# A Review of Distribution System State Estimation Methods and Their Applications in Power Systems

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## Abstract

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## 1. Introduction

#### 1.1. Motivation

#### 1.2. Survey of the Literature

`–`Rao lower bound analysis, were proposed by the authors in [14]. One of the state estimation methods, i.e., the WLS method and fast heuristic optimization algorithm were discussed in [3]. A discussion on the optimal allocation of measuring units using a multi-objective evolutionary algorithm was proposed by the authors in [4]. A method of dynamic state estimation (DSE) optimization in accordance with back/forward sweep-based load flow calculations was discussed in paper [5]. A new PMU-DSSE formulation to estimate NEVs was proposed in [6].

## 2. Distribution Phasor Measurement Units

## 3. Distribution System State Estimation

## 4. Mathematical Formulation of Distribution System State Estimation

_{i}and θ

_{i})

_{i}is the injected real power at bus “i” and Q

_{i}is an injective reactive power at bus “i”, then

^{(0)},$\overline{e}=[{\left.\begin{array}{ccc}{e}_{1}& {e}_{2}& {e}_{3}\end{array}.......{e}_{n}\right]}^{T}$. [94].

## 5. Conclusions and Future Scope

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Ref. No. | Authors | Proposed Work/Technique/Method |
---|---|---|

[2] | Louis | Investigation of error covariance in DSE with the help of an augmented complex Kalman filter (ACKF). |

[14] | G. Wang | The Cramer–Rao is lower bound in order to indicate the unbiased estimator’s performance was proposed. |

[75] | Carquex, Rosenberg and Bhattacharya | Firstly, in order to improve the accuracy, the PASE method with EnKF has been proposed. |

[36] | Jiao | IEEE 14-bus and 33-bus distribution systems were tested by the proposed heuristic algorithm and indicated an acceleration of up to 50% inaccuracy |

[37] | Hassannejad Marzouni, Zakariazadeh and Siano | In order to show the exact robustness of the method proposed by the authors, some conditions have to be developed, and, to achieve this, the Monte Carlo simulation is used |

[38] | Švenda, Strezoski and Kanjuh | Real-time measuring points were optimized to improve accuracy and, for this purpose, the authors proposed a heuristic algorithm thus optimizing the deployment of the real-time measurement points |

[39] | De Oliveira-De Jesus, Celeita and Ramos | The estimation of NEVs, a novel PMU-DSSE formulation, was proposed. |

[40] | Ahmad | The performance analysis of WLS (static estimator), as well as EKF and UKF (dynamic state estimators), was proposed. |

[41] | Deoliveira-Dejesus | Earthing resistances are incorporated as both state variables and field measurements in the optimization problem. |

[42] | Baran and McDermott | The operating condition can be estimated using the BCSE method, i.e., branch current-based state estimation. |

[43] | Chusovitin, Polyakov and Pazderin | Performance analysis of two different models of the grid with respect to the state estimation results. |

[44] | S. Wang and Liu | The advantages of the proposed hybrid algorithm of the state estimation were clarified in the numerical simulation process using the IEEE 13-bus system. |

[45] | Ramesh | Two aspects, i.e., of a smart meter placement and hybrid state estimator were proposed and an algorithm was formulated and verified with both the IEEE and the TNEB benchmark systems. |

[46] | Soares | The proposed technique was evaluated by calculating the mean percentage errors of the estimated pseudo measurements. |

[35] | Haughton and Heydt | A state estimation algorithm in smart distribution systems was proposed. |

[47] | Gholami | The reliability of satisfying accuracy constraints was postulated |

[48] | Zhou | A study of the mathematical model and methods of state estimation of the electricity-gas interconnected integrated energy system was proposed; in addition to this, distribution state estimation calculations were formulated. |

[49] | Carcangiu | In order to improve the accuracy of distribution state estimation, a load forecasting model based on an artificial neural network was proposed. |

[55] | Carquex, Rosenberg and Bhattacharya | First, in order to improve accuracy, the PASE method with EnKF was proposed |

[50] | L. Liu | A novel information fusion estimation methodology for distributed networked systems. |

[51] | Khan, Rehman, and Ahmad | A methodology where branch currents were considered to be state variables was proposed and working for a weak meshed distribution system was presented. |

[52] | Da Silva | A low-voltage power distribution system in the state estimation domain was analyzed |

[12] | Prasad and Kumar | A detailed discussion of state estimation methods, computational intelligence techniques, and heuristic algorithms for state estimation was proposed. |

