Constant Voltage Model of DFIG-Based Variable Speed Wind Turbine for Load Flow Analysis

Abstract

At present, the penetration of wind-driven electric generators or wind power plants (WPPs) in electric power systems is getting more and more extensive. To evaluate the steady state performances of such power systems, developing a valid WPP model is therefore necessary. This paper proposes a new method in modeling the most popular type of WPP, i.e., DFIG (doubly fed induction generator)-based WPP, to be used in power system steady state load flow analysis. The proposed model is simple and derived based on the formulas that calculate turbine mechanical power and DFIG power. The main contribution of the paper is that, in contrast to the previous models where the DFIG power factor has been assumed to be constant at unity, the constant voltage model proposed in this paper allows the power factor to vary in order to keep the voltage at the desired value. Another important contribution is that the proposed model can be implemented in both sub-synchronous and super-synchronous conditions (it is to be noted that most of the previous models use two different mathematical models to represent the conditions). The case study is also presented in the present work, and the results of the study confirm the validity of the proposed DFIG model.

1. Introduction

The application of variable speed wind turbines for electricity generation has been increasing in recent years. This increasing application is mainly because a variable speed WPP can extract wind energy in a more optimal way than a fixed speed WPP. Variable speed operation of a WPP can be achieved through the use of DFIG or PMSG (permanent magnet synchronous generator) as its main energy converter. However, currently, the DFIG application is more popular because it costs less than PMSG [1,2]. In the operation of the DFIG, two different control modes (i.e., power factor control mode and voltage control mode) are often adopted. In power factor control mode, the DFIG power factor is kept constant during operation, while the voltage magnitude varies within allowable limits. On the other hand, in voltage control mode, the voltage magnitude is kept constant, and the DFIG power factor is allowed to vary to keep the voltage at desired value [3,4,5,6].

To be able to study or analyze power systems embedded with WPP, modeling of the power system components, including the WPP, is necessary. In power system load flow analysis, a traditional power plant is usually modeled as a PV bus model. However, since the WPP does not have the capability of controlling active power output, this PV bus model is no longer applicable for WPP. Therefore, in order that the analysis can properly be carried out and the system steady state performances can correctly be assessed, formulation and development of the WPP model are necessary.

In the context of WPP steady state load flow model, several interesting techniques have been proposed. References [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18], for example, report some of the recent methods. In [7,8,9], multiple-node models of asynchronous generator-based WPP for load flow analysis are proposed. By applying the proposed methods in [7,8,9], a conventional load flow solver can be employed to solve the load flow problem. However, input data to the load flow solver needs to be modified to incorporate the WPP data. References [10,11,12,13,14,15] discuss various steady state models of fixed speed WPP for load flow analysis. In the method [10,11,12,13,14,15], the developed mathematical model is combined with the load flow formulation of a system without WPP. The combined equations are then simultaneously solved using some iterative techniques to obtain the solution to the load flow problem.

References [4,5,6,16,17,18] propose several models of DFIG-based WPP for load flow analysis. In [4], a three-phase model of DFIG to be used in unbalanced distribution system load flow (DSLF) analysis is proposed. Reference [5] proposes an iterative technique to integrate DFIG in load flow analysis. The proposed model in [5] is developed based on the DFIG equivalent circuit. In [6], a framework for incorporating DFIG-based WPP in load flow analysis of distribution systems has been proposed. The proposed model in [6] is also developed based on the DFIG equivalent circuit, and the forward–backward sweep technique has been employed to obtain the load flow solution. A steady-state model of DFIG-based variable speed WPP for three-phase load flow analysis is investigated and presented in [16]. The sequence components theory has been used in deriving the proposed model. Refs. [17,18] proposes a simple technique for modeling DFIG-based WPP to be used in power system steady-state load flow studies. Development of the WPP model in [17,18] is carried out based only on power formulations of the WPP.

Table 1. Previously published models of DFIG-based WPP.

