# A Novel Multi-Area Distribution State Estimation Approach for Active Networks

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## Abstract

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## 1. Introduction

- Requiring high computational speed processors;
- Requiring large data storage units;
- Requiring a low latency communication system to transfer large amounts of data among the field agents and control center;
- Subjecting to a single point of failure risk.

- Usually, real-time measurements in the distribution network are limited;
- Unlike transmission systems, a large share of consumed energy in the distribution network is fed through the upstream substations. Consequently, despite the existence of normally closed tie-lines in ADNs with meshed topology, hierarchical strategies will play an effective role in the coordination phase of decentralized SE procedures;
- Generally, the division of the network is mainly performed according to the topological and geographical criteria. On the other hand, there is a flexible topology in the ADNs by switching tie-lines. However, the base topology of the network is radial, and the internal buses of zones resulting from the division of the network should belong to the same feeder.

- Introducing a new HDSE procedure for improving the accuracy of SE results and the reliability and latency of CISs’ in ADNs;
- Proposing a new approach for modifying the local voltage estimation of the zone’s internal buses according to the coordinated results of border buses;
- Considering the existence of normally closed tie-lines (networks with meshed topology) in the proposed decentralized SE method for ADNs.

## 2. Active Distribution Networks State Estimation

## 3. Proposed Hierarchically Distributed SE

- Each zone is equipped with adequate measurement devices to guarantee the observability of its local sub-network. Therefore, in the case of communication failure and loss of coordination phase, the states of each zone can be calculated with the minimum required data;
- All voltage measurements in the overlapped buses (shared bus between neighboring zones) are taken by the PMUs or µPMUs. If only traditional measurements are used, due to lack of phase angle synchronization between zones, each zone estimator considers one of its internal buses as a slack bus, and the local SE process estimates the voltage phase angles of its local buses refer to this phase angle reference. Then, in the coordination phase, the zone which includes the substation bus is considered as the phase angle reference for other zones and according to the difference between voltage phase angle estimations in common buses of neighboring zones, the estimated voltage phase angles of the neighboring zone can be shifted sequentially.

#### 3.1. Level of Zone Overlapping

- Topological and geographical criteria;
- The similarity of the zones size (for minimizing SE execution time);
- Existence of overlapped bus and/or branch between zones for coordination of local estimates;
- Existence of measurement devices in common buses to minimize the information exchange between neighboring zones.

_{com}), local SE of zone 1 (z

_{com1}), and local SE of zone 2 (z

_{com2}), can be represented by the following equations

#### 3.2. The Architecture of Proposed HDSE

**local voltage estimations**and

**coordination of the local SE results**. The ZEs in all zones of the network perform the first step of the proposed HDSE process. However, the duty of coordinating the local SE results is assigned to FCs and SCs units. Information exchange in the proposed structure is a combination of centralized and distributed strategies. Therefore, it is expected that this method integrates the advantages of both centralized and decentralized strategies and results in better accuracy than a distributed strategy. All of the FCs and the SC for each substation are proposed to be placed in the substation and use one shared database. Moreover, due to exploiting the hierarchical structure in the proposed method, in the cases that one of ZEs or FCs/SC units fails to perform its performance, their related FC/SC and the control center can be used as the backup unit, respectively.

#### 3.3. Local Voltage Estimation

#### 3.4. Coordination of the Local SE Results

**FC’s revisable (FCR) zones**and

**SC’s revisable (SCR) zones**. Then, the FCs and SCs attend to coordinate the local voltage estimation of their related ZEs. Indeed, the first group of zones is coordinated by the related FC (there is one FC for each feeder). These zones do not include the substation bus or the buses that are connected to the neighboring substations (by tie-lines). However, the zones that fall into the second group include the aforementioned buses as a part of their border buses and are coordinated by the SC. In Figure 3, Zone 3 is the FCR zone of Feeder 1, and Zones 5 and 6 represent the FCR zones of Feeder 2 in a typical ADN; However, other zones of the network (Zones 1, 2, and 4) fall into the second group of zones (SCR zones).

## 4. Test Case and Simulation Results

- Number of generated noisy measurements sets: 10,000;
- Maximum error of the measurements:
- ○
- Synchrophasor measurements: 0.7% for voltage magnitude and 0.7 centiradian (crad) for voltage phase angle.
- ○
- Power flow measurements (active and reactive): 3%.
- ○
- Pseudo-measurement (DG power outputs and load power consumption): 50%.

