**1. Introduction**

Traditionally, synchronous generators have provided frequency control reserves, which are released under power imbalance conditions to recover grid frequency [1]. In fact, any generationdemand imbalance leads the grid frequency to deviate from its nominal value, which can cause serious scale stability problems [2]. With the significant penetration of renewables, mainly wind power plants, a proportional capacity of the system reserves must be provided by these new resources [3]. In this way, reference [4] considers that wind power plant participation in grid frequency control is imminent. However, wind turbines usually include back-to-back converters, and they are electrically decoupled from the grid through power electronic converters [5]. Consequently, with the significant integration of wind power into power systems, grid frequency tends to degrade progressively due to the reduction of the grid inertial responses [6]. Therefore, this new scenario presents a preliminary reduction of reserves from conventional generation units, mainly in weak and/or isolated power systems with high renewable resource penetration [7,8]. Moreover, these problems would be exacerbated in micro-grids, with a high share of power-electronically interfaced and thus a low grid inertia [9,10]. Under this framework, frequency control strategies must be included in wind power plants to provide additional

active power under disturbances [11]. These new strategies would allow us to integrate Variable Speed Wind Turbines (VSWTs) into these services, replacing conventional power plants by renewables [12] and maintaining a reliable power system operation [13]. Most of the proposed strategies for VSWTs are based on 'hidden inertia emulation', enhancing their inertia response [14–16]. According to the specific literature, '*Fast power reserve emulation*' has been proposed as a suitable solution. It is based on supplying the kinetic energy stored in the rotating masses to the grid as an additional active power, being subsequently recovered through an under-production period (recovery) [17–19]. Different studies can be found to discuss the definition of overproduction period and the transition from overproduction to recovery period [20–25]. These studies are mainly focused on analyzing the inertia reduction problem on isolated power systems [20,21,23–27]. However, there is a lack of contributions focused on large interconnected power systems with high wind power penetration [28]. These new scenarios are in line with current wind generation units, covering more than 20% in different power systems. Moreover, renewables have accounted for more than 50% at different times in some European countries such as Spain, Portugal, Ireland, Germany or Denmark [29].

In general, synchronous generators inherently release or absorb kinetic energy as an inertial response to imbalance situations [24]. However, to recover the grid frequency at the nominal value, an additional control system is needed as well [30]. Automatic Generation Control (AGC) is thus considered as one of the most important ancillary services in power systems. AGC is used to match the total generation with the total demand, including power system losses [31]. Over the last decade, different authors have proposed several control strategies and optimization techniques. A modified AGC for an interconnected power system in a deregulated environment is described in [32]. A similar contribution can be found in [33], where an energy storage system is added to a multi-area power system, and the *I* controller gains are optimized by using the Opposition-based Harmony Search algorithm. A teaching-learning process based on an optimization algorithm to tune both *I* and *PID* controller parameters in single and multi-area power systems is described in [34]. In [35], a hybrid fuzzy PI controller is proposed for AGC of multi-area systems, yielding significant improvements compared to previous approaches. In [36], the gray wolf optimization method is proposed to tune the controller gains of an interconnected power system. This solution presented a more suitable tuning capability than other population-based optimization techniques. An optics inspired optimization algorithm is proposed in [37] and compared to other optimization algorithms, reaching a better performance for maximum overshoot and settling time values. However, in these contributions, only thermal, gas and hydro-power plants are considered from the supply side [32–36]. Therefore, multi-area power system modeling by including wind power plants are required to simulate frequency excursions under power imbalance conditions. Consequently, and by considering previous contributions, this paper analyzes different power imbalance situations and the corresponding frequency deviations in a multi-area interconnected power system with high wind power penetration. The main contributions of the paper are summarized as follows:


The rest of the paper is organized as follows: Section 2 presents the frequency control strategy for VSWTs. The implemented multi-area interconnected power system is described in Section 3. The results are provided and widely discussed in Section 4. Finally, the conclusions are presented in Section 5.

