Random load fluctuations and collapse probability of a power system operating near codimension 1 saddle-node bifurcation

For a power system operating in the vicinity of the power transfer limit of its transmission system, effect of stochastic fluctuations of power loads can become critical as a sufficiently strong such fluctuation may activate voltage instability and lead to a large scale collapse of the system. Considering the effect of these stochastic fluctuations near a codimension 1 saddle-node bifurcation, we explicitly calculate the autocorrelation function of the state vector and show how its behavior explains the phenomenon of critical slowing-down often observed for power systems on the threshold of blackout. We also estimate the collapse probability/mean clearing time for the power system and construct a new indicator function signaling the proximity to a large scale collapse. The new indicator function is easy to estimate in real time using PMU data feeds as well as SCADA information about fluctuations of power load on the nodes of the power grid. We discuss control strategies leading to the minimization of the collapse probability.Comment: 5 pages, 1 figure, submission to IEEE PES General Meeting 201

Critical slowing-down as indicator of approach to the loss of stability

We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations of the system state vector are driven by random variations of loads and intermittent renewable generation. In the vicinity of collapse the power system experiences so-called phenomenon of critical slowing-down characterized by slowing and simultaneous amplification of the system state vector fluctuations. In generic case of a co-dimension 1 bifurcation corresponding to the threshold of instability it is possible to extract a single mode of the system state vector responsible for this phenomenon. We characterize stochastic fluctuations of the system state vector using the formal perturbative expansion over the lowest (real) eigenvalue of the system power flow Jacobian and verify the resulting expressions for correlation functions of the state vector by direct numerical simulations. We conclude that the onset of critical slowing-down is a good marker of approach to the threshold of global instability. It can be straightforwardly detected from the analysis of single-node autostructure and autocorrelation functions of system state variables and thus does not require full observability of the grid.Comment: Shorter version submitted to IEEE SmartGridComm 2014; 6 pages, 4 figures, discussion of autostructure functions adde

Calculation of the Autocorrelation Function of the Stochastic Single Machine Infinite Bus System

Critical slowing down (CSD) is the phenomenon in which a system recovers more slowly from small perturbations. CSD, as evidenced by increasing signal variance and autocorrelation, has been observed in many dynamical systems approaching a critical transition, and thus can be a useful signal of proximity to transition. In this paper, we derive autocorrelation functions for the state variables of a stochastic single machine infinite bus system (SMIB). The results show that both autocorrelation and variance increase as this system approaches a saddle-node bifurcation. The autocorrelation functions help to explain why CSD can be used as an indicator of proximity to criticality in power systems revealing, for example, how nonlinearity in the SMIB system causes these signs to appear.Comment: Accepted for publication/presentation in Proc. North American Power Symposium, 201

A Backend Framework for the Efficient Management of Power System Measurements

Increased adoption and deployment of phasor measurement units (PMU) has provided valuable fine-grained data over the grid. Analysis over these data can provide insight into the health of the grid, thereby improving control over operations. Realizing this data-driven control, however, requires validating, processing and storing massive amounts of PMU data. This paper describes a PMU data management system that supports input from multiple PMU data streams, features an event-detection algorithm, and provides an efficient method for retrieving archival data. The event-detection algorithm rapidly correlates multiple PMU data streams, providing details on events occurring within the power system. The event-detection algorithm feeds into a visualization component, allowing operators to recognize events as they occur. The indexing and data retrieval mechanism facilitates fast access to archived PMU data. Using this method, we achieved over 30x speedup for queries with high selectivity. With the development of these two components, we have developed a system that allows efficient analysis of multiple time-aligned PMU data streams.Comment: Published in Electric Power Systems Research (2016), not available ye

The Estimation of Nodal Power Supply Reliability through the Network Connectivity by Complex Network Method

The paper studies the reliability of the power system from the perspective of node loads. The reliability of the whole system can be estimated by evaluating the power supply reliability of each node. A measure, connectivity observed at load node (Ci), is proposed. Ci is calculated through a recursion equation by evaluating the generation capacity that can be transferred from the further neighbor to the nearest neighbor of load node i. IEEE-30 bus system is taken as a test system. We calculated the index of 7 load nodes at 2 different load levels with different N-1 failures. The test results show that the variation of the index and that of the percentage load shedding at selected load nodes show good consistency