A Framework for Dynamic Stability Analysis of Power Systems with Volatile Wind Power

We propose a framework employing stochastic differential equations to facilitate the long-term stability analysis of power grids with intermittent wind power generations. This framework takes into account the discrete dynamics which play a critical role in the long-term stability analysis, incorporates the model of wind speed with different probability distributions, and also develops an approximation methodology (by a deterministic hybrid model) for the stochastic hybrid model to reduce the computational burden brought about by the uncertainty of wind power. The theoretical and numerical studies show that a deterministic hybrid model can provide an accurate trajectory approximation and stability assessments for the stochastic hybrid model under mild conditions. In addition, we discuss the critical cases that the deterministic hybrid model fails and discover that these cases are caused by a violation of the proposed sufficient conditions. Such discussion complements the proposed framework and methodology and also reaffirms the importance of the stochastic hybrid model when the system operates close to its stability limit.Comment: The paper has been accepted by IEEE Journal on Emerging and Selected Topics in Circuits and System

Investigating the Impacts of Stochastic Load Fluctuation on Dynamic Voltage Stability Margin Using Bifurcation Theory

This paper studies the impacts of stochastic load fluctuations, namely the fluctuation intensity and the changing speed of load power, on the size of the voltage stability margin. To this end, Stochastic Differential-Algebraic Equations (SDAEs) are used to model the stochastic load variation; bifurcation analysis is carried out to explain the influence of stochasticity. Numerical study and Monte Carlo simulations on the IEEE 14-bus system demonstrate that a larger fluctuation intensity or a slower load power changing speed may lead to a smaller voltage stability margin. Particularly, this work may represent the first attempt to reveal the influence of the time evolution property of the driving parameters on the voltage stability margin in power systems

The Effect of the Uncertainty of Load and Renewable Generation on the Dynamic Voltage Stability Margin

In this paper, the impact of stochastic load and renewable generation uncertainty on the dynamic voltage stability margin is studied. Stochastic trajectories describing the uncertainty of load, wind and solar generation have been incorporated in the power system model as a set of Stochastic Differential-Algebraic Equations (SDAEs). A systematic study of Monte Carlo dynamic simulations on the IEEE 39-Bus system has been conducted to compute the stochastic load margin with all dynamic components active. Numerical results show that the uncertainty of both demand and generation may lead to a decrease on the size of the dynamic voltage stability margin, yet the variability of renewable generators may play a more significant role. Given that the integration of renewable energy will continue growing, it is of paramount importance to apply stochastic and dynamic approaches in the voltage stability study.Comment: Accepted in 2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe

Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks with Renewables

Considering the increasing penetration of renewable energy sources and electrical vehicles in utility distribution feeders, it is imperative to study the impacts of the resulting increasing uncertainty on the delivery capability of a distribution network. In this paper, probabilistic available delivery capability (ADC) is formulated for a general distribution network integrating various RES and load variations. To reduce the computational efforts by using conventional Monte Carlo simulations, we develop and employ a computationally efficient method to assess the probabilistic ADC, which combines the up-to-date sparse polynomial chaos expansion (PCE) and the continuation method. Particularly, the proposed method is able to handle a large number of correlated random inputs with different marginal distributions. Numerical examples in the IEEE 13 and IEEE 123 node test feeders are presented, showing that the proposed method can achieve accuracy and efficiency simultaneously. Numerical results also demonstrate that the randomness brought about by the RES and loads indeed leads to a reduction in the delivery capability of a distribution network.Comment: 10 pages, 4 figures, journal paper accepted by IEEE Transactions on Power System

Probabilistic Power Flow Calculation using Non-intrusive Low-rank Approximation Method

In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, probability density function) of the PPF solutions. This method aims at building up a statistically-equivalent surrogate for the PPF solutions through a small number of power flow evaluations. By exploiting the retained tensor-product form of the univariate polynomial basis, a sequential correction-updating scheme is applied, making the total number of unknowns to be linear rather than exponential to the number of random inputs. Consequently, the LRA method is particularly promising for dealing with high-dimensional problems with a large number of random inputs. Numerical studies on the IEEE 39-bus, 118-bus, and 1354-bus systems show that the proposed method can achieve accurate probabilistic characteristics of the PPF solutions with much less computational effort compared to the Monte Carlo simulations. Even compared to the polynomial chaos expansion method, the LRA method can achieve comparable accuracy, while the LRA method is more capable of handling higher-dimensional problems. Moreover, numerical results reveal that the randomness brought about by the renewable energy resources and loads may inevitably affect the feasibility of dispatch/planning schemes.Comment: 12 pages, 5 figures, Accepted by IEEE Transactions on Power Systems on January 27, 2019. arXiv admin note: text overlap with arXiv:1810.0815