Emulation of an Isolated Wind Energy Conversion System: Experimental Results - Final Report

DAAD Short-Term Research Internship

Final Report

02 February – 24 August – 2007

Author

Roberto Galindo del Valle

Supervisor:

Prof. Dr.-Ing. W. Hofmann

Chemnitz, Germany, August 24th, 2007

Final Report of the Short Term Research Internship at Chemnitz University of Technology February, 2nd 2007 – August, 24th 2007

DAAD Short-Term Research Scholarship Roberto Galindo del Valle 2

TABLE OF CONTENTS

1 Introduction 4

2 Considered Activities 4

3 System Description 5

4 Modifications made to the Experimental Test Bench 7

4.1 First Modification 7

4.2 Second Modification 8

4.3 Last Modification Proposal 9

5 Design and Simulation of the PI Controllers for the Isolated System 10

5.1 Controllers associated with the Doubly-Fed Induction Generator (DFIG) 10

5.1.1 Rotor Current Controllers 11

5.1.2 Stator Voltage Controller 12

5.2 Controllers associated with the Front End Converter (FEC) 14

5.2.1 FEC Current Controllers 14

5.2.2 dc-Link Voltage Controller 15

6 Experimental Results obtained with the PI Controllers 16

6.1 Controllers associated with the Doubly-Fed Induction Generator (DFIG) 17

6.1.1 Rotor Current Controllers 17

6.1.2 Stator Voltage Controller 17

6.2 Controllers associated with the Front End Converter (FEC) 18

6.2.1 FEC Current Controllers 18

6.2.2 dc-Link Voltage Controller 18

6.3 Experimental Tests Concerning the Operation of the Complete System 19

6.3.1 Connection of the Complete System 19

6.3.2 Decreasing of the q Component of the FEC Current 21

6.3.3 Speed Ramp 22

6.3.4 Load Ramp 23

6.3.5 Dependency of the Generated Voltage on the Component q of the Rotor Current

23

6.3.6 Turn-off Procedure 23

7 Experimental Assessment of the Black Start Capability 24

7.1 Self-Excitation of the Doubly-Fed Induction Generator 24



7.2 dc-Link pre-charge by using the Self-Excitation Phenomenon 26

7.3 Use of the Self-Excitation Phenomenon for Black Start Purposes 26

8 Analysis of the Operating Conditions for Minimum Copper Losses 27

9 Proposed Implementation Method for the Sliding Mode Controllers 28

9.1 Background: The Considered Design Method for Sliding Mode Controllers 28

9.2 The Proposed Implementation Method 29

10 Conclusions 29

11 References 31

Appendix “Optimal distribution of the reactive power” 32



1 Introduction This document is associated with the short-term research internship the author have carried out at Chemnitz University of Technology in order to implement the control of an Isolated Wind Energy Conversion System. This internship has been developed in the laboratory of the Department of Electrical Machines and Drives, belonging to the Faculty of Electrical Engineering, under the supervision of Professor Wilfried Hofmann. For readability reasons this document is organized as follows: In Section 2 a brief list and summary of the considered activities is presented. In Section 3 the considered system is described. In Sections 4 to 9 a more detailed account of the main activities is given. Finally, the conclusions of this work are presented and a list of possible future related works or activities is proposed.

2 Considered Activities During the short-term internship this Report is related to, the next activities were carried out:

1. Collaboration for the commissioning of the new back-to-back (B2B) converter for the test bench of interest. At the same time, a first approach to the used software platform and some theoretical analysis were considered.

2. Proposal and execution of the necessary modifications in order to add to the test bench the capability of isolated system emulation. Two different, and subsequent, modifications were proposed and carried out to give the test bench some emulation flexibility for it to be able to function as an isolated system. These modifications consisted in the addition of a switch that reconfigures the system wiring to change from grid connected to isolated system. It is thought that a third modification is necessary in order to enhance the test bench capabilities. With this modification it would be possible to test the black-start capabilities of the isolated system, which consist in the ability to star from zero, in a completely independent way. The modifications proposed are presented in Section 4.

3. Design and simulation of PI controllers for the isolated WECS. Classical PI controllers were designed for the different subsystems of the isolated WECS by using the root locus method. These controllers were subsequently simulated in MatLab/Simulink. This is considered in Section 5.

4. Implementation of the designed PI controllers by using the dSpace platform, which is briefly presented in Section 6.

5. Isolated WECS experimental tests. Several experimental tests regarding start, turn off, step responses, and regulation performance were considered. The results are given in Section 6.

6. Assessment of some experimental issues associated with the black start of the isolated WECS. Several tests were carried out in order to reproduce the self-excitation of the electrical generator and to verify its usefulness for the black start capability. The results of this activity are considered in Section 7.

7. In accordance with the features of the considered isolated WECS, an analysis of the operating conditions for minimizing the electrical losses in the copper wires, and some associated experimental tests were carried out. This is presented in Section 8.

8. An implementation method for some sliding mode controllers –which were designed in México–, and an associated theoretical result, were developed. Unfortunately, time was not enough to implement these controllers and no experimental results were obtained. This topic is presented in Section 9.



3 System Description In this work it has been considered an isolated WECS, which is depicted in Fig. 3.1. In this system, energy is collected by a wind turbine (WT), whose blades convert the kinetic energy contained in the air flow into mechanical energy which is transferred to a doubly-fed induction generator (DFIG) by a rotational movement through a drive train (DT). The DT increases the rotational speed using a gear box (GB). The DFIG transforms the received mechanical energy into electrical one in order to supply an isolated load (both main and auxiliary). The system operation is controlled by a B2B converter. The B2B is composed by two bi-directional AC-DC converters connected by their backs through a capacitive dc-link. At this first stage, only a main star-connected resistive load has been considered and the WT has been emulated by a speed-controlled dc motor. In the WECS, the front end converter (FEC) manages the power flow between rotor and stator circuits by a cascaded control system, in which the inner loop controls the converter currents and the outer one regulates the dc-link voltage. In a similar way, the machine side converter (MSC) uses a cascaded control system in order to control de DFIG current, in the inner loop, and the generated voltage, in the outer one. Originally, this scheme has been taken from [Peña et al., 1996c], but some modifications have been considered.

MSC FEC

DFIGGB

WT

Back-to-back Converter

VCM1

VCM2

VCM3

Controller 1 (SMC)

Controller 2 (PIs)

LegendWT = Wind Turbine.GB= Gear Box.DFIG = Doubly Fed Induction Generator.MSC= Machine Side Converter.FEC= Front End Converter.VCM= Voltage and Current Measurement.

Auxiliary LoadMain Load

Low SpeedSide

High SpeedSide

Stator

Rotor

Fig. 3.1. Wind Energy Conversion System (WECS) to supply an isolated load.

In the considered WECS, the active power flow can suffer some changes which depend on the operating speed, as shown in Figs. 3.2 and 3.3. The DFIG has a synchronous speed, which is imposed by its design, i.e. the generator number of poles and by the electric frequency of the signals the DFIG is designed to work with. The flow of the mechanical, stator, and rotor powers is defined to be positive when it is directed towards the DFIG and negative in the opposite case. In addition, the power is considered positive when it is directed towards the FEC and outwards the MSC, otherwise it is negative. This way, under normal operating conditions, mechanical power is always being injected to the system (Pm>0), whilst stator is invariably producing active power (Ps<0). Furthermore, when the DFIG is operating at a speed lower than the synchronous (i.e. sub-synchronous operation), Ps is delivered to the load and to the FEC (PL>0 and Pfec>0), whilst the FEC transfers its power to the DFIG rotor through the MSC (Pmsc>0 and Pr>0), as shown in Fig. 3.2. On the other hand, when the DFIG is operating at a speed higher than the synchronous one (super-synchronous operation), the load active power is supplied by both the stator and the FEC (PL>0 and Pfec<0). The FEC active power is



received from the rotor through the MSC (Pmsc<0 and Pr<0), as shown in Fig. 3.3. With respect to the reactive power flow, at this moment it can only be said that the DFIG requires some magnetizing reactive power, which can be provided by the stator and/or the rotor. If one of them provides a reactive power higher than the magnetizing one, then the other will be able to deliver the excess to its associated circuit. At the same time, the filter capacitor is producing a generated-voltage dependant reactive power (in almost the same quantity needed for the DFIG magnetizing), whilst the FEC and the MSC are able to consume or to produce reactive power under certain limits. Furthermore, the load reactive power is arbitrary and dictated by the users necessities.

