# Frequency Regulation and Coordinated Control for Complex Wind Power Systems

Authors: Cheng Guo; Delin Wang
Journal: Complexity
 (2019)

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## Abstract

With the development of complex renewable energy systems, the frequency control and regulation of the power grid powered by such renewable energies (e.g., wind turbine) are more critical, since the adopted different power generators can lead to frequency variations. To address the frequency regulation of such power grids, we will present a variable coefficient coordinated primary frequency regulation scheme for synchronous generator (SG) and doubly fed induction generator (DFIG). The variable adjustment coefficient of DFIG is defined according to the current reserve capacity, which can be applied to adjust different operation conditions to regulate the frequency variation within a predefined allowable range. Since the DFIG can make full use of the reserve wind power in the system frequency regulation, the proposed method can address both the frequency regulation response and the economic performance. Simulation results indicate that the proposed coordinated control scheme can achieve satisfactory frequency regulation response and lead to reduced demand for frequency regulation of SG.


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## Body

## 1. Introduction

The wind power industry in all countries of the world is developing at a relatively fast speed. By 2050, 100% renewable energy can be supplied to the world, of which wind power accounts for 40% [1, 2]. This indicates that wind energy will gradually become the main source of renewable energy in the future. Today, wind power technology is relatively mature; however, wind power has a highly uncertain nature because wind speed is greatly affected by environmental conditions such as temperature and airflow changes. The connection of more wind power to power grid not only has many problems in the operation of the wind farm itself but also brings difficulties to the operation and regulation of the power grid [3, 4]. The traditional doubly fed induction generator- (DFIG-) based wind turbine does not have frequency regulation capability because its rotor speed is completely decoupled from the system frequency. Thus, the inertial response and frequency regulation capability of the power grid are influenced in this configuration. Nowadays, some wind power industries in developed countries have required that wind farms should have a certain frequency regulation capability by proposing advanced strategies. However, it is recognized that the adjustable frequency range of DIFG-based wind turbines is seriously limited by the wind speed [5]. Moreover, the wind power is usually included in the frequency regulation, making it a complicated process during the coordination with the traditional synchronous generators [6].To address the above issues, many efforts have been done to investigate the feasibility to incorporate wind power into power grid frequency regulation in recent years by developing advanced control strategies and frequency regulation schemes [7, 8]. In [9–11], the potential problems caused by the large-scale wind power integration were introduced, and the recent research progress of two essential related aspects, control strategy and frequency regulation capability, has been reviewed. In terms of DFIG control designs, the authors of [12–15] proposed using proportional, differential controller (PD controller) to construct a primary frequency regulation controller on the rotor side, where the corresponding converter was designed, so that DFIG can adapt quickly to the frequency changes induced in the system. Moreover, after developing speed control schemes, the authors of [16–18] proposed several composite frequency control schemes for variable speed wind turbines by combining the variable pitch control approaches and virtual inertial control methods. In [19], the variable droop is introduced to enhance the primary frequency contribution of wind turbine generators (WTG), and the droop parameter of every WTG is regulated to optimize the power output according to the reserve power margin available. In [20], a reduced-order model-based integrated controller method was suggested, which can provide inertial response and primary frequency control for WTG. This controller allows for a coupled control of torque and pitch angle at all speed range of DFIGs. In [21], simulation results indicate that the inertial term can be omitted, and the synthetic inertia strategy reduces to a very fast droop control strategy. It is noted that all the above-mentioned methods have been proposed from either the perspective of the wind farms or the internal control synthesis of wind turbines to study the possibility and validity of using wind power in the frequency regulation of power grid. However, when the wind power with variable frequency is incorporated into the power grid as a new type of frequency regulation power supply, the economic performance of the DFIG-based wind turbines and the ability of system frequency regulation should be considered simultaneously. Therefore, in order to obtain better power grid response and frequency modulation ability, it is necessary to coordinate the frequency regulation outputs between the DFIGs and the synchronous generators, according to the adjustable frequency capacity of DFIG-based wind turbines under different wind speeds. In fact, this idea has been recognized as one of emerging research topics as it can improve the wind frequency regulation.Inspired by the above discussion, this paper explores the feasibility of using DFIGs to implement frequency regulation from the point of view of the adjustment coefficient. We found that the adjustable frequency wind turbines can effectively undertake the frequency regulation responsibility of the power grid. We propose a coordinated primary frequency regulation strategy between the synchronous generators and the DFIG-based wind turbines by using the variable coefficients. The strategy considers the influence of wind speed variation upon DFIG’s wind energy acquisition and improves the maximum power point tracking (MPPT) [22, 23] operation mode of traditional DFIG. In the MPPT region, DFIG achieves deloading operation by controlling the rotor speed to deviate from MPPT operating point; in the constant power region, DFIG operates in deloading operation by controlling the pitch angle so as to reserve active power for DFIG to participate in primary frequency regulation of power grid. This strategy takes into account the frequency regulation ability and economic performance. In the allowable range of frequency variations, the DFIG can make full use of spare capacity to participate in the system frequency regulation. It can not only reduce the frequency regulation pressure of the synchronous generators but also reduce the wind power curtailment indirectly. Finally, the simulation result demonstrates the effectiveness of the proposed strategy. The main contribution of this paper is to introduce a variable coefficient coordinated frequency regulation for SG and DFIG, which can adapt to different operation conditions to make full use of the reserve wind power, and address both the frequency regulation response and the economic performance.The structure of this paper is described as follows: Section2 provides the system modeling and problem formulation. Section 3 presents the coordinated control scheme for generators. The coordinated frequency regulation strategy is given in Section 4, and numerical simulations are shown in Section 5. Finally, some conclusions are given in Section 6.


