An Approximately Optimal Algorithm for Scheduling Phasor Data Transmissions in Smart Grid Networks

In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure in the electric grid. The problem is cast in the framework of the classic job scheduling with precedence constraints. The optimization setup comprises the number of phasor measurement units (PMUs) to be installed on the grid, a weight associated with each PMU, processing time at the control center for the PMUs, and precedence constraints between the PMUs. The solution to the PMU placement problem yields the optimum number of PMUs to be installed on the grid, while the processing times are picked uniformly at random from a predefined set. The weight associated with each PMU and the precedence constraints are both assumed known. The scheduling problem is provably NP-hard, so we resort to approximation algorithms which provide solutions that are suboptimal yet possessing polynomial time complexity. A lower bound on the optimal schedule is derived using branch and bound techniques, and its performance evaluated using standard IEEE test bus systems. The scheduling policy is power grid-centric, since it takes into account the electrical properties of the network under consideration.Comment: 8 pages, published in IEEE Transactions on Smart Grid, October 201

A Framework for Phasor Measurement Placement in Hybrid State Estimation via Gauss-Newton

In this paper, we study the placement of Phasor Measurement Units (PMU) for enhancing hybrid state estimation via the traditional Gauss-Newton method, which uses measurements from both PMU devices and Supervisory Control and Data Acquisition (SCADA) systems. To compare the impact of PMU placements, we introduce a useful metric which accounts for three important requirements in power system state estimation: {\it convergence}, {\it observability} and {\it performance} (COP). Our COP metric can be used to evaluate the estimation performance and numerical stability of the state estimator, which is later used to optimize the PMU locations. In particular, we cast the optimal placement problem in a unified formulation as a semi-definite program (SDP) with integer variables and constraints that guarantee observability in case of measurements loss. Last but not least, we propose a relaxation scheme of the original integer-constrained SDP with randomization techniques, which closely approximates the optimum deployment. Simulations of the IEEE-30 and 118 systems corroborate our analysis, showing that the proposed scheme improves the convergence of the state estimator, while maintaining optimal asymptotic performance.Comment: accepted to IEEE Trans. on Power System

Optimal PMU Placement for Power System Dynamic State Estimation by Using Empirical Observability Gramian

In this paper the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability Gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search (MADS) algorithm. The implementation, validation, and also the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. The proposed method is tested on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. Under optimal PMU placements an obvious observability transition can be observed. The proposed method is also validated to be very robust to both load fluctuations and contingencies.Comment: Accepted by IEEE Transactions on Power System

Optimal Placement of Phasor Measurement Units for Power Systems Using Genetic Algorithm

Power grids require monitoring to operate with high efficiency while minimizing the chances of having a failure. However, current monitoring scheme which consists of SCADA (Supervisory Control and Data Acquisition), accompanied with conventional meters distributed throughout the grid, is no longer sufficient to maintain an acceptable operation of the grid. This is evident from the multiple failures and blackouts that happened and are still happening in grids worldwide. This issue became more severe due to systems being operated near their limits (to reduce costs and due to the increase in electricity demands), as well as, the addition of renewable energy sources, which usually have abrupt changes. Smart grids were introduced as a solution to this issue by the inclusion of Wide Area Monitoring System (WAMS), which is mainly based on Phasor Measurement Units (PMU), which are measurement devices that provides synchronized time stamped measurements with high sending rate which significantly improves the monitoring of the grid. However, PMUs are relatively expensive (considering both direct and indirect costs incurred). Thus, it is desired to know the minimum number of PMUs required for achieving certain monitoring criteria. Thus, Optimal PMU Placement (OPP) formulates an optimization problem to solve this issue. In the literature of OPP, multiple objectives and constraints are considered, based on desired criteria. In this thesis, a review of OPP is made, followed by the application of selected algorithms (Integer Linear Programming and Genetic Algorithm) on various test systems as a verification and then applying it to Qatar Grid, to compare between different considerations as well as gain insight about the possible PMU placements for Qatar Grid. The contribution of this thesis is introducing a modified fitness function for the Genetic Algorithm that provides more diverse results than previous papers, while incorporating for various considerations like Zero Injection Buses, Conventional Measurements and current branch limit. It also analyzes the results of current branch limit and provides new plots describing their effects