MSC FEC

LZ

1Z 2ZcjX

sP

LP FP

fecPmscP

rP

sQ

rQ

LQFQ

mscQ fecQ

cQ

DFIG

mP

Fig. 3.2. Power flow in the isolated system during sub-synchronous operation.

MSC FEC

LZ

1Z 2ZcjX

sP

LP FP

fecPmscP

rP

sQ

rQ

LQFQ

mscQ fecQ

cQ

DFIG

mP

Fig. 3.3. Power flow in the isolated system during super-synchronous operation.

Accordingly with the above mentioned comments, the per-phase power flow is described by the expressions (3.1)-(3.7).

0s L FP P P+ + = (3.1)

2F fecP P P= + (3.2)

fec mscP P= (3.3)

1msc rP P P= + (3.4)

0s L FQ Q Q+ + = (3.5)



2F C fecQ Q Q Q= + + (3.6)

1msc rQ Q Q= + (3.7)where: P stands for the active power [W] and Q for the reactive power

[VAR], whilst the variables are identified by using the subscript: s for the stator, r for the rotor, L for the load, fec for FEC, msc for the MSC, C for the filter capacitor, 1 for the elements that connect the MSC with the rotor and 2 for the ones that connect the FEC with the stator.

4 Modifications made to the Experimental Test Bench 4.1 First Modification Initially, the test bench was only able to emulate a grid-connected WECS, in which both the stator and the rotor circuits1 were connected to the secondary of the input transformer. This way, the first proposed and executed modification was a very simple one, which consisted in the addition of a switch in order to change the connection of both the stator and the rotor circuits from the secondary of the input transformer to an isolated load. This situation is shown in Fig. 4.1, in which the two-position switch S5 is used to select the type of application of interest: grid-connected or isolated. At this stage, only star-connected resistive loads have been considered.

Fig. 4.1. Electrical diagram of the test bench after the first modification was made. The two-position switch S5 was introduced to change the emulated system from grid-connected to isolated.

1 In this document “rotor circuit” means the circuit formed by the LC filter, the back-to-back AC↔AC converter and the DFIG rotor terminals.

Umrichter

LC - Filter

Trafo380V/0..400V

DSAG

Netz400 V50 HzS1

250 A500V

S4100 A500V

S3, Sks25 A

500V

1

2

S3 - Schalter Zustand0 Stillstand1 Generator Anlaß2 Normale Betrieb

LfLf

C fC f

S225 A500V

Crow-bar

F1250 A

0

AA

VVAA

VV

RWR NWR

Vorladung

VV

GZK

U_n400V

I_s25A I_n

25AU_s400V

U_r400V

AA

VV

S_v

S_ü

I_dc-+25A

+

U_1600V

R_v

_

F_v25 A

GS-Schiene/Batterie GZK

+

_

Synchronisierung

Chopper

LrLr

GSM

Ein

Aus

M entor

Lufter

Feld

S_Feld

K1

3x Ir 3x In

2x Un

Udc

16A

25A63A

Schirmung

AA

VV

Strommessung

Spannungsmessung

Strommessanzeige

Spannungsmessanzeige20A

40A

40A

AA

VV

250 A

Verteiler

Vorladung

3x Is

VV U_2600V

Isolated Load1 2

S525 A500V

First modification



4.2 Second Modification In a second stage, it was desired to add more flexibility to the test bench, in order for it to be able to emulate an isolated system or two kind of grid connected ones. In Fig. 4.2.1 a schematic diagram is presented, in which it can be seen that if the points I and II are connected to B and D, respectively, then both the stator and the rotor circuits are tied to the secondary of the input transformer. On the other hand, if the points I and II are connected to A and D, respectively, then the stator is connected to the grid, whilst the rotor circuit (through the FEC) is connected to the secondary of the transformer. Finally, the isolated system operating mode is achieved by connecting the points I and II to B and C, respectively.

IsolatedLoad

MSC FEC

DFIG

Electrical Grid

Transformer

AI II

D

B C

L1 L2r 1 r 2

Cf

Fig. 4.2.1. Schematic diagram of the test bench after the second modification was made. It was introduced a new three-position switch to configure the emulated system as a: (1) grid-connected system with both the stator and the rotor circuits tied to the secondary of the input transformer [connecting I to B and II to D], or (2) grid connected with the stator tied to the mains and the rotor circuit to the secondary of the transformer [connecting I to A and II to D], or (3) an isolated system with both the stator and the rotor circuits tied to the load [connecting I to B and II to C].

In accordance with this objective, the former switch S5 was substituted with a three-position one, as shown in Fig. 4.2.2. This new switch S5 is able to change the configuration of the system in such a way that it can operate as a grid connected system in the two different and previously described forms or, in position 3, as an isolated system. It must be remarked that the used switch has a smaller rated current than the previous one. Furthermore, at the present the reference for the generated voltage measurement (for control purposes) must be manually connected by using a wire from the stator central point to the reference of the stator measurements (for the oscilloscope) in the frontal control panel or from the central point of the load to the reference of the stator measurements in the mentioned panel. It is only necessary for the isolated system emulation, so that wire should not be used in grid-connected operation.



Fig. 4.2.2. Electrical diagram of the test bench after the second modification was made. The new three-position switch S5 was introduced to configure the emulated system as a: (1) grid-connected system with both the stator and the rotor circuits tied to the secondary of the input transformer, or (2) grid connected with the stator tied to the mains and the rotor circuit to the secondary of the transformer, or (3) an isolated system with both the stator and the rotor circuits tied to the load.

4.3 Last Modification Proposal A third modification could be carried out in the test bench in order for it to be able to connect/disconnect the load in the isolated system emulation and to connect/disconnect the filter capacitors to/from the FEC through the filter inductors. This way, the load could be fed after the start transient and the capacitors could be used for initial self-excitation of the generator (see Section 7.3), respectively. It is thought that all this can be achieved by using again the former switch S5, which could be internally reconfigured in a proper fashion, as shown in Fig. 4.3. In this figure the switch has been renamed as S6 and considered as composed of two three-phase switches: S6-I for the isolated load and S6-II for the filter capacitors. In addition, it is believed that the remaining contact in switch S5 could be used to connect the reference for stator voltage measurement to the central point of the input transformer or to the central point of the stator, in grid connected or isolated system emulation, respectively.

Umrichter

LC - Filter

Trafo380V/0..400V

DSAG

Netz400 V50 Hz

S1250 A500V

S4100 A500V

S3, Sks25 A500V

1

2


LfLf

C fC f

S225 A500V

Crow-bar

F1250 A

0

AA

VVAA

VV

RWR NWR

Vorladung

VV

GZK

U_n400V

I_s25A I_n

25AU_s400V

U_r400V

AA

VV

S_v

S_ü

I_dc-+25A

+

U_1600V

R_v

_

F_v25 A


+

_

Synchronisierung

Chopper

LrLr

GSM

Ein

Aus

M entor

Lufter

Feld

S_Feld

K1

3x Ir 3x In

2x Un

Udc

16A

25A63A

Schirmung

AA

VV

Strommessung

Spannungsmessung

Strommessanzeige


40A

40A

AA

VV

250 A

Verteiler

Vorladung

3x Is

VV U_2600V

Isolated LoadI II

S516 A500V

Second modification

A

B

D

C

Position 1: I-B , II-D (Grid Connected)

Position 2: I-A , II-D (Grid Connected)

Position 3: I-B , II-C (Isolated)



Fig. 4.3. Electrical diagram of the test bench, in which switch S6 can be used to connect/disconnect the load to/from the generator and to connect/disconnect the filter capacitors to/from the FEC through the filter inductors.

