Minimum Short-Circuit Ratios for Grid Interconnection

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

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Minimum Short-Circuit Ratios for Grid Interconnection of Wind Farms with Induction Generators Romeu Reginatto and Carlos Rocha, member IEEE

Abstract—This paper concerns the problem of determining the minimum value for the short-circuit ratio which is adequate for the interconnection of a given wind farms to a given grid point. First, a set of 3 criteria is defined in order to characterize the quality/safety of the interconnection: acceptable terminal voltage variations, a minimum active power margin, and an acceptable range for the internal voltage angle. Then, the minimum shortcircuit ratio requirement is determined for 6 different induction generator based wind turbines, both fixed-speed (with and without reactive power compensation) and variable-speed (with the following control policies: reactive power, power factor, and terminal voltage regulation). The minimum short-circuit ratio is determined and shown in graphical results for the 6 wind turbines considered, for X/R in the range 0−15, also analyzing the effect of more/less stringent tolerances for the interconnection criteria. It is observed that the tighter the tolerances the larger the minimum short-circuit ratio required. For the same tolerances in the interconnection criteria, a comparison of the minimum shortcircuit ratio required for the interconnection of both squirrel-cage and doubly-fed induction generators is presented, showing that the last requires much smaller values for the short-circuit ratio. Index Terms—Induction generators, wind power generation, wind farms, grid interconnection, short-circuit ratio.

I. I NTRODUCTION Wind energy integration into the power systems is continuously growing. Penetration levels of 20% to 30% have been reached in certain regions in Europe [1] and this continuous growth has demanded for advancements in several directions in order to guarantee a safe interconnection of wind energy in the network. Transmission and distribution network companies specify particular technical regulations for connecting wind farms to the network, according to their local and/or regional network characteristics, wind penetration levels and company policies. A comparison of several European regulations can be found in [2], [3]. Technical regulation usually specify operating characteristics that wind farms have to comply with. Such operating characteristics are influenced by several factors, including the wind energy conversion system technology, the control policy adopted, the power of the wind farm, and characteristics of the This work was partially supported by PTI Ciˆencia e Tecnologia, Itaipu Technological Park (PTI), Foz do Iguac¸u. R. Reginatto and C. Rocha are with the Center for Engineering and Exact Sciences of Western Paran´a State University (UNIOESTE), Av. Tancredo Neves, 6731, CP 1511, PTI/Bloco 14, 88856-970, Foz do Iguac¸u, Paran´a, Brazil (e-mail: [email protected]; [email protected]).

point of common connection (PCC). Even though it is simple to admit that such influence does exist, the determination of the exact way in which it happens is rather difficult. In [4] terminal voltage variations and voltage flicker were analyzed with respect to the point of common connection (PCC) parameters, namely the short-circuit power (Ssc ) and the X/R ratio. For a range of X/R ratios, values of Ssc were determined for which the terminal voltage variation and voltage flicker would comply with given limits. Based on such results, values of X/R ratio that would lead to the smallest Ssc were identified in the range 1.3−2.8. The case of a fixed-speed wind turbine both stall and pitch regulated was considered. The doubly-fed induction generator variable speed wind turbine (DFIG-VSWT) has recently gained a significant application in large wind farms[3], even though fixed-speed wind turbines equipped with squirrel cage induction generators (SQIG-FSWT) are still in use in medium size wind farms. The DFIG allows a full control of the main generator variables by acting on the rotor voltages and currents through DCAC converters. Proceeding in such a way, control policies including active power regulation [5], reactive power and/or voltage control [6], [7] besides other approaches [8] have been considered. In [9] the analysis of wind farm grid integration was extended to the DFIG-VSWT case with reactive power regulation, besides considering the influence of reactive power compensation in the SQIG-FSWT case. Moreover, a set of 3 criteria was employed to characterize the interconnection of a wind farm to the grid, namely: acceptable terminal voltage variations, a minimum active power margin relative to the maximum power transferable to the grid, and an acceptable range for the internal voltage angle. The satisfaction of such interconnection criteria was referred to as a safe interconnection, and conditions for it were numerically determined for a particular wind farm. The analysis was extended in [10] to evaluate the individual effect of each interconnection criterion, i.e., the determination of the limits imposed by each interconnection criterion on the integration level of wind power. It was seen that the tolerance on voltage variation has a major impact on such limits. The amount of wind power that can be connected to a grid point was then determined as the composite effect of the individual criteria. The analysis in [10] included both power factor and voltage regulation control policies for the DFIG-VSWT. In this paper, the analysis is turned to the determination of the minimum SCR required in order for wind farms to comply

