Keyou Wang

Power System Voltage Regulation via STATCOM Internal Nonlinear Control

A new internal STATCOM control based on feedback linearization is proposed. The feedback linearization controller is developed without any simplifying assumptions to the STATCOM model. The proposed control is validated on the IEEE 118-bus system with full-order generator and network models as opposed to a small test system. Furthermore, the proposed control is benchmarked against published results. Lastly controllability issues associated with a singularity in the feedback linearization control (FBLC) coordinate transformation is identified, and a solution is provided to avoid instability.

Numerical simulation of Stochastic Differential Algebraic Equations for power system transient stability with random loads

This paper summarizes numerical methods for Stochastic Differential Algebraic Equations (SDAEs) with which power system are modeled. The loads are modeled as random variables which appear in algebraic equations. The properties of numerical methods for Differential Algebraic Equations (DAE) and Stochastic Differential Equations (SDE) are reviewed and the first-order backward euler method is proposed for SDAE in power system transient stability simulation. Illustration examples are given on a single-machine-infinite-bus (SMIB) system.

The Fokker-Planck Equation for Power System Stability Probability Density Function Evolution

This paper presents an analysis of the evolution of the probability density function of the dynamic trajectories of a single machine infinite bus power system. The probability density function can be used to determine the impact of random (stochastic) load perturbations on system stability. The evolution of the state probability density function over time leads to several interesting observations regarding stability regions as a function of damping parameter. The Fokker-Planck equation (FPE) is used to describe the evolution of the probability density of the states. The FPE is solved numerically using PDE solvers (such as finite difference method). Based on the results, the qualitative changes of the stationary density produce peak-like, ridge-like and other complicated shapes. Lastly, the numerical FPE solution combined with SMIB equivalent techniques lay the framework extended to the multimachine system.

A Versatile Probability Model of Photovoltaic Generation Using Pair Copula Construction

Photovoltaic (PV) generation is increasingly popular in power systems. The nonlinear dependence associated with a large number of distributed PV sources adds the complexity to construct an accurate probability model and negatively affects confidence levels and reliability, thereby resulting in a more challenging operation of the systems. Most probability models have many restrictions when constructing multiple PV sources with complex dependence. This paper proposes a versatile probability model of PV generation on the basis of pair copula construction. In order to tackle the computational burden required to construct pair copula in high-dimensional cases, a systematic simplification technique is utilized that can significantly reduce the computational effort while preserving satisfactory precision. The proposed method can simplify the modeling procedure and provide a flexible and optimal probability model for the PV generation with complex dependence. The proposed model is tested using a set of historical data from colocated PV sites. It is then applied to the probabilistic load flow (PLF) study of the IEEE 118-bus system. The results demonstrate the effectiveness and accuracy of the proposed model.

A Feedback Linearization Based Unified Power Flow Controller Internal Controller for Power Flow Control

Abstract This article presents a feedback linearization based controller design methodology for a unified power flow controller to achieve rapid reference signal tracking in the internal control level. Feedback linearization is a non-linear control technique based on the differential geometry theory and overcomes the drawback of traditional linear proportional-integral control, which is typically tuned for one specific operating condition. In this article, feedback linearization control is developed for the unified power flow controller dynamic model via an appropriate coordinate transformation, and linear quadratic regulator control is then applied on the transformed linear system. The proposed control is validated via a detailed device-level simulation on an 11-bus system and a large scale simulation on the IEEE 118-bus and 300-bus systems. The proposed control is benchmarked against proportional-integral control.

Applying probabilistic collocation method to power flow analysis in networks with wind farms

In power systems with a high wind power penetration, probabilistic load flow analysis is a fundamental problem for system planning and operation due to the uncertainty and fast fluctuation of wind speed. This paper proposes probabilistic collocation method (PCM) for load flow analysis with a penetration of wind farms. The orthogonal polynomials are utilized to generate the approximation of the random variable of interest as the function of uncertainty parameters. The proposed method is a computational efficient solution to provide quite an accurate approximation for the given probability distribution of system response. Therefore the method can significantly reduce the computational time compared to the traditional brute force Monte Carlo approach. Illustration examples are given on the IEEE 39 bus system to show the effectiveness of the proposed method.

Feedback linearization internal control for the unified power flow controller

This paper presents a feedback linearization based controller design methodology for a unified power flow controller (UPFC) to achieve rapid reference signal tracking in the internal level. Feedback linearization control (FBLC) is a nonlinear technique based on differential geometry theory and overcomes the drawback of traditional PI control linearzing at one specific operating condition. FBLC is applied on UPFC dynamic model via an appropriate coordinate transformation and LQR control is then applied on the transferred linear system. The proposed control is validated on the IEEE 118-bus system with full-order generator and network models.

Fokker-Planck equation application to analysis of a simplified wind turbine model

This paper presents a new method to evaluate the stochastic dynamic model of the wind turbine system using stochastic differential equations (SDE). The wind speed is described by the Rayleigh distribution which is constructed as the stationary solution of a one-dimensional nonlinear SDE. The dynamic model of the wind turbine system can be combined with this SDE of wind speed to expand to multi-dimensional stochastic differential equations. The time evolution of the probability density function of the system is described by the Fokker-Planck equation (FPE) which can be derived from the corresponding stochastic differential equations. The procedure is illustrated using a constant-speed wind turbine model with squirrel cage induction generator.

Investigation on singularity of stochastic differential algebraic power system model

This paper presents the results of the investigation of the singularity of power systems with random loads. The power system is modeled with stochastic differential algebraic equations (SDAE). This is the extension of singularity induced bifurcation analysis in the deterministic DAE model. This paper explores the probability of loss of voltage causality. The WECC 3-machine-9-Bus system is used to illustrate the impact of diffusion coefficients on voltage stability.

A stochastic model for power system transient stability with wind power

There has been continuous development of methods for evaluating transient stability of power system incorporating wind farms. A stochastic model of power systems with wind farms is proposed in this paper. The model takes into account both of the random initial values and stochastic noise of wind speed, with which power system transient stability analysis is modeled as a stochastic initial value problem (SIVP). Monte Carlo trials transform the model into stochastic differential algebraic equations (SDAEs). An implicit numerical method for SDAEs is discussed, which is similar to implicit trapezoidal integration for deterministic differential algebraic equations (DAEs). Case studies illustrating the proposed model are tested on the IEEE 39-bus 10-machine system. The simulation results demonstrate that the proposed model can provide comprehensive description of stochastic excitation of wind farms.