Ref.	Model Description	Notes
[4]	Based on analytical representation of wind turbine, voltage source converters, and wound rotor induction machine	▪ Unity power factor (UPF) operation ▪ For balanced and unbalanced systems
[5]	Based on equivalent circuit of DFIG	▪ UPF operation, and two models are needed to represent sub- and super-synchronous speeds ▪ For balanced systems
[6]	Based on equivalent circuit of DFIG	▪ UPF operation, and two models are needed to represent sub- and super-synchronous speeds ▪ For balanced systems
[17]	Based on sequence components	▪ UPF operation, and two models are needed to represent sub- and super-synchronous speeds ▪ For balanced and unbalanced systems
[18]	Based on WPP power formulations	▪ UPF operation ▪ For balanced systems
[19]	Based on WPP power formulations	▪ UPF operation ▪ For balanced systems

summarizes the previously published models of DFIG-based WPP for load flow analysis.

In this paper, a new steady state model of DFIG-based WPP for load flow analysis is proposed. Similar to the model in [17,18], in the present work, derivation of the proposed mathematical model is also based on the DFIG power formulas and turbine mechanical power formula. The process of the model development is relatively straightforward, and therefore, the resulted model is quite simple and can easily be incorporated into the power system load flow analysis. The main contributions of the present work can be described as follows: (i) In contrast to the model in [4,5,6,16,17,18], where DFIG power factor has been assumed to be constant at unity, the constant voltage model proposed in this paper allows the power factor to vary to keep the voltage at the desired value; (ii) The proposed model can be implemented in both sub-synchronous and super-synchronous conditions (it is to be noted that references [5,6,16] use two different mathematical models to represent the conditions).

2. DFIG-Based WPP

The basic structure of a DFIG-based WPP is shown in Figure 1 [3,17,18,19,20,21]. In Figure 1, P_m is turbine power, P_S and Q_S are stator powers, P_R and Q_R are rotor powers, and P_g and Q_g are WPP output powers. Moreover, in Figure 1, RSC and GSC stand for rotor side converter and grid side converter, respectively. As mentioned earlier, the DFIG system is normally operated at a constant voltage magnitude or a constant power factor. In constant voltage operation mode, the DFIG terminal voltage magnitude is kept constant during operation. However, in constant power factor operation mode, the DFIG power factor is held constant during operation. In this mode, three power factors (i.e., unity, leading, and lagging power factors) are usually adopted in the operation. In unity power factor mode, the reactive power in the stator of WRIG (wound rotor induction generator) is zero (or Q_g = 0); therefore, there is no reactive power exchange between the WPP and power grid. In lagging power factor mode, the DFIG absorbs reactive power from the power grid (or Q_g is negative). On the other hand, in leading power factor mode, the DFIG delivers reactive power to the power grid (or Q_g is positive), and, consequently, can support the system reactive power demand and voltage profile improvement.

Figure 2 and Figure 3 show the steady state equivalent circuits of WRIG [3,17,18,19,20,21]. To include turbine mechanical power and rotor power in the WRIG equivalent circuit, the equivalent circuits in Figure 2 and Figure 3 are modified to those given in Figure 4 and Figure 5 [3,18,19,20,21,22]. In the figures, V_S and I_S are stator voltage and current, V_R and I_R are rotor voltage and current, R_S and X_S are stator resistance and reactance, R_R and X_R are rotor resistance and reactance, R_c and X_m are core circuit resistance and reactance, S_S is stator complex power, I_M is core circuit current, and s is WRIG slip. Based on Figure 4 and Figure 5, the following formulas that calculate turbine mechanical power and rotor power can be shown to be valid:

$$P_m=\left[V_R{I}_R^{*}-R_R{I}_R{I}_R^{*}\right]\frac{1-s}{s}$$

(1)

and:

$$P_R+js{Q}_R=V_R{I}_R^{*}$$

(2)

where Q_R is, as mentioned before, the reactive power produced by the DFIG rotor seen from the stator side.

Furthermore, by looking at Figure 1, the WPP active power output is DFIG stator active power minus DFIG rotor power, or:

$$P_g=P_S-P_R$$

(3)

and the WPP reactive power output is:

$$Q_g=Q_S$$

(4)

Based on Figure 2, Figure 3, Figure 4 and Figure 5, the electrical power in DFIG stator is:

$$S_S=P_S+j{Q}_S=V_S{I}_S^{*}$$

(5)

3. Modeling of DFIG-Based WPP

The proposed constant voltage model of DFIG-based WPP will be developed based on the formulas described in Section 2. On using (2) and (3) in (4) and (5), the formulas of WPP active and reactive power outputs become:

$$P_g=Re(V_S{I}_S^{*})-Re(V_R{I}_R^{*})$$

(6)

$$Q_g=Im(V_S{I}_S^{*})$$

(7)