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

Fig. 1. Simplified representation of a wind farm connection to the network.

with given tolerances for the interconnection criteria. For a given turbine technology and control policy, the satisfaction of the interconnection requirements can be verified for each short-circuit ratio (SCR) and X/R ratio. It is of particular interest the minimum value of the SCR that allows such satisfaction, since this may reduce costs in the wind farm grid interconnection. Also, interconnection requirements may be either more or less stringent depending upon the particular facility and/or interconnection rules. Three different tolerance levels are considered to show its influence on the minimum SCR both for SQIG-FSWT, with and without reactive power compensation, and DFIG-VSWT, with 3 different control policies: reactive power regulation, power factor regulation, terminal voltage regulation. The paper is organizes as follows. Section II introduces modeling and systems considerations which allow to develop theoretical properties of different operation and control policies for the wind turbines in section III. The main results on the analysis of the minimum SCR are given in section IV. Section V provides concluding remarks II. M ODELING AND S YSTEM C ONSIDERATIONS Figure 1 shows a simplified representation of the connection of a wind farm to the grid, here represented as a single DFIGbased wind turbine (DFIG-VSWT). The network viewed from the PCC is represented by its static equivalent (infinite bus with a series impedance) and represented by its short-circuit power (Ssc ) and X/R ratio. Let the nominal power of the wind farm be represented by Pn and consider the short-circuit ratio (SCR) Ssc SCR = . (1) Pn Several aspects are related to the SCR in the connection of wind farms to the grid. On one hand, there are aspects of the wind conversion system, including the technology and the control policies employed. On the other hand, there are aspects of the power system to which the wind farm is connect to, like the line length and capacity, for instance. In general, interconnection regulations impose constraints on the control and operation of wind conversion system so that certain technical, safety and quality requirements for the system are kept within given tolerances[2], [3]. A large SCR would in general favor the possible satisfaction of such

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requirements. Unfortunately, a large SCR would also mean a costly solution, since it would imply in a large capacity connection point relative to the actual wind farm nominal active power. The goal in this paper is to determine the minimum SCR that would comply with a set of interconnection requirements. The analysis is carried out for wind farms equipped with induction generators based wind turbines, both fixed-speed (SQIG-FSWT) and variable-speed (DFIG-VSWT). For the present analysis, the requirements considered are relative to the static behavior of the system. The DFIG can be represented by its 3rd order simplified model given the synchronous reference frame by [11], [12]
−1 ωs Xm E˙ d = Ed − (Xs − X ′ )Iqs + sωs Eq − Vqr To Xr
−1 ωs Xm E˙ q = Eq + (Xs − X ′ )Ids − sωs ed + Vdr To Xr 1 ω˙ r = (Tmg − (Eq Iqs + Ed Ids ) − F ωr ) 2H

(2) (3) (4)

and Vds Vqs

= =

Ed − Rs Ids + X ′ Iqs ′

Eq − Rs Iqs − X Ids

(5) (6) X2

where To = Xr /ωs Rr , s = 1−ωr , X ′ = σXs , σ = 1− Xs m Xr ; Xs , Xr and Xm are the stator, rotor, and magnetizing reactance, respectively; Rs , Rr are the stator and rotor resistance; H is the inertia constant; F is the damping; Tmg is the mechanical torque; Vdr , Vqr are rotor voltage components; Vds , Vqs , Ids , Iqs are stator voltage and current components, respectively. Letting E˜ = Ed + jEq to represent the internal voltage and similar notation for the stator and rotor voltages and currents, the following equation can be derived from (2)-(6) V˜s

=

sXr ˜ E Xm

=

˜ − (Rs + jX ′ )I˜s E

V˜r + Rr I˜r

(7) (8)

The rotor circuit of the DFIG is connected to the grid through a back-to-back converter allowing the exchange of power between the rotor and the grid and, at the same time, the control of the active and reactive power delivered by the stator. In the model (7)-(8), the rotor side converter is used to impose rotor voltages/currents which determine the internal ˜ which, in its turn, determine stator generated active voltage E and reactive power. The grid side converter keeps a constant DC voltage in the converters by regulating the active power exchange with the grid. The converter power factor can be controlled to produce/absorb reactive power in an amount limited to the converter rating. Considering this equilibrium condition, the system of Figure 1 can be represented by the equivalent circuit model shown in Figure 2.

