Effect of Wind Generation Uncertainty on Voltage Stability - A Singular Value Analysis

Transmission systems worldwide were designed predominantly for operation with conventional synchronous generation but are now evolving to include the integration of large amounts of renewable generation. These generators are sited at resource-rich locations, causing a geographical shift in power injections into transmission systems, in some cases, subjecting them to undue stress. In many transmission systems, the capacity to integrate wind resources has been exhausted. In these circumstances, assessing the effect of the uncertainty inherent in wind forecasts with respect to system voltage stability is very important. This paper proposes a method for providing such an assessment. Using an optimal power flow algorithm, a Hessian matrix of the power balance equations is determined, which linearly relates changes in the minimum singular value of the system Jacobian to changes in bus-wise real power injections. This relationship is then employed for examining the effect of the uncertainty in the wind power forecast with respect to system voltage stability. The proposed method has been applied for studying these effects in IEEE 6-bus, 57-bus, and 118-bus systems. The same systems were also investigated using the minimum singular values of the system Jacobian matrix. The comparison of results from two methods demonstrates the effectiveness of the proposed technique.