Abstract—In order to avoid stability problems, LVRT

requirements (Low Voltage Ride Through) demand Wind

Energy Conversion Systems (WECS) to remain connected to the

grid in the presence of grid voltages dips. Because 88% of the

grid failures are asymmetrical, positive and negative sequence

components have to be controlled to fulfill LVRT requirements.

This paper present a comparison between synchronous and

stationary reference frame control strategies for an active front-

end converter of a grid connected WECS working under grid

fault conditions. The mathematical analysis and design

procedure of both control system are presented in this work.

Experimental results obtained from a 3kW prototype are fully

discussed in this paper. The experimental implementation is

realized using a novel implementation of a voltage sag generator

which is based on a 3x4 Matrix Converter

Index Terms—Low Voltage Ride Through, Resonant

Controllers, Wind Energy Conversion Systems, Voltage Sag

Generators.

I. INTRODUCTION

IND ENERGY has become one of the industries with

the greatest and fastest growth in the renewable energy

sector [1]. The wind energy production capacity for the whole

world in 2012 was 282-GW [1]. Moreover, the penetration of

wind energy is steadily increasing. A good example is Spain,

where the average wind energy penetration has been 11%,

13.8%, and 16% in 2008, 2009, and 2010, respectively [x]–

[x]. Therefore, some rather strict grid codes are enforced in

countries with relatively high penetration of wind energy, in

order to regulate the connection of large wind energy parks to

generation and transmission systems. In these grid-codes,

Low-Voltage Ride-Through (LVRT) requirements demand

wind-power plants to remain connected in the presence of

grid-voltage dips, contributing to keep grid voltage and

frequency stable. According with [2], [3], [4], in the presence

of a grid-voltage dip, the requirements of the LVRT control

strategy are:

To maintain the WECS connected to the grid, when the

line voltage is inside the boundaries specified in Fig.

1(a).

To support voltage regulation in the power system. This

is accomplished through the consumption/injection of

reactive power by the grid side converter (see Fig. 3).

Typically only 12% of the grid-faults are symmetrical;

therefore, LVRT control system has to be able to deal with

positive and negative sequence currents and voltages. Several

Control systems for LVRT operation have already been

presented in [5], [6], [7], [8]. In most of these papers the

controllers are based on revolving synchronous rotating d-q

axe where the negative and positive sequences are transformed

2014 Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER)

Analysis of Synchronous and Stationary Reference

Frame Control Strategies to Fulfill LVRT Requirements

in Wind Energy Conversion Systems

Matías Díaz

University of Chile

Av. Tupper #2007

Santiago, PC PC 8370451 , Chile

Email: matias.diaz@ing.uchile.cl

Roberto Cárdenas

University of Chile

Av. Tupper #2007

Santiago, PC PC 8370451 , Chile

Email: rcd@ieee.org

W

a)

a)

b)

Fig. 1. LVRT Requirements of the Spanish grid code. (a) Limit of the grid

voltage dip. (b) Demanded Reactive Current in function of grid-voltage dip.

into dc signals and controlled using standard PI regulators.

Resonant controllers (RC) are well suited to manage positive

and negative sequence components of grid voltage [9], [10],

but no attention has been paid to stationary axis based control

systems under grid fault condition, in order to study WECS

LVRT requirements fulfillment.

This paper is focused on the comparison of synchronous

and stationary reference frame based control strategies to

fulfill the LVRT requirements for a system similar to Fig.

1(a). The system is composed of a wind turbine connected to

the grid through a low voltage two level Back to Back

converter. Low voltage two-level voltage-source converters

are the most used topology in WECS [11], [12], [13], [14]. In

this work it is assumed that the dc-link voltage is fairly

constant, both in steady state and under grid fault conditions

[2]. Therefore, grid-side and generator-side operations are

decoupled and only the control of the grid-side converter is

considered.

II. CONTROL STRATEGY

When a grid-voltage dip appears, the power injected to the

grid is decreased as a function of the voltage reduction,

therefore is not possible to supply to the grid all the power

produced by the machine. An active power surplus is stored in

the dc-link, resulting in an unacceptable dc-link voltage

increase that can be dangerous to the Back-to-Back converter.

Furthermore, the unbalance between the power generated and

the power supplied to the grid induces an increase in the speed

of the generator due to the mismatch between the mechanical

input power and electrical output power [2], [15], [16]. To

avoid this, Back-to-Back power converters are usually

equipped with a dc-link-voltage limiter unit (Crow-Bar,

Braking Chopper) [13], [14]. Therefore, generator side

converter and/or dc-link Crow Bar regulate the active power

surplus through grid-voltage dips, and the assumption of

decoupled generator-grid side converter is realistic [2], [17].

