PMU-Based FOPID Controller of Large-Scale Wind-PV Farms for LFO Damping in Smart Grid

Due to global warming problems and increasing environmental pollution, there is a strong tendency to install and apply renewable energy power plants (REPPs) around the world. On the other hand, with the increasing development of information and communication technology (ICT) infrastructures, power systems are using these infrastructures to act as smart grids. In fact, future modern power systems should be considered as smart grids with many small and large scale REPPs. One of the main problems and challenges of the REPPs is uncertainty and fluctuation of electrical power generation. Accordingly, a suitable solution can be combination of different types of REPPs. So, the penetration rate of large-scale wind-PV farms (LWPF) is expected to increase sharply in the coming years. Given that the LWPFs are added to the grid or will replace fossil fuel power plants, they should be able to play the important roles of synchronous generators such as power low-frequency oscillation (LFO) damping. In this paper, an LFO damping system is suggested for a LWPF, based on a phasor measurement unit (PMU)-based fractional-order proportional–integral–derivative (FOPID) controller with wide range of stability area and proper robustness to many power system uncertainties. Finally, the performance of the proposed method is evaluated under different operating conditions in a benchmark smart system.


I. INTRODUCTION
Global warming, environmental pollutions and other destructive effects of fossil fuels-based power generation have led to a growing focus on the use of renewable energies around the world [1]. So, a growing trend can be seen in establishing and exploiting renewable energy power plants (REPPs) [2], [3]. This type of power plants is usually integrated with the main grid to increase generation capacity with low pollution. Moreover, they may replace conventional power plants in some cases [4], [5]. In other words, in future systems, the REPPs will play an important role in electrical power generation.
The associate editor coordinating the review of this manuscript and approving it for publication was Youngjin Kim .
On the other hand, information and communication technology (ICT) infrastructures are rapidly developing, and also with the help of artificial intelligence (AI) systems, power systems can be considered as smart grids [6], [7]. A smart grid includes three layers. A power system layer, a control system layer and a communication infrastructure layer [6]. In transmission level, smart grids are based on wide-area measurement systems (WAMSs) that receive most of their desired data through the phasor measurement units (PMUs) [6]. The application of PMUs can reduce many uncertainties of REPPs, considering their accurate measurements, which can be used for any control system.
Despite the various benefits of renewable energy resources, some of the inherent characteristics of this type of energy VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ resources are considered as challenges in their efficient use and are obstacles to proper efficiency and reliability in electricity generation [5]. For example, non-everlasting winds at the proper speed and the lack of solar irradiation at whole times are some of the challenges which can reduce the generation efficiency in the large-scale photovoltaic farms (LPFs) and large-scale wind farms (LWFs). This causes high uncertainty in the power generation by these types of power plants [5]. Large-scale hybrid wind-PV farm (LWPF) is regarded as a fundamental solution for these challenges [8], [9]. These types of REPPs include two generator units, wind turbine generators (WTGs) and photovoltaic (PV) generators (PVGs). The hybrid application of WTGs and PVGs increases the efficiency and reliability of electrical power generation than the separated application of LPFs and LWFs [8], [9]. In order to exploit REPPs, two important issues need to be addressed. The operation of these power plants causes many changes in the characteristics of power systems such as stability. Given that REPPs are inverter-based, so they reduce mechanical inertia and can increase the risk of LFOs in the power system [10]- [13]. Moreover, given the replacement of REPPs with the conventional power plants, many of the existing capabilities in the synchronous generators, such as low-frequency oscillation (LFO) damping by power system stabilizer (PSS) should be performed by them. Therefore, the REPP needs to be able to mitigate the LFOs by a supplementary controller.
In many papers, the LFO damping through the LPFs and LWFs has been studied [14]- [20]. Given that the control model of the LWPF is different from the control model of conventional REPPs, it is necessary to investigate this issue separately, which has been investigated in [21], and a simple lead-lag controller (LLC) has been suggested as a power oscillation damping controller (PODC).
Although the LLC is very cheap and very common, it provides a smaller stability area than modern controllers and also has low robustness against grid uncertainties. One of the types of modern controllers that have been studied recently is the fractional-order proportional-integral-derivative (FOPID) controller, which is the general structure of proportionalintegral-derivative (PID) controllers [22]. The FOPID controller is mathematically based on the fractional-order calculus [22]- [30]. Due to the inherent characteristics of the FOPID controllers, these types of controllers have a wide stability region. In addition, it is highly robust against power system uncertainties. In recent years, the application of this type of controller in the case of automatic generation control (AGC) [31], load-frequency control (LFC) [32], and LFOs damping by synchronous generators [33], FACTS devices [34], and LPFs [35], [36], has been the subject of many researches.
In this paper, the implementation of the PMU-based FOPID controller in the control loop of the LWPF for LFOs damping is proposed. For this purpose, an optimized tuning method based on teaching-learning-based optimization (TLBO) is proposed to obtain the values of the FOPID controller parameters. Finally, the performance of the controller is evaluated in various operating conditions and against different uncertainties in a smart grid.
The rest of the paper is organized as follows. Section 2 provides an overview of the LWPF, its benefits, and models for power system studies. The introduction of the FOPID controller and the concept of fractional-order calculus are given in Section 3. Also, the use of the FOPID controller as a PODC is proposed in section 4. Moreover, tuning of the proposed PODC, simulation, and performance evaluation are presented and discussed in Section 5. The conclusions are drawn in Section 6.

