load | Rigid | Chemical plant | 20.05% |

6 | Load | Rigid | Water works | 8.32% |

7 | Load | Elasticity | School, energy storage | 36.69% |

8 | Power generation | Elasticity | Wind power, energy storage | 28.96% |

9 | Load | Rigid | Mechanical plant | 9.13% |

10 | Load | Rigid | Food processing plant | 10.14% |

11 | Load | Elasticity | Commercial and self-built photovoltaic energy storage | 46.68% |

12 | Load | Rigid | Government office | 31.24% |

13 | Power generation | Rigid | Wind force | 16.21% |

14 | Load | Elasticity | Textile factory, belt energy storage | 16.46% |

15 | Load | Rigid | Paper mill | 8.83% |

16 | Power generation | Rigid | Photovoltaic power | 5.49% |

17 | Load | Elasticity | Cotton textile mill | 30.13% |

18 | Power generation | Rigid | Basin runoff is a small hydropower group | 10.25% |

19 | Power generation | Elasticity | Biomass power generation | 60.14% |

20 | Load | Rigid | Small textile mills | 14.32% |

21 | Load | Rigid | Automobile manufacturers | 10.93% |

22 | Load | Rigid | Energy storage battery manufacturer | 4.16% |

23 | Load | Rigid | Steel processing plant | 2.86% |

24 | Load | Rigid | Commercial office building | 20.57% |

25 | Load | Elasticity | Auto parts manufacturer, PV | 29.12% |

26 | Power generation | Elasticity | Gas-fired power generation | 63.17% |

27 | Power generation | Elasticity | Comprehensive energy demonstration park | 79.23% |

Family Members | List of Load Nodes | List of Power Generation Nodes |
---|---|---|

1 | 1, 2, 7, 9, 11, 17 | 4, 8 |

2 | 5, 15 | 19 |

3 | 6, 10, 12 | 13, 32 |

4 | 14, 21, 23, 33, 35 | 36 |

5 | 20, 22, 25 | 18, 26, 29 |

6 | 24, 30, 31 | 3 |

7 | 27, 28, 34 | 16 |

Node Number | Node Type | Voltage Level | Main Parameters (Installed Capacity, in MW) |
---|---|---|---|

3 | Cascading hydropower | 110 kV | 2 × 3.5 + 3 × 1.25 + 3 × 0.63 + 2 × 0.32 + 4 × 0.5 |

8 | Wind farm | 35 kV | 16 × 2 + 1 × 1.5 + 5, Storage: 16 |

19 | Biomass power generation | 35 kV | 8 × 1.5 + 4 × 3 + 3 × 5 |

26 | Gas-fired power generation | 10 kV | 4 × 4.5 + 6 × 1.5 |

32 | Photovoltaic power station | 10 kV | 1.2 × 5, Storage: 3.6 |

36 | Storage capacity and power station | 110 kV | 6 × 4.6 + 4 × 2.5 + 8 × 1.25 |

7 | Class II load | 10 kV | Storage: 1.5. Installation capacity: 3 |

11 | Class II load | 35 kV | Light: 1.2 × 3, Storage: 2, Installed capacity: 6.3 |

14 | Class I load | 110 kV | Storage: 3.5. Installation capacity: 4.6 |

25 | Class I load | 110 kV | Light: 1 × 4, installed capacity: 7.83 |

27 | Class II load | 35 kV | Light: 1 × 14, Storage: 12, Gas: 8 × 1.5, Heat: 0.4 × 6 Installed capacity: 34 |

28 | Class II load | 35 kV | Light 1.2 × 6, Storage: 10. Pile: 10 × 0.18 + 12 × 0.035 Installed capacity: 16 |

30 | Three types of load | 10 kV | Storage: 2. Installation capacity: 2.4 |

34 | Class II load | 35 kV | Storage: 6. Installation capacity: 6.3 |

35 | Class II load | 10 kV | Storage: 3.2, Pile: 6 × 0.36 + 14 × 0.24, installed capacity: 4.2 |

Generation Node | Active Power (MW) | Capacity (MW) |
---|---|---|

3 | 13.2019 | 15.28 |

4 | 16.6745 | 18.48 |

8 | 17.9025 | 38.5 |

13 | 6.8876 | 30 |

16 | −0.066 | 20 |

18 | 10.5206 | 12.48 |

19 | 19.968 | 39 |

26 | 9.936 | 27 |

29 | −0.1478 | 16 |

32 | 0.0443 | 6 |

36 | 40.3172 | 47.6 |

Node Name | Voltage | Phase Angle | Node Name | Voltage | Phase Angle |
---|---|---|---|---|---|

BUS1 | 1 | 0 | BUS19 | 1.011764051 | −31.1464 |

BUS10 | 0.989535501 | −19.7508 | BUS20 | 1.011727813 | −31.1951 |

BUS11 | 1.019591909 | −23.7891 | BUS21 | 1.001133166 | −38.2493 |

BUS2 | 1.011749759 | −31.1677 | BUS26 | 0.991429899 | −41.5284 |

BUS22 | 1.001028601 | −38.277 | BUS27 | 1 | −27.8 |

BUS23 | 0.988518931 | −30.1358 | BUS28 | 1.019514092 | −16.4535 |

BUS24 | 0.988722183 | −30.0071 | BUS29 | 1.01950393 | −16.4518 |

BUS25 | 0.991470488 | −41.5135 | BUS34 | 1.019493038 | −16.4671 |

BUS3 | 0.967180274 | −41.2169 | BUS4 | 0.991399466 | −41.513 |

BUS51 | 0.994779656 | −41.5325 | BUS5 | 1.009353618 | −22.8737 |

BUS9 | 0.994544278 | −28.8754 | BUS50 | 1.033333767 | −31.8241 |

BUS12 | 0.990260647 | −11.9921 | BUS52 | 0.994779656 | −41.5325 |

BUS13 | 1.002626092 | −37.9659 | BUS6 | 0.989535501 | −19.7508 |

BUS14 | 0.998759999 | −31.5197 | BUS30 | 0.988722183 | −30.0071 |

BUS15 | 1.039171437 | −30.079 | BUS31 | 1 | −41.2368 |

BUS16 | 0.977696715 | −20.1593 | BUS33 | 1 | −10.7673 |

BUS17 | 1.046380497 | −5.50664 | BUS7 | 1 | −10.6603 |

BUS18 | 1.019633416 | −23.8103 | BUS8 | 0.989868176 | −20.2014 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, P.; Dong, J.; Zhu, Y.
Mixed Linear Model of a Safety Dispatch Model in an Active Distribution Network for Source–Grid–Load Interactions. *World Electr. Veh. J.* **2023**, *14*, 159.
https://doi.org/10.3390/wevj14060159

**AMA Style**

Jiang P, Dong J, Zhu Y.
Mixed Linear Model of a Safety Dispatch Model in an Active Distribution Network for Source–Grid–Load Interactions. *World Electric Vehicle Journal*. 2023; 14(6):159.
https://doi.org/10.3390/wevj14060159

**Chicago/Turabian Style**

Jiang, Peng, Jun Dong, and Yuan Zhu.
2023. "Mixed Linear Model of a Safety Dispatch Model in an Active Distribution Network for Source–Grid–Load Interactions" *World Electric Vehicle Journal* 14, no. 6: 159.
https://doi.org/10.3390/wevj14060159