5 Design and Simulation of the PI Controllers for the Isolated System 5.1 Controllers associated with the Doubly-Fed Induction Generator (DFIG) The control system associated with the DFIG is configured in cascade, with current controllers in the inner loop and an indirect stator voltage controller in the outer one. In the design of the PI controllers it has been used the well-known dq model of the induction machine, whose equations can be written in the following scalar form:

sdsd s sd e sq

dv r idtλω λ= − +

(5.1.1)

sq

sq s sq e sd

dv r i

dtλ

ω λ= + + (5.1.2)

( ) rdrd r rd e r rq

dv r idtλω ω λ

′′ ′ ′ ′= − − +

(5.1.3)

( ) rq

rq r rq e r rq

dv r i

dtλ

ω ω λ′

′ ′ ′ ′= + − + (5.1.4)

( )sd ls sd rdL M i Miλ ′= + + (5.1.5)

( )sq ls sq rqL M i Miλ ′= + + (5.1.6)

Umrichter

LC - Filter

Trafo380V/0..400V

DSAG

Netz400 V50 Hz

S1250 A500V

S4100 A500V

S3, Sks25 A500V

1

2


LfLf

C fC f

S225 A500V

Crow-bar

F1250 A

0

AA

VVAA

VV

RWR NWR

Vorladung

VV

GZK

U_n400V

I_s25A I_n

25AU_s400V

U_r400V

AA

VV

S_v

S_ü

I_dc-+25A

+

U_1600V

R_v

_

F_v25 A


+

_

Synchronisierung

Chopper

LrLr

GSM

Ein

Aus

M entor

Lufter

Feld

S_Feld

K1

3x Ir 3x In

2x Un

Udc

16A

25A63A

Schirmung

AA

VV

Strommessung

Spannungsmessung

Strommessanzeige


40A

40A

AA

VV

250 A

Verteiler

Vorladung

3x Is

VV U_2600V

Isolated LoadI II

S516 A500V

Third modification

A

B

D

C

Position 1: I-B , II-D (Grid Connected)

Position 2: I-A , II-D (Grid Connected)

Position 3: I-B , II-C (Isolated)

S625 A500V

S6-II

S6-I



( )rd lr rd sdL M i Miλ′ ′ ′= + + (5.1.7)

( )rq lr rq sqL M i Miλ′ ′ ′= + + (5.1.8)

where: and, , , , , , , , , , , sq rq sq rq sq rqsd rd sd rd sd rdv v v v i i i i λ λ λ λ′ ′ ′ ′ ′ ′ are the dq

compo-nents of the stator and the rotor voltages [V], currents [A], and flux linkages [H·A], respectively; and s rr r′ are the stator and rotor winding resistances [Ω], and ls lrL L′ are leakage inductances corresponding to a stator or rotor winding [H], M is the magnetizing inductance [H], ωe is the angular speed of the reference frame [rad/s], and ωr is the angular speed of the axes associated with the rotor variables [rad/s]. The symbol (’) denotes that the rotor variables are referred to the stator.

Furthermore, the control system considers a synchronous reference frame aligned with the stator flux, which implies the following:

sd s s sd rd msL i Mi Miλ λ ′= = + = (5.1.9)

0sq s sq rqL i Miλ ′= + = (5.1.10)

s lsL L M= + (5.1.11)

where: s sd sqjλ λ λ= + is the stator flux vector and ims is the magnetizing

current.

Additionally, the αβ components of the stator-flux linkages are obtained by using the following expression:

( )s s s sv r i dtλ• • •= − ⋅∫ (5.1.12)

where: • = α or β.

5.1.1 Rotor Current Controllers In order to get a model for the design of the rotor current controllers, it is possible to solve (5.1.9)-(5.1.10) for the stator currents, an then to substitute them into (5.1.7) and (5.1.8) to write the rotor flux linkages in terms of the rotor currents. Then the rotor flux linkages can be substituted into (5.1.3) and (5.1.4) to obtain:

dr

dr r dr r slip r qrdiv r i L L idt

σ ω σ′

′ ′ ′ ′ ′ ′= + − (5.1.13)

( )

qr

qr r qr r slip ms r dr

div r i L Mi L i

dtσ ω σ

′′ ′ ′ ′ ′ ′= + + +

(5.1.14)

where: ( )slip e rω ω ω= − ,

2

1s r

ML L

σ = −′

, and r lrL L M′ ′= + (5.1.15)

This way, the controllers can be designed by using the next model:

rr r r r

div r i Ldt

σ •• •

′′′ ′ ′ ′= +

(5.1.16)

where: • = d or q. and the actual control signals will be given as:

* dr dr slip r qrv v L iω σ′′ ′ ′= − (5.1.17)

( )* qr qr slip ms r drv v Mi L iω σ′′ ′ ′= + + (5.1.18)



in which the terms that appear in (5.1.13)-(5.1.14) but are omitted in (5.1.16) are used as feed-forward signals. The root locus method was used to tune the current controllers in order to obtain a response with settling time approximately equal to ts=27ms. The values of the system parameters are given in the TABLE I, in the Appendix. Fig. 5.1.1 shows the root locus plot, in which it can be seen that the closed loop system will have a natural frequency equal to ωn=166 rad/s. Fig 5.1.2 presents the step response of the simplified model (5.1.16) when controller (5.1.19) is used. It can be noticed that the rising time is approximately tr=10ms, whilst settling time is ts=40ms, which is caused by the natural limitations of the root locus method, in accordance with its assumption that the system has a second order transfer function.

( ) 38.5 3465 scIrG s = + (5.1.19)

Fig. 5.1.1. Root locus of the current control loop. Fig. 5.1.2. Step response of the system (5.1.16) with the controller (5.1.19).

TABLE I. Parameters used in the controllers design. Parameter Value Parameter Value

rs 1.54 Ω Ls 148e-3 H r’r 0.9 Ω L’r 141e-3 H M 139e-3 H nsr 2.4 r1 0.4 Ω L1 20e-3 H r2 1.4 Ω L2 8e-3 H C0 6600 uF

Where: nsr is the stator to rotor turns ratio.

5.1.2 Stator Voltage Controller The stator voltage is regulated indirectly by controlling the magnetizing current, which is achieved by manipulating the d-component of the rotor current. This is a consequence from the equation (5.1.1) as it is shown in (5.1.19). However, to do this it is necessary to assume that the stator resistance voltage drop is negligible, which implies that some error will exist as long as this assumption is not completely fulfilled.

sq s s sq e sd s sq e ms e msv v r i r i Mi Miω λ ω ω= = + = + ≈ (5.1.19)

To obtain a model to design the stator voltage controller it is necessary to solve (5.1.9) for isd and to substitute it in (5.1.1). After a proper algebraic manipulation it is possible to write the following:



1ms SS ms rd sd

S

diT i i vdt r

σ+′+ = + (5.1.20)

where: and =1s s

S Ss

L LTr M

σ= + (5.1.21)

The controller has been tuned by using the root locus method and requiring a settling time approximately equal to ts=0.7s. Fig. 5.1.3 shows the root locus plot, in which it can be noticed that the natural frequency of the closed loop system will be ωn=9.2 rad/s. Fig 5.1.4 presents the step response of the simplified model (5.1.20) when controller (5.1.22) is used. It can be seen that the rising time is approximately tr=0.3s and that the settling time agrees reasonably well with the requested one.

( ) 0.2 8 scVsG s = + (5.1.22)

Fig. 5.1.3. Root locus of the magnetizing current (or indirect stator voltage) control loop.

Fig. 5.1.4. Step response of the system (5.1.20) with the controller (5.1.22).

On the other hand, the q component of the rotor current can be considered as a degree of freedom and, in fact, it is used to force the reference frame orientation. Initially, the approach used by [Peña et al., 1996a-1996c] was used, which consists in to solve (5.1.10) for i'rq in order to obtain the expression (5.1.23), with which the proper set-point can be calculated.

Srq sq

Li iM

′ = − (5.1.23)

However, the parameters uncertainty did not allow to achieve a good performance. In order to cope with this, (5.1.10) can be solved for isq and substituted into (5.1.2) to obtain the model (5.1.24). By using it, a controller can be tuned , which should be able to force the orientation.

sq srq sq e sd

S

d M r i vdt Lλ

ω λ′= + − (5.1.24)

The controller has been tuned by using the root locus method and requesting a settling time approximately equal to ts=4s, because it was considered more important the disturbance rejection capability than a faster response. Fig. 5.1.5 shows the corresponding root locus plot, which shows that the closed loop natural frequency is ωn=1 rad/s. Fig 5.1.6 presents the step response of the simplified model (5.1.23) when controller (5.1.25) is used. Note that the rising time is ts=0.1s, whilst settling time is around 1s.



( ) 40 40 sc sqG sλ = + (5.1.25)

Fig. 5.1.5. Root locus of the magnetizing current (or indirect stator voltage) control loop.

Fig. 5.1.6. Step response of the system (5.1.20) with the controller (5.1.22).

This way, with the controllers (5.1.19) and (5.1.25) the reference frame position can be imposed for it to be equal to an angle which is obtained through direct integration of the desired frequency, see (5.1.24). This angle is used in all the reference frame transformations.

