1. Introduction
Renewable energy sources (RESs) are being increasingly implemented into power grids to realize sustainable energy generation systems. Photovoltaic generators (PVs) and Type III and IV wind turbine generators (WTGs) are typically connected to the grid via inverters. These inverter-based resources (IBRs) can help reduce the usage of fossil-fuel-based thermal power generators; however, they decrease system inertia. Low-inertia systems are vulnerable to disturbances, which can reduce the stability of the power supply. Consequently, virtual inertia control (VIC), which emulates the behavior of a machine or generator with rotational inertia in an IBR, was proposed to increase inertia [
1,
2].
VIC can be theoretically applied to the inverter to establish the grid connection of the IBR regardless of the type of DC-side power source (e.g., battery energy storage, PV, and WTG). However, the performance of the VIC partially deteriorates when it is implemented in PVs and WTGs based on the operating condition and the structure of the control system.
For WTGs, there are two types of VIC implementations without additional energy storage. The first is a combination with the de-loading operation [
3,
4]. Typically, the output of the WTG is maximized according to the wind conditions such that it does not exceed the rated output. Consequently, the output cannot be increased for an inertial response emulation by the VIC. De-loading (i.e., the intended decrease in output) can be implemented to accommodate for the increasing output. The acceleration and deceleration of the wind turbine (WT) and an increase in the pitch angle of the blades are effective means of achieving headroom. The pitch angle control is adopted for primary frequency control reserve from [
5], and for the headroom for droop-based grid-forming control from [
6]. The hybrid methodology of over-speeding and pitch angle control is also proposed in [
7,
8]. In these implementations, the VIC can change the WTG output within the reserved capacity, and its effectiveness is expected to be equivalent to that of the VIC embedded in the battery energy storage for disturbances despite the decrease in the capacity ratio of the WTG.
The second type of implementation involves temporarily using the stored energy in the WT and capacitor in the DC-link for the inertial response emulation. The release of the stored energy decreases the rotating frequency of the WT and DC-link voltage and ultimately leads to the loss of operation. To avoid this, the process of recovering the energy loss must be driven after the VIC response. In [
9,
10], the WTG output is controlled to decrease the stepwise after the output increase by VIC with a pre-determined time constant. Ref. [
11] adopts ramp change in the output decrease. In [
12], the output decrease for the recovering is triggered by a specified magnitude of decrease in the rotating frequency. The recovery of the operational condition of WTG can be obtained owing to the controllers typically embedded in the WTG, maximum power point tracking (MPPT), and pitch angle control. Since the behavior of these controllers depends on the wind condition, the recovery process also depends on it. The control system of the WTG is divided into four modes based on the wind condition as Regions 1–4 [
13,
14,
15];
- −
Region 1: Stopped (Wind speed is lower than the cut-in wind speed),
- −
Region 2: MPPT operation (Wind speed is between the cut-in and rated wind speed),
- −
Region 3 Rated output operation (Wind speed is between the rated and cut-out wind speed),
- −
Region 4: Stopped (Wind speed is larger than the cut-out wind speed).
The WTG does not generate power when the wind speed is less than the cut-in wind speed (Region 1) or larger than the cut-out wind speed (Region 4). In Region 2, where the wind speed is greater than the cut-in value and smaller than the rated value, the output of the WTG is maximized by the MPPT. Lastly, in Region 3, the wind speed lies between the rated value and cut-out value, where the output and rotating frequency of the WT is maintained at the rated values by adjusting the pitch angle. The MPPT and the pitch angle controller are functions holding the operational point (i.e., the output and rotating frequency of the WT) at a specified point under a certain wind speed. Therefore, they can help in returning the operation state of the WTG to the nominal state after the VIC responds to the disturbance.
In Region 2, the MPPT helps in the recovery of the operational state. The active power reference is switched from the VIC to MPPT when the rotating frequency of the WT drops to the specified value in [
16]. In [
17,
18], the active power reference is gradually changed to MPPT depending on the rotating frequency. In [
19], the active power reference of the VIC is given as the MPPT curve increased by the amount of the inertial response to be emulated. In the VIC proposed in [
20,
21], the MPPT recovers the operation state after the VIC supplies the inertial response without switching, owing to the difference in the time constant between the VIC and MPPT. In [
22,
23,
24], the DC-link voltage control recovers the energy released from the DC-link capacitance by inertial response emulation. Refs. [
25,
26] propose the hybrid method that MPPT and DC-link voltage control contribute to the recovery. The recovery process possibly deteriorates the performance of the VIC since it cancels out the output change produced by the VIC to compensate for the loss of energy. Ref. [
20] demonstrates that increasing the time constant in MPPT such that it does not lead to the loss of operation can effectively improve the frequency regulation capability of the VIC. However, the criteria required to ensure the success of the recovery process have not been demonstrated thus far.