#### **2. Improving Frequency Control Strategy of Wind Turbines**

According to the specific literature, different methods for VSWTs have been proposed to provide frequency control. Figure 1 summarizes the corresponding solutions to be implemented in wind power plants: (i) de-loading, (ii) droop control and (iii) inertial response [47]. With regard to de-loading control methods, they are based on operating VSWTs below their optimal generation point. A certain amount of active power reserve is thus available to supply additional generation under a contingency [48]. It can be implemented by regulating the pitch angle from *βmin* to a maximum value or by increasing the rotational speed above the Maximum Power Point Tracking (MPPT) speed (over-speeding) [49]. An extension of de-loading strategy applied to Photovoltaic system (PV) taking into account a percentage of the PV power production for back-up reserve can be found in [50]. Secondly, droop control solutions have a significant influence on the frequency minimum value (nadir) and the frequency recovery [51]. The controller is based on considering the torque/power-set point as a function of the frequency excursion (Δ*f*) and the rate of change of frequency (ROCOF) [52–56]. Finally, 'hidden inertia' controllers introduce a supplementary loop into the active power control. This additional loop control is only added under frequency deviations. Both blades and rotor inertia are then used to provide primary frequency response. Different approaches can be found in the specific literature. One solution is based on emulating similar inertia response to conventional generation units, shifting the torque/power reference proportionally to the ROCOF [51,57–60]. Another study uses the fast power reserve emulation. Constant overproduction power is released from the kinetic energy stored in the rotating mass of the wind turbine, with the rotational speed being recovered later through an underproduction period [17,20,21,25,47,61].

**Figure 1.** Wind power plant frequency control: general overview [28,47].

In line with previous contributions, the frequency control strategy for VSWTs implemented in this work is based on the fast power reserve emulation technique developed by the authors in [25]. This approach improves an initial proposal described in [61], by minimizing frequency oscillations and smoothing the wind power plant frequency response. Three operation modes are considered: normal operation mode, overproduction mode and recovery mode, see Figure 2. Different active power (*Pcmd*) values are determined aiming to restore the grid frequency under power imbalance conditions. Figure 2b depicts the VSWTs active power variations (Δ*PWF*) submitted to an under-frequency excursion, being Δ*PWF* = *Pcmd* − *PMPPT*(<sup>Ω</sup>*MPPT*).

**Figure 2.** Wind frequency control strategy and VSWTs' active power variation (Δ*PWF*) [25]; (**a**) frequency control strategy used for VSWTs; (**b**) Δ*PWF* with frequency control strategy.

1. *Normal operation mode*. The VSWTs operate at a certain active power value (*Pcmd*), according to the available mechanical power for a specific wind speed, *Pmt*(<sup>Ω</sup>*WT*). It matches the maximum available active power for this current wind speed *PMPPT*(*VW*); see Figure 2a,

$$P\_{\rm cmd} = P\_{\rm mt}(\Omega\_{\rm WT}) = P\_{\rm MPPT}(V\_{\rm W}).\tag{1}$$

Under power imbalance conditions, and assuming an under-frequency deviation, the frequency controller strategy changes to the overproduction mode and, subsequently, Δ*f* < −<sup>Δ</sup>*flim* → Overproduction.

2. *Overproduction mode*. The active power supplied by the VSWTs involves (i) mechanical power *Pmt* available from the *Pmt*(<sup>Ω</sup>*WT*) curve and (ii) additional active power Δ*POP* provided by the kinetic energy stored in the rotational masses,

$$P\_{cmd} = P\_{mt}(\Omega\_{WT}) + \Delta P\_{OP}(\Delta f). \tag{2}$$

Δ*POP* is estimated proportionally to the evolution of frequency excursion in order to emulate primary frequency control of conventional generation units [26,62]. Most previous approaches assume Δ*POP* as a constant value independent of the frequency excursion [22,23,61]. Moreover, the mechanical power *Pmt* is also considered as constant by most authors, even when rotational speed decreased [20–24,61]. This overproduction strategy remains active until one of the following conditions is met: the frequency excursion disappears, the rotational speed reaches a minimum allowed value, or the commanded power is lower than the maximum available active power,

$$
\begin{pmatrix}
\Delta f & > -\Delta f\_{lim} \\
\Omega\_{WT} & < \Omega\_{WT,min} \\
P\_{cmd} & < P\_{MPPT}(\Omega\_{MPPT})
\end{pmatrix} \to \text{Recovery.}\tag{3}
$$

