**1. Introduction**

The technical regulations about environmental issues and the use of renewable energy sources (RES) set robust planning expansion programs due to the increasing energy demand. This leads to analysis of the system constraints, aiming to avoid instability scenarios defined by the load-ability limits [1]. Voltage stability is of utmost importance in electrical power systems studies and is related to reactive power compensation. In this context, flexible AC transmission system (FACTS) devices have been developed not only to offer a fast dynamic response of reactive power compensation but also to prevent the occurrence of synchronous resonance in large power systems [2,3]. In the literature, it has been reported that static synchronous compensator (STATCOM) presents promising results in dynamic reactive power compensation, voltage regulation and also helping to reduce power fluctuations [4,5].

During transient events, a power system may exhibit low-frequency power oscillation between two or more interconnected areas, also called inter-area oscillations, that are in a range of 0.1–1.0 Hz according to [6]. It is well-known that a STATCOM model not only provides good support of voltage control but can also improve the dynamic performance of the grid during transient events, in other words, is able to enhance the voltage recovery time and limits, and it is expected to have a better performance during power oscillations. As a consequence, a STATCOM is a good alternative to provide power oscillation damping

**Citation:** Rivera, D.; Guillen, D.; Mayo-Maldonado, J.C., Valdez-Resendiz, J.E.; Escobar, G. Power Grid Dynamic Performance Enhancement via STATCOM Data-Driven Control. *Mathematics* **2021**, *9*, 2361. https://doi.org/ 10.3390/math9192361

Academic Editor: Roberto Salvador Félix Patrón

Received: 22 July 2021 Accepted: 1 September 2021 Published: 23 September 2021

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(POD) [7]. This task is commonly carried out using power system stabilizers (PSS) to damp low-frequency power oscillations, which consists of an auxiliary control loop that measures the deviation of frequency. However, this is not the main task of a STATCOM, it is rather an inherent response due to its control design and can also include an additional damping controller [8].

Dynamic reactive power compensation can be an effective way to facilitate the interconnection of RES, especially to comply with grid codes regarding reactive power requirements at the point of common coupling (PCC) [9]. For example, in [10], a control scheme based on the fundamentals of a STATCOM is employed in photovoltaic (PV) power plants to reduce power oscillations in power grids, due to an inverter being able to act as a STATCOM; this enables the mitigation of POD during transient events. In [11], a STATCOM is also used in wind power plants to enhance the dynamic performance of the main oscillating modes; in that work, an adaptive network-based fuzzy inference system (ANFIS) controller is employed. Another proposal focused on POD can be found in [12], where a STATCOM is equipped with energy storage so that the combination of real and reactive power injection offers good robustness during the dynamic response of the power system.

On the other hand, different control strategies have been proposed in the literature to enhance the dynamic response of power systems supported by STATCOMs. Many of those approaches present different attributes according to the employed techniques. In [13], a mechanism of POD is based on auxiliary damping controllers defined by a wavelet neural network (WNN), which offers a reduced complexity due to the number of data used as well as its learning capability. In the same way, in [14], a multi-band controller is employed to deal with POD, which is a coordinated design and is optimized based on the operating conditions of the grid. Most of them have been used to design auxiliary control loops aiming to damp power oscillations, like in [8], which presents a control strategy using an additional damper controller (ADC) based on artificial neural networks and deep deterministic policy gradient (DDPG). In another study reported in [15], a datadriven analysis is carried out to adjust and calculate the control gain to enhance the overall system dynamic response to reduce the power oscillations. In contrast with other proposed control strategies, this work is focused on the full control of the voltage source converter (VSC)-based STATCOM without using auxiliary control loops to enhance the dynamic performance.

This paper presents a fully data-driven controller for a VSC-based STATCOM. The general idea is based on the fact that a STATCOM helps to increase the transient stability; this is feasible using well-coordinated controllers or employing other supplementary control functions. In this context, the proposed approach aims to improve the dynamic performance of a VSC-based STATCOM following the fundamentals of a conventional VSC controller. The contribution is underpinned in a data-driven controller to enhance the transient response of a VSC-based STATCOM under different operating conditions of a two area, four-machine power system. The proposed controller offers robustness and adaptability according to the power system requirements that will be reflected in the dynamic performance.

The proposed data-driven control is able to ensure the demanding performance specifications without any prior knowledge of the system. Among such specifications we can highlight stability as the most important one. It is well-known that model-based techniques are able to ensure stability and general performance. However, the limitation of such approach is the requirement of an existing accurate model of the grid and the power converter as a starting point. For instance, in [16] the small signal model of the system is required to design the controller of a STATCOM based on a multilevel converter. Similarly, in [17] the model of the system is required in order to design an adaptive controller for voltage regulation using a STATCOM. Other newer approaches, such as model predictive control (MPC), also require a detailed modeling of the system in order to work properly as can be corroborated in [18,19], where MPC is used as the control strategy for the mitigation

of voltage unbalance and reactive power control. Robust control can be also categorized as a model-based technique as can be observed in [20,21], where the system-model derivation is an important step of the controller design procedure. In real-life, a power grid is such a complex system that its model, parameters and general dynamics have a high-level of uncertainty. Consequently, the stability conditions obtained from an idealized model can be compromised during extreme scenarios such as the occurrence of faults. Another alternative is the use of classical proportional (P), proportional and integral (PI) and proportional, integral and derivative (PID) tuning rules, which do not require a model to set-up controller gains. The limitation of these rules, however, is the fact that they cannot guarantee stability unless a system model, for example, transfer function or frequency response traces, is provided (see e.g., [22,23]). Motivated by this problem, we developed a data-driven control technique that is able to ensure performance specifications and by all means stability, as in a model-based technique. Nevertheless, we replace the requirement of a model, by matrices constructed from data and stability conditions provided in terms of linear matrix inequalities (LMIs), which can be easily set-up and numerically solved by traditional MATLAB (Version R2021a, MathWorks, Natick, MA, USA) toolboxes such as Yalmip (free toolbox developed by Dr. Johan Lofberg).

The present paper is organized as follows. In Section 2, a theoretical background is discussed, which sets the basis of the proposed data-driven controller. The conventional state-space model is replaced by data, which is discussed in Section 3; it includes modeling and parametric identification. Section 4 describes the data-driven control design. The conventional and data-driven VSC is derived in Section 5, which includes the development of the state-space model, also known as the model-based. The case of study is depicted in Section 6, which describes the system that is going to be used to test the data-driven controller. In addition, Section 6 also includes the results, and the tests are focused on three aspects: voltage reference changes, power oscillation damping during transient faults, and load shedding. The data-driven controller performance is compared to the conventional controller, which is a state-space model described in [24]. Finally, Section 7 presents the conclusion of the data-driven controller performance.

## **2. Theoretical Background**

In this section, we introduce the main notation and theoretical elements that constitute the basis of the proposed data-driven controller.
