this paper presents a probabilistic optimal power flow (popf) algorithm considering different uncertainties in a smart grid. different uncertainties such as variation of nodal load, change in system configuration, measuring errors, forecasting errors, and etc. can be considered in the proposed algorithm. by increasing the penetration of the renewable energies in power systems, it is more essent...

this paper presents a probabilistic confidence-interval based method for optimal placement of shunt capacitors in distribution networks by considering probabilistic characteristics of loads. the main objective function are reducing loss and improving the voltage profile. backward forward sweep method has been employed to obtain the power flow results in distribution system. in addition, integer...

Optimal Reactive Power Dispatch (ORPD) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. Due to the stochastic behavior of loads, the ORPD requires a probabilistic mathematical model. In this paper, Monte Carlo Simulation (MCS) is used for modeling of load uncertainties in the ORPD problem. The problem is formulated as a nonlinear constrained mul...

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on non-parametric Bayesian inference-based uncertainty propagation approach, called (GP). We also suggest new type sensitivity Subspace-wise Sensitivity, using observations the ...

optimal reactive power dispatch (orpd) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. due to the stochastic behavior of loads, the orpd requires a probabilistic mathematical model. in this paper, monte carlo simulation (mcs) is used for modeling of load uncertainties in the orpd problem. the problem is formulated as a nonlinear constrained mul...

This paper is devoted to revealing some properties of the probabilistic optimal power flow (POPF) problem. In conjunction with Hermite polynomial model, Nataf transformation introduced map POPF problem independent standard normal space. Firstly, a multivariate model employed represent function relationship between inputs and outputs. Then, moment matching equations are derived characterize unce...