II. OVERVIEW OF LWPF
The LWPFs are the new type of REPPs which are extensively used in the near future considering their higher efficiency and reliability, compared to the conventional REPPs [8], [9]. The hybrid application of WTGs and PVGs reduces the uncertainty of power generation [8], [9]. As shown in Figure 1, when PV generation decreases, the WTG may compensate for the shortage of the PV generation, and vice versa [37].
Note that various types of small-scale hybrid generation systems are currently in operation. The LWPFs consist of four basic components including PVGs, WTGs, inverters, and controllers [1]. This type of power plants includes a separate controller for each generator and a central controller for the whole power plant. Each controller receives command signals from the central controller [38], [39]. Figure 2 illustrates the schematic structure of the LWPF.
Given that the converter-based units are connected to the grid by inverters, their dynamic is too fast and can usually be ignored in stability studies. Thus, their converted energy is assumed to be constant [38], [39]. Usually, the inverters of LWPFs are modeled as the current-controlled current 94954 VOLUME 9, 2021 sources [38], [39]. In some software packages, this model is available as a static generator. As mentioned, the fourth component of the LWPF is the controllers, which play a fundamental role in the system response during the dynamic conditions. Thus, the modeling of the LWPFs controller is essential to analyze the grid stability.

A. POWER FLOW MODEL
To study the behavior of a power grid, which has an LWPF, it is needed to have a power flow model of the LWPF. As mentioned, the LWPF consists of PVGs and WTGs, each of which includes smaller units. For example, a PVG unit includes many photovoltaic PV panels and inverters. In order to conduct power flow study, the total number of units is necessary to be considered as an equivalent unit in which its rated power is equal to the sum of the rated powers of individual units. This model is called simple aggregated model [38], [39]. As shown in Figure 3, the simple aggregated model can be used for power flow analysis. Also, each unit is considered as a conventional generator for the LWPF, which involves PVG and WTG units. The connecting point to the power system is called point of common coupling (PCC).

