NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Doubly Fed Induction Generator 

in an Offshore Wind Power Plant 

Operated at Rated V/Hz

Preprint

Eduard Muljadi, Mohit Singh, 

and Vahan Gevorgian

To be presented at the IEEE Energy Conversion Congress and 

Exhibition

Raleigh, North Carolina

September 15-20, 2012

Conference Paper

NREL/CP-5500-55573

June 2012
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1

Abstract—This paper introduces the concept of constant 

volt/hertz operation of offshore wind power plants (WPPs). The 

deployment of offshore WPPs requires power transmission from 

the plant to the load center inland. Because this power 

transmission requires submarine cables, there is a need to use 

high-voltage direct current (HVDC) transmission, which is 

economical for distances greater than 50 km. In the concept 

presented here, the onshore substation was operated at 60 Hz 

synced with the grid, and the offshore substation was operated at 

variable frequency and voltage, allowing the WPP to be operated 

at constant volt/hertz. In this paper, a variable frequency at rated 

volt/hertz operation was applied to a Type 3 doubly fed induction 

generator (DFIG) wind turbine generator. The size of the power 

converter at the turbine can be significantly reduced from 30% 

of the rated power output in a conventional Type 3 turbine to 5% 

of the rated power. The DFIG allows each turbine to vary its 

operating speed with respect to the other turbines. Thus, small 

wind diversity within the WPP can be accommodated by the 

DFIG, and the collector system frequency can be controlled by 

HVDC to follow large variations in average wind speed.

Index Terms—wind turbine generator, variable speed, 

induction generator, HVDC, HVAC, renewable energy

I. INTRODUCTION

he use of high-voltage direct current voltage-sourced 

converters (HVDC-VSC) has been proposed for offshore 

power systems, including renewable energy resources [1]–[3],

because these systems become more economical than 

alternating current systems for transmission over distances 

greater than 50 km in an offshore environment. Although the 

dynamics of the high-voltage direct current (HVDC) itself are

important [4], [5], we focused our investigation on the wind 

turbine and plant operation. The use of HVDC confers another 

advantage in that it is able to operate at variable frequency: 

several studies have proposed different control algorithms 

with the wind power plant (WPP) interconnected with HVDCVSC [6], [7].

Figure 1 illustrates the layout diagram of the offshore WPP. In 

our proposed control strategy, the HVDC connecting the 

offshore WPP substation was operated at variable frequency at 

constant volt/hertz, and the onshore substation was operated at 

60 Hz connected to the grid inland. The collector system 

frequency and voltage followed the average wind speed. In 

previous work [8], we reported on constant volt/hertz

operation of fixed-speed turbines; in this paper, we 

concentrate on Type 3 doubly fed induction generator (DFIG) 

turbines. At rated frequency, the collector system voltage level 

was 34.5 kV, 60 Hz. At the turbine level, the pad mounted 

transformer converted the voltage to the generator voltage 

level, for example, 4160 V, 60 Hz at rated frequency. The 

operating frequency and the voltage at the collector system 

changed, but the ratio of the voltage to the frequency was

constant. In this paper, the performance of DFIG at rated 

volt/hertz operation and the size of the power converter 

needed for rated volt/hertz operation is explored in 

comparison to conventional DFIGs operated at 60 Hz. Results 

from dynamic simulations performed to illustrate the control 

algorithms proposed for HVDC, electrical generator and 

power converter, and aerodynamic controls are shown. 

In this analysis, we assumed that the wind speed was

relatively uniform over an offshore wind plant, compared to 

an onshore plant, because of elimination of surface roughness 

and terrain effects. Wake may affect the validity of this 

assumption, particularly when the wind is directed along the 

turbine rows. Observed power losses due solely to wake can 

be up to 10% for closely spaced wind plants [9]. In [10], the 

authors presented an analysis of variable frequency (though 

not constant volt/hertz) offshore plant operation and included

a discussion of wake effects as well. In our analysis, we 

considered that the average wind speed measurements had 

already incorporated the wake-linked reductions. Wake effects 

may also increase the diversity of wind speed within the plant, 

but the 5% power converter discussed here is able to 

accommodate the 10% speed variation between turbines 

because of wake effects.

Because of the decoupling of the plant from the grid by the 

HVDC link, the HVDC grid side converter assumed the 

responsibilities of ensuring that low-voltage and fault ridethrough criteria were met. Fault and low-voltage operation is 

not examined in this paper.