## 2. System Formulation and Problem Statement

In this paper, the studied system includes the synchronous generator (SG) and DFIG-based wind turbine generator (WTG). The connection structure between SG and WTG is shown in Figure1(a). The WTG system for primary frequency regulation consists of aerodynamics model, pitch angle control system as shown in Figure 1(b), DFIG with supplementary controller to realize inertial response, and lookup tables to compute maximum and deloading power.Figure 1
Structure of power system including wind turbines and main controller.
(a)
Wiring diagram of WTG and SG (b)
Improved pitch angle control structureIn Figure1(b),f is the current frequency, fN is the rated frequency, ω∗r is the expected angular velocity, ωr is the current angular velocity, β0 is the reserved pitch angle for load shedding, Kβ is the proportional coefficient, Tβ is the time constant of the controller, and βmax and βmin are the maximum and minimum limit of pitch angle. Compared with the traditional pitch angle control, the frequency response link of pitch angle is added, and the frequency deviation of power grid is used as input. By adjusting the pitch angle to respond to the frequency change, DFIG-based wind turbines can provide long-term power support for the power grid.A simplified aerodynamic model is used when the electrical behavior of the wind turbine is the main interest of the study. The relationship between the wind speed and the aerodynamic torque can be described as(1)TW=12ρπR3v2CPθ,λwhere Tw is the aerodynamic torque extracted from the wind, ρ is the air density,R is the wind turbine rotor radius, v is the equivalent wind speed, θ is the pitch angle of the rotor, λ is the tip speed ratio, and Cp is the aerodynamic efficiency of the rotor.Numerical approximations have been developed to calculateCp for given values of θ and λ. Here the following approximation is used as(2)CPθ,λ=0.22116λi-0.4θ-5.0e-12.5/λiwhere(3)λi=11/λ+0.08θ-0.035/θ3+1Actually, the dynamic characteristics of DFIG and power grid are decoupled in conventional MPPT control method; the wind turbines cannot respond to the system frequency changes. However, the rotational inertia stored in WTG is remarkable; hence, there exists the waste of rotational inertia of DFIG rotor on the traditional operation mode. However, if there is an appropriate operation condition, it can be fully released and utilized through proper control strategy to support the system stability. The aim of this paper is to develop a new control strategy for WTG to participate in the primary frequency regulation, and the coordinated control strategy between SG and DFIG for primary frequency regulation is explored.


## 3. Coordinated Control of Synchronous Generators and DFIG-Based Wind Turbines

### 3.1. Frequency Regulation Characteristics

According to the primary frequency regulation principle of SG, the adjustment coefficient, namely,RW, of the DFIG-based wind turbine is defined as(4)RW=-ΔfΔPWwhere ΔPW is the frequency regulation of DFIG and Δf is the frequency variation of system.When a synchronous generator and a DFIG-based wind turbine are connected in parallel, the relationship between the frequency regulation characteristic and the active power allocation among generators can be illustrated in Figure2. In the figure, ABD¯ represents the adjusting characteristic curve of the synchronous generator. ACE¯ represents that of the DFIG-based wind turbine. We suppose that the total load of the system is ΣPL, which is corresponding to the line segment CB¯ in the figure. When the system frequency is fN, the load carried by the synchronous generator is PG1, and the load carried by the wind turbine is PW1, such that(5)PG1+PW1=∑PLFigure 2
Frequency regulation characteristics of synchronous generator and DFIG-based wind turbine in parallel operation mode.After the system load increases ΔPL and then is stable atf1, the power output increase of the synchronous generator is ΔPG and the total generated power output is PG2; the power output increase of the wind turbine is ΔPW and the total power output is PW2. The sum of the increased power output of two generators is ΔP. According to Figure 1 and (4), we can obtain(6)ΔPG∗ΔPW∗=RW∗RG∗where ΔPG∗ and ΔPW∗ represent the per unit values of power output of the synchronous generator and DFIG-based wind turbine, respectively; RG∗ and RW∗ are the per unit values of adjustment coefficients of the synchronous generator and DFIG-based wind turbine, respectively.According to (6), when a synchronous generator and a DFIG are operated in parallel mode and the power increments of generators are retained at their respective per unit values, the power allocation between the SG and DFIG-based wind turbine is inversely proportional to the respective adjustment coefficients. That is, the generator with smaller adjustment coefficient has larger load increment, while the generator with larger adjustment coefficient has smaller load increment. Thus, the following can be concluded: (1) when a synchronous generator and a DFIG-based wind turbine run in parallel, the DFIG-based wind turbine participating in the frequency regulation can effectively reduce the frequency regulation pressure of the synchronous generator; (2) the frequency regulation output of the synchronous generator and DFIG-based wind turbine can be coordinated by adjusting the ratio of RG∗ to RW∗.


### 3.2. Coordinated Control Strategy after DFIG-Based Wind Turbine Connected to the Power Grid

In the primary frequency regulation, the frequency regulation output of the synchronous generator is given by(7)ΔP=-1R∗ΔffNPNwhere Δf is the system frequency deviation, fN is the system rated frequency, R∗ is the per unit value of adjustment coefficient, and PN is the rated capacity of the generator.When a DFIG andn synchronous generators are operated in parallel, according to (7), the adjustment equations are given as follows:(8)ΔPGi=-1Ri∗ΔffNPGiNi=1,2,…,n(9)ΔPW=-1RW∗ΔffNPWNwhere ΔPGi and ΔPW are the frequency regulation outputs of synchronous generator i and DFIG-based wind turbine, respectively; PGiN and PWN are the rated capacity of synchronous generatori and DFIG-based wind turbine, respectively.In the steady state, when the frequency variation of the whole system is Δf, the frequency regulation output of all generators in the system ΔPΣ can be calculated as(10)ΔPΣ=∑i=1nΔPGi+ΔPWFrom (8)-(10), we can obtain(11)ΔPΣ=-ΔffN∑i=1nPGiNRi∗+PWNRW∗If all generators involved in the system are replaced by an equivalent generator, the frequency regulation output of the system is(12)ΔPΣ=-1RΣ∗ΔffNPΣNwhere RΣ∗ is the equivalent adjustment coefficient and PΣN is the total capacity of the system. From (8) and (9), we can derive(13)-Δf∗=Ri∗ΔPGiPGiN=RW∗ΔPWPWN=RΣ∗ΔPΣPΣNBased on (11) and (12), one can further obtain(14)RΣ∗=PΣN∑i=1nPGiN/Ri∗+PWN/RW∗Equations (12) and (15) illustrate that, from the point of view of the whole power network, when the capacity connected to the system is a constant, the smaller adjustment coefficient of each parallel operation generator is, the smaller equivalent adjustment coefficient RΣ∗ of the system will be, and the larger unit power regulation is, the better ability of primary frequency regulation will be; on the contrary, the larger adjustment coefficient of each parallel operation generator is, the larger equivalent adjustment coefficient RΣ∗ of the system will be, and the smaller unit power regulation is, the weaker ability of primary frequency regulation will be. From (13), when the system load changes, the power of each generator can be determined as(15)ΔPi=RΣ∗ΔPΣPΣN×PGiNRi∗When the wind turbines that have no frequency regulation ability are connected to the power grid,PWN/RW∗≈0, and RW∗ goes to infinity. Then the remaining synchronous generators use differential control schemes. If more wind turbines with no frequency regulation ability replace traditional synchronous generators, which are connected to the power grid, then we know that PWN/RW∗=0 and RΣ∗ of the system will become larger. Hence, connecting the large-scale wind turbines with no frequency regulation ability to the power network will obviously reduce the frequency regulation capability of the system.