The recovery process in Region 3 varies from that in Region 2. The energy released from the WT is compensated by increasing the energy captured from the wind by decreasing the pitch angle. The performance of the VIC is not expected to deteriorate significantly since the change in the output of the WTG produced by the VIC does not need to be pulled back rapidly. However, previous studies conducted in this field have not analyzed the influence of pitch angle control on the VIC, although [
20] analyzes the influence of MPPT on the performance of the VIC in Region 2 in detail. Therefore, in this study, to clarify the performance of the VIC-embedded WTG in Region 3, the effect of pitch angle control on the frequency-regulating capability of the VIC-embedded WTG in Region 3 was analyzed from a theoretical perspective as novel research, and a simulation was then performed to verify this theoretical estimation. The key parameters (i.e., the wind speed, MPPT time constant, and control gain of the pitch angle control) were changed in wide ranges, and the boundary of the success of the recovery process was clarified. Furthermore, the influence of the MPPT in Region 2 was also analyzed for a wide range of responsivity, and the operation stabilities of Regions 2 and 3 were compared.
The power system model in the simulation comprises two synchronous generators with a speed governor and voltage controller and a WTG with a virtual synchronous machine (VSM), which comprises a VIC algorithm, pitch angle control, and MPPT. The frequency stability and operation stability of the WTG are evaluated for the disturbance of the trip of a synchronous generator, while the control parameters of the MPPT, pitch angle control, and wind speed are varied.
2. Model of Wind Power Generation with Virtual Inertia Control
Figure 1 shows the configuration of the WTG model used in the simulation, which is developed proprietary with [
27,
28] for the WTG model, MPPT, and pitch angle control. The wind turbine is connected to a permanent magnet synchronous generator (PMSG), and full-rated back-to-back converters are used to establish the grid connection. This is called a Type-IV or Type-D connection [
27,
28]. The converter on the WT side is designated as the rotor-side converter (RSC), and that on the other side is designated as the grid-side converter (GSC). The VSM is embedded in the GSC, and the RSC contributes to the DC-voltage regulation.
2.1. Wind Turbine
The output power of the wind turbine,
, is expressed as follows:
where
denotes the air density,
denotes the wind turbine radius,
denotes the power coefficient, and
denotes the wind speed.
is defined as the ratio of the wind turbine output to the power of the wind, and it depends on the pitch angle,
, and tip-speed ratio,
.
is expressed as follows [
27]:
where
denotes the angular frequency of the wind turbine.
Figure 2 depicts the operational point of the 2.5 MW-rated WTG, whose specifications are listed in
Table 1. The WTG comprises four different regions of operation, as described in
Section 1. In Region 2, the output increases with the increase in the wind speed since the wind energy also increases. In Region 3, the output is constant at the rated output of the WTG regardless of the wind speed.
Figure 3 presents the power curves of the WTG based on the wind speed and MPPT profile, which is a trajectory of the maximum power point (MPP) at each wind speed. Here, the pitch angle,
, is zero to extract the maximum energy from the wind. The power curves are described based on (1), (2), and (3). The MPPT-profile curve can be derived by solving
. The tip speed ratio and power coefficient at the MPP,
and
, are constant, regardless of the wind speed, and are given as follows:
The MPPT-profile
is determined from Equations (1), (3)–(5) by eliminating the wind speed,
, as follows:
In Region 2, the operation point of the wind turbine is set at the MPP based on the variation of the wind speed. The pitch angle is maintained at zero, as explained above. In Region 3, the operational point of the WTG is maintained at the rated output and angular frequency by adjusting the pitch angle.
2.2. Wind Turbine Controller
The left part of
Figure 1 depicts the wind turbine controller, which comprises an MPPT function and a pitch angle controller. There are various types of MPPTs [
29]; in this study, we adopted the power feedback method, in which the reference of the WT output,
, is updated based on Equation (6) by measuring the angular frequency,
.
The output reference of the GSC, , is determined via a PI controller such that the output of the PMSG, , converges to the reference from the MPPT function, . The first lag component with the time constant, , was intentionally added in series with the PI controller to adjust the response of the MPPT. If the MPPT has fast responsivity, the operational point of the WTG is strongly held to the MPP, and the inertial response of the VSM is suppressed. The lag component is used to ensure the appropriate VSM performance.
The pitch angle control is activated when the angular frequency of the WT exceeds the rated value, and it changes the pitch angle of the blades of the wind turbine from 0° to 90° to ensure that the angular frequency converges to the rated value. The controller also contains a ramp limiter to prevent a rapid change in the pitch angle.
2.3. Rotor Side Converter (RSC) Control
The center part of
Figure 1 depicts the RSC controller, which comprises the DC-link voltage and reactive power control blocks in the outer loop and current control in the inner loop. The d-axis current reference,
, is computed by the PI-based DC-link voltage controller. The q-axis current reference,
, is computed by a reactive power controller. The current controller presents basic functionalities [
30], and the d and q-axis currents are controlled to the reference value without interference.