In this paper, the following sequence occurs. In section II, 

the doubly fed induction generator is explored based on steady 

state characteristics, and the size of the power converter 

needed for rated volt/hertz operation is explored in 

comparison to conventional DFIG operated at 60 Hz. Section 

III describes the dynamic simulation we performed to 

illustrate the control algorithms proposed for HVDC, electrical 

generator and power converter, and aerodynamic controls.

Individual WTGs

HVDC Link

Grid

Substation platform 

and collector system

Anemometer 

masts

Figure 1. Offshore WPP connected via HVDC to the grid

Doubly Fed Induction Generator in an Offshore 

Wind Power Plant Operated at Rated V/Hz

E. Muljadi, Fellow, IEEE, M. Singh, Member, IEEE, and V. Gevorgian, Member, IEEE

T
2 

II. TYPE III WIND TURBINE—DOUBLY FED INDUCTION 

GENERATOR WITH A PARTIAL RATING POWER CONVERTER

Recently, the use of wound rotor induction machines has 

been revived in the form of an induction generator for wind 

turbine applications. With the power converter connected to 

the rotor winding, the induction generator can be operated at 

variable speed at partial load. A physical connection of the 

DFIG system is shown in Figure 2 below. 

Figure 2. Physical connection diagram of a DFIG wind turbine 

generator 

A. Basic Equations 

From the equivalent circuit shown in Figure 3, we derived 

the equations to determine the size of power converter needed. 

Figure 3. Per-phase equivalent circuit of the induction generator 

From the equivalent circuit, the induced rotor emf Er is 

proportional to the winding ratio and to the rotor frequency. In 

a locked rotor condition (slip=1), the stator-to-rotor winding 

relationship is similar to a transformer. As the slip gets 

smaller, the rotor voltage decreases. The relationship to the 

stator emf Es can be written as 

࢘࢓ࡱ

࢙࢓ࡱ

ࢋ࢘ࡺ࢙ ൌ

ࢋ࢙ࡺ

 [1] ࢋࣂ࢏ࢋ

The current ratio is not affected by the rotor frequency and can 

be written as 

࢘ࡵ

࢙ࡵ

ࢋ࢙ࡺ ൌ

ࢋ࢘ࡺ

 [2] ࢋࣂ࢏ࢋ

The ratio of the actual rotor impedance to the stator referred 

rotor impedance is 

࢘ࢆ

ᇲ࢘ࢆ

ࢋ࢙ࡺ൤࢙ ൌ

ࢋ࢘ࡺ

൨

૛ [3] 

The useful active power at the stator side can be computed as 

࢙࢓ࡱ࢙࢓ࡵReሾ ൌ ࢙࢓ࡼ

 [4] ሿ כ

The real power at the rotor side can be computed as 

࢘࢓ࡱ࢘࢓ࡵReሾ ൌ ࢘࢓ࡼ

 [5] ሿ כ

By substitution, we can get the following equation 

࢙࢓ࡱ࢙࢓ࡵ࢙Reሾ ൌ ࢘࢓ࡼ

 [6] ሿ כ

Or 

 [7] ࢙࢓ࡼ࢙ൌ ࢘࢓ࡼ

Of the total air gap power of the generator, only a small 

fraction is dissipated in the rotor circuits. The mechanical 

power that is driven by the wind turbine is 

ࢎࢎࢎࢎࢎࢉࢋ࢓ࡼ ൌ ሺ࢙࢓ࡼ െ ࢘࢓ࡼሻ ൌ ሺ૚െ࢙ሻ࢙࢓ࡼ

[8] 

Thus, mechanical/aerodynamic power generated by the wind 

turbine is converted into electrical power with the majority of 

the power delivered to the grid via the stator winding and a 

fraction of it delivered via the rotor output power. For 

example, assume the turn ratio of the stator-to-rotor winding 

relationship is one. The DFIG is to be operated at + 30% slip. 

The power converter to be used must have about 30% rated 

voltage and 100% rated current. The implication is that to use 

a DFIG in variable speed with slip variation between -30% to 

+30%, the size of the power converter is about 30% of the 

rated power of the induction generator. 

B. Operation at Rated Volt/Hertz 

From the equivalent circuit shown in Figure 3 and the 

equations presented in the previous section, the size of the 

power converter is based on the designed slip range, the 

effective turn ratio, and the rated output power. 