## 3.1. Frequency Regulation Characteristics

According to the primary frequency regulation principle of SG, the adjustment coefficient, namely,RW, of the DFIG-based wind turbine is defined as(4)RW=-ΔfΔPWwhere ΔPW is the frequency regulation of DFIG and Δf is the frequency variation of system.When a synchronous generator and a DFIG-based wind turbine are connected in parallel, the relationship between the frequency regulation characteristic and the active power allocation among generators can be illustrated in Figure2. In the figure, ABD¯ represents the adjusting characteristic curve of the synchronous generator. ACE¯ represents that of the DFIG-based wind turbine. We suppose that the total load of the system is ΣPL, which is corresponding to the line segment CB¯ in the figure. When the system frequency is fN, the load carried by the synchronous generator is PG1, and the load carried by the wind turbine is PW1, such that(5)PG1+PW1=∑PLFigure 2
Frequency regulation characteristics of synchronous generator and DFIG-based wind turbine in parallel operation mode.After the system load increases ΔPL and then is stable atf1, the power output increase of the synchronous generator is ΔPG and the total generated power output is PG2; the power output increase of the wind turbine is ΔPW and the total power output is PW2. The sum of the increased power output of two generators is ΔP. According to Figure 1 and (4), we can obtain(6)ΔPG∗ΔPW∗=RW∗RG∗where ΔPG∗ and ΔPW∗ represent the per unit values of power output of the synchronous generator and DFIG-based wind turbine, respectively; RG∗ and RW∗ are the per unit values of adjustment coefficients of the synchronous generator and DFIG-based wind turbine, respectively.According to (6), when a synchronous generator and a DFIG are operated in parallel mode and the power increments of generators are retained at their respective per unit values, the power allocation between the SG and DFIG-based wind turbine is inversely proportional to the respective adjustment coefficients. That is, the generator with smaller adjustment coefficient has larger load increment, while the generator with larger adjustment coefficient has smaller load increment. Thus, the following can be concluded: (1) when a synchronous generator and a DFIG-based wind turbine run in parallel, the DFIG-based wind turbine participating in the frequency regulation can effectively reduce the frequency regulation pressure of the synchronous generator; (2) the frequency regulation output of the synchronous generator and DFIG-based wind turbine can be coordinated by adjusting the ratio of RG∗ to RW∗.


## 3.2. Coordinated Control Strategy after DFIG-Based Wind Turbine Connected to the Power Grid

In the primary frequency regulation, the frequency regulation output of the synchronous generator is given by(7)ΔP=-1R∗ΔffNPNwhere Δf is the system frequency deviation, fN is the system rated frequency, R∗ is the per unit value of adjustment coefficient, and PN is the rated capacity of the generator.When a DFIG andn synchronous generators are operated in parallel, according to (7), the adjustment equations are given as follows:(8)ΔPGi=-1Ri∗ΔffNPGiNi=1,2,…,n(9)ΔPW=-1RW∗ΔffNPWNwhere ΔPGi and ΔPW are the frequency regulation outputs of synchronous generator i and DFIG-based wind turbine, respectively; PGiN and PWN are the rated capacity of synchronous generatori and DFIG-based wind turbine, respectively.In the steady state, when the frequency variation of the whole system is Δf, the frequency regulation output of all generators in the system ΔPΣ can be calculated as(10)ΔPΣ=∑i=1nΔPGi+ΔPWFrom (8)-(10), we can obtain(11)ΔPΣ=-ΔffN∑i=1nPGiNRi∗+PWNRW∗If all generators involved in the system are replaced by an equivalent generator, the frequency regulation output of the system is(12)ΔPΣ=-1RΣ∗ΔffNPΣNwhere RΣ∗ is the equivalent adjustment coefficient and PΣN is the total capacity of the system. From (8) and (9), we can derive(13)-Δf∗=Ri∗ΔPGiPGiN=RW∗ΔPWPWN=RΣ∗ΔPΣPΣNBased on (11) and (12), one can further obtain(14)RΣ∗=PΣN∑i=1nPGiN/Ri∗+PWN/RW∗Equations (12) and (15) illustrate that, from the point of view of the whole power network, when the capacity connected to the system is a constant, the smaller adjustment coefficient of each parallel operation generator is, the smaller equivalent adjustment coefficient RΣ∗ of the system will be, and the larger unit power regulation is, the better ability of primary frequency regulation will be; on the contrary, the larger adjustment coefficient of each parallel operation generator is, the larger equivalent adjustment coefficient RΣ∗ of the system will be, and the smaller unit power regulation is, the weaker ability of primary frequency regulation will be. From (13), when the system load changes, the power of each generator can be determined as(15)ΔPi=RΣ∗ΔPΣPΣN×PGiNRi∗When the wind turbines that have no frequency regulation ability are connected to the power grid,PWN/RW∗≈0, and RW∗ goes to infinity. Then the remaining synchronous generators use differential control schemes. If more wind turbines with no frequency regulation ability replace traditional synchronous generators, which are connected to the power grid, then we know that PWN/RW∗=0 and RΣ∗ of the system will become larger. Hence, connecting the large-scale wind turbines with no frequency regulation ability to the power network will obviously reduce the frequency regulation capability of the system.


