Research on Optimal Placement of µPMUs in Distribution Networks Based on State Estimation Accuracy

With the gradual penetration of distributed generation, the distribution network faces increasing challenges in terms of safety and reliability. Micro-Phasor Measurement Units <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mu \text{PMU})$</tex>, due to their high accuracy and strong real-time capabilities, have become an important tool for improving the monitoring capability of distribution networks. However, due to their high cost, the optimal placement of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu \text{PMUs}$</tex> is particularly important. This paper proposes an optimization method for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu\text{PMU}$</tex> placement based on the E-optimal criterion design. The goal is to improve the operational accuracy and stability of the distribution network by minimizing the state estimation errors. The method employs a two-step state estimation algorithm: in the first step, a preliminary state estimation is performed using pseudo-measurements, followed by a linear state estimation using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu\text{PMU}$</tex> measurement data in the second step. The final result yields the state variables and error covariance of the distribution network. The E-optimal criterion based on the covariance is used as the objective function, with the number of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu \text{PMUs}$</tex> as a constraint, forming an optimization mathematical model. By introducing relaxation variables, the original problem is transformed into a semidefinite programming (SDP) problem for solution. The effectiveness of the method is validated through a case study using the IEEE 33-bus system.