*e e dtθ ω= ∫ (5.1.24)

where: * *2e efω π= is the desired angular frequency.

5.2 Controllers associated with the Front End Converter (FEC) The FEC control system is considered in a stator-voltage reference frame, which implies that a decoupled control of the active and the reactive power can be achieved. The scalar equations of this subsystem in the considered reference frame are [Peña et al., 1996b]:

2 2 2

ndnd nd e nq sd

div r i L L i vdt

ω= − − + + (5.2.1)

2 2 2

nqnq nq e nd

div r i L L i

dtω= − − −

(5.2.2)

where: and, , , nq nqnd ndv v i i are the dq components of the FEC voltages [V], and

currents [A], respectively; r2 and L2 are the elements that connect the FEC with the stator, in [Ω], and [H], respectively.

Originally, [Peña et al., 1996c] propose the use of the angle (5.1.24) to estimate the stator voltage vector position, by adding π/2 to θe. However, in the laboratory test bench better results were obtained when a PLL was used to determine the stator voltage vector position.

5.2.1 FEC Current Controllers The FEC current controllers were tuned by using the root locus method and the next model:

2 2

nn n

div r i Ldt

•• •′ = − −

(5.2.3)

where: • = d or q. whilst the actual control signal is given by:



* 2 nd nd e nq sdv v L i vω′= + + (5.2.4)

*2nq nq e ndv v L iω′= − (5.2.5)

Fig. 5.2.1 shows the corresponding root locus plot. In this case, the natural frequency of the closed loop system will be ωn=317 rad/s. It was required a settling time of ts=18ms. Fig 5.2.2 presents the step response of the simplified model (5.2.3) when controller (5.2.6) is used. It can be observed that the rising time is approximately tr=8ms and that the settling time is approximately ts=20ms.

( ) 2.5 800 scIfecG s = + (5.2.6)

Fig. 5.2.1. Root locus of the FEC current control loop. Fig. 5.2.2. Step response of the system (5.2.3) with the controller (5.2.6).

5.2.2 dc-Link Voltage Controller The dc-link voltage control is achieved by considering that the FEC ac input mean power in (5.2.7) equates its dc output power in (5.2.8), which is fed to the dc-link, and recalling that the fundamental amplitude of the output voltage of a three-phase voltage source inverter depends on its dc-link voltage and on its modulation index, as shown in (5.2.9). This way, by manipulating (5.2.7)-(5.2.9), a mathematical relationship between the d component of the FEC current and its dc output current can be established, which is presented in (5.2.10).

32fec nd ndP v i=

(5.2.7)

0 02dcP V I= (5.2.8)

102

ˆfund fec fecV m V= (5.2.9)

02

34

fecnd

mI i=

(5.2.10)

where: Pfec is the FEC input mean power [W], Pdc is the FEC output power [W], 2 1 2 3o fec na fec nb fec ncg gg i i iI + += is the FEC output current [A], V0

is the dc-link voltage [V], ˆfund fecV is the amplitude of the fundamental

of the FEC output voltage [V], gfec i is the gate signal applied to the i-th upper FEC switch (i=1, 2, 3), and mfec is the FEC modulation index.

Furthermore, the dc-link voltage depends on its capacitance and on the FEC and the MSC currents, as given in the following expression:



( )0

0 00 02 01

1 1dV I Idt C C

I= −= (5.2.11)

where: C0 is the dc-link capacitance [F], I02 is the FEC output current [A], and I01 is the MSC input current [A].

In accordance with the previous paragraphs, dc-link voltage can be controlled by manipulating the d component of the FEC current, and the associated model is obtained if (5.2.10) is combined with (5.2.11):

0

0

34

fecnd

mdV idt C

= (5.2.12)

where the MSC input current is considered as a disturbance. The controller has been tuned by using the root locus method and requiring a settling time approximately equal to ts=1s, because it was considered more important the controller disturbance rejection capabilities than a faster response. It was considered a modulation index equal to mfec=0.75. Fig. 5.2.3 shows the root locus plot. It can be noticed that the closed loop system will have a relatively small natural frequency ωn=6.53 rad/s. Fig 5.2.4 presents the step response of the simplified model (5.2-10) when controller (5.2-13) is used. Note that the rising time is tr=200ms whilst the settling time is approximately ts=1s.

( ) 0.1 0.5 scVdcG s = + (5.2.13)

Fig. 5.2.3. Root locus of the FEC current control loop. Fig. 5.2.4. Step response of the system (5.2.3) with the

controller (5.2.6).

6 Experimental Results obtained with the PI Controllers The designed controllers were discretized by using the trapezoidal method, and implemented in a dSpace DS1103 Board with a sampling frequency of 1.5kHz, and a switching frequency of 4050 Hz. This board contains a master IBM PowerPC processor running at 1 GHz and a slave Texas Instruments TMS320F240 DSP running at 20 MHz. Furthermore, amongst other remarkable features, the board has 36 ADC channels (20 with 16-bit resolution and 16 with 10-bit resolution), and 50-bit for digital IO purposes. Additionally, the board can be programmed by using Real Time Interface (RTI) blocks from the Simulink environment, which makes quicker and easier the implementation tasks. In the following subsections some experimental results are presented.



6.1 Controllers associated with the Doubly-Fed Induction Generator (DFIG) 6.1.1 Rotor Current Controllers The rotor current controllers, given in (5.1.19), were tested by using periodic pulses of 5A. The dc-link was fed by using the pre-charger (at 330V, connected to the grid) and the DFIG was running at 1400 rpm driven by the dc-motor. At first instance, the behavior was not exactly the expected, so the initial tuning was taken as a base for an experimental adjustment, which produced a proportional gain of Kp=50 and an integral one of Ki=4500, which represents an increment of 30% in both gains. Fig. 6.1.1 shows the response of i'rd when 5A pulses are given as set-points. It can be seen that the rising time is 11 ms and the settling time is 37 ms. Fig. 6.1.2 presents the analogous test for i'rq, in which similar results are observed. It was noticed that the feed-forward terms considered in (5.1.17) and (5.1.18) do not have a great impact on the controllers behavior. Although it could be caused by the parameters uncertainties, it is believed that the main cause is that expressions (5.1.17) and (5.1.18) are only valid when the right orientation has been caught. However, in the used scheme i'rq is used to force the orientation during normal operation, but during these tests the synchronous reference frame was not aligned with the stator flux vector.

Fig. 6.1.1. Response of the i'rd controller to a 5A pulse test. Fig. 6.1.2. Response of the i'rq controller to a 5A pulse test.

6.1.2 Stator Voltage Controller The controller in (5.1.22) was tested by using a dc-link voltage of 330 V, maintained by the pre-charger (connected to the grid), whilst the dc-motor was driven the DFIG at 1400 rpm. The current controllers were previously started with their references set to cero, and a resistive load of 40 Ω was used. Fig. 6.1.3 shows the start of the voltage controller with a ramp from 0 to 120 Vrms in 5 s. It can be seen that the d component of the stator voltage is not zero, because the stator resistance is not negligible, which produces an average stator voltage error of approximately 6% in the steady state. In addition, it can be noticed that both the d and the q components of the rotor currents increase with the same pattern as the q component of the stator voltage. In the case of i'rd it is because this component is driving the stator voltage, see (5.1.19)-(5.1.20). In the case of i'rq it is because of the expression (5.1.23). It must be recalled that stator flux orientation is used, which results in the association of the q components with the active power, whilst the d components are linked to the reactive one. This way, for the stator voltage to be able to increase it is necessary to furnish some additional magnetizing, which is provided by i'rd. Meanwhile, as stator voltage increases, the active power consumed by the



resistive load is also increasing. This produces an increment in isq which, in accordance with (5.1.23), makes i'rq bigger. Fig. 6.1.4 presents the response of the stator voltage controller to a pulse from 140 V to 220 V (peak). It can be observed that the settling time is around 1s, which is similar to the one requested during the controller design (0.7s). The components of the rotor currents show a behavior similar to the one described in the previous paragraph.

Fig. 6.1.3. Start of the stator voltage controller. Fig. 6.1.4. Response of the stator voltage controller to a pulse of 80 V in the set-point.

