Power distribution systems receive bulk electrical power from transmission systems and supply them to consumers. Over the last few decades, the introduction of electric vehicles, photovoltaic generation, and newer technologies have created several challenges in controlling and operating these systems. Efficient operation of these systems requires monitoring the system to estimate the current system state (values of system variables used to describe its behaviour at that time instant). These estimates are also required to take appropriate corrective actions. However, assessing the system’s state is challenging because of the lack of measurements from the distribution system. Previous works have utilized the concepts such as weighted least squares to solve this problem. However, these methods have some disadvantages, particularly in cases where very few measurements exist, which is typical of distribution systems. Therefore, in this work, the researchers, which include Mr. Rahul Madbhavi, from the Department of Electrical Engineering, Indian Institute of Technology Gandhinagar, Palaj, Gujarat, India, Prof. Balasubramaniam Natarajan, from the Department of Electrical and Computer Engineering, Kansas State University, Manhattan, USA, and Prof. Babji Srinivasan, from the Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India, propose a new tensor-based approach to solve this problem.
Mr. Rahul Madbhavi 
Prof. Balasubramaniam Natarajan 
Prof. Babji Srinivasan
A matrix is a mathematical concept wherein numbers are arranged in the form of rows and columns. Measurements from the distribution system can be arranged in the form of a matrix. These measurement matrices can be collected to form a 3-dimensional arrangement of numbers by placing the matrices one over another. Such an arrangement is called a tensor. However, since few measurements are taken from the system, many values will be missing in the tensor. Therefore, it is required to fill these missing measurements to estimate the system’s state at all time instants. This process of filling the missing measurements in a tensor is called tensor completion.
Since the numbers in the tensor are measurements from the distribution system, they must satisfy the power-flow equations, which are a set of equations that explain the behaviour of the system. Thus, in this experiment, for the first time, the system model has been incorporated into tensor completion to estimate the state of the distribution system. Also, the tensor can be assumed as a collection of multiple 3-dimensional blocks. This work also describes how this tensor can be divided into blocks to improve the state estimation. Such a division helps create more intermediate measurements (pseudo measurements), which can improve the accuracy of state estimation. Furthermore, the mode of viewing the tensor, for example, along rows, columns or time, provides different insights into the data. Therefore, this work explores how some views of the tensor are more structured and thus are more critical in reducing estimation errors. Finally, this work also introduces a method to scale the numeric values of the tensor to make the method more sensitive to changes in all variables. This scaling is necessary because measurements of the system can be of different magnitudes and make the technique biased towards some quantities.
These methods have been checked on the IEEE 33-, 37- node distribution systems and a 100-node test network. The methods were found to be more accurate than existing methods. This model can be extended to other networks with suitably designed tensors and constraints in the optimization.
Article by Akshay Anantharaman
Here is the original link to the paper:
https://ieeexplore.ieee.org/document/9247155
