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Evaluation of conservation voltage reduction (CVR) factor is critical to peak load reduction, 556 energy conservation, and many CVR-related power system control/optimization strategies. This paper proposes a novel robust CVR factor evaluation method using soft constrained gradient analysis based on time-varying load modeling and real utility field measurements. Firstly, the time-varying ZIP parameter identification is formulated as an over-determinant problem composed of first-order gradient with respect to each coefficient and soft constraints representing temporal correlation of loads in each time step, in order to improve the robustness and smoothness of CVR factor evaluation. Then, problems in time series are coordinated with a sliding window approach. A necessary condition for selecting the smallest window size is proposed and strictly proved to guarantee the existence and uniqueness of the solution of time-varying load modeling problem. Finally, time-varying CVR factors are accurately and robustly calculated with field measurements and the identified load model. Case studies are performed using sufficient field measurements obtained from two real utilities. Unlike existing methods that require a large number of measurements to obtain precise estimation of CVR factor, the proposed method is sufficiently accurate even when the measurements are limited or of low time resolution. Further, the accuracy and robustness of the proposed approach are validated under different types of uncertainties and compared with other existing data processing and CVR factor evaluation methods. [ABSTRACT FROM AUTHOR]

A new smooth model is proposed in this paper to eliminate the non-differentiability of several types of limits in power flow models. The proposed smooth model accurately represents power system static models with limits as a continuously differentiable function. Analytic results are developed to show that each solution of the proposed smooth model is arbitrarily close to a solution of the corresponding original power flow model with limits. The proposed smooth model includes a wide range of devices with physical limits, such as generators, transformers, HVDCs, phase shifters, and shunts. In addition, it is shown that every generic static bifurcation in the original model is transformed into a saddle-node bifurcation in the smoothed model. Hence, the search for bifurcations in voltage stability assessment can be greatly simplified. Several numerical studies of the proposed smooth model on a 9241-bus power system and on a 13659-bus power system have shown promising results. [ABSTRACT FROM AUTHOR]