## 4. Coordinated Strategy for Frequency Regulation

The primary frequency regulation control system coordinated by DFIGs and synchronous generators is shown in Figure2. The overall system consists of three control modules: (1) area A: in this area, the power is constant; then through tuning the pitch angle action system, the active power output of DFIGs can be adjusted to adapt the change of the system frequency; (2) area B: this area is the maximum power point tracking module. It can realize the ability of power reservation by switching the running profile of the DFIG and adjusting the active power of the DFIG to participate in the frequency regulation according to the tuning variable adjustment coefficient; (3) area C: this area is the coordinated control module for the synchronous generator. According to the system frequency deviation, we choose the corresponding adjustment coefficient and coordinate the frequency regulation output between the synchronous generators and DFIGs.


### 4.1. Control Strategy of Primary Frequency Regulation with DFIG-Based Turbine

In this paper, the traditional operation mode of DFIG is modified and improved. In the maximum power point tracking area, the DFIG controls deloading operation through increasing or reducing the rotor speed. While in the constant power area, it can reserve the active power by adjusting the pitch angle, so that the DFIG has the frequency regulation capacity.


#### 4.1.1. Maximum Power Point Tracking Control

Inspired by the principle of synchronous generator speed governor, a primary frequency regulation controller attached to the rotor side converter of a wind turbine is designed in this paper. We make the DFIG-based wind turbine whose load is reduced by 20% operate at the current wind speed, which is shown in area A in Figure3. In this figure, ωr is the corresponding rotor speed at the current wind speed, Popt′ is the suboptimal power when the wind turbine’s load is reduced by 20%, Rω is the adjustment coefficient of the DFIG maximum power point tracking module,f is the real-time frequency of the system, fN is the rated frequency of the system,K1 is the gain value, ΔPω is the frequency regulation power of DFIG-based wind turbine corresponding to the system frequency variation, and PΣ is the sum of suboptimal power Popt′ and frequency regulation power ΔPω.Figure 3
Primary coordinated frequency regulation structure of DFIG and synchronous generator.For the wind turbines, the frequency regulation power corresponding to the frequency variation is(16)ΔPω=-ΔfRω=ΔfΔf0P0DFIG-based wind turbines can participate in the frequency regulation as the traditional synchronous generators if the variable adjustment coefficient is tuned at the maximum power point tracking area, and the adjustment coefficient can be adjusted automatically according to the current wind speed to determine the amount of frequency regulation power.


#### 4.1.2. Control Strategy in Power Constant Area

In this paper, we introduce the regulation coefficient of the pitch angle. Through improving the traditional pitch angle control system, the DFIG can also realize the function of deloading reservation in the power constant area to respond to the system frequency variation. In the constant power area, deloading operation of DFIG can be achieved by presetting the pitch angleβ0, which is calculated by the following equation:(17)1-d%0.44sin⁡πλc-315=0.44-0.0167β0sin⁡πλc-315-0.3β0-0.00184λc-3β0where the tip speed ratio of DFIG-based wind turbine is defined as λc=Rωmax/v.According to the principle of synchronous generator governor, we design the controller of pitch angle for area B as shown in Figure3. In the figure, βω is the pitch angle of the DFIG-based wind turbine when the power is constant. Δf is the difference between the system’s current frequency f and the rated frequency fN. Rβ is the static adjustment coefficient of pitch angle.K2 is the gain value. In the power constant area, the improved pitch angle control system enables DFIG to adapt to the current wind speed by adjusting the pitch angle according to its characteristic.When the DFIG-based wind turbine is involved in the frequency regulation, the movement range of pitch angle is(18)Δβ=-ΔfRβ=ΔfΔf0β0In the constant power area, the variable adjustment coefficient between the pitch angle and the frequency characteristic is introduced and tuned. DFIG-based wind turbines can respond to the system frequency variation through changing mechanical power captured by the DFIG according to the variation of system frequency. Thus, DFIG is able to participate in the frequency adjustment process.


### 4.2. Coordinated Strategy of Primary Frequency Regulation between DFIG and Synchronous Generator

For the system with multiple generators, the frequency adjustment can be coordinated and achieved by those generators which have frequency regulation ability. When DFIG-based wind turbines are connected to the system, it is necessary for the traditional generators to detect the inclusion of these new generators. When the system frequency changes, part of the frequency regulation power will be allocated to the wind turbines according to the wind speed [24, 25] and the induced frequency deviation. Therefore, it is necessary to divide the frequency regulation region of the system according to the magnitude of the system frequency deviation.The control and coordination strategies of the synchronous generators are shown in area C in Figure2. The basic methods are summarized as follows.( 1 ) When the system is in the normal operation region and the frequency deviation is within the allowable range (0.2 Hz), if DFIG-based wind turbines are used in the frequency regulation and deloading operation, it will lead to a wind power curtailment and reduction of the wind power’s economic efficiency. In general, the adjustment coefficient of SG is between 0.03 and 0.05. In this case, in order to reduce the frequency regulation output of SGs, we set the regulation coefficient RG to 0.05, so that the more reserved power of DFIG-based wind turbines will be used for the frequency regulation and the “abandoned air” will be reduced. In particular, in the power constant area, the reserved power of DIFG-based wind turbines is larger, and thus the adjustable frequency power output will be increased as well.( 2 ) The frequency deviation is large when the system is in the emergency regulatory area. In order to make the system run stably and accelerate the recovery of system frequency, the synchronous generators and DFIG-based wind turbines should be used in the system frequency regulation as much as possible. The adjustment coefficient of the synchronous generator is usually set to 0.03, so that the DFIGs participate in the system frequency regulation as much as possible according to the current wind speed.The above-mentioned coordinate control strategies for the studied system with DFIGs and synchronous generator can be implemented by using the following steps:( 1 ) Measure the system frequency and calculate the frequency variations( 2 ) If the frequency variation is larger than 0.2 Hz, we set the adjustment coefficient of the SG as 0.03; otherwise, we set the adjustment coefficient of the SG as 0.05( 3 ) Measure the rotor’s speed ωr of the DIFG under the current wind speed( 4 ) If ωr > ωmax, we can calculate the pitch adjusting coefficient Rβ in the constant area based on (17) and then apply the obtained Rβ to the pitch operation system( 5 ) If ωr ≤ ωmax, we can calculate the pitch adjusting coefficient Rω in the maximum power tracking area based on (17) and then apply the obtained Rω to the pitch operation system( 6 ) Calculate the primary frequency regulation of the synchronous generator, ΔPG, based on the result of Step (2) and the primary frequency regulation of DFIG, ΔPW, based on Step (4) or (5). Then we obtain the total frequency regulation of the system as ΔPΣ=ΔPG+ΔPW.The practical implementation of the proposed algorithm can be found in Figure4.Figure 4
Flow chart of the proposed algorithm.