6.2 Controllers associated with the Front End Converter (FEC) 6.2.1 FEC Current Controllers In order to test the FEC current controllers, given by (5.2.6), the dc-link was driven by the pre-charger at 330V (connected to the grid). Initially, the controllers were tested only by making them to produce a voltage in the filter capacitors. Under this conditions, it was noted that the feed-forward compensation does not have any effect on the controllers performance. It occurs because the model of that system is not the same what was considered during the controllers design. So, in order to test the current controllers the FEC subsystem was synchronized with and connected to the electric grid. The right orientation was obtained by using a PLL, whilst the dc-link voltage was regulated at 400V. Fig. 6.2.1 shows the response of the FEC subsystem to a 3A pulse in the inq set-point. Apparently, the response is almost the same no matters whether the feed-forward is used or not. However, Fig. 6.2.2 presents a zoomed view in the time interval around the positive edge of the pulse. Here, it is possible to observe that the rising time of the controlled current is almost 10ms, whilst its settling time is around 25 ms, which agrees reasonably well with the values requested during the design. Furthermore, it can be noticed that in the best case the feed-forward compensation reduces the ind current peak in almost 0.5A. In addition, it can be seen that ind increases during the inq pulse in order to compensate the dc-link voltage drop, and that it gets negative in order to diminish the dc-link voltage when the pulse disappears. Finally, Figs. 6.2.1 and 6.2.2 show that the dc-link voltage controller is able to reject the disturbance in almost 500 ms.

6.2.2 dc-Link Voltage Controller The dc-link voltage controller, given by (5.2.13), was tested under the same conditions described in the previous section. In the test, a pulse from 400V to 450V was applied to the set-point of the dc-



link voltage controller, which at the same time constitutes a disturbance for the inq controller. Figs. 6.2.3 and 6.2.4 show the obtained results. In particular, in Fig. 6.2.3 it can be seen that the rising time is approximately 180 ms, whilst the settling time is around 700ms. Both of them are similar to the obtained in the simulations. Furthermore, it is possible to observe that the dc-link voltage increases in the rising edge of the pulse because ind provides the necessary active power, and that it decreases during the falling edge because ind gets negative, indicating that the active power is leaving the FEC. On the other hand, the pulses in the dc-link voltage constitutes a disturbance for the inq controller, whose effects can be diminished by the use of feed-forward compensation, as it can be seen in Fig 6.2.4. In this figure it is possible to observe that a reduction of almost 1A can be obtained by the use of the feed-forward compensation.

Fig. 6.2.1. Response of the inq controller to a 3A pulse in the set-point.

Fig. 6.2.2. Zoom in the time interval around the rising edge of the 3A pulse in the set-point of the inq controller.

Fig. 6.2.3. Response of the dc-link voltage controller to a 50 V pulse in the set-point.

Fig. 6.2.4. Zoom in the time interval around the rising (top) and in the falling (bottom) edges of the 50V pulse in the set-point of the dc-link voltage controller.

6.3 Experimental Tests Concerning the Operation of the Complete System 6.3.1 Connection of the Complete System In this test a star-connected 40 Ω resistive load has been used, whilst the dc-motor was driven the DFIG at 1400rpm and the dc-link was initially maintained around 330V by the pre-charger (connected



to the grid). Then the DFIG control system was started by enabling the current controllers with their references set to 0. After that, the orientation enforcement (which uses i'rq to assure that λsq will be equal to 0), and the stator voltage controller are enabled. Next, a ramp in the set-point of desired voltage (Vs

*) from 0 to 120 Vrms is applied, as in Fig. 6.1.3. Afterwards, the FEC current controllers were enabled with their references initially set to 0. Then, the FEC currents are controlled to produce 120Vrms in the filter capacitors, in phase with the stator voltage. This is achieved by setting the ind reference to a relatively small negative value (to face the copper losses) and the inq reference to a negative value which enables the FEC to “consume” the reactive power associated with the filter capacitors (= –ωe

*· Cf · Vs*, where Cf is the filter capacitance). Once the steady state has been reached

in both subsystems, they are connected to each other, whilst the pre-charger is disconnected from the dc-link and the dc-link voltage controller is enabled. Figs. 6.3.1-6.3.4 present the results of this experiment. The connection was carried out around t=1s. It can be seen in Fig. 6.3.1 that after the connection the dc-link voltage drops because it was disconnected from the pre-charger. In consequence a decrement in the generated stator voltage and some variations in the system currents are produced, as shown in Fig. 6.3.2. In this figure it can be observed that the reactive power associated currents (isd, i'rd, and inq) remain almost the same and that their variations are produced only by the transient in the generated voltage. Indeed, it is possible to figure out that the DFIG magnetizing is furnished completely through the rotor (isd=0), whilst the FEC is still “consuming” the reactive power of the filter capacitors.

Fig. 6.3.1. Transient behavior in stator and dc-link voltages during connection.

Fig. 6.3.2. Transient behavior in stator, rotor and FEC currents during connection.

On the other hand, the active power related currents (isq, i'rq, and ind) must increase their magnitudes in order for them to be able to increase the dc-link voltage, whilst the DFIG continues supplying both the load and the FEC subsystem. In the end, the steady state value of isq is slightly bigger than the previous one, because now the stator is supplying not only the load, but also the FEC. The same can be said of i'rq, whilst ind assumes a positive value because it must furnish the necessary active power to the dc-link, for it to be able to transfer this power to the DFIG rotor through the MSC. Finally, Fig. 6.3.3 shows that the mentioned current increments makes the electromagnetic torque magnitude to increase, in order to extract more mechanical power to transfer it to the electrical system. Meanwhile, the dc-motor speed control system sees this torque increment like a disturbance, as it can be noticed in Fig. 6.3.4.



Fig. 6.3.3. Transient behavior in electromagnetic torque during connection.

Fig. 6.3.4. Transient behavior in DFIG speed during connection.

It is worthwhile to comment that the load voltage and current magnitudes remained almost unchanged during the connection procedure. The measured phase voltage was 113 Vrms with a THD of 2.1% before the connection, and 112Vrms with a THD of 1.2% after it, which represent a regulation error of approximately 6%. This decrement on the harmonic pollution is caused by the LC filter and it can be observed in Fig. 6.3.1. The load current was 2.93 Arms with a THD of 6%, before the connection, and 2.94 Arms with a THD of 9% after it. These measurements were taken by using a Fluke 41 Power Harmonics Analyzer.

6.3.2 Decreasing of the q Component of the FEC Current In order to visualize the relationship between the reactive power related currents (isd, i'rd, and inq) an experiment was designed. After the start and connection were carried out, and the steady state was reached, as commented in the previous sections, an increasing ramp in the inq set-point from –3 to 0 was applied to the corresponding controller. The DFIG speed was 1400 rpm, whilst the stator voltage was regulated at 120 Vrms and the dc-link voltage at 330V. The load resistance was 40 Ω. The results are given in Figs. 6.3.5 and 6.3.6. Fig. 6.3.5 shows that both the generated voltage and the dc-link voltage remain relatively unchanged. The same can be said of the active power related currents (isq, i'rq, and ind), as it can be seen in Fig. 6.3.6. The observed changes are caused because of the imperfect decoupling between active and reactive power, since stator resistance is not negligible, and the stator flux oriented reference frame do not exactly comply with Unq=0. Theoretically, this situation only applies for the DFIG related variables, because in the FEC control system a stator voltage oriented reference frame is used. On the other hand, with respect to the reactive power currents, in Fig. 6.3.6 it is noticed that isd increases as inq increases, which is caused by the fact that the FEC is not anymore consuming all the reactive power produced by the filter capacitors. In the end, when inq reaches 0, all the filter capacitors reactive power is being used to magnetize the DFIG. Because of this, i'rd decreases from its initial value to a smaller one, with which the MSC is able to provide to the DFIG the remaining magnetizing power. If inq increases beyond 0, then there would be an excess of reactive power, which could be used to feed the load or to increase isd which would imply that the DFIG would be receiving an amount of reactive power bigger than the necessary for magnetizing. This would produce a decrement in i'rd under 0, which would imply that the rotor would be furnishing reactive power to the MSC.



Fig. 6.3.5. Transient behavior in electromagnetic torque during connection.

Fig. 6.3.6. Transient behavior in DFIG speed during connection.