B. DYNAMIC MODEL
From the beginning of the development of REPPs, the lack of access to a comprehensive and generic dynamic model has been a major problem in studying the power system stability. First, research models or models created by power plant owners were used [40]. These models had their own problems although they could satisfy the study requirements in many cases.
However, the lack of a generic, accessible, and flexible model, which could be used for a variety of REPPs, was evident before expanding the establishment and development of REPPs [38]. Although different models have been presented by well-known companies and institutes later [41]- [43], the model that introduced by General Electric (GE) and accepted by Western Electricity Coordinating Council (WECC), called first-generation generic model, is regarded as the leading one [41], [42]. Since 2010, WECC has initiated to develop this model for further flexibility and adapt it to a wide range of control strategies for the possibility of modeling different types of equipment for power plants.
The result was second generation generic model (SGGM) presented in 2012 [43]. The block diagram of the SGGM is shown in Figure 4.
Due to the increasing tendency to use the hybrid REPPs (HREPPs), WECC and Electric Power Research Institute (EPRI) conducted some studies to present a generic model for this type of power plants. Ultimately, an initial model called generic dynamic model of HREPPs was presented by them [38], [39]. This model, which was based on  the SGGM, is currently under development [38]. Generally, these models consist of three basic modules as follows [39]: • Renewable energy generator/converter (REGC). • Renewable energy electrical control (REEC). • Renewable energy plant control (REPC). The creation of a dynamic model for HREPPs was based on the development of the REPC module. This module is the model of a central controller that sends control signals to other controllers [38], [38]. In other words, in the dynamic model of HREPP, the central controller can send control signals to several different controllers. Figure 3 shows the schematic structure of the REPC module in the dynamic model of HREPP [38]. Therefore, this model can be used to model the LHWPF. As shown in Figure 1, the LWPF consists of three main controllers, a PVG controller, a WTG controller and a central controller. The dynamic model of the LWPF is shown in Figure 5.
It should be noted that the SGGM and the HREPP dynamic model have the ability to model a wide range of inverter-based generators [38], [39]. Therefore, the modules defined in these models have differences according to the generator type, so each of the modules has a specific version. In this study, the versions of REPC, REEC, REGC modules are B, B, and A, respectively [39].

III. SURVEY ON FOPID CONTROLLER
The FOPID controllers are based on fractional-order calculus, which is a famous mathematical concept that generalizes conventional integer-order calculus into arbitrary orders. This issue has a history of more than 300 years, yet its application in different fields has been realized only recently due to its implementation complexity in reality [22]- [30].
Fractional differential equations based on fractional-order calculus have emerged as one of the most important areas of interdisciplinary interest in recent years [20]- [25]. The fractional-order differentiator, which can be denoted by a general fundamental operator as a general form of differential and integral operators, is defined as follows [22]: where, q indicates the fractional-order. Also, a and t are the lower and upper limits of D, respectively. Note that q can be a complex number. There are three popular definitions for the fractional-order differentiator, Grunwald Letnikov (GL) definition, Riemann Liouville (RL) definition, and Caputo definition [22]. The GL definition is as follows: where, n is the integer value that satisfies the condition and n-1 < q < n. In addition, function represents the Euler's Gamma function as indicated in (4). Also, operator [ ] in (2) indicates a floor function [22], [25].

A. FOPID CONTROLLER
The general form of the PID controller is the FOPID controller. This controller provides higher robustness and stability area than common controllers due to the extra degrees of freedom resulting from the orders of fractional integral λ, and fractional derivative δ [22]. As shown in Figure 6, the FOPID controller is the expansion of the PID controller [22].   The conventional PID controller has three variables (K P , K I , and K D ) while the FOPID has five variables (K P , K I , K D , λ, and δ). The ability to manage model uncertainties in non-linear applications, more flexibility in tuning, and high disturbance rejection are other advantages of the FOPID controller [20], [24]. The fractional-differential-equation of this type of controller is expressed as follows [22], [29]: Also, the transfer function C(s), in Laplace form is as below: where, E(s) is the input and U (s) is the output. As well as, K P , K I and K D represent the proportional, integral, and derivative gains of the FOPID controller. Moreover, λ and δ display the fractional-orders of integral and derivative. The controller structure has been shown in Figure 7 [22].

B. STABILITY OF FRACTIONAL-ORDER SYSTEMS
The fractional-order systems stability is somewhat different from the integer-order systems, duo to the inherent characteristics of fractional-order calculus. In a stable fractionalorder system, the roots may be located in the right side of the imaginary axis.
The state-space model of fractional-order linear-time invariant system is stated as bellow [30], [44]: where, x ∈ R n , u ∈ R m and y ∈ R p are the state vector, vector of system inputs and vector of system outputs. For an n-th order system with m inputs and p outputs, A ∈ R n×n , B ∈ R n×m and C ∈ R p×n are the system matrix, input matrix and output matrix. Also, q = [q 1 , q 2 , . . . , q n ] T is the fractional-orders vector. The stability condition for a fractional-order system based on Matignon's Stability Theorem can be presented as bellow [30], [44]: The fractional-order system in (9) and (10) is stable if and only if: where, eig(A) represents the eigenvalue of matrix A. The stability area of fractional-order system depends on the value of q [31], [45]. Given that, in FOPID controllers, the fractionalorders, λ and δ, are between 0 and 1, so this type of controllers has a wide range of stability area as shown in Figure 8.