## 4.1. Control Strategy of Primary Frequency Regulation with DFIG-Based Turbine

In this paper, the traditional operation mode of DFIG is modified and improved. In the maximum power point tracking area, the DFIG controls deloading operation through increasing or reducing the rotor speed. While in the constant power area, it can reserve the active power by adjusting the pitch angle, so that the DFIG has the frequency regulation capacity.


### 4.1.1. Maximum Power Point Tracking Control

Inspired by the principle of synchronous generator speed governor, a primary frequency regulation controller attached to the rotor side converter of a wind turbine is designed in this paper. We make the DFIG-based wind turbine whose load is reduced by 20% operate at the current wind speed, which is shown in area A in Figure3. In this figure, ωr is the corresponding rotor speed at the current wind speed, Popt′ is the suboptimal power when the wind turbine’s load is reduced by 20%, Rω is the adjustment coefficient of the DFIG maximum power point tracking module,f is the real-time frequency of the system, fN is the rated frequency of the system,K1 is the gain value, ΔPω is the frequency regulation power of DFIG-based wind turbine corresponding to the system frequency variation, and PΣ is the sum of suboptimal power Popt′ and frequency regulation power ΔPω.Figure 3
Primary coordinated frequency regulation structure of DFIG and synchronous generator.For the wind turbines, the frequency regulation power corresponding to the frequency variation is(16)ΔPω=-ΔfRω=ΔfΔf0P0DFIG-based wind turbines can participate in the frequency regulation as the traditional synchronous generators if the variable adjustment coefficient is tuned at the maximum power point tracking area, and the adjustment coefficient can be adjusted automatically according to the current wind speed to determine the amount of frequency regulation power.


### 4.1.2. Control Strategy in Power Constant Area

In this paper, we introduce the regulation coefficient of the pitch angle. Through improving the traditional pitch angle control system, the DFIG can also realize the function of deloading reservation in the power constant area to respond to the system frequency variation. In the constant power area, deloading operation of DFIG can be achieved by presetting the pitch angleβ0, which is calculated by the following equation:(17)1-d%0.44sin⁡πλc-315=0.44-0.0167β0sin⁡πλc-315-0.3β0-0.00184λc-3β0where the tip speed ratio of DFIG-based wind turbine is defined as λc=Rωmax/v.According to the principle of synchronous generator governor, we design the controller of pitch angle for area B as shown in Figure3. In the figure, βω is the pitch angle of the DFIG-based wind turbine when the power is constant. Δf is the difference between the system’s current frequency f and the rated frequency fN. Rβ is the static adjustment coefficient of pitch angle.K2 is the gain value. In the power constant area, the improved pitch angle control system enables DFIG to adapt to the current wind speed by adjusting the pitch angle according to its characteristic.When the DFIG-based wind turbine is involved in the frequency regulation, the movement range of pitch angle is(18)Δβ=-ΔfRβ=ΔfΔf0β0In the constant power area, the variable adjustment coefficient between the pitch angle and the frequency characteristic is introduced and tuned. DFIG-based wind turbines can respond to the system frequency variation through changing mechanical power captured by the DFIG according to the variation of system frequency. Thus, DFIG is able to participate in the frequency adjustment process.


## 4.1.1. Maximum Power Point Tracking Control

Inspired by the principle of synchronous generator speed governor, a primary frequency regulation controller attached to the rotor side converter of a wind turbine is designed in this paper. We make the DFIG-based wind turbine whose load is reduced by 20% operate at the current wind speed, which is shown in area A in Figure3. In this figure, ωr is the corresponding rotor speed at the current wind speed, Popt′ is the suboptimal power when the wind turbine’s load is reduced by 20%, Rω is the adjustment coefficient of the DFIG maximum power point tracking module,f is the real-time frequency of the system, fN is the rated frequency of the system,K1 is the gain value, ΔPω is the frequency regulation power of DFIG-based wind turbine corresponding to the system frequency variation, and PΣ is the sum of suboptimal power Popt′ and frequency regulation power ΔPω.Figure 3
Primary coordinated frequency regulation structure of DFIG and synchronous generator.For the wind turbines, the frequency regulation power corresponding to the frequency variation is(16)ΔPω=-ΔfRω=ΔfΔf0P0DFIG-based wind turbines can participate in the frequency regulation as the traditional synchronous generators if the variable adjustment coefficient is tuned at the maximum power point tracking area, and the adjustment coefficient can be adjusted automatically according to the current wind speed to determine the amount of frequency regulation power.


## 4.1.2. Control Strategy in Power Constant Area

In this paper, we introduce the regulation coefficient of the pitch angle. Through improving the traditional pitch angle control system, the DFIG can also realize the function of deloading reservation in the power constant area to respond to the system frequency variation. In the constant power area, deloading operation of DFIG can be achieved by presetting the pitch angleβ0, which is calculated by the following equation:(17)1-d%0.44sin⁡πλc-315=0.44-0.0167β0sin⁡πλc-315-0.3β0-0.00184λc-3β0where the tip speed ratio of DFIG-based wind turbine is defined as λc=Rωmax/v.According to the principle of synchronous generator governor, we design the controller of pitch angle for area B as shown in Figure3. In the figure, βω is the pitch angle of the DFIG-based wind turbine when the power is constant. Δf is the difference between the system’s current frequency f and the rated frequency fN. Rβ is the static adjustment coefficient of pitch angle.K2 is the gain value. In the power constant area, the improved pitch angle control system enables DFIG to adapt to the current wind speed by adjusting the pitch angle according to its characteristic.When the DFIG-based wind turbine is involved in the frequency regulation, the movement range of pitch angle is(18)Δβ=-ΔfRβ=ΔfΔf0β0In the constant power area, the variable adjustment coefficient between the pitch angle and the frequency characteristic is introduced and tuned. DFIG-based wind turbines can respond to the system frequency variation through changing mechanical power captured by the DFIG according to the variation of system frequency. Thus, DFIG is able to participate in the frequency adjustment process.