For asymmetrical grid-voltage dip conditions, a separation

sequence method is required to guarantees correct grid

frequency detection due to the second harmonics produced by

the negative sequence is reflected in the grid-frequency

estimation [18], [19].

To improve the performance of the PLL, positive sequence

extraction is included in some advanced 3-phase PLL

structures, such as the 3-phase enhanced PLL (EPLL), double

second order integrator PLL (DSOGI-PLL), decoupled double

synchronous reference frame PLL (DDSRF-PLL), delayed

signal cancellation PLL (DSC-PLL) [20].

Delayed-signal-cancellation (DSC) is probably the best

suited method to separate sequences [21], [22]. This method

presents an intrinsic delay of T/4 and is described in the Fig. 3.

Regarding DSC, the PLL is employed to synchronize the

active Front-End converter to positive sequence of the grid

voltage at the Point of Common Coupling (PCC) [23], [24]

and [25].

III. CURRENTS REFERENCES CALCULATION

The apparent power at grid terminal, calculated considering

three-leg unbalanced system with positive -and negative-

sequence components, is show in (7):

(

) (

) (1)

The superscripts (c), (p), and (n) are used to denote the

complex conjugate of the current vector, positive-sequence

component and negative-sequence component, respectively.

Developing the previous equation and separating real and

imaginary parts:

(2)

(3)

and are the grid average active and reactive power.

Furthermore, and as it is well known, an unbalanced grid-

voltage dip produces double frequency components in both

active power as reactive power, represented by

,

,

.

A. Synchronous Reference Frame Current Reference

Calculation

According to [26], (11)-(12) could be expressed in function

of sequence components voltages/currents in d-q frame as

follow:

Fig. 2. (a) Wind generator connected to the grid through a Back-to-Back

converter. (b) Grid-Connected Front-End Converter.

Fig. 3. Delay Signal Cancellation Method.

(

) (4)

(5)

(6)

(7)

(8)

(9)

The system described by (4) - (9) has four degrees of

freedom (

) to control six variables (

, , . Therefore it is necessary to

make a choice of variables according to the control objectives.

Mainly, the reference currents are setting to regulate average

active and reactive power and to eliminate the

double frequency oscillations in the active power ( ).

Reactive power oscillations ( , ) are not controlled in

any case. Therefore, it is possible to write (4)-(7) in matrix

notation:

[

]

[

]

[

]

(

(10)

B. Stationary Reference Frame Current Reference

Calculation

Follow the same procedure, it is possible to demonstrate

that (2)-(3) can be represented by sequence component

voltages/currents in the natural frame:

(11)

(12)

(13)

(14)

(15)

(16)

The apparent power at Front-End converter terminal follows

the same structure than (2) and (3), and the next expression

gives the power balance at the Front-End terminals (see Fig.

8):

(17)

is the apparent power dissipated in the filter. It contains

average active and reactive power terms and cosine and sine

component oscillating with double grid frequency. The active

powers dissipated in the filter are obtained from [21], [27].

(

) (18)

(

) (

) (19)

(

) (

) (20)

Where is the average active power dissipated in the

filter, and are the double frequency active power

components.

It is also important to note that the system described by

(11)-(16) has four degrees of freedom (

) to

control six variables ( . In this

case, reactive power oscillations ( ) are not

controlled again.

Two different current references methods are presented.

The first one, considers that the Front-End converter supplies

the oscillating active power to the filter, which results in zero

oscillating active power components on the grid side, i.e.

.

[

]

[

]

[

] (21)

In the second case, the oscillating powers flow from the grid

into the filter, therefore oscillating active power components

are regulated to zero at the Front-End terminals,

and .

[

]

[

]

[

]

(22)

IV. SYNCHRONOUS REFERENCE FRAME CONTROL (SYN-RFC)

This strategy is based in [6], [8]. Implementations for

LVRT fulfillment can be found in recent literature [27], [28]

and [29]. Positive and negative-sequence components are

regulated by independent rotational frame PI controllers.

“Positive sequence current controller” rotates , that

correspond to the angle of the positive sequence voltage

component, founded by DSC-PLL. “Negative sequence

current controller” rotates with - . A schematic of the d-q

control is represented in Fig. 4. Proportional Integral (PI)

controllers are used since they have correct behavior

controlling dc variables.

For improving the performance of the PI controller, cross-

coupling terms and voltage feedforward are considering.

V. STATIONARY REFERENCE FRAME CONTROL (ST-RFC)

Mainly, all strategies used in LVRT are based on

conventional d-q frame control systems explained in previous

section. Instead synchronous reference frame, the use of

stationary reference frame current controllers based on RC is

presented and development in this section.

Fig.4: Synchronous Reference Frame Control Strategy.