If we had operated the collector system in a variable 

frequency mode while maintaining rated volt/hertz, the 

operating magnetizing flux would have been constant at its 

rated value. The voltage rating of the power converter can be 

computed from its rated frequency and the maximum 

operating slip. For example, consider a DFIG designed to 

operate at +5% slip variation with rated voltage at 4160 V, 60 

Hz. The voltage rating of the power converter would be 208V 

operating at 60 Hz (1.0 p.u. rated frequency). 

If we connected the DFIG to a variable frequency source at 

rated volt/hertz and the frequency of the collector system was 

varied down to 30Hz (0.5 p.u.), the voltage at the rotor Emr at 

5% slip condition would be 5% x 0.5 x 4160 V = 104 V. Then, 

if the power converter was rated at 208 V, the operating slip 

range at 30 Hz could be increased to +10% slip without 

exceeding the rated voltage (10% x 0.5 x 4160 V = 208 V) of 

the power converter at 60 Hz. As shown in Figure 4, there was 

additional headroom to increase the range of operating slip at 

rated volt/hertz operation in the low operating frequency 

(corresponding to low wind speed). 
3

To illustrate the concept, a typical DFIG was operated both 

at conventional operation (constant frequency at 60 Hz) and at 

variable frequency at constant rated volt/hertz. The DFIG was 

operated at unity power factor at its stator winding output.

Figure 4. Voltage Emr variation at the rotor winding

Figure 5. Stator output power versus rotor speed

In Figure 5, a typical output power of the stator winding 

was plotted against rotational speed. The first curve (solid red 

line) is a conventional doubly fed induction generator operated 

at 60Hz with the rotor slip operated within + 30% slips. The 

next two curves (dashed blue and dot-dashed green lines) are 

the converter (rotor winding) output power with the operation 

of the wind turbine generator (WTG) kept at rated volt/hertz

with the slip kept constant at -5% and +5% respectively. The 

last curve is the total output power from the stator winding and 

from the rotor winding, shown as a solid thick black line with 

the WTG operated at maximum performance coefficient 

(Cp_max). There were several observations worth noting:

• The difference between the total output power (solid 

black line) and the stator output power was the output 

power delivered by the rotor winding via the power 

converter.

• The size of the power delivered via the power 

converter was proportional to the slip and the output 

stator power.

• The total output power of the WTG crossed the output 

power of the stator winding, indicating that below 

synchronous rotor speed, the output of the power 

converter flows into the rotor winding, crossing the air

gap, and into the grid via the stator winding. Above 

synchronous speed, the output of the power converter 

flows out of the rotor winding and is delivered to the 

grid via the power converter.

• Operating at lower slips (5%), the proportion of the 

output power from the rotor winding at rated speed 

was larger than the conventional operation with 

maximum operating slip of 30%. 

• The size of the power delivered via the converter was 

determined by the maximum operating slip allowed by 

the operating design.

C. Power Converter Sizing

As shown in Figure 6, the ratio of the output power from 

the rotor to the output power from the stator was proportional 

to the operating slip. In the case of conventional operation of 

DFIG, the ratio of the power showed a linear line, as expected.

On the other hand, if we maintained the operating slip 

constant, the rated volt/hertz operation showed a constant ratio 

(e.g., +5% or -5%).

Figure 6. Ratio of P_rotor/P_stator versus rotor speed

Ideally, it is expected that all WTGs will operate at a very 

narrow slip. Although wind speed in an offshore WPP is 

generally consistent, there is a small diversity among wind 

speed from turbine to turbine; thus, realistically, the operating 

slips of individual turbines may vary between -5% and 5%.

The power converter sized at 5% of the rated stator power 

would be sufficient to cover the diversity range in an offshore 

WPP.

In Figure 7, the output of the power converter is shown as a 

function of the rotor speed. The positive sign indicates that the 

output power flows out of the rotor winding; the negative sign 

indicates that the output power flows into the rotor winding.

Note that in an ideal situation, when the wind speed is totally 

0.4 0.52 0.64 0.76 0.88 1

0

0.1

0.2

0.3

0.4

60Hz, Slip = +/- 30%

Rated V/Hz, Slip = - 5%

Rated V/Hz, Slip = + 5%

Rotor Voltage vs Rotor Speed

Rotor Speed (p.u.)

Voltage Emr (p.u.)