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

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where Qs is the stator reactive power. By acting on the stator reactive power, power factor and terminal voltage control can also be regulated [6], [7]. A. Squirrel-cage Induction Generators

Fig. 2.

DFIG equivalent circuit representation.

The grid side converter is represented by a controlled current source, with magnitude and angle determined by the rotor active power and converter power factor, respectively. With balanced active power flow through both converters and assuming a unitary power factor for the grid side converter, the current flowing from the converter to the network is given by Pr 6 θs (9) I˜g = Vs where Pr is the rotor active power and Vs 6 θs is the terminal voltage. The rotor side converter is represented by an ideal voltage source connected to the rotor. The rotor voltage results from the specific control policy adopted. If the rotor voltage is set to zero the equivalent circuit representation of Figure 2 reduces to the case of a SQIG. The sharing of active power by the stator and rotor of the DFIG is determined by the generator slip frequency [13], [14], according to Pr = −sPs (10) where s is the slip, and Ps is the stator active power. For supersynchronous speed, s < 0 and the generator supplies active power to the grid by both stator and rotor circuits. For subsynchronous speed, s > 0 and the rotor circuit absorbs active power from the network. Then, the total generated active power is 1−s Pr (11) s The generated active power depends on the available wind speed. In order to maximize the generated active power, in general the maximum power tracking (MPT) [15] strategy is employed, in which the generated active power is maximized for the available wind speed by allowing the wind turbine speed to vary in accordance with the wind speed. Active power can also be regulated within the available wind power [5]. By acting on the rotor side converter, the reactive power delivered by the stator can be controlled [14], [5]. Under the assumption that the grid side converter power factor is unitary, the total reactive power delivered by the generator to the grid is [13], [14] Q = Qs (12) P = Ps + Pr = (1 − s)Ps = −

In the case of a SQIG-FSWT the generated active power depends upon the mechanical torque provided by the wind turbine rotor. For a given mechanical torque, the generator reactive power and terminal voltage result from the network an machine characteristics. The equilibrium condition can be calculated by solving the equivalent circuit of Figure 2 with V˜r = 0, together with Te = Eq Iqs + Ed Ids = Tmg . A closed form solution for this problem is given in [16] and is employed in this paper. B. DFIG-VSWT with Reactive Power Regulation When the DFIG-VSWT is operated with reactive power regulation, the generator bus bar can be viewed as a PQ bus. Active power is determined by the available wind speed and control settings whereas reactive power is determined by control settings. Let S = P + jQ be the complex power transfered from the generator to the network, then S = V˜s I˜s∗ = (V˜s V˜s∗ − V˜s V∞ )/(R−jX). Solving this equation, the stator voltage V˜s = Vsr + jVsi is found to satisfy the relation 2 Vsr

− V∞ Vsr

Vsi V∞ − P X + QR = + Vsi2 − (P R + QX) =

0 0

(13) (14)

The maximum power transfer to the network Pk can be found from (14) as the limiting value for which a real solution for Vsr exists. This value is computed as s " # Ssc β 4Q 1 2Q 2 Pk = +β 1+ + (15) 2 X/R β Pcc X/R Pcc where

p 1 + (X/R)2 β= X/R

and the following fact has been used p 2 V∞ = Ssc R 1 + (X/R)2 C. DFIG-VSWT with Power Factor Regulation Another operating control polity for DFIG-VSWT is the power factor regulation. This case can be treated as a special case of reactive power regulation in which the reactive power is varied according to the generated active power. Let F P be a given power factor, then the generator reactive power has to satisfy √ 1 − FP2 Q= P =fP (16) FP The generator can still be considered as a PQ bus, similarly as the reactive power regulation case. The terminal voltage can be determined from (13)-(14) considering the reactive power

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

given by (16). The maximum power transfer, in this case, can be computed as " # p Ssc (1 + f X/R + βF ) 1 + (X/R)2 (17) Pk = 2 (f − X/R)2