Therefore, based on (1), (2), (6) and (7), the proposed constant voltage model of DFIG-based WPP is:

$$s{P}_m+(1-s)R_R{I}_R{I}_R^{*}-(1-s)Re(V_R{I}_R^{*})=0$$

(8)

$$s{Q}_R-Im(V_R{I}_R^{*})=0$$

(9)

$$P_g-Re(V_S{I}_S^{*})+Re(V_R{I}_R^{*})=0$$

(10)

$$Q_g-Im(V_S{I}_S^{*})=0$$

(11)

It is to be noted that I_S and I_R in (8)–(11) can be expressed in terms of V_S and V_R (see Appendix A). In the load flow analysis, mathematical model (8)–(11) is then combined with the following nodal equations of system without WPP [23]:

$$P_{Gi}-P_{Li}-{\displaystyle \sum _{j=1}^n\left|V_i\right|\left|Y_{ij}\right|\left|V_j\right|cos({\delta }_i-{\delta }_j-{\theta }_{ij})}=0$$

(12)

$$Q_{Gi}-Q_{Li}-{\displaystyle \sum _{j=1}^n\left|V_i\right|\left|Y_{ij}\right|\left|V_j\right|sin({\delta }_i-{\delta }_j-{\theta }_{ij})}=0$$

(13)

In (12) and (13), P_G and Q_G are power generations, P_L and Q_L are power demands, |V| and δ are voltage magnitude and angle, |Y| and θ are magnitude and angle of bus admittance matrix element, and n is number of system buses.

Table 2. Equation and variable.

Bus Type	Equation(s)	Known Variable	Unknown Variable
Slack	(9)	|V| and δ = 0°	PG and QG
PV	(9)	PG and |V|	δ and QG
PQ	(9)	PG = QG = 0	|V| and δ
WPP	(8) and (9)	|V| = |VS|, s and Pm	δ = δS, PG = Pg,QG = Qg, QR, Re(VR) and Im(VR)

gives detail of the equations to be solved as well as the variables to be determined in the complete formulation of load flow analysis for system embedded with DFIG-based WPP. It is to be noted that V_S in (10) and (11) is also the voltage at WPP bus (i.e., V = |V|∟δ). In constant voltage mode of operation, the magnitude of this voltage (|V| = |V_S|) is known or specified at a certain value.

4. Case Study

4.1. Test System

The case study is based on 5-bus power system with total three phase loads of 1215 MW and 600 MVAR [23]. The system data are given in

Table 3. Test system line data (in pu).

Line	Sending Bus	Receiving Bus	Series Impedance
1	1	3	0.042 + j0.168
2	1	4	0.031 + j0.126
3	2	3	0.031 + j0.126
4	2	4	0.053 + j0.210
5	2	5	0.084 + j0.336
6	4	5	0.063 + j0.252
1	1	3	0.042 + j0.168

and

Table 4. Test system bus data (in pu).

Bus	|V|	δ	Generation	Load	Note
1	1.07	0	-	0.65 + j0.30	Slack
2	1.06	-	1.8 + j-	0.70 + j0.40	PV
3	-	-	0	1.15 + j0.60	PQ
4	-	-	0	0.85 + j0.40	PQ
5	-	-	-	0.70 + j0.30	PQ

. The system is then modified by adding a WPP at bus 5 via a step-up transformer with an impedance of j0.05 pu (see Figure 6). The WPP consists of 100 identical DFIG-based wind turbine generator (WTG) units. Data of the WTG unit are given in

Table 5. WTG unit data.

Turbine	Blade length: 40 m Rated power: 3.0 MW Speed: Cut-in: 4 m/s; Rated: 14 m/s; Cut-out: 23 m/s
Gearbox	Ratio: 1/90
Generator	Type: DFIG Rated power: 3.0 MW Pole pairs: 2 Voltage: 690 Volt Resistances/Reactances (in pu): RS = 1; XS = 25; RR = 1; XR = 25; Rc = 3000; Xm = 350
Transformer	Impedance (in pu): j5

. This WTG unit data is adopted from [18]. Base value of 100 MVA has been used for all data in pu.