0.4 0.52 0.64 0.76 0.88 1

0

0.333

0.667

1

60Hz, Slip = +/- 30%

Rated V/Hz, Slip = - 5%

Rated V/Hz, Slip = 5%

P_total

Stator Power vs Rotor Speed

Rotor Speed (p.u.)

P_stator (p.u.)

0.4 0.52 0.64 0.76 0.88 1 − 0.4

− 0.2

0

0.2

0.4

Ratio(P_converter/P_stator) vs Rotor Speed

Rotor Speed (p.u.)

P_converter/P_stator (p.u.)

0

Additional 

headroom 

to increase 

the slip 

range to 

+10% Emr at rated freq. 

at 5% slip
4 

uniform within the WPP, the rotor power of the WTG is 

practically zero, with the operating frequency matching the 

variation of the wind speed. 

Figure 7. Rotor power output versus rotor speed 

In Figure 7, the rating can be computed from the apparent 

power of the power converter. As shown, the apparent power 

is determined by the allowable operating slips. It indicates that 

with rated volt/hertz operation in an offshore WPP with 

uniform wind speed, we can size the power converter at lower 

rating, i.e., 5% instead of 30%, as in the conventional 

operation. (The frequency is fixed at 60 Hz.) 

Figure 8. Power converter rating as a function of rotor speeds 

D. Control Algorithm 

 1) HVDC Control and WTG Control Deployment 

From the control diagram shown we showed that the sizing 

of the power converter is based on the designed slip range and 

operation at rated output power. The slip schedule and the 

rating of the power converter can be computed as 

ࢊࢋ࢚ࢇ࢘ࢌ ൌ ሻࢌሺ࢞ࢇ࢓࢖࢏࢒࢙

࢞ࢇ࢓࢙ ࢌ

[9] 

The rating of the power converter can be sized at 

ࡳࢀࢃ࡭ࢂࡹ࢞ࢇ࢓࢙ ൌ ࢘ࢋ࢚࢘ࢋ࢜࢔࢕ࢉ࡭ࢂࡹ

[10] 

TABLE I 

MAXIMUM OPERATING SLIP FOR DIFFERENT OPERATING FREQUENCIES USING 

RATED VOLT/HERTZ WITH 5% MAXIMUM SLIP AT RATED FREQUENCY

HVDC Operating 

Frequency 

Maximum 

Operating Slip 

Range of the Rotor 

Speed 

1.0 p.u. +5% 0.95 p.u.–1.05 p.u. 

0.75 p.u. +6.66% 0.70 p.u.–0.80 p.u. 

0.50 p.u. +10% 0.45 p.u.–0.55 p.u. 

0.25 p.u. +20% 0.20 p.u.–0.30 p.u. 

If we operate the collector system in a variable frequency 

mode while maintaining rated volt/hertz, the operating 

magnetizing flux will be maintained constant at its rated value. 

As shown in Figure 9, the WTG controller measured the 

operating frequency at the collector system. The frequency 

was used to compute the maximum allowable operating slip 

by using Table 1 presented above. The calculated maximum 

slip was then used to compute the maximum rotational speed 

at any operating frequency. When this maximum rotational 

speed was exceeded, the pitch controller adjusted the 

rotational speed to operate within allowable operating range. 

The optimum operation of a wind turbine can be expressed 

as the target power Ptgt and written as 

 [11] ૜࢓࣓ࢊ࢔࢏࢝࢑ ൌ ࢚ࢍ࢚ࡼ

where ݇௪௜௡ௗ ൌ ଵ

ଶ ܥߩ௔௠௣௫ߨܴ௔௟௕ௗ௘

ହ ൬ ଵ

்ௌோ೟೒೟ ൰

ଷ

The tip speed ratio can be computed as 

ൌ ࡾࡿࢀ

ࢋࢊࢇ࢒࢈ࡾ ࢓࣓

ࢊ࢔࢏࢝ࢂ

[12] 

where TSRtgt is the target tip speed ratio where Cp = Cpmax.

The tip speed ratio shown in Equation 12 has a specific 

value called TSRtgt that corresponds to maximum aerodynamic 

efficiency Cpmax. TSRtgt is a constant value approximately 

between 8 and 9 for a commercial turbine. Thus, by keeping 

the tip speed ratio or the ratio between rotational speed (or 

operating frequency) to the wind speed, we can keep the 

operation of the WTG at maximum aerodynamic efficiency 

Cpmax. 