A RC have a couple of purely imaginary poles, with a

resonant frequency of , found by the DSC-PLL. In the z-

plane, a RC controller has the follow transfer function [9],

[10]:

( ) ( )

( ) ( )

(23)

Where: represents the distance between the pole and zero;

represent the sampling time; is the controller gain.

A schematic of the proposed control is represented in Fig. 5

Positive and negative-sequence components are regulated by

the same RC. Each RC regulate line current get the current

reference calculated according to the method explain in

previous section. In this strategy, line current and voltages are

measured and trigonometric functions required to transform

from - to d-q coordinates (and vice versa) are not used for

the implementation.

RCs are designed using root locus in the z-plane. The

controllers should have an appropriate dynamic response

during grid-voltage dips, therefore, a second order lead lag

network is added for improvement of dynamic behavior [10].

The expression for the controller considering RC and lead lag

network is presented in (24):

(24)

The controller presented in (25) has been designed

considering: =500µs, closed loop poles damping

coefficientof 0.35, =100π rads-1, =5 , =0.5 . The

root locus of the proposed control system is shown in Fig. 7:

(25)

If the frequency at the PCC “ ” is proportioned for the

DSC-PLL, (25) represents a Self Tuning Discrete Resonant

Controller that can be easily implemented in a digital signal

processor.

VI. EXPERIMENTAL IMPLEMENTATION

The experimental system attempts to emulate the WECS

presented in Fig. 1(b) through the implementation of a low

power grid-connected Front-End converter. The SVM

algorithm, d-q based controllers, RC and all control structures

were implemented using a DSP based board and a FPGA –to

generate signal IGBT drivers, IGBT’s dead time, hardware

protection–. The DSP board used in this application is based

on a TMS320C67 processor. For data acquisition purposes a

board with ten analogue to digital channels and 1-

conversion time is interfaced to DSP.

αβabc

~

αβabc

αβ

abc~ ~

DSC

DSC

+

-

-

+

PI

αβ

dq

αβ

dq

PI

+

+

+

+-

Positive Sequence Current Controller

DSC

DSC+

-

-

+

PI

αβdq

αβ

dq

PI

+

+

+-

Negative Sequence Current Controller

αβdq

αβdq

Current

References

Calculation

PLL

+

+

Fig.5: Stationary Reference Frame Control Strategy

Fig.6: Root locus for controller shown in (25).

A 3-kW grid-connected two-level Front-End converter is

used. The switching frequency is set to 2-kHz. Discrete RC’s

and PI regulators have been calculated for 500-us sample time.

Three Hall-Effect voltage transducers are used to measure the

grid and dc-link voltages. Also, two Hall-Effect current

transducers are used to measure the grid currents. The Front-

End converter is connected to the grid using a first order filter

of 20-mH 0.5-Ω.

The grid-voltage dips have been produced a using a novel

3-kVA Matrix Converter Voltage Sag Generator, implemented

on a DSP board based on a high performance TI TMS320C67

processor, capable of a performance of 1350MFLOPS. For

data acquisition purposes an external board, with ten Analogue

to Digital (ADC) channels of 14bits, 1-μs conversion time

each, is interfaced to the DSP.

VII. EXPERIMENTAL RESULTS

This section presents experimental results for the system

shown in Fig.7. This Experimental Rig has been tested under

grid-voltage dip type B and C conditions [30]. Different tests

are carried out to validate the proposal strategy and to

compare it with the traditional d-q control scheme presented

in Fig.4. In all the cases, active power, line current and

reactive power responses are presented. The sag conditions

have duration of 140-ms and are produced by the Matrix

Converter based VSG. In state steady, the voltage in the PCC

is controlled to 110-V (rms value), the active power is set to

1-kW and the reactive power reference is controlled to 0-

kVA, in order to work with unitary power factor.

Test 1: 35% Grid-voltage dip type B.

Fig. 8 shows that Syn-RFC strategy is able to keep the

control through the grid-voltage dip. There is not presence of

double-frequency oscillations in active power (calculations

presented in (22) are also valid for synchronous reference

frame), but reactive power presents double frequency

oscillations that flows between the grid and the filter. At the

fault time appearance, the active power delivered to the grid

is 0-kW, and the Front-End starts to support to the grid

voltage through reactive power injection. When the fault is

over, the systems come back to state steady references.

The same behaviour is observed in waveforms presented in

Fig.9. In this case, St-RFC strategy is utilised. During the

grid-voltage sag condition, the active power delivered to the

grid is 0-kW and the Front-End to support to the grid voltage

through reactive power injection. For both strategies, line

currents are slightly distorted and unbalance during the sag,

mainly due to the control objective is to regulate the power

and not the current.