IV. IMPLEMENTATION OF PMU-BASED FOPID-PODC
In this paper, a FOPID controller is suggested to damp LFOs by the LWPF. The FOPID-PODC is implemented in the central controller of the LWPF. Also, the input signals are received from PMUs, so the controller function is based on a WAMS [6], [7]. As indicated in Figure 9, two various points are proposed for the FOPID-PODC in the central controller model called REPC_B model. Each of these points is considered based on the LWPF control mode for reactive power/voltage control. Point 1 is suggested, if the control mode is voltage control. Therefore, the PCC is considered as a PV bus. Moreover, point 2 is suggested, if the reactive power control mode 94958 VOLUME 9, 2021 is selected for the LWPF operation mode. So, the PCC is considered as a PQ bus.

V. CASE STUDY
To further investigate the issue, it is necessary to evaluate the performance of the proposed controller in a benchmark test system. Therefore, having the necessary information about the power system is necessary for the first step to design the proposed controller.

A. TEST SYSTEM
There are various benchmark grids for LFO studies; the most important and well-known one is the two-area system [45], [46]. In this study, this system with a secure communication infrastructure is considered as a smart grid. As depicted in Figure 10, the LWPF is connected to bus 6.  It should be noted that this bus is considered as the PCC. Also, only generator G2 has a PSS in the excitation system. The specifications of the mentioned system are given in Table 1.  As mentioned, the test system has a secure communication infrastructure layer. Therefore, the grid uses a WAMS to measure the desired signals. The required signals are measured by PMUs, connected to the generator buses, and transmitted to the phasor data concentrator (PDC) for data  processing. Finally, required signals are sent to the relevant equipment by the WAMS. It is clear that signal transmission has a time delay that needs to be considered in studies. In this paper, the time delay is assumed to be constant. Also, the values of the LWPF parameters, excitation system of synchronous generators, and PSS of generator G2 are given in the appendix. Other data is in accordance with the specifications of the two-area system in [46].
In this study, the LWPF control mode for reactive power/ voltage control is defined as voltage control mode [39], [43]. In this mode, the point 1 is considered for the FOPID-PODC. Moreover, governor response mode, up and down regulation, is selected as the active power/frequency control mode. Note that the variation of generators speed across the two areas is considered as the input signal of the FOPID-PODC [47]. Also, the time delay of the signal transmission among PMUs, PDC and FOPID-PODC is considered as constant time delay, T m , which is 100 ms [48].

B. TUNING OF PMU-BASED FOPID-PODC
One of the most important challenges of the FOPID controllers is their tuning. The presence of fractional-order parameters in the differential equation and a large number of parameters make it impossible to use conventional tuning methods.
So far, two methods have been used for the FOPID controller tuning in different power systems studies. The rule-based methods are based on approximation and numerical methods are based on optimization [49]. The first group is based on the approximation of the fractional-order  function to an integer-order function [49]. Another group uses the optimization algorithms by considering an objective function (OF) and determining the optimal values of the parameters [49].     integral of the time-weighted absolute error (ITAE) index, is considered as follows [50]: (12) where, N L denotes the number of loading conditions. Also, the ITAE index is as follows: where, t presents the time variable and t sim denotes the simulation time, which is 20 s in this paper [51]. In addition, e(t) is the error function. Note that there are several generators in the smart grid, so, the OF should consider the effect of all of them [52]. For this purpose, the sum of the speed deviation of the generators is considered as an error function, as follows [50], [52]: where, n G indicates the number of grid generators and ω G indicates the speed deviation of the generator G. The optimization is implemented by applying a large disturbance to the test system for three loading conditions. Therefore, a three-phase short circuit event at bus 8 is considered for 100 ms; because this event creates the most severe short-circuit current in the transmission lines of the test system. Table 2 presents the loading conditions. Note that the loading conditions are considered based on steady-state stability. For optimal adjustment of the FOPID-PODC, (12) must be minimized subject to parameters constraints listed in Table 3.
In this study, the TLBO algorithm is used for optimal tuning of the proposed controller [53], [54]. The optimization process is in accordance with the flowchart in Figure 11.
Also, Particle swarm optimization (PSO) algorithm and genetic algorithm (GA) were used to compare the   results [55], [56]. The results of the implementation of optimization algorithms are shown in Figure 12. As shown in this figure, the best value of the OF is obtained by the TLBO. Table 4 lists the best values of the OF obtained by the three algorithms. Also, Table 5 presents the optimal values of the FOPID-PODC parameters based on TLBO.

