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An affine arithmetic (AA) method is proposed in this paper to solve the optimal power flow (OPF) problem with uncertain generation sources. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a probability density function (pdf). The proposed AA-based OPF problem is used to determine the operating margins of the thermal generators in systems with uncertain wind and solar generation dispatch. The AA-based approach is benchmarked against Monte Carlo simulation (MCS) intervals in order to determine its effectiveness. The proposed technique is tested and demonstrated on the IEEE 30-bus system and also a real 1211-bus European system. [ABSTRACT FROM AUTHOR]

This paper presents a novel method based on affine arithmetic (AA) for voltage stability assessment of power systems considering uncertainties associated with operating conditions, which may be attributed to intermittent generation sources, such as wind and solar. The proposed AA-based method reduces the computational burden as compared to Monte Carlo (MC) simulations, and also improves the accuracy as compared to some analytical approaches. The proposed method is tested using two study cases: first, a 5-bus test system is used to illustrate the proposed technique in detail, and thereafter a 2383-bus test system to demonstrate its practical application. The results are compared with those obtained using MC simulations to verify the accuracy and computational burden of the proposed AA-based method, and also with respect to a previously proposed technique to estimate parameter sensitivities in voltage stability assessment. [ABSTRACT FROM PUBLISHER]

This paper presents a novel framework based on range arithmetic for solving power flow problems whose input data are specified within real compact intervals. Reliable interval bounds are computed for the power flow problem, which is represented as an optimization model with complementary constraints to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. It is demonstrated that the lower and upper bounds of the power flow solutions can be obtained by solving two determinate optimization problems. Several numerical results are presented and discussed, demonstrating the effectiveness of the proposed methodology and comparing it to a previously proposed affine arithmetic based solution approach. [ABSTRACT FROM PUBLISHER]