#
Optimal Selection of Metering Points for Power Quality Measurements in Distribution System^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

- The proposition of an equivalent model and formulation of the optimization problem. The model should allow for expressing measurement goals in an analytical form. Usually, it requires a simplified model of the grid. In order to define the optimization problem, a criterion should be selected and formulated in an analytical form.
- Solving the optimization problem—which requires selecting the solving method. In most cases, the problem does not have an analytical solution, so numerical methods are utilized. Due to the problem complexity, heuristic methods are preferred. It is also assumed that a sequential approach can be utilized to find a near-optimal solution.

#### 1.2. Literature Review

- State estimation (SE) problem, also referred to as power flow (PF) or load flow analysis,
- Fault detection (FD) based on voltage event recording and analysis,
- Harmonics flow analysis, also referred to as harmonic state estimation (HSE).

**.**However, it is possible to build an equivalent model of the network so that the dependence of the RMSE on the metering points can be expressed a mixed-integer linear problem with constraints. The optimization criterion can incorporate estimation errors and the metering system’s cost (including all expenses). In [16], the method is compared with two other methods using a standard IEEE 13-node test feeder and another 33-node radial grid. The method is thoroughly explained. However, the process of building the equivalent model seems to be very complex and may be difficult to apply in practice.

#### 1.3. Contribution and Paper Organization

## 2. Materials and Methods

#### 2.1. Selected Methods

- Kirchhoff current law criterion states that current in a line can be computed by the summation of currents in other lines. It means that in a node comprising n lines, only n−1 can be monitored without losing the system’s observability.
- Customer connection point—when a PQ parameter exceeds limits, it may affect customers. Therefore, branch customers connected to it should be selected to monitor with a high priority.
- The number of branches fed form a node. Elements near the supply source are more important for monitoring due to the total number of elements connected.
- Connection point (the beginning) of a branch—allows for monitoring all branches elements when a meter is installed in the node. It increases the observability of the system.

- Observability analysis using an iterative procedure referred to as index method. Nodes are selected based on mutual connection analysis in a way that the total observability is maximized. This stage decreases the number of nodes to analyze in the next stage. It comes from the assumption that the optimal solution can be found from a reduced set of nodes.
- Optimization procedure finds a minimal set of nodes to monitor, having preselected those chosen in Stage 1. The procedure minimizes a fitness function which depends on the number of used meters (in this stage) and the metering redundancy, i.e., the number of meters that can monitor a single node. The fitness function is nonlinear, and the optimization procedure also has to keep constraints related to observability. Therefore, there is no analytical solution, and heuristic algorithms should be used for the performance reason. In [38], binary particle swarm optimization (BPSO) procedure is used for this task, but any other solver for binary problems can also be used.

#### 2.2. Test Grids

- IEEE test feeders: 13-node, 34-node, and 37-node test feeder [48],
- A typical MV feeder in an urban area.

- for IEEE 13-node: 650, 632, 617, and 680,
- for IEEE 34-node: 800, 802, 806, 808, 812, 814, 850, 816, 824, 828, 830, 854, 852, 832, 858, 834, 860, and 836.

#### 2.3. Implementation

## 3. Results

#### 3.1. Application to the IEEE 37-Node Test Feeder

#### 3.2. Application to Others IEEE Test Feeders

#### 3.3. Application to a Typical MV Distribution Feeder

## 4. Discussion

## 5. Conclusions

- the definition of the state and the state vector,
- observability analysis.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AHP | Analytic Hierarchy Process |

ASE | Adaptive State Optimization |

BILP | Binary Integer Linear Programming |

BPSO | Binary Particle Swarm Optimization |

CE | Complete Enumeration |

CEER | Council of European Energy Regulators |

CIGRE | International Council on Large Electric Systems |

DSO | Distribution System Operator |

FD | Fault Detection |

GA | Genetic Algorithm |

HSE | Harmonic State Estimation |

HV | High Voltage |

LV | Low Voltage |

MRA | Meter Reach Area |

MV | Medium Voltage |

PF | Power Flow |

PMU | Phasor Measurement Unit |

PSO | Particle Swarm Optimization |

PQ | Power Quality |

RMSE | Root Mean Squared Error |

SE | State Estimation |

SVD | Singular Value Decomposition |

TMRA | Topological Meter Reach Area |

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**Figure 1.**Schematic diagram of the test grids: (

**a**) IEEE 37-node test feeder; (

**b**) a typical MV feeder in an urban area.

**Figure 2.**Measurement locations selected by the discussed methods: (

**a**) elements selected by the method 1; (

**b**) nodes selected to monitor by method 2.

**Figure 4.**Application results to IEEE 13-node test feeder: (

**a**) elements selected by the Method 1; (

**b**) nodes selected to monitor by Method 2; (

**c**) nodes for voltage metering and branches for current metering selected by Method 3.

**Figure 5.**Application results to IEEE 34-node test feeder: (

**a**) elements selected by the Method 1; (

**b**) nodes selected to monitor by Method 2; (

**c**) nodes for voltage metering and branches for current metering selected by Method 3.

**Figure 6.**Results of the method applied to a typical feeder in an urban area: (

**a**) elements selected by the Method 1; (

**b**) nodes selected to monitor by Method 2; (

**c**) nodes for voltage metering and branches for current metering selected by Method 3.

Method 1 | Method 2 | Method 3 | |
---|---|---|---|

MV feeder (Simple grid) | 8 m (10 m ^{1}) | 9 m (14 m ^{1}) | 8 m (13 m ^{1}) |

IEEE 13-node | 9 m | 15 m (6 m ^{2}) | 13 m (4 m ^{2}) |

IEEE 34-node | 28 m | 35 m (12 m ^{2}) | 41 m (18 m ^{2}) |

IEEE 37-node (Complex grid) | 26 m | 38 m (13 m ^{2}) | 41 m (16 m ^{2}) |

^{1}without the preinstalled meters;

^{2}selected directly by the method, without the required load metering.

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**MDPI and ACS Style**

Piatek, K.; Firlit, A.; Chmielowiec, K.; Dutka, M.; Barczentewicz, S.; Hanzelka, Z.
Optimal Selection of Metering Points for Power Quality Measurements in Distribution System. *Energies* **2021**, *14*, 1202.
https://doi.org/10.3390/en14041202

**AMA Style**

Piatek K, Firlit A, Chmielowiec K, Dutka M, Barczentewicz S, Hanzelka Z.
Optimal Selection of Metering Points for Power Quality Measurements in Distribution System. *Energies*. 2021; 14(4):1202.
https://doi.org/10.3390/en14041202

**Chicago/Turabian Style**

Piatek, Krzysztof, Andrzej Firlit, Krzysztof Chmielowiec, Mateusz Dutka, Szymon Barczentewicz, and Zbigniew Hanzelka.
2021. "Optimal Selection of Metering Points for Power Quality Measurements in Distribution System" *Energies* 14, no. 4: 1202.
https://doi.org/10.3390/en14041202