  This letter presents a technique to calculate the variance of algebraic
variables of power system models represented as a set of stochastic
differential-algebraic equations. The technique utilizes the solution of a
Lyapunov equation and requires the calculation of the state matrix of the
system. The IEEE 14-bus system serves to demonstrate the accuracy of the
proposed technique over a wide range of variances of stochastic processes. The
accuracy is evaluated by comparing the results with those obtained with Monte
Carlo time domain simulations. Finally, a case study based on a 1479-bus
dynamic model of the all-island Irish transmission system shows the
computational efficiency of the proposed approach compared to the Monte Carlo
method.