From Equation 11, we derived the equation of the output 

current for constant volt/hertz. Assuming a unity power factor 

operation at rated volt/hertz, the power equation can also be 

written as 

 [13] ࢙ࡵ࢙ࢂ૜ ൌ ࢍ࢚࢝ࡼ

From Equation 11 and Equation 13, we derived the output 

current as 

࢓࣓ ࡵ࢑ ൌ ࢙ࡵ

૛ [14] 

where ݇ூ ൌ ௄ೢ೔೙೏௉

଺௏ೄషೝೌ೟೐೏

 (Note: P here denotes the number of poles.)

0.4 0.52 0.64 0.76 0.88 1 − 0.08

0.04

0.16

0.28

60Hz, Slip = +/- 30%

Rated V/Hz, Slip = - 5%

Rated V/Hz, Slip = 5%

Rotor Power vs Rotor Speed

Rotor Speed (p.u.)

P_rotor (p.u.)

0

0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

Apparent Power from Converter vs Rotor Speed

Rotor Speed (p.u.)

S (p.u.)
5 

a) Plant level control flowchart 

b) Turbine level control flowchart 

c) Turbine level control block diagram 

Figure 9. Control implementation 

The torque can be expressed by modifying Equation 11 as 

follows 

࢓࣓ࢊ࢔࢏࢝࢑ ൌ ࢚ࢍ࢚ࢀ

૛ [15] 

From Equation 14 and Equation 15, we can see that the output 

current of the WTG is proportional to the electromagnetic 

torque of the generator; thus, the stator current is a convenient 

way to observe the electromagnetic torque. The power 

converter will always be controlled to follow the target power 

based on the operating speed. With this control algorithm, the 

aerodynamic output power will be optimized and the turbine 

will be operated in the Cpmax operating mode. More detail 

derivation of target power can be found in many literatures 

(e.g., [1]–[5]). 

Consider the operating condition of a DFIG connected to a 

grid of 60 Hz when the rotor winding is connected to a 

variable frequency source. The operating slip varies from -

0.25 p.u. to +0.25 p.u. The rotor speed of the low speed shaft 

reaches synchronous speed of the generator at 0.8p.u. 

(shownas Point A in Figure 10. The actual generator’s 

synchronous speed is 1,200 rpm (6 pole, 60 Hz). Thus, the 

generator is operated between 900 rpm and 1500 rpm, which 

correspondsto 0.6 p.u. to 1.0 p.u. at the low speed shaft. The 

power converter needed is 25% of the rated power of the 

generator. The operation of the WTG is depicted by the area 

covered by horizontal stripes. 

Consider the operating condition of a DFIG connected to a 

grid of 60 Hz when the rotor winding is connected to a power 

converter. The operating slip varies from -0.05 p.u. to +0.05 

p.u. The operation of the WTG is depicted by the area covered 

by gray shade. The synchronous speed is shown as Point B in 

Figure 10 (rotor speed=0.95 p.u.). The operation of this WTG 

is much narrower than the one with 25% rating power 

converter. However, the power converter for this operation is 

sized at only about 5% of the full rating of the generator. The 

operation of the WTG is depicted by the area covered by 

vertical stripes, with operating speed ranges from 0.9 p.u. to 

1.0 p.u. 

Figure 10. Variable speed operation at constant 60 Hz grid and 

variable speed operation at variable grid frequency. 
6

If the collector system was connected to a substation with 

an HVDC transmitting power from an offshore WPP inland, 

the operating frequency of the collector system would be 

adjustable. As shown in Figure 1, the HVDC was operated at 

rated volt/hertz, allowing the collector system voltage and 

frequency to vary with time. The operation of the WTG is 

depicted by the area covered by gray shade, with operating 

speed ranges between 0.9 p.u. and 1.0 p.u. Note that the area 

can be moved along the speed axis by changing the operating 

frequency of the HVDC at the offshore substation.

TABLE II

COMPARISON BETWEEN 60 HZ OPERATION AND HVDC OPERATED AT RATED 

VOLT/HERTZ

60 Hz

Operation

HVDC at rated

V/Hz

Rotor Speed 0.6p.u.–1.0p.u. 0.2p.u.–1.0p.u.

Power Converter 25% 5%

The operation of the WTG is depicted by the moving area 

covered by vertical stripes, with the operating speed varying

within 5% with respect to the operating synchronous speed.