6.3.3 Speed Ramp In order to verify the system operation over the speed range a test was carried out, in which the DFIG was driven from 1200 rpm to 1800 rpm, whilst the stator voltage was regulated at 120 Vrms and the dc-link voltage at 350 V. The considered load resistance was 40 Ω. Fig. 6.3.7 shows the DFIG speed, and the typical phase inversion in the rotor currents when the generator crosses the synchronous speed, around t=4s. Fig. 6.3.8 presents the behavior of the powers in the system, calculated by using the measured currents and voltages. In particular, it can be noticed that load power is maintained almost without a change. There is a little increment when the speed starts to grow because the active stator power decreases, which diminish the voltage drop in the stator resistance. As speed increases, a power redistribution is taking place, in such a way that the stator has to manage a smaller power because the rotor decreases its demands until synchronous speed is crossed. After this, the rotor stops the consumption and starts to generate power. This way, the load power is supplied by both the stator and the rotor. In fact, the inversion in the rotor flow was not immediately observed when the DFIG crossed the synchronous speed and it is believed that it was caused by the external elements that are connected between the MSC and the rotor. Also, in Fig. 6.3.8 it can be observed that the power managed by the MSC and the FEC (Pr and Pfec) is approximately equal to each other, which allows to the dc-link to maintain its average value.

Fig. 6.3.7. Speed of the DFIG and three-phase rotor currents during the speed ramp test.

Fig. 6.3.8. Behavior of the calculated powers during the speed ramp test.



6.3.4 Load Ramp The system was also tested by increasing the load (i.e. by decreasing the load resistance). During this test, the DFIG was driven by the dc-motor at 1900 rpm, the stator voltage was regulated to 150Vrms and the dc-link voltage at 400V. Once the steady state was reached, the load resistance was decreased from 40 Ω to 26.5 Ω approximately. Fig. 6.3.9 shows the behavior of the estimated powers, and it can be observed that the increase in the load power is mainly supplied by the stator, since the rotor power only changes in a relatively small amount. On the other hand, before the load ramp the actual generated voltage was 140Vrms with a THD of 1.4%, the load current was 3.62 Arms with a THD of 3.8%, and the three-phase load power was 1.53kW. After the test, the actual generated voltage was 137Vrms with a THD of 1.3%, the load current was 5.14 Arms with a THD of 2.5%, and the three-phase load power was 2.13kW. This measurements were taken by using a Fluke 41 Power Harmonics Analyzer.

6.3.5 Dependency of the Generated Voltage on the Component q of the Rotor Current The expression (5.1.23) gives the relationship between isq and i’rq in the implemented control scheme. Furthermore, and because of the stator flux orientation, these two currents are directly linked to the active power, and to the electromagnetic torque. In accordance with this, it was considered worthwhile to characterize experimentally the relationship between the generated voltage and i’rq. This way, the system was operated at several speeds and in each one the stator voltage was varied, whilst the dc-link voltage was regulated at 400 V. Fig. 6.3.10 shows the experimental curves obtained during these tests. It can be noticed that as higher the speed is as lower i’rq must be in order to obtain a given stator voltage.

Fig. 6.3.9. Behavior of the estimated powers during the load ramp test.

Fig. 6.3.10. Dependency of the generated voltage on the q component of the rotor current (i’rq).

6.3.6 Turn-off Procedure In order to disconnect the system in an easy way, a turn off procedure was proposed. It consists in an algorithm to decrease the set-points of the generated stator voltage and of the dc-link voltage. The slopes of the decreasing ramps were chosen for the stator voltage to be 0 in almost 20 s, whilst the dc-link voltage decreases to 0 in almost 30 s. Figs. 6.3.11 and 6.3.12 show the experimental data obtained during a turn off. It can be noticed that both the stator and dc-link decrease monotonically until a point is reached in which the dc-link voltage in not able anymore to furnish the required power in order to maintain both the stator and dc-link voltages in their set-points. Then the currents increase for them to be able to recover the control. However, the dc-link is discharged by their control efforts.



Fig. 6.3.11. Stator voltage and rotor currents behavior during the turn off.

Fig. 6.3.12. dc-link voltage and FEC currents behavior during the turn off.

7 Experimental Assessment of the Black Start Capability 7.1 Self-Excitation of the Doubly-Fed Induction Generator During this internship some basic experiments were carried out, whose purpose was to verify the black start capability of the DFIG. The black start consists in the system ability to start from zero in a completely independent way, which is specially important in an isolated system. Because of this, it was considered the self-excitation of the DFIG. The self-excitation (SE) is a well-known phenomenon that is used by squirrel-cage generators in some WECSs. It requires the use of a static reactive power compensator (usually a three-phase capacitor bank) connected to its stator terminals. So, SE consists in a voltage build up originated either by the residual magnetic flux in the machine or by the initial charge in the capacitor bank. This process, can be considered as the response of a resonant circuit, composed by the machine windings and the capacitor bank [Levi & Liao, 2000]. This way, when the induction generator starts to run, there will be a voltage in its stator (produced by the residual magnetism in the rotor circuit or by the initial charge in the capacitors); this voltage creates a small capacitor current flow. Straight afterwards, the current increases the stator voltage, which produces a higher current, and so forth until a steady state is reached [Bansal, 2005]. This steady state is set by the intersection of the induction generator magnetization curve and the capacitor load line. Furthermore, during the voltage build up, the magnetizing inductance varies until it takes a saturated value. In fact, it is the magnetizing inductance behavior which stabilizes the growing transient and let the generated voltage and current to continue to oscillate at a particular steady state frequency and amplitude [Seyoum et al., 2002 and 2003]. In [Bansal, 2005] and [Singh, 2004] some very good references concerning the self-excited induction generator (SEIG) can be found. In the considered tests, the SE was initiated both by the sudden connection of the capacitor bank to the stator, whilst the DFIG was running at a constant speed, and by increasing the speed whilst the capacitor bank is already connected to the stator. The following observations were made:

1. If the DFIG is running at a constant speed, maintaining its rotor terminals short-circuited, and the capacitor bank is suddenly connected to its stator the SE phenomenon appears at 900 rpm when a ∆-connected capacitor bank is used, and at 1600 rpm when a Y-connected capacitor is considered. Some experimental results are given in TABLE II, peak values are considered.



TABLE II. Experimental values obtained when the DFIG is running at a constant speed and the capacitor bank is suddenly connected.

Connection Speed (rpm) Phase Voltage (V) Phase Current (A) 900 186 7 1000 220 9.4 1100 255 11

∆

1200 290 13 1600 350 4.1 Y 1700 382 4.8

2. If the DFIG speed is increased by a ramp, with its rotor terminals short-circuited, whilst the capacitor bank is connected to its stator then the SE occurs at 880 rpm when a ∆-connected capacitor bank is used, and at 1350 rpm when a Y-connected capacitor is considered. Fig. 7.1 shows some of the experimental results.

For this test the DFIG speed was increased form 1300rpm to 1500rpm, whilst the star-connecter capacitor bank was tied to its stator. It is interesting to note that in the steady state the voltage amplitude is equal to the rated one (310 Vpeak), whilst the current takes the necessary value for the DFIG to be able to receive the magnetizing power and to furnish the copper losses, as it can be seen in the bottom of Fig. 7.1.

Fig. 7.1. Stator voltage, currents and powers during the self-excitation phenomenon.

Although the considered experiments were mainly qualitative, some things can be said about the self-excitation. It has been shown in [Seyoum et al., 2002 and 2003] that in an unloaded induction generator with a capacitor bank connected to its stator the self-excitation can only be produced when an eighth order equation has at least one root with positive real part. The coefficients of this equation depends on the DFIG parameters, on the generator speed, on the external capacitance and its initial charge, and on the residual flux in the rotor. They consider that there are three variable quantities: the mechanical speed, the external capacitance, and the magnetizing inductance, which they have previously characterized in the laboratory. This way, by using a searching algorithm they are able to plot a Capacitance vs. Speed curve. To find each point they consider fixed the capacitance and start to vary the speed, until a root with positive real part is found. It is interesting to note that they do not consider it, but the Routh criteria could be used in order to try to find an algebraic expression to determine a general relationship between the capacitance and the operating speed for the DFIG self-excitation to occur.



7.2 dc-Link pre-charge by using the Self-Excitation Phenomenon Once the SE was tested, the next step was to verify if it is possible to charge the dc-link by using SE. The following conclusions were drawn:

1. If the DFIG speed increases from 0 to 1500 rpm when the ∆-connected capacitor bank and the FEC are connected to its stator, then the SE phenomenon can appear and, at the same time, it is able to pre-charge the dc-link by using the anti-parallel diodes in the FEC. The Y-connected capacitor bank is not able to achieve it.