- Different pre-defined decompositions of the network: Generally, based on the amount of available budget for equipping zones with the local processing units, communication infrastructures, and measurement devices, the number of zones and their sizes (number of internal buses of zones) can be determined in the network. Obviously, the number of zones and their sizes are inversely related to each other, and increasing the number of zones leads to a decrease in their sizes. In this simulation, two predefined network division types are assumed as follow:
- Different operating conditions of the network:
- ○
- Network topology (meshed or radial).
- ○
- Presence of distributed generations.

- Different measurement scenarios:
- ○
- Case I: Measurement points in the substation and overlapped buses are considered as stated before (in Section 4).
- ○
- Case II: Measurement points in Case I plus voltage measurements in the end buses of tie-lines are considered.

#### 4.1. Accuracy of the Proposed HDSE

#### 4.2. Runtime of the Proposed HDSE

_{LSE}, t

_{FC}, and t

_{SC}are the runtimes of LSE, FCs, and SC, respectively. Moreover, t

_{CPM1}and t

_{CPM2}are the runtimes of the coordination phase in Method 1 and Method 2, respectively.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Shared elements between neighboring zones and their separation method to perform independent local SEs: (

**a**) level of zone overlapping between neighboring zones, (

**b**) boundary of Zone 1 and (

**c**) boundary of Zone 2.

**Figure 3.**Sub-networks of feeder coordinators (FCs) and substation coordinator (SC) in a typical active distribution network (ADN).

**Figure 4.**Flowchart of the coordination phase in the proposed Hierarchically Distributed state estimation (HDSE) procedure.

**Figure 7.**Power flow results of the test case with meshed topology: (

**a**) voltage magnitude and (

**b**) voltage phase angle.

**Figure 8.**Estimation errors of the HDSE method for the test network with meshed topology: (

**a**) average voltage magnitude percentage errors (AVMPE) and (

**b**) average voltage phase angle absolute errors (AVPAE).

**Figure 9.**Evaluated errors in the test network with meshed topology, case 2 measurement scenario and type 1 decomposition method: (

**a**) AVMPE and (

**b**) AVPAE.

**Figure 10.**Evaluated errors in the test network with radial topology, case 2 measurement scenario and type 2 decomposition method: (

**a**) AVMPE and (

**b**) AVPAE.

**Figure 11.**Error comparison for different decentralized SE methods in different scenarios described in Table 1: (

**a)**normalized average AVMPE and (

**b**) normalized average AVPAE.

**Figure 12.**Comparison of normalized runtimes for different decentralized SE methods in different scenarios.

Case | Network Topology | DG Grid Connection | Network Decomp. Type | Meas. Scenario |
---|---|---|---|---|

1 | Mesh | ✓ | 1 | 2 |

2 | Mesh | ✓ | 1 | 1 |

3 | Mesh | ✓ | 2 | 2 |

4 | Mesh | ✓ | 2 | 1 |

5 | Radial | ✓ | 1 | 2 |

6 | Radial | ✓ | 1 | 1 |

7 | Radial | ✓ | 2 | 2 |

8 | Radial | ✓ | 2 | 1 |

9 | Radial | 🗶 | 1 | 2 |

10 | Radial | 🗶 | 1 | 1 |

11 | Radial | 🗶 | 2 | 2 |

12 | Radial | 🗶 | 2 | 1 |

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**MDPI and ACS Style**

Gholami, M.; Tehrani-Fard, A.A.; Lehtonen, M.; Moeini-Aghtaie, M.; Fotuhi-Firuzabad, M.
A Novel Multi-Area Distribution State Estimation Approach for Active Networks. *Energies* **2021**, *14*, 1772.
https://doi.org/10.3390/en14061772

**AMA Style**

Gholami M, Tehrani-Fard AA, Lehtonen M, Moeini-Aghtaie M, Fotuhi-Firuzabad M.
A Novel Multi-Area Distribution State Estimation Approach for Active Networks. *Energies*. 2021; 14(6):1772.
https://doi.org/10.3390/en14061772

**Chicago/Turabian Style**

Gholami, Mohammad, Ali Abbaspour Tehrani-Fard, Matti Lehtonen, Moein Moeini-Aghtaie, and Mahmud Fotuhi-Firuzabad.
2021. "A Novel Multi-Area Distribution State Estimation Approach for Active Networks" *Energies* 14, no. 6: 1772.
https://doi.org/10.3390/en14061772