20 18 16 14 12 scr

where p βF = (1 + f X/R)2 + (f − X/R)2

6 4

An interesting control and operating policy for DFIGVSWT is the terminal voltage regulation, which allows the wind farm to better contribute to system support. In this operating policy, active power is determined by the available wind speed and control settings whereas the terminal voltage is determined by control settings. Thus, the generator bus bar reduces to a PV bus. The generated active power, in this case, satisfies the relation i h Vs 1 V∞ β X/R

Vs X − cos(θs ) + sin(θs ) V∞ R

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D. DFIG-VSWT with Voltage Regulation

P = Ssc

4

(18)

The terminal voltage angle θs varies according to the generated active power, while Vs and V∞ are regulated, thus considered constant. The corresponding angle for a given active power is given by   P V∞ Vs θs = −θz + cos−1 cos(θz ) − (19) V∞ Ssc Vs where θz = tan−1 (X/R). Taking the derivative of P with respect to θs , in (18), and equating to zero, the maximum power transfer to the network can be deduced as " # Vs Vs 1 p Pk = Ssc +1 (20) V∞ V∞ 1 + (X/R)2

which occurs for θs = π − θz . In the voltage regulation case it is important to consider the generator limits to deliver/absorb reactive power. This limits are due to apparent power limits of the generator and current limits of the converters. If terminal voltage is kept constant, it can be demonstrated that the apparent power is monotone and increases with the generated active power. So, the worst case for the generator limits occurs at maximal generated active power. III. I NTERCONNECTION P ROPERTIES Grid interconnection requirements for wind farms, in general, constrain static and transient behavior of the unit with the goal of preserving the power system operation and energy quality. It is not the goal of this paper to dwell upon such interconnection regulations and the reader is referred to [17], [2], [3], [18] for further details. The purpose of this paper is to evaluate minimum SCRs that would comply with a set of criteria that characterize the quality of the interconnection, which, in this paper, is stated on the basis of static stability properties of the system. The following 3 criteria are considered: 1) Voltage variation. A range of allowable terminal voltage variation, given in terms of the inequality Vmin ≤ Vs ≤ Vmax , where Vmin and Vmax are given constants.

2 0

0

5

X/R

10

15

Fig. 3. Combination of the 3 criteria to determine the minimum SCR for the case of a DFIG-VSWT: terminal voltage variation (solid); active power margin (dashed); and internal voltage angle (dotted).

2) Active power margin. The wind farm nominal active power Pn is sufficiently smaller than the maximum power transferable to the network (Pk ) at the PCC, as given by the relation Pn ≤ Pk /(1 + MP ), where MP is a given margin. 3) Internal voltage angle limit. The value of the angle δ ˜ = E 6 δ should lie within the of the internal voltage E range 0 ≤ δ ≤ δmax , where δmax is a given constant. The active power margin can be determined from the PV curve at the wind farm connection bus, once the short-circuit power Ssc and X/R ratio are known. To evaluate the voltage variation and internal voltage angle, a range of active power operating condition has to be considered. Since the active power generated by the wind farm depends upon the available wind speed and since the wind speed may vary substantially, such range is considered from 0.1pu to 1.05pu of the nominal wind farm active power. The range allows for a 5% overload and neglects the very low generated active power. The minimum SCR are to be determined so that all three criteria are satisfied, i.e., Vmin ≤ Vs ≤ Vmax and 0 ≤ δ ≤ δmax for all operating conditions ranging from 0.1pu to 1.05pu of generated active power, and Pn ≤ Pk /(1 + MP ). An interconnection satisfying these requirements is also referred to as being safe, in this paper. The Figure 3 illustrates such situation for the case of a DFIG-VSWT with reactive power regulation. Each curve in the figure shows the minimum SCR required to satisfy each of the 3 interconnection criteria for the X/R ratio up to 15. The region above all 3 curves defines all values of SCR and X/R ratio that comply with the safe interconnection requirements stated previously, and can be considered as a region of safe interconnection. The curve limiting such a region determines the minimum SCR for the safe interconnection of such a wind farm, in this case based on DFIG-VSWT. IV. M INIMUM SCR S

FOR WIND FARM GRID

INTERCONNECTION

In the previous section, 6 different cases of induction generator based wind farms were introduced: SQIG-FSWT with 3 possible power factor compensation; and DFIG-VSWT