## 4.2. Coordinated Strategy of Primary Frequency Regulation between DFIG and Synchronous Generator

For the system with multiple generators, the frequency adjustment can be coordinated and achieved by those generators which have frequency regulation ability. When DFIG-based wind turbines are connected to the system, it is necessary for the traditional generators to detect the inclusion of these new generators. When the system frequency changes, part of the frequency regulation power will be allocated to the wind turbines according to the wind speed [24, 25] and the induced frequency deviation. Therefore, it is necessary to divide the frequency regulation region of the system according to the magnitude of the system frequency deviation.The control and coordination strategies of the synchronous generators are shown in area C in Figure2. The basic methods are summarized as follows.( 1 ) When the system is in the normal operation region and the frequency deviation is within the allowable range (0.2 Hz), if DFIG-based wind turbines are used in the frequency regulation and deloading operation, it will lead to a wind power curtailment and reduction of the wind power’s economic efficiency. In general, the adjustment coefficient of SG is between 0.03 and 0.05. In this case, in order to reduce the frequency regulation output of SGs, we set the regulation coefficient RG to 0.05, so that the more reserved power of DFIG-based wind turbines will be used for the frequency regulation and the “abandoned air” will be reduced. In particular, in the power constant area, the reserved power of DIFG-based wind turbines is larger, and thus the adjustable frequency power output will be increased as well.( 2 ) The frequency deviation is large when the system is in the emergency regulatory area. In order to make the system run stably and accelerate the recovery of system frequency, the synchronous generators and DFIG-based wind turbines should be used in the system frequency regulation as much as possible. The adjustment coefficient of the synchronous generator is usually set to 0.03, so that the DFIGs participate in the system frequency regulation as much as possible according to the current wind speed.The above-mentioned coordinate control strategies for the studied system with DFIGs and synchronous generator can be implemented by using the following steps:( 1 ) Measure the system frequency and calculate the frequency variations( 2 ) If the frequency variation is larger than 0.2 Hz, we set the adjustment coefficient of the SG as 0.03; otherwise, we set the adjustment coefficient of the SG as 0.05( 3 ) Measure the rotor’s speed ωr of the DIFG under the current wind speed( 4 ) If ωr > ωmax, we can calculate the pitch adjusting coefficient Rβ in the constant area based on (17) and then apply the obtained Rβ to the pitch operation system( 5 ) If ωr ≤ ωmax, we can calculate the pitch adjusting coefficient Rω in the maximum power tracking area based on (17) and then apply the obtained Rω to the pitch operation system( 6 ) Calculate the primary frequency regulation of the synchronous generator, ΔPG, based on the result of Step (2) and the primary frequency regulation of DFIG, ΔPW, based on Step (4) or (5). Then we obtain the total frequency regulation of the system as ΔPΣ=ΔPG+ΔPW.The practical implementation of the proposed algorithm can be found in Figure4.Figure 4
Flow chart of the proposed algorithm.


## 5. Simulations

In order to verify the effectiveness of the proposed frequency regulation strategy, we use Matlab/Simulink to carry out simulations, where the simulated model includes 4-generator and 2-area power grid [26]. The structure of this test system is shown in Figure 5. The power grid model consists of 3 traditional synchronous generators with a rated power of 700MW, and the inertial time constant is 6.5s. In addition, a DFIG-based wind turbine with equivalent capacity 800×15MW is connected to bus 2; the upper limit of active power per unit is 1, and the capacities of load L1 and L2 are 1200MW and 1800MW, respectively. The variable pitch time constant of the wind turbine is 3s and the rated wind speed is 12m/s. In the model, the DFIG-based wind turbine is operated in the condition of reducing 20% load, and there is a load jump on L1 at the time of 40s. In practical situations, wind farm participating in frequency regulation is generally selected in rich wind area. Moreover, when the scale of wind farm is very large, the gathering effect of wind energy is also significant as it can decrease the fluctuation of wind speed and output power. Accordingly, the wind speed becomes flatter. In this paper, the major focus is on the feasibility analysis of participation of wind turbine in frequency regulation; hence, we select a constant wind speed in the simulation. In this simulation, the output active power of DFIG and SG is per unite value based on SB.Figure 5
The structure of 2-area test system.


### 5.1. Load Variation in Maximum Power Point Tracking Area

Two cases are simulated in this study: (a) the frequency variation is less than 0.2 Hz and (b) the frequency variation is larger than 0.2 Hz.In case (a), the wind speed is set to 9m/s. At the time of 40s, the applied load suddenly increases by 300MW, and then the frequency has a deviation less than 0.2Hz. The adjustment coefficients of the SG,RG, are set to 0.03, 0.04, and 0.05, respectively. The corresponding simulation results are shown in Figure 6.Figure 6
Simulation results of the maximum power tracking area when frequency change is less than 0.2Hz.
(a)
Frequency variation (b)
Output of synchronous generators (c)
Output of DFIG-based wind turbine (d)
Pitch angle variationIn Figure6, we find that the frequency regulation output of the SG is gradually reduced as long as the adjustment coefficient increases (Figure 6(b)), while the frequency regulation output of the DFIG-based wind turbine is gradually increased (Figure 6(c)). From the point of view of the system frequency recovery, the frequency recovery response is the best when we set RG=0.03 as shown in Figure 6(a). However, if the adjustment coefficient of the SG is small, the frequency regulation output of DFIG is limited as shown in Figure 6(c). When we set RG=0.05, the frequency can also be retained within a bound around 0.2Hz, and the system frequency is relatively stable. Therefore, in order to increase the frequency regulation output of the DFIG-based wind turbines as much as possible and make full use of the restored power of the DFIG-based wind turbine for frequency regulation, we can take RG=0.05. The pitch angle variation is also shown in Figure 6(d). The fluctuations shown in Figure 6 are due to the fact that the system is operated in the MTTP area and the frequency variation is larger than 0.2 Hz, so that it will take some transient periods to achieve a new steady state because of the limited control effect of ∆f.In case (b), the wind speed is also 9m/s. At the time of 40s, the applied load suddenly increases by 600MW; the frequency has a deviation larger than 0.2Hz. The adjustment coefficients of the synchronous generator are also the same as (a). The corresponding simulation results are shown in Figure7. According to Figure 7(a), the frequency recovery response is the best when we set RG=0.03. When the frequency change is greater than 0.2Hz, the system is in the emergency frequency modulation stage, and the ultimate goal is to improve the frequency recovery effect of the system. All synchronous generators and DFIGs should output power as much as possible, which are shown in Figures 7(b) and 7(c). According to the frequency recovery effect of Figure 7(a) and the pitch angle variation shown in Figure 7(d), the adjustment coefficient of the synchronous machine should be set as RG=0.03.Figure 7
Simulation curves of the maximum power tracking area when frequency change is greater than 0.2Hz.
(a)
Frequency variation (b)
Output of synchronous generators (c)
Output of DFIG-based wind turbine (d)
Pitch angle variation