The synchronous speed of the WTG changes with the HVDC 

operating frequency. For example, the synchronous speed is 

shown as Point B in Figure 10. When the HVDC frequency is 

moved to 0.4 p.u., the operating maximum slip variation is +

7.5%, and the operating rotor speed ranges between 0.325 p.u. 

and 0.475 p.u. Thus, as summarized in Table II, with the 

variable frequency collector system, a wider speed range of 

operation can be achieved with a small size power converter.

The converter size is very important, especially for a large 

wind turbine in offshore wind power deployment.

 2) Pitch Control Activation

The pitch controller must be deployed to shed some of the 

aerodynamic power, thus limiting the slip and consequently

keeping the stator current from exceeding the rated stator 

current. If the pitch angle is not changed, eventually the 

overload current may develop enough heat to cause insulation 

failure and short-circuit the stator winding. In addition, the 

power converter switches have very firm limits on current 

conduction capability.

If a wind turbine received a significantly higher wind speed 

than the VW-ave used to determine the frequency and voltage, it

would generate a higher output power and the output current 

could exceed the rated current. To protect an individual wind 

turbine from operating at an overload condition, pitch needs to 

be controlled to stay below its rated output current.

III. DYNAMIC SIMULATIONS

A. HVDC Control Implementation

A dynamic simulation of the HVDC control was 

implemented at the offshore substation. The dynamic 

simulations shown examined the behavior of one wind turbine 

under volt/hertz control; however, if wind diversity within the 

plant was assumed to be small, this turbine’s behavior would 

have been representative of the plant’s behavior. In Figure 11, 

the frequency of the collector system varied based on the 

average wind speed measured. This variation was computed 

based on Equation 12 presented above and illustrated in the

control block diagram shown in Figure 9.

The frequency was controlled to follow the wind speed 

variation to achieve maximum Cp operation for the majority of 

the turbines within the WPP. Similarly, the operating voltage 

was computed based on the variation of the frequency to 

maintain constant and rated volt/hertz, so that all the 

transformers and generators operated around rated flux and 

avoided magnetic saturation. Note that the operating 

frequency was limited at its rated frequency, which 

corresponds to the rated wind speed. Above rated wind speed, 

the frequency was constant, and the rotor speed was limited to 

its rated speed by controlling the pitch angle of the blades, 

limiting aerodynamic power from the wind.

B. WTG Electrical Control Implementation

The DFIG was operated at constant reactive power. The 

output power of the DFIG was controlled to follow the target 

power based on the variation of the rotational speed. (Refer to 

Equation 11 to compute the target power Ptgt and the control 

diagram shown in Figure 9.) The output power and reactive 

power of the DFIG is shown in Figure 12. The real and 

reactive power output of the DFIG was controllable 

independently and instantaneously. The WTG was operated 

with a combination of implementing electrical control of the 

power converter and aerodynamic control (pitch actuator). The 

output current as described in Equation 14 and Equation 15 

was proportional to the electromagnetic torque. By comparing 

Figure 13 and Figure 14, we observed the relationship 

between the output current and the electromagnetic torque. 

Figure 11. Variation of the wind speed and its corresponding 

frequency and voltage

0 50 100 150

6

8

10

12

14

16

18

time (s)

Wind Speed (m/s)

0 50 100 150

20

40

60

time (s)

Frequency (Hz)

0 50 100 150

0.4

0.6

0.8

1

time (s)

RMS Voltage (pu)
7

Figure 12. Real and reactive power output of the WTG

Figure 13. Output current of the WTG

C. WTG Aerodynamic Control Implementation

Figure 9 illustrates the aerodynamic control. The pitch angle 

was controlled to ensure that the rotor speed did not exceed 

the prescribed maximum operating slip (e.g., 5%); however, as 

described in Figure 4, there was headroom to double this 

maximum operating slip (to 10%) at half the rated speed.

Figure 13 shows that the pitch was successfully controlled 

to limit the rotational speed as obvious in the higher wind 

speed region, where the frequency of the collector system 

reached its limit, and the rotational speed was successfully 

limited by the aerodynamic control implemented via pitch 

controller.

Figure 14. The torque, rotational speed, and pitch angle

D. Harmony Among the HVDC Control, Electrical WTG 

Control, and Aerodynamic WTG Control

The harmony among different controls of the entire WPP is

illustrated in Figure 15. Consider the performance coefficient 

curve shown in Figure 15. In the lower wind speed region, the 

HVDC controlled the frequency to follow the wind speed 

average. The voltage output was also controlled so that the 

collector system connected to the HVDC at the onshore 

substation generated rated volt/hertz, ensuring that the 

electromagnetic fluxes within the WPP avoided saturation.