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

with 3 possible control policies: reactive power, power factor, and terminal voltage regulation. Also, 3 criteria were stated as measures of the quality of the interconnection of wind farms to the grid. The goal in this section is to study the minimum SCR required to comply with such interconnection criteria, for all 6 cases of different technology/control policies: SQ0 - A SQIG-FSWT with no power factor compensation. SQN - A SQIG-FSWT with no load power factor compensation. SQF - A SQIG-FSWT with full load power factor compensation. DFQ - A DFIG-VSWT with reactive power regulation set to Q = 0. DFP - A DFIG-VSWT with power factor regulation set to 0.95 leading power factor. DFV - A DFIG-VSWT with terminal voltage regulation set to Vt = 1pu. To better illustrate the effect of the interconnection criteria, the minimum SCRs are obtained for 3 different cases: •

•

•

Case A. Representative of a wind farm interconnection with tight limits: 0.95 ≤ Vs ≤ 1.05, MP = 2, 0 ≤ δ ≤ 30o . Case B. Representative of a wind farm interconnection with medium limits: 0.9 ≤ Vs ≤ 1.1, MP = 1, 0 ≤ δ ≤ 38o . Case C. Representative of a wind farm interconnection with loose limits: 0.85 ≤ Vs ≤ 1.15, MP = 0.5, 0 ≤ δ ≤ 45o .

The active power margin limits are modified in the SQIGFSWT case to MP = 1, 0.5 and 0.3, respectively. This is done since for SQIG-FSWT, in general, it is not possible to obtain large active power margins. The results are obtained for a wind farm equipped with 10 generators of 2MW, whose equivalent model has the following parameters: 690V , 50Hz, 4 poles, H = 3.5s, Xm = 3.95279pu, Xls = 0.09241pu, Xlr = 0.09955pu, Rs = 0.00488pu, Rr = 0.00549pu. Base values are: Vb = 690V and Pb = 20M W . An individual 0.69/11kV transformer is connected to each turbine, with 5.9% leakage reactance. The whole wind farm is connected to the grid by a 11/33kV transformer with leakage reactance 10%. The following considerations are made regarding the wind farm electric and control structure:

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generation) and full load (nominal active power generation). For the sake of content clarity, throughout the paper we refer to the minimum value of the minimum SCR curve as SCRmin , and to the value of the X/R ratio where it is attained as X/Rmin . We also define SCR0 and SCR∞ as the value of the SCR for X/R = 0 and X/R = 15, respectively, the last being an approximation of the SCR limit as X/R → ∞. Finally, SCRmax represents the maximum value of the SCR in the whole range considered 0 ≤ X/R ≤ 15. Minimum SCR curves for the SQIG-FSWT case are shown in the Figures 4, 5, and 6. Figure 4 corresponds to the case without power factor compensation. Case A almost do not appear in the plot because it requires a very high SCR. The minimum SCR for cases B and C stay bellow 13, for the whole range of X/R ratio analyzed. Notice that the minimum SCR curves attain a minimum value for X/R close to 1. For other values of X/R, the SCR ratio has to increase in order for the system to comply with the given interconnection criteria. As it might be expected, the tighter the tolerance tolerance of the interconnection requirements, the larger the minimum SCR required, as the figure shows. Nonetheless, such dependence is nonlinear, in the sense that changes in the limits of the interconnection criteria lead to not proportional changes in the SCR. In Figure 5 the minimum SCR obtained for the no load power factor compensation is provided. The general profile of the minimum SCR is similar to the case without power factor compensation, although with a slight difference in its magnitude. Again, the case A results in very large minimum SCRs, which is mostly due to the active power margin requirement. The case with full load power factor compensation is shown in Figure 6. Again, the overall profile is similar, although with different magnitudes of the minimum SCR. Once again, as the case goes from A to C, the minimum SCR curve moves downward, i.e., lower SCR are required in order to ac less stringent limits of the interconnection criteria. In general, SRC0 1, the addition of reactive power compensation reduces the minimum SCR, which is desirable. However, for X/R < 1, the effect is opposite. Fortunately, X/R < 1 is not a common situation in practice.