2. The Y-connected capacitor bank is able to pre-charge the dc-link if SE is firstly initiated and the test-bench pre-charger is used when the steady state has been reached. It is shown in Fig. 7.2, in which the DFIG is running at 1425 rpm, after the SE establishment, and the pre-charger is used in t=1.5s. It can be observed that the DFIG speed decreases, because the dc-link is seen as a load suddenly connected and the dc-machine torque has to increase in order to maintain the speed constant. Fig. 7.3 presents the behavior of the stator variables. It van be noticed that the stator voltage suffers a momentary decrement in its amplitude, whilst the d component of the stator current, increases its magnitude, in order to increase the torque for it to be able to furnish the additional active power which is necessary to charge the dc-link. Once the dc-link is charged, the system returns to its previous steady state.

Fig. 7.2. dc-link voltage and DFIG speed during the pre-charge.

Fig. 7.3. Behavior of the stator variables during the pre-charge.

7.3 Use of the Self-Excitation Phenomenon for Black Start Purposes Based on the previous experiments it is believed that the black start may be achieved by using the Y-connected capacitor bank, which is already connected in the test bench, in order to produce the initial SE. For it to be possible it would be necessary to carry out the modification proposed in Section 4.3, in order to be able to initially disconnect the capacitor bank from the FEC. Once the SE has occurred and the dc-link has been pre-charged, the switch S6-II can be closed in order to re-connect the capacitor bank with the FEC and it can start to pulse. The next step is to connect the MSC. It has been thought that it will be a critical point, because SE could be lost during the change from rotor short-circuited to MSC connected.



8 Analysis of the Operating Conditions for Minimum Copper Losses It has been observed that there is a perfect decoupling between active and reactive power in the FEC subsystem, because a stator voltage oriented reference frame is used, whilst there is an imperfect decoupling in the DFIG-MSC subsystem, because a stator flux oriented reference frame is considered. This decoupling in fact depends on the negligibility of the stator resistance voltage drop: as bigger the machine is as better the decoupling will be. In accordance with the used orientation, in the FEC subsystem the d-component is associated with the active power, and the q-component with the reactive one. At the same time, in the DFIG-MSC subsystem the opposite is valid. In the isolated system, once the generated stator voltage is set, the (active) power required from the mechanical subsystem is mainly imposed by the load, and its distribution between the stator and the rotor is dictated by the operating speed. On the other hand, the load may consume or produce some reactive power, but the DFIG is continuously demanding the magnetizing power (which may be fed through the stator or through the rotor or through both of them), and the filter capacitors are producing a generated-voltage dependant reactive power (in almost the same quantity needed for the DFIG magnetizing). In addition, the FEC and the MSC are able to produce or to consume reactive power under certain limits. In Section 6.3.2 some associated experimental results have been shown. From the analysis of these results, we see that it is possible to use the q-component of the FEC current in order to modify the reactive power distribution in the whole system. In this way, the system efficiency can be increased by the proper selection of the value of the q-component of the FEC current vector, as shown in Fig. 7.4. If the aim of the reactive power distribution is to reduce the cupper losses, then the following proposition can be derived, whose proof is presented in the Appendix.

Proposition 1. Suppose that the voltage drop in the stator resistance is negligible, which implies that the active and reactive powers in the stator and the rotor are decoupled. Consider the PI controllers designed in Section 5 for the entire system. If the set-point for the q-component of the FEC current vector is given by (8.1) then the cupper losses given by (8.2) are minimized.

* eFECq

e

ViR

= −

1 2s rCuL r rP P P P P= + + +

( ) ( )21 2e s s rR r L M r r r′ ′= + + +

( )( )1 2 1e s s rV I r I L M r r′ ′= − +

1 Cq LqI i i= −

( )2 1ms sI i L M I= −

(8.1)

(8.2)

(8.3)

(8.4)

(8.5)

(8.6)

Fig. 7.4. Dependency of the system efficiency on the q-component of the FEC current vector.

where: PCuL are the system cupper losses, Prs, Prr, P1, and P2 are the cupper losses in the resistances of the stator, the rotor, the wire connecting the MSC with the DFIG, and the wire in the inductor of the LC Filter, respectively.



Currently, the experimental results do not agree with the predicted ones, and the causes are being analyzed. It is believed that one possible cause is that in the considered machine the stator resistance voltage drop is not negligible. Other cause could be some error in the efficiency calculation.

9 Proposed Implementation Method for the Sliding Mode Controllers 9.1 Background: The Considered Design Method for Sliding Mode Controllers In the past it has been proposed a theoretical proposition which is based on the work of [Utkin, 1993], [Utkin et al., 1999] and [Zhang et al., 2000]. This proposition is useful to design sliding mode controllers for a class of systems which receive three-phase feeding from a voltage source inverter and whose model is given by expressions (9.1).

( )C C D D

ddt

= + +i

Ai B v B v (9.1.1)

*1,2 = −s y y (9.1.2)

C C D D= + +y Ci D v D v (9.1.3)

Where: i is the state vector, [ ]T

C dC qCv v=v is the control vector (which is applied to the system by the voltage

source inverter in the form of a three-phase set), [ ]T

D dD qDv v=v is a disturbance, y is the output vector

and *y is its set-point. The corresponding dimensions are: n∈i , 21,2 , ∈s y , n n×∈A ,

2, nC D

×∈B B , 2 n×∈C and 2 2,C D×∈D D .

Based on the Theorem 10.3 presented in [Utkin et al., 1999], the following proposition has been drawn.

Proposition 2. If D1,2 is a non-singular matrix given in (9.1.10) and the components of F1,2 in (9.1.11) are bounded, then there is a value for the dc-link voltage V0 –given in (9.1.6)– which is high enough to drive the system (9.1.1) towards the origin 1,2 =s 0 in a finite time, by using the control (9.1.4) and the transformation (9.1.5).

( )*1123 02C UV sign=v s (9.1.4)

* * * *1,2 1 2 3

T

U U U Us s s+ ⎡ ⎤= = ⎣ ⎦s D s (9.1.5)

( ) ( )* * *12

0 0 * * *

9 max2 2

T T TU U U

UlU mU nU

V Vs s s

⎛ ⎞⎡ ⎤+ ⋅ ⋅⎢ ⎥⎜ ⎟⎣ ⎦= > ⋅ ⎜ ⎟+ +⎜ ⎟⎝ ⎠

F s D Q D s

(9.1.6)

with: l m n≠ ≠ y , , 1, 2,3l m n ∈

* * *1 2 3

* 21,23

T

U f f f+ ⋅ = ⎡ ⎤= ⎣ ⎦F D F (9.1.7)

1 32

T T T−+ ⎡ ⎤= ⋅ =⎣ ⎦D D D D D Q (9.1.8)

1231,2 1,2

abc abcdq abc dqαβ αβ

αβ αβ= ⋅ ⋅ ⋅ = ⋅ ⋅D D A A A D A A (9.1.9)

1,2 C Cp= +D D CB (9.1.10)

( ) ( )*1,2 C C D D D Dp p p p= − + ⋅ − ⋅ − −F y C CA i D v D v CB v (9.1.11)



1

1,2 1,2T −

⎡ ⎤= ⋅⎣ ⎦Q D D (9.1.12)

1 1 2 1 223 0 3 2 3 2

abcαβ

− −⎡ ⎤= ⎢ ⎥

−⎣ ⎦A → ( ) ( )3

2

Tabc abcabcαβ

αβ αβ

+= =A A A (9.1.13)

cos sensen cosdq

αβ φ φφ φ

⎡ ⎤= ⎢ ⎥−⎣ ⎦

A → ( ) ( )1 Tdqdq dqαβ αβ

αβ

−= =A A A (9.1.14)

( ) ( ) ( ) ( )* * *1 2 3

Tsign sign s sign s sign s= ⎡ ⎤⎣ ⎦

*s (9.1.15)

where: l is the coefficient belonging to the surface which have a different sign (the other two have the same sign), p is the differentiation operator d /dt, φ θ= for the stator variables, and rφ θ θ= − for the rotor ones; θ is the reference frame position. Furthermore, max() denotes the maximum value and the superscript “+” denotes the pseudo-inverse matrix.

This proposition shows that the control vector can be chosen on the base of the control error sign if a proper transformation is used. This means that the sliding regime can be obtained by direct switching of the control signals.