The power converter of the WTG ensured that the DFIG 

was at maximum operating Cp by following the target power 

expressed by Equation 11. As shown in Figure 15, in the first 

70 s of the simulation, the operating Cp was at its maximum.

As the wind speed increased, the maximum operating 

frequency was reached and the HVDC control was frozen to 

maintain constant voltage and constant frequency 

corresponding to rated volt/hertz.

Because we could not control wind speed, the pitch 

controller was activated when the wind speed increased

beyond its rated, thus avoiding a runaway situation. As shown 

in Figure 14 and Figure 15, the aerodynamic power was well 

maintained by the pitch controller by operating the WTG at a 

much lower aerodynamic efficiency (refer to the Cp between 

70 s and 95 s and between 115 s and 135 s).

Figure 15. Performance coefficient Cp and aerodynamic power

IV. CONCLUSIONS

Rated volt/hertz operation for an offshore WPP takes 

advantage of the availability of the HVDC-VSC to vary the 

frequency and voltage at the collector system. This paper 

investigates Type 3 WTG (DFIG) operated under rated 

volt/hertz. With uniform wind speed in an offshore WPP, the 

size of the power converter at each WTG can be minimized by 

matching the frequency of the collector system to the wind 

speed average. The use of a small power converter at 5% of its 

rated power proved to be sufficient for the wind speeds under 

consideration with possible additional slip range in lower wind 

0 50 100 150

1

2

3

time (s)

Real Power (MW)

0 50 100 150

-1

0

1

time (s)

Reactive Power (MVAR)

0 50 100 150 1

1.5

2

time (s)

RMS Current (kA)

0 50 100 150

-1.5

-1

-0.5

0

time (s)

Torque (pu)

Aero Tq

EM Tq

0 50 100 150

0.6

0.8

1

time (s)

Speed (pu)

Turb Spd

Gen Spd

0 50 100 150

0

5

10

time (s)

Pitch Angle (deg)

0 50 100 150

0

0.2

0.4

time (s)

CP

0 50 100 150

0

1

2

3

4

time (s)

P

aero (MW)
8

speed. The combination of controllers (HVDC, power 

converter, and pitch control) makes it possible to smooth out 

the output during transients, thus allowing a better mechanical 

compliance between the wind turbine and the generator while 

maintaining the Cpmax operation up to rated wind speeds.

V. FUTURE PLAN

At the conclusion of this study, we plan to test the concept 

at the National Renewable Energy Laboratory’s Energy 

System Integration Facility using small-scale units and Real 

Time Digital Simulator system with hardware in the loop.

Eventually, a field test is necessary to verify the control 

systems at our test site (National Wind Technology Center) 

using our 9MVA Grid Control Simulator. In future work, we 

will quantify the benefit of implementing this concept from 

the energy yield point of view, and also study the impact on 

WPP dynamics of various control schemes.

VI. ACKNOWLEDGMENT

This work was supported by the U.S. Department of Energy 

under Contract No. DE-AC36-08-GO28308 with the National 

Renewable Energy Laboratory.

VII. REFERENCES

[1] Bodin, A. “HVDC Light—A Preferable Power Transmission System for 

Renewable Energies.” Proceedings of the 2011 Third International 

Youth Conference on Energetics; July 7–9, 2011, Leiria, Portugal.

[2] Rui, O; Thon, J.; Sand, H.; Waalman, J.G.; Bjerknes, O.J.; and Karijord,

K. “Design and Operation of an Offshore Node Connected to Wind 

Parks, Oil Platforms as Well as a Multiterminal HVDC Grid.” Ninth 

International Workshop on Large-Scale Integration of Wind Power into 

Power Systems as well as on Transmission Networks for Offshore Wind 

Power Plants, Oct. 18-19, 2010, Québec City, Canada.

[3] MacLeod, N.M.; Barker, C.D.; and Kirby, N.M. “Connection of 

Renewable Energy Sources through Grid Constraint Points using HVDC 

Power Transmission Systems.” 2010 IEEE PES Transmission and 

Distribution Conference and Exposition, April 19–22, New Orleans, 

Louisiana.