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Let us now turn to the DFIG-VSWT case. Results are given in Figures 8-10 for the 3 control policies considered: reactive power regulation, power factor regulation, and terminal voltage regulation, respectively. As for the SQIG-FSWT, the minimum SCR curves show a V-like shape, having a minimum value in the range 1-3 of the X/R ratio, depending on the control policy. For the reactive power regulation control policy (Fig. 8), a stringent tolerance of the interconnection criteria (from case C to case A) increases the X/R value at which the minimum of the SCR curve is attained, i.e., X/Rmin moves to the right. It can be seen that the effect of the tolerance of the interconnection requirements is more uniform and smaller in magnitude for X/R > 3 than for X/R < 1. In other words, SCR∞ is close to SCRmin , whereas both differ considerably than SCR0 . Such behavior is quite different than the SQIG-FSWT case, where the smallest influence tends to be close to the minimum point of the SCR curves, increasing as X/R moves away from this point, in both directions. A flat characteristic of the minimum SCR curve implies a low sensitivity of the interconnection requirements on X/R, which can be seen as a robustness property. In the case of power factor regulation (Figure 9), X/Rmin is near to 1 for all cases. Also, the overall shape of the minimum SCR ratio curves present some similarity with the SQIG-FSWT case, although being much smaller for all X/R ratios despite the active power margins being more stringent. It is also important to notice that the power factor, in this case, is regulated at 0.95 lagging, meaning that the DFIG is absorbing reactive power from the network. Reactive power absorption occurs also in the SQIG-FSWT case, which may explains the similarity of the curves, but notice that for the DFIG-VSWT the power factor is constant for all values of generated active power, whereas it varies in the SQIG-FSWT case. Compared to the reactive power regulation of the DFIGVSWT, the SCR curves here (Fig. 9), present a much larger variation for X/R > X/Rmin . In this case, SCRmin differs considerably than SCR∞ , which tends to be closer to SCR∞ than it is for the active power regulation case. Also notice that X/Rmin varies with cases A, B, and C, much more for the reactive power regulation than for the power factor regulation.

20 20

18

18

16

16

14

14 12

10 scr

scr

12

8

8

6

6

4

4

2 0

10

2 0

5

X/R

10

15

Fig. 7. Effect of reactive power compensation on the minimum SCR for SQIG-FSWT, case B. Power factor compensation: Without - solid; no load dashed; full load - dotted.

0

0

5

X/R

10

15

Fig. 8. Minimum SCR for DFIG-VSWT with reactive power regulation with Q = 0. Case A - solid line; Case B - dashed line; Case C - dotted line

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

20 18 16 14

scr

12 10 8 6 4 2 0

0

5

X/R

10

15

7

with slight differences in the range 0.5 ≤ X/R ≤ 2.5. The vertical part of the minimum SCR curve is related to the current limitation for voltage regulation. For small values of X/R ratio, in this case, X/R < 2.5, it may not be possible to attain voltage regulation for any SCR. At best, there is a range of SCRs where it is possible. This is the only situation, among all analyzed, in which the growth of the SCR implies violating an interconnection criteria. This is because in order to keep the voltage regulated, the generator is obligated to inject reactive current into the grid, according to the generated active power and according to the grid equivalent impedance. The reactive current is specially high for low X/R ratios, thus reaching the current limits.

Fig. 9. Minimum SCR for DFIG-VSWT with power factor regulation with P F = 0.95 lagging power factor. Case A - solid line; Case B - dashed line; Case C - dotted line

20 18 16 14

20 12 scr

18 10

16 8 14 6 scr

12 4 10 2 8 0 6

0

5

X/R

10

15

4 2 0

0

5

X/R

10

15

Fig. 10. Minimum SCR for DFIG-VSWT with terminal voltage regulation with Vt = 1pu. Case A - solid line; Case B - dashed line; Case C - dotted line

The minimum SCRs for the voltage regulation case are given in Figure 10. Some remarks are in order since this is a special case. The terminal voltage is kept constant due to the voltage regulation characteristic of the wind turbine. Then, as long as the voltage regulation is possible, the terminal voltage will necessarily satisfy any voltage variation criterion. Thus, what is important to consider here as a criterion is not the terminal voltage variation, but the possibility of regulating the terminal voltage. Since the generator has current limitations, it is possible that the regulation of the terminal voltage can not be maintained for all possible operating conditions ranging from 0 to rated active power generation. Thus, instead of the voltage variation criterion, it is here considered the minimum SCR required in order for the voltage regulation to be possible considering the apparent power limitation of the wind turbine. The result in Figure 10 considers that the wind turbine can operate at rated active power with at most 0.9 power factor, either leading or lagging. First notice from Fig. 10 a main change in the V-like shape of the minimum SCR curve, as compared to all other previous plots. Recall that the terminal voltage in this case is regulated at 1 p.u. This requirement prevails over all other criteria in determining the minimum SCR curves. Thus, it is seen that the curves are quite similar in all A, B, and C cases considered,