### 5.2. Load Variation in Constant Power Area

Two cases at the constant power areas are simulated in this study: (a) the frequency variation is larger than 0.2 Hz, and (b) the frequency variation is less than 0.2Hz.In case (a), in the constant power area, the wind energy captured by DFIG is mainly regulated by adjusting the pitch angle controlled by the pitch control mechanism. The wind speed is set as 15m/s. At the time of 40s, the load suddenly increases by 600MW; then the frequency has a deviation more than 0.2Hz. The adjustment coefficients of SG,RG, are set as 0.03, 0.04, and 0.05 respectively. The simulation results are shown in Figure 8.Figure 8
Simulation diagram of the power constant area when frequency variation is greater than 0.2Hz.
(a)
Output of synchronous generators (b)
Output of synchronous generators (c)
Output of synchronous generators (d)
Pitch angle variationIn Figure8, when RG is set as 0.03, the frequency recovery performance is the best among these three cases and the frequency deviation can be retained within a bound 0.02Hz as shown in Figure 8(a). Because the frequency deviation is more than 0.2Hz at one period during the process of frequency recovery, the magnitude of the frequency deviation is larger than the normal value. Thus, the system enters in the emergency control phase. In order to make the system frequency recover better, the DFIG-based wind turbine can make full use of the restored power for frequency regulation when the power is constant, the wind speed is fast, and the DFIG has much reserved power. From the frequency recovery result in Figure 8(a), when we take RG=0.03, the DFIG-based wind turbine and synchronous generators can participate in the frequency regulation as much as possible (Figure 8(b)). Figure 8(c) also shows that the output of DFIG wind turbines has reached the upper limit of active power per unit. Thus, we can put 20% of the reserved power into the frequency regulation as a part of the frequency regulation power, such that the minimum value of the frequency drop and the steady-state deviation responses have been significantly improved. Figure 8(d) provides the corresponding pitch angle variation.In case (b), the wind speed is set as 15m/s. At the time of 40s, the load suddenly increases by 300MW; the frequency has a deviation less than 0.2Hz. The adjustment coefficients of SG,RG, are set to 0.03, 0.04, and 0.05, respectively. The simulation results are shown in Figure 9. When the system frequency is reduced within 0.2Hz, the frequency can be restored well when RG = 0.03, 0.04, and 0.05 according to the frequency variation in Figure 9(a). Figure 9(d) shows that when RG = 0.05, the action range of pitch angle is the largest, reaching 2.8°, and the reserve power of DFIG released amounts to 0.07 pu (Figure 9(b)), which reduces the steady-state frequency deviation of the system to 0.15 Hz. This shows that the DFIG effectively reduces the power change rate of SG in the initial stage of frequency change (Figure 9(c)) and can continuously provide active power effective support for power grid.Figure 9
Simulation diagram of the power constant area when frequency variation is less than 0.2Hz.
(a)
Frequency variation (b)
Output of synchronous generators (c)
Output of DFIG-based wind turbine (d)
Pitch angle variationIn the process of frequency modulation, the reserve power of DFIG can be fully used for frequency regulation by increasing the power output of DFIG, thus indirectly reducing the wind abandonment. The simulation results of Figure9 show that when the frequency varies within the allowable range, the larger the RG value is, the smaller the static adjustment coefficient Rβ of pitch angle will be. The range of pitch angle action will be larger, and the frequency regulation capability of DFIG will be enhanced, so that it can undertake more power output and further reduce the steady-state frequency deviation of power grid.


