Optimal PMU Placement via Quantum Optimization

Phasor Measurement Units (PMUs) are essential for real-time monitoring and improving grid observability. Determining the optimal PMU installation is critical, especially as the penetration of renewable energy resources increases, as the Optimal PMU Placement (OPMUP) can guarantee full system observability and reduce the installation cost. However, identifying the optimal PMU installation is a prototypical combinatorial optimization problem, requiring substantial classical computational resources. Furthermore, the significant expansion of the grid in terms of renewable energy integration makes the determination of optimal PMU placement increasingly computationally intensive. In this work, a hybrid quantum-classical approach, Quantum Approximate Optimization Algorithm (QAOA), is developed to effectively solve the optimal PMU installation problem under normal and channel limitation scenarios. A tailored objective function is proposed for quantum optimization, which takes into account both PMU placement cost and system observability constraints. To analyze the observability of QAOA-generated solution distributions, recursion-based Depth-First Search and Breadth-First Search algorithms are proposed for normal and channel-limited scenarios. These methods determine solution feasibility on classical computers with O(N + M) complexity, outperforming the O(N²) complexity of inequality-based approaches, where N and M denote the number of buses and branches, respectively. In addition, the proposed quantum optimization framework can significantly reduce the computational complexity from the polynomial or exponential levels required by previous classical methods, i.e., O(RN) on quantum circuits and O(R(M + N)) on classical resources, where R is the repetition times of quantum circuits executions. The proposed method is tested on IEEE 9-, 14-, 24-, and 30-bus systems, where better installation results are achieved compared to the state-of-the-art results, providing a new baseline for further quantum studies in OPMUP. Furthermore, a landscape optimization strategy is introduced to improve QAOA solution quality. This approach also reduces the time cost of quantum computing resources, making it more efficient for current quantum applications. Additionally, parameter studies are conducted to identify key factors influencing QAOA performance. This work is expected to lay the foundations for addressing challenging power system problems through quantum technology in the Noisy Intermediate Scale Quantum (NISQ) era.