Fig. 11. Effect of control policies on the minimum SCR for DFIG-VSWT, case B. Regulation: reactive power - solid; power factor - dashed; terminal voltage - dotted.

Figure 11 compares the 3 control policies for DFIG-VSWT in terms of the minimum SCR. For X/R > 2.5 the voltage regulation strategy leads to the smallest SCRs, followed by the reactive power regulation. Moreover, for both control policies the profile is quite flat, thus presenting low sensitivity to the specific value of X/R. For X/R < 2.5, there is no such predominance. The smallest SCR is attained by any of the 3, each for specific ranges of the X/R ratio. V. C ONCLUDING

REMARKS

This paper has considered the determination of minimum SCRs for grid interconnection of wind farms. Results were provided for both SQIG-FSWT and DFIG-VSWT. Minimum SCRs were determined so as to comply with 3 interconnection criteria: a maximum range of terminal voltage variation; a minimum active power margin relative to the maximum active power that could be transfered to the network; and a maximum range for the internal voltage angle. The general profile of the minimum SCR ratio curve is a V-like shape, attaining a minimum value for X/R in the range 1−3. It also attains its maximum value either for very small or very large values of X/R ratio. Only the DFIG-VSWT with voltage regulation differs from such profile. The minimum SCR curve tends to be flatter for X/R > X/Rmin , i.e., for values of X/R grater than the point where the curve attains its minimum value. The flattest behavior occurs for DFIG-VSWT with reactive power and voltage

THE 8TH LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009

regulation. Such characteristic shows less sensitivity of the minimum SCR with respect to the value of X/R ratio. The behavior is rather diverse for X/R smaller than approximately 2.5, where the minimum SCR tends to increase as X/R goes to zero. The influence of the interconnection criteria was analyzed by choosing 3 different set of values for their limits. It was observed that tight tolerances in the interconnection criteria tend to require larger SCRs. Moreover, for the same tolerances, the minimum SCR for DFIG-VSWT tend to be much smaller than for SQIG-FSWT. The DFIG-VSWT with terminal voltage regulation can be considered as the one that requires the smallest SCR to comply with the interconnection requirements. However, voltage regulation may not be attainable for small SCR due to current limitations of the induction machine and the grid side converter. The range at which the minimum point of the minimum SCR curves is attained (1-3 of the X/R ratio) is close to typical values of the X/R ratio for distribution network interconnection. On one hand it may a favorable point, since a small SCR is required in this case. On the other hand, it may be unfavorable since the minimum SCR tends to be very sensitive to the X/R ratio in such range and may vary considerably, depending on the technology and control policy. R EFERENCES [1] L. Soder, L. Hofmann, A. Orths, H. Holttinen, Y. Wan, and A. Tuohy, “Experience from wind integration in some high penetration areas,” IEEE Trans. Energy Conversion, vol. 22, no. 1, pp. 4–12, Mar 2007. [2] J. Matevosyan, T. Ackermann, S. Bolik, and L. Soder, “Comparison of international regulations for connection of wind turbines to the network,” Wind Energy, vol. 8, no. 3, pp. 295–306, 2005. [3] T. Ackermann, Ed., Wind power in power systems. England: John Wiley & Sons, 2005. [4] S. Lundberg, “Electrical limiting factors for wind energy installations,” Master Dissertation, Chalmers University of Technology, Gothenburg, Sweden, 2000. [5] G. Tarnowski and R. Reginatto, “Adding active power regulation to wind farms with variable speed inductions generators,” in IEEE PES Anual Meeting, Tampa, FL, Dezembro 2007. [6] M. P´alsson, T. Toftevaag, K. Uhlen, and J. Tande, “Control concepts to enable increased wind power penetration,” in IEEE PES General Meeting, Toronto, Canad, July 2003, pp. 1984–1990. [7] P. Cartwright, L. Holdsworth, J. Ekanayake, and N. Jenkins, “Coordinated voltage control strategy for a doubly-fed induction generator (DFIG)-based wind farm,” IEE Proc. Gener. Transm. Distrib., vol. 151, no. 4, pp. 495–502, July 2004. [8] H. T. Le and S. Santoso, “Analysis of voltage stability and optimal wind power penetration limits for a non-radial network with an energy storage system,” in Power Engineering Society General Meeting, Tampa, FL, June 2007, pp. 1–8. [9] R. Reginatto, A. S. Bazanella, and M. Zanchettin, “Regi˜oes de penetrac¸ a˜ o segura de gerac¸a˜ o e´olica com aerogeradores de induc¸a˜ o,” in XVII Brazilian Conference on Automatica, Juiz de Fora, MG, 2008. [10] R. Reginatto, M. Zanchettin, and M. Tragueta, “Analysis of safe integration criteria for wind power with induction generators based wind turbines,” in 2009 IEEE PES General Meeting, Alberta, CA, July 2009. [11] A. Feij´oo, J. Cidr´as, and C. Carrillo, “A third order model for the doublyfed induction machine,” Electric Power Systems Research, vol. 56, pp. 121–127, 2000. [12] L. Holdsworth, X. Wu, J. Ekanayake, and N. Jenkins, “Direct solution method for initialising doubly-fed induction wind turbines in power system dynamic models,” IEE Proc. Generation, Transmission and Distribution, vol. 150, no. 3, pp. 334–342, May 2003. [13] S. M¨uller, M. Deicke, and R. W. de Doncker, “Doubly fed induction generation systems for wind turbines,” IEEE Ind. Applic. Magazine, pp. 26–33, May-June 2002.

