Calculation Of Critical Point Of Power System Static Voltage Stability Based On Direct Method

The calculation of critical point, also called maximum power point, is an importan issue in the field of power system static voltag stability research. With the exact critical point calculated, the loading margin to voltage collapse can be determined and the margin sensitivity with respect to control parameter can be used for preventive and corrective control against voltage instability.At the critical point, the Jacobian matrix of conventional power flow equations becomes singular. To overcome this difficulty, two method have been applied to compute this kind of points. One is continuation method, which gets the approximate critical point through tracing the PV curve. The main disadvantage is time-consuming feature which make it unsuitable for online application . The other is direct method, also called Newton method, which gets the exact point by solving a set of nonlinear determination equations. Currently, the direct method is not widely used mainly because that the dimension of the determination equations is twice as the dimension in continuation method, which needs more CPU memory and time to compute. In addition, the estimation of initial value is another difficulty, divergence will occur when the initial guess is too far from the solution.In this dissertation, a new matrix reduction technique is presented to directly calculate the critical point. The feature of this algorithm is that the original Newton iterative equations which is of (2n+1) dimensions can be solved through (n+1) dimensional linear equations. Compared with the older method, this approach significantly reduces the computational efforts and is more suitable for online application in bulk power systems using sparse technique. In addition, an effective scheme is also proposed to estimate the initial value of state variables and right eigenvector of critical point, which exploit the second derivative of load parameter .To assess the voltage stability under branch outage contingency, this dissertation presents a new technique for critical point tracing. With branch admittance as the continuation parameter this method can trace through the critical curve, which is made up of critical points, from pre-contingency case to post-contingency case using predictor and corrector. All equations in prediction and correction can be solved using matrix reduction technique, which significantly reduces the dimension to half of the original.A new method is also derived to compute the sensitivity of loading margin to voltage collapse with respect to any parameters. Differing from the traditional one, this method does not need to compute the left eigenvector associated with the zero eigenvalue of power flow Jacobian matrix, evaluated at critical point. What's neededis just to solve a system of linear equations with extended power flow Jacobian matrix on the left-hand side. Avioding the iteration step to compute left eigenvector, this method is more simple and more suitable for on-line steady state voltage stability analysis.