4.2. Calculations of Slip and Turbine Power

Machine slip and turbine mechanical power can be calculated using the formulas given in [17]. In the present work, it is assumed that the turbine tip speed ratio (λ) is 8.0, and turbine coefficient performance (C_P) is 0.50. Therefore, the mechanical power produced by each turbine is:

$$P_m=0.5(1.225)(\pi {40}^2)V_w^3(0.5)$$

(14)

The machine slip is:

$$s=1-\frac{(2)(8)V_w}{(100\pi )(1/90)(40)}$$

(15)

Table 6. Generator slip and turbine power.

Vw (m/s)	s	Pm (MW)	ΣPm (MW)
8	0.0833	0.7882	78.82
9	−0.0313	1.1222	112.22
10	−0.1459	1.5394	153.94

shows the results of machine slip and turbine mechanical power calculations for three wind speed values (i.e., 8, 9 and 10 m/s). These results (i.e., P_m and s) will be used in the load flow study discussed in Section 4.4.

4.3. WPP Aggregation

To simplify the load flow analysis, the group of WTG units in Figure 6 is aggregated into a single machine equivalent (note: aggregation technique as discussed in [3] has been used in the aggregation process). In the WPP single machine representation (see Figure 7), parameters of the WRIG equivalent are:

$$R_{S,ek}=1/100=0.01 \mathrm{pu}$$

(16)

$$X_{S,ek}=25/100=0.25 \mathrm{pu}$$

(17)

$$R_{R,ek}=1/100=0.01 \mathrm{pu}$$

(18)

$$X_{R,ek}=25/100=0.25 \mathrm{pu}$$

(19)

$$R_{c,ek}=3000/100=30 \mathrm{pu}$$

(20)

$$X_{M,ek}=350/100=3.5 \mathrm{pu}$$

(21)

The impedance of pad mount transformer in the single machine equivalent is:

$$Z_{T,ek}=j5/100=j0.05 \mathrm{pu}$$

(22)

4.4. Load Flow Results and Discussion

Using the WPP single machine representation, a load flow study is then carried out for various values of wind speed listed in Table 6. In addition, in the study, the WPP terminal voltages have been specified to some values ranging from 0.95 to 1.0 pu. Results of the study are given in

Table 7. Rotor power and DFIG power loss (V_w = 8 m/s).

|VS| (pu)	ΣPR (MW)	ΣQR (MVAR)	DFIG Loss
			MW	MVAR
0.95	7.6218	81.5364	9.6055	93.5515
0.96	7.6755	95.8748	10.0061	97.6761
0.97	7.7397	110.9682	10.4326	102.3248
0.98	7.8145	126.8189	10.8850	107.4996
0.99	7.8999	143.4289	11.3636	113.2021
1.00	7.9959	160.8002	11.8682	119.4341

,

Table 8. Stator power, WPP output and power factor (V_w = 8 m/s).

|VS| (pu)	ΣPS (MW)	ΣPg (MW)	ΣQg (MVAR)	Power Factor
0.95	76.8364	69.2145	−12.0151	0.9853 (lag)
0.96	76.4894	68.8139	−1.8013	0.9997 (lag)
0.97	76.1272	68.3874	8.6434	0.9921 (lead)
0.98	75.7495	67.9350	19.3193	0.9619 (lead)
0.99	75.3563	67.4564	30.2268	0.9126 (lead)
1.00	74.9477	66.9518	41.3661	0.8507 (lead)

,

Table 9. G1+G2 output and line loss (V_w = 8 m/s).

|VS| (pu)	G1+G2 Output		Line Losses
	MW	MVAR	MW	MVAR
0.95	1168.2577	704.3137	22.4722	92.2987
0.96	1168.1939	692.1300	22.0078	90.3287
0.97	1168.1962	679.9542	21.5836	88.5976
0.98	1168.2645	667.7863	21.1994	87.1057
0.99	1168.3989	655.6265	20.8554	85.8533
1.00	1168.5996	643.4748	20.5514	84.8409

,

Table 10. Rotor power and DFIG power loss (V_w = 9 m/s).

|VS| (pu)	ΣPR (MW)	ΣQR (MVAR)	DFIG Loss
			MW	MVAR
0.95	−2.7852	84.1153	9.8841	101.1058
0.96	−2.7405	97.9311	10.2655	104.7983
0.97	−2.6852	112.5033	10.6728	109.0165
0.98	−2.6193	127.8338	11.1061	113.7620
0.99	−2.5428	144.9246	11.5655	120.0365
1.00	−2.4556	161.7777	12.0510	125.8415