2.4. Grid Side Converter (GSC) Control
The right side of
Figure 1 depicts the GSC controller, which comprises a VSM and grid voltage controller in the outer loop and a current controller in the inner loop. The virtual impedance block is the interface between the inner and outer loops. The VSM is designed based on the equation of motion of the synchronous generator, also known as the swing equation, which is expressed as follows:
where
,
, and
denote the inertia constant, damping constant, and deviation of the angular frequency from the nominal value of the virtually simulated synchronous generator in the control system, respectively. The reference to the rotor angle,
, represents the output of the VSM and corresponds to the phase angle of the internal induced voltage. The magnitude of the internal voltage,
, is determined by the grid voltage control, in which the voltage at the point of interconnection (POI),
, is maintained at the reference value, which is modified via the droop controller. The voltage reference is converted to the current reference,
, in the virtual impedance block, as shown below:
Here, the bold face indicates the phasor expression. and denote the resistance and reactance components of the virtual impedance, respectively. In the VSM algorithm, the voltage source with the emulated internal voltage, , is assumed to be connected to the POI with voltage, , via the virtual impedance, .
The active power reference signal of the GSC, , is input to the VSM as the virtual mechanical input. Subsequently, the output of the GSC, , follows in the steady state, whereas the virtual inertial response is added in the transient state after the fault occurrence. In the GSC controller, the virtual rotor angle reference, , is used as a reference for Park’s transformation. A phase-locked loop (PLL) is not used in this case since is computed in the VSM block. This is one of the main requirements for grid-forming inverters.
3. Influence of Wind Turbine Control on the VSM Performance
When the VSM mounted in the GSC responds to a disturbance, such as when a generator trips, the change in the active power of the GSC reduces the DC voltage and the rotating frequency of the WT since the change in the GSC output is provided by the electrostatic energy stored in the capacitance of the DC circuit and the kinetic energy of the WT. The decrease in the rotating frequency leads to a decrease in the output of the wind turbine corresponding to the power curve, and the rotating frequency is further decreased. This negative cycle can completely halt the operation of the WTG.
However, the MPPT and the pitch angle control can recover the operational point to one before the disturbance occurs.
Figure 4a depicts an instance of the recovery process in Region 2. When the VSM increases the WTG output in the event of a generator trip, the rotating frequency of the WT,
, decreases with the decrease in the mechanical output,
(A->B). Simultaneously, the MPPT decreases the output reference,
, along with the MPPT profile (A->C), and the PMSG output,
, follows
over time, corresponding to the time constant of the MPPT. Since the input of the PMSG becomes larger than the output, the PMSG starts accelerating to the initial operational point (B->A) based on the dynamics of the PMSG:
where
denotes the inertia constant of the WT,
denotes the gear ratio at the gear box, and
denotes the number of pole pairs of PMSG. The large time constant of the MPPT causes a loss of operation of the WTG.
Figure 4b depicts the recovery process in Region 3. Assuming the same event described in Region 2,
and
are first decreased (A→B). The pitch angle control responds to the change and decreases the pitch angle,
, based on the logic shown in
Figure 1, leading to the increase in
(B→C). The WT accelerates (C→D), and when
exceeds the rated value,
, the pitch angle control increases
to decrease
(D→E) and decelerate WT (E→A). Since the pitch angle changes in conjunction with the rotating frequency of the WT, the locus of the operational point is expected to be close to a solid line, as shown in
Figure 4b. The operational point returns to the initial point while describing the spiral if the pitch angle control responds quickly to the change in the rotating frequency of the WT.
The recovery process in Region 3 has not been discussed in previous research. This paper logically indicates how the pitch angle control contributes to the process based on the characteristics of the WTG, MPPT, and the pitch angle control. The following simulation study is performed to confirm that the operational point can be restored as explained above and to explain its dependencies on the MPPT, pitch angle control, and wind speed.
6. Conclusions
This study analyzed the performance of a wind turbine generator with a virtual synchronous machine (WTG-VSM). We primarily focused on the influence of the wind speed and control parameters of the MPPT and pitch angle control in the event of a frequency drop caused by a tripped generator. The WTG-VSM can provide an inertial response like a synchronous generator by using the rotating energy in the WT, but the consumed energy must be restored to avoid a loss of operation of WTG. The MPPT and pitch angle control were originally provided with a function that holds a specified operational state in the constant wind speed condition. They are expected to help in recovering the operational state after the VSM responds to the disturbance.
The theoretical consideration based on the characteristics of the WTG and simulation demonstrates that the MPPT and pitch angle control basically contribute to recovering the energy released from the WT for the inertial response emulation by the VSM. Furthermore, it is observed that the VSM performance during short-term frequency regulation immediately after a disturbance can be improved by slowing down the responsivity of the MPPT and the pitch angle control. Conversely, the slow response of those controllers deteriorates the long-term frequency regulation capability of the VSM since the energy released from the WT increases as the response slows down. Additionally, the simulation demonstrates that the recovery process fails and the operation of the WTG stops if the responsivity is set considerably slow.
Those findings indicate that the parameters of VSM, MPPT, and pitch angle control need to be tuned considering the interaction among them to maintain the stable operation of the WTG and maximize the VSM performance. The results of the research are expected to be a guideline for that. On the other hand, determining the optimal parameterization and criteria for the stability of the operation was a considerable challenge. The verification of the simulation results through an experimental study is also important for future work.