100

101

102

103

104

105

-400

-300

-200

-100

0

P.M.: 41.6 deg

Freq: 6.8e+003 rad/s

Frequency (rad/s)

Ph

ase

(d

eg

)

-300

-200

-100

0

100

G.M.: 3.33 dB

Freq: 8.35e+003 rad/s

Stable loop

Open-Loop Bode for (6)

Ma

gn

itu

de

(d

B)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.26e3

2.51e3

3.77e3

5.03e36.28e3

1.26e3

2.51e3

3.77e3

5.03e36.28e3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Real Axis

Root Locus for (6)

Ima

g A

xis

0.85 0.9 0.95 1

-0.05

0

0.05

0.1

Zoom Root Locus for (6)

x

Plant

RC

Pole

xo

RC

ZeroLL

Zero

Fig. 7. Experimental System.

Fig. 8: Syn-RFC responses for 50% Grid-Voltage Dip Type B. Up: Grid

Voltage. Medium: Grid Currents. Lower: Active and Reactive Power.

Fig. 10: Syn-RFC responses for 30% Grid-Voltage Dip Type C. Up: Grid

Voltage. Medium: Grid Currents. Lower: Active and Reactive Power.

The responses using Syn-RFC are presented in Fig. 10. In

this case, a grid-voltage dip type C is tested. At the beginning

of the sag, phases A and C drop from 110 to the 35 .

In order to fulfil LVRT, the reference to reactive power

injection through the grid-voltage dip is 0.5 kVA.

Fig.11 presents the performance of St-RFC to the same

grid-voltage sag condition. Both strategies to allow grid

voltage support by reactive injection while the grid-voltage

dip is present. However, St-RFC presents slightly better

dynamic behaviour. At the appearance/clearance fault time -

using Syn-RFC- line current reaches 14 A, almost 3 times the

rated value. With St-RFC line current overshoot is lower,

reaching 9 A at the clearance fault time. An amplified view of

the line current is presented in Fig.13.

The time required by the DSC method to separate the

positive and negative sequences is very short, and it is

included within the sampling time (500 us) of the DSP

controller. Hence, this calculation time does not affect the

control dynamics.

Fig.9: St-RFC responses for 50% Grid-Voltage Dip Type B. Up: Grid

Voltage. Medium: Grid Currents. Lower: Active and Reactive Power.

Fig. 11: St-RFC responses for 30% Grid-Voltage Dip Type C. Up: Grid

Voltage. Medium: Grid Currents. Lower: Active and Reactive Power.

However, when a fault appears, inaccurate values are feeding

to the control systems during of the period. An amplified

view of the line current is shown in Fig.12.

Fig. 12: St-RFC responses for 30% Grid-Voltage Dip Type C. Left: Current response at fault appearance time. Right: Current response at fault clearance

time.

VIII. CONCLUSIONS

A comparison between Syn-RFC and a novel control

strategy, dealing with sequence components under unbalanced

voltage conditions, have been presented in this paper.

Proposed control strategy (St-RFC) is based on the use of

Resonant Controllers to regulate line currents in stationary

frame and is able to fulfill LVRT requirements.

According to experimental results, both strategies present

correct performance under unbalance grid-voltage conditions.

This fault conditions have been generated by a Matrix

Converter based VSG. In all the cases, the voltage sags

generated do not present peaks, transient effects or low

reliability. Therefore, the good performance of the novel VSG

has been ratified to test LVRT capability in grid-connected

systems.

Syn-RFC and St-RFC strategies are able to keep the system

grid-connected and to support grid-voltage through reactive

power injection when grid-voltage sag appears. Therefore,

both strategies meet LVRT requirements. However, St-RFC

strategy has slightly better dynamic behavior. St-RFC is more

stable and faster than Syn-RFC, mainly due to the lead lead

network, added to the RC in order to increase the dynamic

behaviour and stability. Also, St-RFC is simpler than Syn-

RFC. A single RC could be used to regulate the positive and

negative sequence current and no transform from d-q to α-β

are needed. Additionally, for LVRT control, orientation along

any of the voltage or current vectors is not required and a PLL

is implemented only to obtain the grid-frequency which is

used to tune the resonant controller.

DSC presents a delay of T/4, which does not affect under

steady-state operation, but makes an inexact sequence

separation during the firts 5-ms (T=20-ms) after the

appearance of any grid-voltage dip. During this 5-ms,

inaccurate values are fed back to the control system. The

result of these inaccuracies can be observed in all responses

(currents and power), and explain the presence of non-desired

values during the 5-ms after at the appearance and clearance

fault time. Despite of the inaccuracies produced by DSC

method and the Voltage Sag Generator System, the results

obtained are acceptable for all the tests.

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