,

Table 11. Stator power, WPP output and power factor (V_w = 9 m/s).

|VS| (pu)	ΣPS (MW)	ΣPg (MW)	ΣQg (MVAR)	Power Factor
0.95	99.5506	102.3359	−16.9905	0.9865 (lag)
0.96	99.2141	101.9545	−6.8672	0.9977 (lag)
0.97	98.8621	101.5472	3.4867	0.9994 (lead)
0.98	98.4947	101.1139	14.0718	0.9905 (lead)
0.99	98.1118	100.6545	24.8881	0.9708 (lead)
1.00	97.7133	100.1690	35.9362	0.9413 (lead)

,

Table 12. G1+G2 output and line loss (V_w = 9 m/s).

|VS| (pu)	G1+G2 Output		Line Losses
	MW	MVAR	MW	MVAR
0.95	1133.1415	703.4212	20.4774	86.4307
0.96	1133.0480	691.1966	20.0025	84.3293
0.97	1133.0198	678.9779	19.5671	82.4647
0.98	1133.0572	666.7654	19.1711	80.8372
0.99	1133.1602	654.5590	18.8147	79.4472
1.00	1133.3288	642.3589	18.4978	78.2951

,

Table 13. Rotor power and DFIG power loss (V_w = 10 m/s).

|VS| (pu)	ΣPR (MW)	ΣQR (MVAR)	DFIG Loss
			MW	MVAR
0.95	−18.7417	90.7664	10.3241	112.3397
0.96	−18.7072	103.9612	10.6831	115.5376
0.97	−18.6621	117.9130	11.0681	119.2614
0.98	−18.6064	132.6235	11.4792	123.5127
0.99	−18.5402	148.0945	11.9163	128.2932
1.00	−18.4632	164.3281	12.3796	133.6045

,

Table 14. Stator power, WPP output and power factor (V_w = 10 m/s).

|VS| (pu)	ΣPS (MW)	ΣPg (MW)	ΣQg (MVAR)	Power Factor
0.95	124.8742	143.6159	−21.5734	0.9889 (lag)
0.96	124.5497	143.2569	−11.5763	0.9968 (lag)
0.97	124.2098	142.8719	−1.3484	0.99996 (lag)
0.98	123.8544	142.4608	9.1107	0.9980 (lead)
0.99	123.4836	142.0237	19.8013	0.9904 (lead)
1.00	123.0972	141.5604	30.7236	0.9772 (lead)

and

Table 15. G1+G2 output and line loss (V_w = 10 m/s).

|VS| (pu)	G1+G2 Output		Line Losses
	MW	MVAR	MW	MVAR
0.95	1090.0827	704.6664	18.6986	83.0931
0.96	1089.9490	692.3759	18.2059	80.7996
0.97	1089.8802	680.0894	17.7520	78.7410
0.98	1089.8762	667.8070	17.3370	76.9178
0.99	1089.9372	655.5289	16.9609	75.3302
1.00	1090.0633	643.2551	16.6237	73.9787

. It is to be noted that the power factors in Table 8, Table 11 and Table 14 are determined after the load flow analysis has been completed, and they are calculated based on the WPP active and reactive power outputs as follows:

$$PF=cos\left(a tan\frac{Q_g}{P_g}\right)$$

(23)

It can be seen from the tables that all of the power factors are above 0.85, which are considered to be good power factors.

Some of the results in Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14 and Table 15 are also presented in graphical forms (see Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18) to make a better observation. Figure 8 shows the variation of DFIG rotor active power. It can be seen from the figure that DFIG rotor active power (P_R) is almost not affected by the improvement of WPP voltage. It can also be seen that, at a wind speed of 8 m/s, the rotor active power is positive, which indicates that the DFIG is at sub-synchronous condition (DFIG rotor absorbs the active power). On the other hand, at wind speeds of 9 and 10 m/s, the rotor active power is negative, which indicates that the DFIG is at super-synchronous condition (DFIG rotor delivers the active power). It is to be noted that the wind speeds of 8, 9, and 10 m/s have been selected in the study to investigate the DFIG in two normal operating conditions, i.e., sub- and super-synchronous conditions. Only those three values are chosen because they already represent the conditions.