C. SIMULATION AND PERFORMANCE EVALUATION
In this section, scenarios are presented to evaluate the performance of the FOPID-PODC. The scenarios have been defined in such a way that they cause the LFOs in the grid. However, the severity of events is not the same. Note that, in conventional power systems, these events are caused by natural or technical reasons. In smart grids, system hacking and cyber-attacks can also cause these events. The scenarios are listed in Table 6.
To analyze the controller performance to damp the LFOs, the four mentioned scenarios are simulated for two modes with and without controller. The results are depicted in Figures 13 to 16.
As the simulation results indicate, the proposed controller has a good effect on LFOs damping. The results also show that the FOPID-PODC damps the frequency and voltage oscillations well.

1) GENERATION UNCERTAINTY OF LWPF
As mentioned in the introduction, one of the main challenges of REPPs is their production uncertainty [2], [3]. Although using the LWPF reduces this uncertainty, it cannot be ignored. Therefore, the performance of the LWPF for LFOs damping should be examined in conditions where the power generation     As the simulation results indicate, despite the reduction in the LWPF generation capacity, there is the necessary to damp the LFOs and the proposed FOPID-PODC is effective.

2) UNCERTAINTY OF TIME DELAY OF INPUT SIGNAL
One case, which must be considered in smart grids, is time delay of communication signals. Although with the development of communication infrastructures and the creation of new technologies in ICT, the amount of time delay is reduced, it cannot be ignored, as shown in Table 7 [57]. The time delay of the FOPID input signal may cause the controller malfunction [58]. To avoid this problem, the controller must have the necessary robustness against time delay uncertainty. In this subsection, the robustness of the FOPID-PODC of the LWPF in various time delays is investigated. As indicated in Figure 21, the proposed FOPID-PODC shows high robustness against different time delays of the input signal in four scenarios.

3) UNCERTAINTY OF SYSTEM LOADING
One of the most important uncertainties of power systems is system loading, which can affect the proper performance of equipment. Switching, relocating system loads, and outage of loads as well as adding new loads to the system are issues that undermine the certainty of the power system loading condition. Accordingly, it is necessary that the proposed FOPID-PODC has sufficient robustness against this type of uncertainty. So, the performance evaluation of the FOPID-PODC under different system loadings is required. As indicated in Figure 22, the proposed FOPID-PODC shows high robustness against 10% variation in system loading for four scenarios.
The results show the proper performance of LWPF to damp the LFOs. It can also be concluded that the proposed FOPID-PODC controller has sufficient robustness to some smart grid uncertainties.

VI. CONCLUSION
In smart grids, there is a great demand for electrical power generation by REPPs. In fact, the integration of REPPs is the foundation of future power systems. Despite all advantages of the REPPs, the uncertainty of electricity generation and generation fluctuations are the main challenges in the operation of this type of power plants. One way to meet this challenge, is to use LWPFs. This paper showed that with the widespread use of LWPFs around the world, these types of REPPs can well damp the LFO of modern power systems that is one of the main tasks of synchronous generators. For this purpose, in this paper, a PMU-based FOPID-PODC was proposed, which showed good performance in simulations compared to the conventional controllers.