A Data-driven Approach for the Design of Wide-Area Damping Controllers

Abstract

The growing complexity of interconnected power systems, with significant penetration of intermittent renewable sources, makes the tasks of devising power system models and defining the operating point challenging. In this context, the large amount of data available from wide-area monitoring systems (WAMS) encourages the application of data-driven methods to power system stability and control. In the present work, a data-driven control design method, called Virtual Reference Feedback Tuning (VRFT), is formulated to design oscillation damping controllers for power systems using remote input signals from phasor measurement units (PMU). The only requirement is a reference model for the closed-loop dynamics. A strategy is proposed to build such model, based on the characteristics of the inter-area mode and measured output response. The use of remote signals in a wide-area damping controller (WADC) approach leads to very efficient inter-area damping controllers. Also, the fast-solving characteristic of the method is explored in an online implementation, where a previously designed controller is re-tuned to re-establish the damping performance after a change in operating condition. The proposed method is tested with two IEEE benchmark power systems, with one having a high penetration of Inverter-Based Source (IBS) generation. In both cases, the critical inter-area oscillation mode is successfully damped.

Appendices

Appendix A Detailed Reference Model Build

Considering the typical poorly damped response presented in Fig. 4, the natural frequency of the dominant oscillation mode can be estimated by $\omega _n={\omega }/{\sqrt{1-\zeta _0^2}}$, where $\omega =2\pi /{\Delta t_3}$ is the damped frequency, and $\zeta _0$ is the damping ratio of the measured signal, estimated using the following logarithm decrement formula for any two adjacent peaks

$$\begin{aligned} \zeta _{0} = \left( 1 + \frac{2\pi }{\ln \left( {p_2}/{p_3}\right) }\right) ^{-1/2}. \end{aligned}$$

(A1)

The second and third peaks are chosen to avoid the nonlinear dynamics of the first swing.

The delay of the reference model is adjusted so the instant of the first peak of its step response matches the instant of the first positive peak of the measured signal ($p_1$), as follows

$$\begin{aligned} Td=\Delta t_2 - t_{M,p1}, \end{aligned}$$

(A2)

where

$$\begin{aligned} t_{M,p1}=\sin ^{-1}\left( \sqrt{1-\zeta ^2}\right) /\omega \end{aligned}$$

(A3)

is the instant of the first peak of the step response of the model (9) without the delay.

The gain K is chosen so that the first peak of the response of M(s) is close to $p_1$ (amplitude of the first peak of the measured output), as follows

$$\begin{aligned} K={p_1}/{y_{M,p1}}, \end{aligned}$$

(A4)

where

$$\begin{aligned} y_{M,p1}=u_{s} \omega _{n} e^{{-\zeta \theta }/{\sqrt{1-\zeta ^2}}}, \end{aligned}$$

(A5)

is the amplitude of first peak of the step response of the model (9) with $K=1$, for a given step input of amplitude $u_{s}$, and $\theta =\sin ^{-1}(\sqrt{1-\zeta ^2})$.

Appendix B Wind Generation

Wind power plants are modeled by variable speed synchronous generators connected to the grid via a voltage source converter and a transformer (same used for the original generators), as illustrated in Fig. 18. This configuration is also known as Type IV wind generator (Ayyanar and Vittal, 2012).

Fig. 18

Schematic of Type 4 wind turbine generator with variable speed synchronous generators. Adapted from CEPEL and Eletrobras (2020)

Fig. 19

AVR of the wind turbine synchronous generator

We used the built-in synchronous wind generator model (GSE) of the software ANATEM, with each turbine operating with 0.75 pu capacity of a 850 MVA rated power. The wind power plants are introduced here to model the reduction of the total inertia of the system caused by a high penetration of IBS generation. This effect together with the removal of the two PSS associated with the original generators, have a significant impact on the damping performance of The 39-Bus New-England Test System. To include the wind generation without interfering in the power flow condition of the system, the wind power plants are composed of 392 (bus 30) and 991 (bus 33) wind turbines in parallel, keeping the original power generation at those buses. At each Type 4 wind turbine, the synchronous generator is equipped with a first-order AVR as the one illustrated in Fig. 19.