Preventive Control of Electric Power System State Variables by the Methods of Probabilistic Load Flow

Probability Constrained Load Flow on the Basis of Tracing Method

“…The validity of the assumption about the normal law is based on the fact that the dependent state variables are the functions of a great number of random arguments. When a variable has the distribution law other than the normal law, such a shift can be obtained by the approximation of the probability density curve with respect to three or more moments with the use of Gram-Charlier series expansion [4]. The interval is compared with the known feasible interval of a change in the variable.…”

“…where: -vectors of dependent variables, that contain magnitudes and phases of voltages, and independent variables or controls, which include active and reactive power sources and transformer ratios. Problem (3)(4)(5)(6) is solved using the combination of the reduced gradient and quadratic programming methods [6]. The specific feature of the solution vector obtained lies in the change in the values of virtually all the control vector components.…”

“…The greater the difference between the minimum singular values of the Jacobian matrix and the rest of the singular values, the more grounds we have to conclude that the variables are of a sensor character with respect to the maximum components of the right singular vector related to the minimum singular value [3]. In the second approach applied in this research, the response of random variables to the disturbances can be studied by linear and nonlinear analytical methods of probabilistic load flow [4].…”