Optimal PMU Placement Using CPLEX and YALMIP

In power systems, optimal PMU (Phasor Measurement Unit) placement is a critical challenge aimed at achieving full system observability with minimal equipment cost. The integration of CPLEX and YALMIP tools provides an efficient methodology for solving this optimization problem computationally.

PMU placement is typically formulated as an Integer Linear Programming (ILP) problem, where the objective is to determine the minimum number and optimal locations of PMUs to ensure complete monitoring of all network buses. CPLEX serves as a high-performance commercial solver for handling large-scale ILP problems, while YALMIP acts as a flexible MATLAB modeling layer that simplifies optimization model formulation and solver interfacing.

Using YALMIP, engineers can declaratively define binary decision variables (representing PMU installation status at each bus), observability constraints (ensuring voltage phasor measurement coverage for each node), and optimization objectives (minimizing total PMU count). The toolbox automatically translates the model into CPLEX-compatible format through commands like `optimize` and `value`, handling solver configuration and result extraction. This approach facilitates rapid prototyping with MATLAB syntax such as:
`x = binvar(nBuses,1); % Binary decision variables`
`Objective = sum(x); % Minimize PMU count`
`Constraints = [A*x >= 1]; % Observability constraints`
The framework supports extensions for complex scenarios including zero-injection buses and communication constraints through modified constraint matrices.

This integrated workflow enables researchers and engineers to efficiently validate diverse PMU configuration strategies, enhancing power system monitoring capabilities and grid reliability through computationally optimized solutions.