Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

Abstract

The static voltage stability margin (SVSM) of a power system considering the uncertain fluctuation range of wind farm (WF) output can be described as an interval value called the SVSM interval. A multi-objective optimal control model for SVS of a power system considering the interval uncertainty of WF output is proposed. The objective functions of the model are to increase the central value and reduce the fluctuation range of the SVSM interval, and the decision variables are the active power output and terminal voltage of generators and the switching capacity of shunt capacitors. Thus, it is a multi-layer optimization model. A parametric approximation (PA) method is used to obtain the approximate functional relationship between the optimal objective function values and the decision variables of the inner-layer and mid-layer optimization models and convert the optimization model into a single-layer bi-objective optimization model. A method for obtaining the continuous Pareto frontier of the bi-objective optimization model is proposed based on the normalized normal constraint and PA methods, and the compromise optimal solution calculated from the continuous Pareto frontier is used as the optimal control scheme. Two methods for improving the calculation efficiency of the PA method are also proposed. Finally, results from experimentation on the IEEE 39-bus system and an actual provincial power grid demonstrate the effectiveness of the proposed method.

A Joint Optimization Model for Transmission Capacity and Wind Power Investment Considering System Security

“…A voltage stability index is presented in [35] based on the P-V curve, where the voltage stability index is computed in terms of the distance between the operating point and saddle point on the P-V curve. A control model for static voltage stability considering the interval uncertainty of wind power output is suggested by [36], where the objective functions are to increase the central value and decrease the fluctuation range. Based on the models presented in the literature, the VSM in scenario 𝑠 for a given investment plan can be computed as follows:…”

Probability confidence correlation analysis for many‐objective optimal operation considering a set of conflict interests

“…where L mi , 𝜇 mi and 𝜎 2 mi need to be obtained by continuous power flow calculation (CPF) as the limit operating values of the system, and the details can be found in literature [44].…”

“…The probability of collapse is calculated by the load margin $$M_{i}=L_{\mathrm{m}i}-L_i$$. With the consideration of the fluctuations of load and wind power, $$M_i$$ also satisfies the normal distribution as: $$$$\begin{equation} M_i \sim N{\big(\mu _{\mathrm{m} i}, \sigma _{\mathrm{m} i}^2\big)}, \end{equation}$$$$where $$L_{\mathrm{m}i}$$, $$\mu _{\mathrm{m} i}$$ and $$\sigma _{\mathrm{m} i}^2$$ need to be obtained by continuous power flow calculation (CPF) as the limit operating values of the system, and the details can be found in literature [44].…”

Coordinated Complex-Valued Encoding Dragonfly Algorithm and Artificial Emotional Reinforcement Learning for Coordinated Secondary Voltage Control and Automatic Voltage Regulation in Multi-Generator Power Systems

“…To mitigate this deficiency, coordinated secondary voltage control (CSVC) has been applied in power systems [21]. The CSVC, which has been introduced by J.P. Paul et al [22], aims to increase voltage stability in highly constrained areas [23]. Consequently, the CSVC can regulate the free variables of the reactive power flow [24].…”