[4] Feltes, C.; Wrede, H.; Koch, F.W.; and Erlich, I. “Enhanced Fault RideThrough Method for Wind Farms Connected to the Grid Through VSCBased HVDC Transmission.” IEEE Transactions on Power Systems (24:

3), Aug. 2009.

[5] Feltes, C., and Erlich, I. “Variable Frequency Operation of DFIG-Based 

Wind Farms Connected to the Grid Through VSC-HVDC Link.” IEEE 

Power Engineering Society General Meeting, June 24–28, 2007, Tampa, 

Florida.

[6] Trilla, L.; Gomis-Bellmunt, O.; Junyent-Ferre, A.; and Sudria-Andreu, 

A. “Analysis of Total Power Extracted with Common Converter Wind 

Farm Topology.” XIX International Conference on Electrical Machines, 

Sept. 6–8, 2010, Rome, Italy.

[7] Jovcic, D. “Interconnecting Offshore Wind Farms Using Multiterminal 

VSC-based HVDC.” IEEE Power Engineering Society General Meeting, 

June 18–22, 2006, Montreal, Quebec, Canada.

[8] Gevorgian, V.; Singh, M.; and Muljadi, E. “Variable Frequency 

Operations of an Offshore Wind Power Plant with HVDC-VSC.”

Preprint. Prepared for IEEE Power Engineering Society General 

Meeting, July 22–26, 2012, San Diego, California: Available at 

http://www.nrel.gov.

[9] Barthelmie, R.J.; Frandsen, S.T.; Nielsen, M.N.; Pryor, S.C.; Rethore, 

P.-E.; and Jørgensen, H.E. “Modeling and Measurements of Power 

Losses and Turbulence Intensity in Wind Turbine Wakes at 

Middelgrunden Offshore Wind Farm.” Wind Energy (10: 6), 2007; pp.

1099-1824.

[10] de Prada Gil, M.; Gomis-Bellmunt, O.; Sumper, A.; and Bergas-Jané, J. 

“Analysis of a Multi-Turbine Offshore Wind Farm Connected to a 

Single Large Power Converter Operated with Variable Frequency.”

Energy (36: 5), May 2011; pp. 3272–3281:

http://www.sciencedirect.com/science/article/pii/S0360544211001769.

VIII. BIOGRAPHIES

Eduard Muljadi (M’82, SM’94, F’10) received his 

Ph.D. in electrical engineering from the University of 

Wisconsin at Madison. From 1988 to 1992, he taught 

at California State University at Fresno. In June 1992, 

he joined the National Renewable Energy Laboratory 

in Golden, Colorado. His current research interests are 

in the fields of electric machines, power electronics, 

and power systems in general with an emphasis on 

renewable energy applications. He is member of Eta Kappa Nu and Sigma Xi,

a Fellow of the Institute of Electrical and Electronics Engineers (IEEE), and 

an editor of the IEEE Transactions on Energy Conversion. He is involved in 

the activities of the IEEE Industry Application Society (IAS), Power 

Electronics Society, and Power and Energy Society (PES). He is currently a 

member of various committees of the IAS, and a member of the Working 

Group on Renewable Technologies and the Task Force on Dynamic 

Performance of Wind Power Generation, both of the PES. He holds two 

patents in power conversion for renewable energy.

Mohit Singh (M’11) received his M.S. and Ph.D. in 

electrical engineering from the University of Texas at

Austin in 2007 and 2011 respectively. His research is 

focused on dynamic modeling of wind turbine 

generators. Dr. Singh is currently working at the 

National Renewable Energy Laboratory (NREL) in

Golden, Colorado, USA, as a post-doctoral researcher in 

transmission and grid integration of renewable energy. 

His current interests include modeling and testing of 

various applications of wind turbine generators and other renewable energy 

resources. He is a member of the IEEE. He is involved in the activities of the

IEEE Power and Energy Society (PES).

Vahan Gevorgian (M’97) graduated from the Yerevan 

Polytechnic Institute in Armenia in 1986. During his 

studies, he concentrated on electrical machines. His 

thesis research dealt with doubly fed induction 

generators for stand-alone power systems. He obtained 

his Ph.D. in electrical engineering from the State

Engineering University of Armenia in 1993. His 

dissertation was devoted to modeling electrical transients 

in large wind turbine generators.

Dr. Gevorgian is a research engineer at the National Wind Technology

Center of the National Renewable Energy Laboratory in Golden, Colorado.

His current research interests include modeling and testing various

applications of small wind turbine–based power systems.