3. *Recovery mode*. With the aim of minimizing frequency oscillations, wind power plants have to move from overproduction mode to recovery mode as smoothly as possible, avoiding abrupt power changes and, subsequently, undesirable secondary frequency shifts [20,22,24,61]. With this aim, the authors' solution described in [25] follows the mechanical power curve *Pmt*(<sup>Ω</sup>*WT*) according to the wind speed instead of the maximum power curve *PMPPT*(<sup>Ω</sup>*WT*) [22]. The power provided by the VSWTs in this mode is based on two periods according to [25]: (i) a parabolic trajectory and (ii) following the *PMPPT* curve proportional to the difference between *Pmt*(<sup>Ω</sup>*WT*) and *PMPPT*(<sup>Ω</sup>*WT*). The normal operation mode then can be recovered when either Ω*MPPT* or *PMPPT*(<sup>Ω</sup>*MPPT*) are respectively reached by the wind turbine.

This strategy was evaluated in [25] and compared to [61] for single-are power system modeling, providing an improved frequency response under power imbalance conditions. This approach is considered in the present paper and extended to a multi-area power system with significant wind power integration into different areas.

#### **3. Power System Modeling**

## *3.1. General Overview*

Traditional power system modeling for frequency deviation analysis under imbalance conditions is usually based on the following expression [63],

$$
\Delta f = \frac{1}{2 \ H\_{eq} \text{ s} + D\_{eq}} \cdot (\Delta P\_{\%} - \Delta P \text{L}),
\tag{4}
$$

where Δ*f* is the frequency variation from nominal system frequency, *Heq* is the equivalent inertia constant of the system, *Deq* is the equivalent damping factor of the loads, and Δ*Pg* − Δ*PL* is the power imbalance. *Heq* is estimated from Equation (5), *Hm* is the inertia constant of *m*-power plant, *SB*,*<sup>m</sup>* is the rated power of the *m*-generating unit, *CG* is the total number of conventional synchronous generators and *SB* is the base power system:

$$H\_{cq} = \frac{\sum\_{m=1}^{CG} H\_m \cdot S\_{B,m}}{S\_B} \,. \tag{5}$$

Transmission level voltage is usually considered for multi-area interconnection purposes through tie-lines. Frequency and tie-line power exchange can vary according to variations in power load demand [64–68]. The total tie-line power exchange between two areas is determined by

$$
\Delta P\_{lie\_{i\bar{j}}} = \frac{2 \cdot \pi \cdot T\_{i\bar{j}}}{s} \cdot (\Delta f\_{\bar{i}} - \Delta f\_{\bar{j}}),
\tag{6}
$$

where *Ti*,*<sup>j</sup>* is the synchronizing moment coefficient of the tie-line between *i* and *j* areas.

When a frequency deviation is detected, the balance between an interconnected power system is determined by generating the Area Control Error signal (*ACE*), expressed as a linear combination of the tie-line power exchange and the frequency deviation [69]

$$ACE\_i = B\_i \cdot \Delta f\_i + \sum\_{\substack{j=1 \\ j \neq i}}^N \Delta P\_{tic\_{i,j'}} \tag{7}$$

where *i*, *j* refers to *i* and *j* areas, respectively, *B* is the bias-factor, Δ*Ptie* is the variation in the exchanged tie-line power and *N* is the total number of interconnected areas. Figure 3 schematically shows these power exchanges for a three-area power system example. Recent contributions focused on a new control logic of the Balancing Authority Area Control Error Limit (BAAL) Standard adopted in the North American power grid can be found in [70].