## 5.1. Load Variation in Maximum Power Point Tracking Area

Two cases are simulated in this study: (a) the frequency variation is less than 0.2 Hz and (b) the frequency variation is larger than 0.2 Hz.In case (a), the wind speed is set to 9m/s. At the time of 40s, the applied load suddenly increases by 300MW, and then the frequency has a deviation less than 0.2Hz. The adjustment coefficients of the SG,RG, are set to 0.03, 0.04, and 0.05, respectively. The corresponding simulation results are shown in Figure 6.Figure 6
Simulation results of the maximum power tracking area when frequency change is less than 0.2Hz.
(a)
Frequency variation (b)
Output of synchronous generators (c)
Output of DFIG-based wind turbine (d)
Pitch angle variationIn Figure6, we find that the frequency regulation output of the SG is gradually reduced as long as the adjustment coefficient increases (Figure 6(b)), while the frequency regulation output of the DFIG-based wind turbine is gradually increased (Figure 6(c)). From the point of view of the system frequency recovery, the frequency recovery response is the best when we set RG=0.03 as shown in Figure 6(a). However, if the adjustment coefficient of the SG is small, the frequency regulation output of DFIG is limited as shown in Figure 6(c). When we set RG=0.05, the frequency can also be retained within a bound around 0.2Hz, and the system frequency is relatively stable. Therefore, in order to increase the frequency regulation output of the DFIG-based wind turbines as much as possible and make full use of the restored power of the DFIG-based wind turbine for frequency regulation, we can take RG=0.05. The pitch angle variation is also shown in Figure 6(d). The fluctuations shown in Figure 6 are due to the fact that the system is operated in the MTTP area and the frequency variation is larger than 0.2 Hz, so that it will take some transient periods to achieve a new steady state because of the limited control effect of ∆f.In case (b), the wind speed is also 9m/s. At the time of 40s, the applied load suddenly increases by 600MW; the frequency has a deviation larger than 0.2Hz. The adjustment coefficients of the synchronous generator are also the same as (a). The corresponding simulation results are shown in Figure7. According to Figure 7(a), the frequency recovery response is the best when we set RG=0.03. When the frequency change is greater than 0.2Hz, the system is in the emergency frequency modulation stage, and the ultimate goal is to improve the frequency recovery effect of the system. All synchronous generators and DFIGs should output power as much as possible, which are shown in Figures 7(b) and 7(c). According to the frequency recovery effect of Figure 7(a) and the pitch angle variation shown in Figure 7(d), the adjustment coefficient of the synchronous machine should be set as RG=0.03.Figure 7
Simulation curves of the maximum power tracking area when frequency change is greater than 0.2Hz.
(a)
Frequency variation (b)
Output of synchronous generators (c)
Output of DFIG-based wind turbine (d)
Pitch angle variation


## 5.2. Load Variation in Constant Power Area

Two cases at the constant power areas are simulated in this study: (a) the frequency variation is larger than 0.2 Hz, and (b) the frequency variation is less than 0.2Hz.In case (a), in the constant power area, the wind energy captured by DFIG is mainly regulated by adjusting the pitch angle controlled by the pitch control mechanism. The wind speed is set as 15m/s. At the time of 40s, the load suddenly increases by 600MW; then the frequency has a deviation more than 0.2Hz. The adjustment coefficients of SG,RG, are set as 0.03, 0.04, and 0.05 respectively. The simulation results are shown in Figure 8.Figure 8
Simulation diagram of the power constant area when frequency variation is greater than 0.2Hz.
(a)
Output of synchronous generators (b)
Output of synchronous generators (c)
Output of synchronous generators (d)
Pitch angle variationIn Figure8, when RG is set as 0.03, the frequency recovery performance is the best among these three cases and the frequency deviation can be retained within a bound 0.02Hz as shown in Figure 8(a). Because the frequency deviation is more than 0.2Hz at one period during the process of frequency recovery, the magnitude of the frequency deviation is larger than the normal value. Thus, the system enters in the emergency control phase. In order to make the system frequency recover better, the DFIG-based wind turbine can make full use of the restored power for frequency regulation when the power is constant, the wind speed is fast, and the DFIG has much reserved power. From the frequency recovery result in Figure 8(a), when we take RG=0.03, the DFIG-based wind turbine and synchronous generators can participate in the frequency regulation as much as possible (Figure 8(b)). Figure 8(c) also shows that the output of DFIG wind turbines has reached the upper limit of active power per unit. Thus, we can put 20% of the reserved power into the frequency regulation as a part of the frequency regulation power, such that the minimum value of the frequency drop and the steady-state deviation responses have been significantly improved. Figure 8(d) provides the corresponding pitch angle variation.In case (b), the wind speed is set as 15m/s. At the time of 40s, the load suddenly increases by 300MW; the frequency has a deviation less than 0.2Hz. The adjustment coefficients of SG,RG, are set to 0.03, 0.04, and 0.05, respectively. The simulation results are shown in Figure 9. When the system frequency is reduced within 0.2Hz, the frequency can be restored well when RG = 0.03, 0.04, and 0.05 according to the frequency variation in Figure 9(a). Figure 9(d) shows that when RG = 0.05, the action range of pitch angle is the largest, reaching 2.8°, and the reserve power of DFIG released amounts to 0.07 pu (Figure 9(b)), which reduces the steady-state frequency deviation of the system to 0.15 Hz. This shows that the DFIG effectively reduces the power change rate of SG in the initial stage of frequency change (Figure 9(c)) and can continuously provide active power effective support for power grid.Figure 9
Simulation diagram of the power constant area when frequency variation is less than 0.2Hz.
(a)
Frequency variation (b)
Output of synchronous generators (c)
Output of DFIG-based wind turbine (d)
Pitch angle variationIn the process of frequency modulation, the reserve power of DFIG can be fully used for frequency regulation by increasing the power output of DFIG, thus indirectly reducing the wind abandonment. The simulation results of Figure9 show that when the frequency varies within the allowable range, the larger the RG value is, the smaller the static adjustment coefficient Rβ of pitch angle will be. The range of pitch angle action will be larger, and the frequency regulation capability of DFIG will be enhanced, so that it can undertake more power output and further reduce the steady-state frequency deviation of power grid.


## 6. Conclusions

In this paper, we presented a control strategy for system with the wind turbines being incorporated into the frequency regulation by further tailoring the primary frequency regulation principle of traditional synchronous generators. The DFIG can provide inertial power support to the power grid and participate in the frequency regulation together with the synchronous generators. Through theoretical analysis and simulation verifications, the following conclusions can be obtained:( 1 ) The wind turbines with adjustable frequency can effectively undertake the frequency regulation responsibility of the power grid, and the frequency regulation output between the synchronous generators and the DFIG-based wind turbines can be coordinated and allocated by adjusting RG∗ and RW∗.( 2 ) The variable difference coefficient of DFIG in different wind speed sections is defined and calibrated. In corresponding to the wind speed changes in real time, the frequency regulation output can be determined considering the current reserved capacity.( 3 ) Through coordinating the frequency regulation output between the DFIG and the synchronous generators, the frequency deviation is retained within the allowable ranges, and the resorted power of the DFIG-based wind turbine can be used for the frequency regulation as much as possible. Those proposed methods can not only meet the demand of the power network frequency regulation but also minimize the “abandoned air” generated by the DIFG load reduction.Future work will focus on validating the proposed coordinate and control strategies under more realistic wind speed and operation scenarios.



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*Source: 8525397-2019-05-16.xml*