[53] | Zamani and Baran | A study of various topological changes in distributed energy systems were proposed |

[54] | M. Liu | State estimation based on the WLS technique was proposed. Analysis of the various effects of installing AMI and PMU for the estimation of accuracy for the DSSE was proposed. |

[55] | Fatima | Testing and verification of a novel two-step MASE algorithm was proposed. |

[56] | Logic and Heydt | The methodology for estimating network parameters was discussed. |

[57] | Dubey, Chakrabarti and Terzija | A novel PS-RHSE algorithm was proposed. |

[58] | Dzafic, Jabr and Hrnjic | A high-performance DSSE method was proposed and analyzed. In addition to this, Hachtel’s matrix method was presented. |

[59] | Almutairi, Miao and Fan | A comparative analysis of the branch current-based DSSE in polar and rectangular coordinates was presented in addition to Micro-PMU measurements. |

[60] | Radhoush, Shabaninia and Lin | The singular value decomposition (SVD) method and Principal component analysis (PCA) algorithm were proposed. |

[61] | Jia, Liu, Tang and Zhang | Analysis of the state of risk in the distribution network was conducted, and safety-related indicators for the distribution network were calculated based on the state estimation results. |

[62] | Majdoub | A detailed overview of the DSSE-based WLS algorithm and evaluation algorithms were presented. |

[63] | Zhang, Wang, Weng and Zhang | Topology identification and estimation of line parameters were conducted by introducing a numerical method. |

[64] | Puddu | The line parameters in a three-phase distribution network were estimated using a PMU-based algorithm, and the method of isolating systematic errors from random errors was presented. |

[65] | Chauhan, Reddy and Sodhi | A prefiltering method was proposed in order to avoid the errors which arise due to the presence of spectral leakage. |

[95] | Dechang Yang | A data-driven optimization approach for a dynamic reconfiguration of the distribution network was proposed. The main advantage of the data-driven optimization approach is that it uses historical data to obtain the optimal control strategy. |

[92] | Hasala Dharmawardena | A distributed data-driven framework based on cellular computational networks (CCN) for power distribution system modeling was presented. |

[93] | Nayara Aguiar, Vijay Gupta | A data-driven technique for the detection of incidents relevant to the operation of energy storage systems in distribution networks was proposed. |

[96] | Matthew J. Reno | The creation of a fundamental change from models based on manual entry to data-driven modeling. |

[97] | H. Xu, A. D. Domínguez-García, V. V. Veeravalli and P. W. Sauer | Development of a data-driven framework for controlling distributed energy resources (DERs) in a balanced radial power distribution system. |

[98] | Rizwan, M.; Waseem, M.; Liaqat, R.; Sajjad, I.A. | Selective particle swarm optimization technique-based model was formulated to reduce distribution loss by optimal sizing and placing of DGs. |

DSSE Method | Advantages | Disadvantages | Applications |
---|---|---|---|

WLS | Simple and fast | Sensitivity issues | Solar PV systems |

LMS | high robustness, less sensitive to data | high computational cost, huge memory usage | PV systems and wind turbine systems |

EKF | used for non-linear systems | Huge system complexity | Solar PV systems, EV charging |

ANN | Good sensitivity and more accuracy | Proper data base is recommended | PV systems and wind turbine, systems |

UKF | Used for non-linear systems | Less recommendation method | PV and Wind |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vijaychandra, J.; Prasad, B.R.V.; Darapureddi, V.K.; Rao, B.V.; Knypiński, Ł. A Review of Distribution System State Estimation Methods and Their Applications in Power Systems. *Electronics* **2023**, *12*, 603.
https://doi.org/10.3390/electronics12030603

**AMA Style**

Vijaychandra J, Prasad BRV, Darapureddi VK, Rao BV, Knypiński Ł. A Review of Distribution System State Estimation Methods and Their Applications in Power Systems. *Electronics*. 2023; 12(3):603.
https://doi.org/10.3390/electronics12030603

**Chicago/Turabian Style**

Vijaychandra, Joddumahanthi, Bugatha Ram Vara Prasad, Vijaya Kumar Darapureddi, Bathina Venkateswara Rao, and Łukasz Knypiński. 2023. "A Review of Distribution System State Estimation Methods and Their Applications in Power Systems" *Electronics* 12, no. 3: 603.
https://doi.org/10.3390/electronics12030603