**Figure 3.** Multi-area power system. (**a**) balanced situation; (**b**) imbalanced situation in Area 1.

## *3.2. Supply-Side Modeling*

From the supply-side, the power systems considered for simulation purposes involve conventional generating units (such as non-reheat thermal and hydro-power) and renewable energy sources (wind and PV power plants). One equivalent generator is used for each type of production to model the supply-side. This assumption is in line with previous contributions focused on frequency strategy control analysis.

The conventional generating unit models considered for simulations can be seen in Figure 4. Taking into account the specific literature, they are modeled according to the simplified governor-based models widely used and proposed in [62]. Parameters are provided in Tables 1 and 2, respectively. The different transfer functions of governor and turbine are indicated in Figure 4.

**Figure 4.** Conventional generation modeling. (**a**) thermal plant model; (**b**) hydro-power plant model.

**Table 1.** Thermal power plant parameters [62].



**Table 2.** Hydro-power plant parameters [62].

Wind power plants are able to provide frequency response according to the strategy discussed in Section 2. An aggregated model for wind power plants is considered for the simulation purposes. They are represented by one equivalent generator, which is generally accepted in the specific literature for frequency response simulations (Figure 5). The equivalent wind turbine has *n*-times the size of each individual wind turbine, with *n* being the number of wind turbines [71,72]. The equivalent wind turbine model is based on [73,74], which have been widely used in recent publications [22,23,25,75–77]. Parameters are shown in Table 3. The remaining renewable generation is modeled through an equivalent PV power plant connected to the grid. It represents a renewable non-dispatchable energy source, following recent contributions [78]. Due to the short period of simulated time (under 5 min), a constant active power provided by this non-dispatchable resource is considered for our analysis.

**Figure 5.** Aggregated wind power plant model with frequency controller.



## *3.3. Area Descriptions*

Figure 6 summarizes the percentages for the different generating units of each area. Previous studies address the problem of multi-area power systems considering only conventional power plants (mainly thermal, hydro-power and gas) and assuming two or three areas [32–36,38–41]. In this work, two different interconnected multi-source power systems are analyzed: (i) a two-area power system (considering only Areas 1 and 2) and (ii) a three-area power system. Both systems allow us to study in detail the relationships between the number of areas and the exchanged power between them when a significant number of renewable energies are considered from the supply-side. A base power of 2000 MW per area is assumed that corresponds to the capacity of each area. In Europe, it is expected that wind and PV will cover up to 30% and 18% of the demand respectively by 2030 [79,80]. Therefore, the integration of these sources in the areas considered in this paper are in line with current European road-maps, having a RES/non-dispatchable integration lying between 25% to 50%. In addition, Δ *Ptiei*,*<sup>j</sup>* is limited to a maximum value of 10%. This limit agrees with recent EU-wide targets, which expect to have an interconnection power of 10% in the year 2020 [46]. Most contributions found in the literature review either do not limit the maximum tie-line power, or it is not indicated [81–84].

**Figure 6.** Generation contribution per area. (**a**) Area 1; (**b**) Area 2; (**c**) Area 3.

*Ti*,*<sup>j</sup>* and *B* values are provided in Table 4 for the two-interconnected areas [30,35] and in Table 5 for three-interconnected areas [30]. The equivalent inertia *Heq* of each area is calculated according to Equation (5), and taking into account the inertia constants of thermal and hydro-power plants indicated in Section 3.2. With regard to the damping factor, the impact of an inaccurate value is relatively small if the power system is stable [85]. Moreover, it is expected to decrease accordingly to the use of variable frequency drives [86]. Table 6 summarizes different values proposed for the damping factor in the literature over recent decades. A value of *Deq* = 1 is considered for simulation purposes, which is in line with recent contributions and is lower than values corresponding to previous works. A general overview of a two-area power system can be seen in Figure 7.




**Table 5.** Interconnected three-area power system parameters [30].



**Figure 7.** Two-area power system modeling for frequency control.