As mentioned before, the DFIG rotor active power (P_R) is almost not affected by the improvement of WPP voltage. However, this is not the case for the reactive power produced by the DFIG rotor (Q_R). The DFIG rotor reactive power is significantly increased with the improvement of WPP voltage magnitude (see Figure 9). This result is expected since more reactive power is needed to obtain a better voltage profile. Power loss in DFIG is also increasing when the WPP voltage goes up (see Figure 10 and Figure 11). The DFIG power loss is calculated using the formula given in Appendix B. This increase in power loss is due to the rise in WRIG currents as the WPP voltage magnitude is raised. As a result, the increase in DFIG active power loss will, therefore, slightly decrease the WRIG stator active power (P_S) and WPP active power output (P_G), as shown in Figure 12 and Figure 13. On the other hand, as the reactive power produced by the DFIG rotor is significantly increased, the WPP reactive power output (Q_G) will also be higher as the WPP voltage magnitude is improved (see Figure 14). This result is also expected, since part of the DFIG rotor reactive power is delivered to the power grid to support the system reactive power demand and voltage improvement.

The active power output of a conventional power plant (G1+G2) is almost not affected by the improvement of WPP voltage (see Figure 15). However, since some portions of system reactive power demand can be supplied by the WPP, the reactive power output of the conventional power plant can therefore be reduced as the WPP terminal voltage increases (see Figure 16). Furthermore, as can be seen from Figure 17 and Figure 18, which show the variation of transmission line power losses, the increase in WPP voltage will reduce the line power losses. It is to be noted that the line loss is proportional to the square of the current flowing in the line. Since the improvement in voltage profile causes the line voltage drop (i.e., the current flowing in the line) to be smaller, the line power loss can therefore be significantly reduced.

From the above results, two important observations regarding the novelty of the main findings can be described as follows. Firstly, the proposed method works well at various specified voltage levels. The DFIG power factors are allowed to vary from lagging to leading power factors to keep the voltage at the specified magnitude. It is to be noted that the DFIG power factor has been assumed constant at unity in most of the previously published methods. Secondly, the proposed model is able to perform properly at both DFIG sub- and super-synchronous speeds. In contrast, some of the previous methods used two different equations to model the DFIG in sub- and super-synchronous conditions. The results also show that with the installation of DFIG-based WPP, in terms of power system steady-state performance, the following advantages can be obtained:

(i)

The improvement in system voltage profile leads to the reduction in transmission line power loss. In turn, this loss reduction will lower the power system operational cost and increase the system efficiency.

(ii)

The decrease in power supply from conventional electric generators. Conventional electric generators are usually fossil fuel-based power plants that are not environmentally friendly. This advantage will, therefore, help in coping with the global climate change issues.

5. Conclusions

In this paper, a new steady state model of DFIG-based WPP for load flow analysis has been proposed. In the present work, the derivation of the proposed mathematical model is based on the formulas that calculate turbine mechanical power and DFIG power. The process of the model development is relatively straightforward; therefore, the resulted model is quite simple and can easily be incorporated into the power system load flow analysis. The main contributions of the paper are:

• In contrast to the previous models, where DFIG power factor has been assumed to be constant at unity, the constant voltage model proposed in this paper allows the power factor to vary to keep the voltage at the specified value. In the present work, various DFIG voltage magnitudes ranging from 0.95 to 1.0 pu have been investigated, and the power factors vary from 0.98 lagging to 0.98 leading.
• The proposed model can be implemented in both sub-synchronous and super-synchronous conditions (it is to be noted that most of the previous models use two different mathematical models to represent the conditions). Three wind speed values (i.e., 8, 9, and 10 m/s) have been studied in this paper. At a wind speed of 8 m/s, the DFIG rotor active power is positive, which indicates that the DFIG is at sub-synchronous condition (DFIG rotor absorbs the active power). On the other hand, at wind speeds of 9 and 10 m/s, the DFIG rotor active power is negative, which indicates that the DFIG is at super-synchronous condition (DFIG rotor delivers the active power).

Case study results confirm the validity of the proposed DFIG model. However, the method in the present work can only be applied to DFIG-based WPP in voltage control mode. In future work, modification of the method so that it can be applied to DFIG-based WPP in power factor control mode can be investigated. This is an interesting research area since the power factor control mode is also often adopted in the operation of DFIG-based WPP.