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[14] G. Tarnowski, “Metodologia de regulao da potncia ativa para operao de sistemas de gerao elica com aerogeradores de velocidade varivel,” Dissertao de Mestrado, PPGEE, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Agosto 2006. [15] J. Amenedo, S. Arnalte, and J. Burgos, “Automatic generation control of a wind farm with variable speed wind turbines,” IEEE Trans. Energy Conversion, vol. 17, no. 2, pp. 279–284, June 2002. [16] D. F. Pereira, “An´alise de estabilidade de sistemas de gerac¸a˜ o e´olica com aerogeradores de induc¸a˜ o com rotor em gaiola,” Master Dissertation, PPGEE, UFRGS, Porto Alegre, RS, Sep. 2007. [17] J. P. da Costa and H. Pinheiro, “Controle do gerador de induo duplamente alimentado durante distrbios na rede eltrica: Crowbar ativo e suporte de reativos,” in XVII Brazilian Conference on Automatica, Juiz de Fora, MG, 2008. [18] ONS, “Requisitos tcnicos mnimos para a conexo rede bsica,” in Procedimentos de Rede: Submdulo 3.6, reviso 4, Set. 2007.

Romeu Reginatto received a Bachelor degree in Electrical Engineering in 1991 from Federal University of Rio Grande do Sul, and Master and Doctor degrees from Federal University of Santa Catarina in 1993 and 2000, respectively, in the area of nonlinear control systems and applications. He is currently a lecturer and researcher in the Center for Engineering and Exact Sciences of Wester Paran´a State University - UNIOESTE, Foz do Iguac¸u, BR, where he leads a research group in Analysis and Control of Electrical Power Systems. R. Reginatto is a member of the Brazilian Society of Automatica (SBA). His current research interests include: wind energy conversion systems, grid integration of wind farms, control systems applications, nonlinear systems.

Carlos Rocha received his Electrical Engineering Bachelor degree in 1996, Master degree in 1999, and PhD degree in 2004, in the Control and Automation area, from Universidade Estadual Paulista J´ulio de Mesquita Filho - UNESP, campus of Ilha Solteira, S˜ao Paulo, Brazil. He is currently a lecturer and researcher in the Western Paran´a State University UNIOESTE, campus of Foz do Iguac¸u, Paran´a, Brazil. C. Rocha is a member of IEEE Power & Energy Society and a member of Cigr´e. He has experience in the Electrical Engineering area, with emphasis in Electrical Power Systems, with the main research interests in: optimization techniques in power systems, transmission lines expansion, electrical systems planning.