9.2 The Proposed Implementation Method During this internship it has been looked for a method to implement the sliding mode controller by using a fixed switching frequency. This has been achieved by using some ideas which were taken from [Gunay, 2002] and [Sabanovic, 2003]. The main difference is that in the cited works it is considered that each switching interval it can be applied whichever of the 6 basic non zero switching vectors (which are also considered in the space vector modulation), and one or two of them are chosen based on some criteria. In the case that is considered here, it cannot be like that because, in accordance with the Proposition 2, the sign of the error is able to decide the control vector to be applied. Otherwise, the intrinsic nature of the sliding mode controllers designed by using Proposition 2 would be ignored. In consequence, each switching interval the sign of the sliding surfaces decides the first vector to be applied, whilst the second one will be the next basic vector in the plane αβ in which the error is considered. In other words, the proposed method considers the two basic vectors that delimit the sector in which the control transformed error is encountered. The six typical sectors associated with space vector modulation are considered. This way, the following proposition was found:

Proposition 3. Consider the system (9.1.1) and an associated sliding mode controller which has been designed by using Proposition 1. If the system parameters contained in D1,2, see (9.1.10), are constant or if they vary in such a way that their changes can be considered negligible during one switching interval, then the duty cycles contained in TABLE III can be used in order to decrease the control error in the maximum amount possible during the considered switching interval.

10 Conclusions This document presents the considered activities during the DAAD Short-Term Scholarship carried out from February, 2nd 2007 to August 24th, 2007. At the beginning of the internship some support was provided in the commissioning of the back-to-back converter for the test-bench. After this, two subsequent modifications were proposed and executed in order to give more flexibility to the test bench for it to be able to emulate an isolated system. Furthermore, a third modification has been recommended in order for the user to be able to evaluate several possibilities for the black start of the isolated system.



TABLE III. Duty Cycles recommended by the Proposition 3 for the SM controllers designed by using Proposition 2.

Sector

Range Basic Vectors Duty Cycles

I 120 3sθ π≤ < 1 0 02 3V= ∠U

2 02 3 3V π= ∠U ( ) ( )1 ,2

0 012

3311 2 2 2

3 3cos cosU

sweq

eq s

f

s V VT T π πθ θ⋅ ⋅= + + + +

U s

2 1swT T T= −

II 123 2 3sπ θ π≤ < 2 02 3 3V π= ∠U

3 02 3 2 3V π= ∠U

1,2

0 0

3312 2 2 2 12cos cos

Usweq f

s V Veq sT T θ θ⋅ ⋅= + +U s

3 2swT T T= −

III 122 3 sπ θ π≤ < 3 02 3 2 3V π= ∠U

4 02 3V π= ∠U

( ) ( )1 ,2

0 012

3313 2 2 2

3 3cos cosU

sweq

eq s

f

s V VT T π πθ θ⋅ ⋅= + − + −

U s

4 3swT T T= −

IV 12 4 3sπ θ π≤ < 4 02 3V π= ∠U

5 02 3 4 3V π= ∠U

( ) ( )1 ,2

0 012

3314 2 2 2

2 3 2 3cos cosU

sweq

eq s

f

s V VT T π πθ θ⋅ ⋅= + − + −

U s

5 4swT T T= −

V 124 3 5 3sπ θ π≤ <

5 02 3 4 3V π= ∠U

6 02 3 5 3V π= ∠U

( ) ( )1,2

0 0 12

3315 2 2 2cos cos

Usweq

eq s

f

s V VT T π πθ θ⋅ ⋅= + − + −U s

6 5swT T T= −

VI 125 3 2sπ θ π≤ < 6 02 3 5 3V π= ∠U

1 0 02 3V= ∠U ( ) ( )1 ,2

0 012

3316 2 2 2

4 3 4 3cos cosU

sweq

eq s

f

s V VT T π πθ θ⋅ ⋅= + − + −

U s

1 6swT T T= −

where: 11,2 1,2 1,2U −= ⋅s D s is the transformed error, ( ) ( )1,2 1 2

2 2U U Us s= +s , ( )2 11

12 tan U Us s sθ −= , eqU is the

equivalent continuous control (which can be obtained by filtering the discontinuous control signal given in

(9.1.4)), ( ) ( )1 2

2 2eq eq eqU U= +U , ( )2 1

1tan eq eqeq U Uθ −= , fsw is the switching frequency, and Tsw = 1/ fsw

is the switching interval.

Next, a set of PI controllers was designed and simulated for the first control approach for the isolated system. After that, these controllers were implemented by using a dSpace board and several tests were carried out in order to assess the isolated system behavior. It is believed that the control system can be further improved, but it could be done in the future. In addition, several tests concerning the self-excitation of the DFIG were carried out and, the possible use of this phenomenon to achieve the black start was considered. However, additional experimentation is still needed in order to determine the self-excitation usefulness for the black start purposes. An analysis of the necessary operating conditions for obtaining the minimum copper losses was considered and some related experimental tests were made. Nonetheless, the experimental results do



not agree with the analytical ones and some additional work is still necessary in order to determine the cause of this. Finally, a method to implement sliding mode controllers by using a fixed switching frequency has been proposed. Nevertheless, time was not enough for it to be proved neither by simulation nor by laboratory experiments.

11 References [Bansal, 2005] Bansal, R.C. “Three-Phase Self-Excited Induction Generators: An Overview,” IEEE Trans. on

Energy Conversion, vol. 20, No. 2, pp 292-299, Jun. 2005. [Gunay, 2002] Gunay, M.: Minimisation of Instantaneous Total Harmonic Distortion of Currents for Three-

phase Switching Power Converters, M. Sc. Thesis, Sabanci University, 89 pp., 2002. [Krause, 1987] Krause, Paul C. : Analysis of Electric Machinery, Mc Graw Hill Company, Singapore, 1987. [Levi & Liao, 2000] Levi, E. and Y.W. Liao, “An experimental investigation of self-excitation in capacitor excited

induction generators,” Elec. Power Sys. Research, Vol. 53, pp. 59-65, 2000. [Peña et al., 1996a] Peña, R.S., Asher, G.M., Clare, J.C., and Cardenas, R.: “A constant frequency constant voltage

variable speed stand alone wound rotor induction generator,” Opportunities and Advances in International Power Generation, Conference Publication No. 419, pp. 111-114, March 1996.

[Peña et al., 1996b] Peña, R.; Clare, J.C. and Asher, G.M.: “Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation,” IEE Proc.-Electr. Power Appl., Vol. 143, No. 3, pp. 231-241, May 1996.

[Peña et al., 1996c] Peña, R.; Clare, J.C. and Asher, G.M.: “A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine,” IEE Proc.-Electr. Power Appl., Vol. 143, No. 5, pp. 380-387, September 1996.

[Sabanovic, 2003] Sabanovic, A.: “Sliding modes in power electronics and motion control systems,” The 29th Annual Conference of the IEEE Industrial Electronics Society, 2003. IECON '03, Volume 13, pp. 997–1002, 2-6 Nov. 200.

[Seyoum et al., 2002] Seyoum, D., Grantham, C.F., Rahman, F. and M. Nagrial, “An Insight into the Dynamics of Loaded and Free Running Isolated Self-Excited Induction Generators,” Proceedings of the Power Electronics, Machines and Drives Conference, pp. 580-585, 16-18 Apr. 2002.

[Seyoum et al., 2003] Seyoum, D., Grantham, C.F., Rahman, F. and M. Nagrial, “The Dynamic Characteristics of an Isolated Self-Excited Induction Generator Driven by a Wind Turbine,” IEEE Trans. on Ind. Applications, Vol. 39, No. 4, pp. 936-944, Jul.-Aug. 2003.

[Singh, 2004] Singh, G.K., “Self-excited induction generator research -a survey,” Elec. Power Sys. Research, Vol. 69, pp. 107-114, 2004.

[Utkin, 1993] Utkin, V.I.: “Sliding mode control design principles and applications to electric drives,” IEEE Transactions on Industrial Electronics, Vol. 40, No. 1, pp. 23 -36, Feb. 1993.

[Utkin et al., 1999] Utkin, V.I.; Guldner, J. & Shi, J.: Sliding Mode Control in Electromechanical Systems, CRC Press, 1999, ISBN. 0-7484-0116-4.

[Zhang et al., 2000] Zhang, Y.; Changxi, Jin and Utkin, V.: “Sensorless sliding-mode control of induction motors,” IEEE Transactions on Industrial Electronics, Vol. 47 , No. 6, pp. 1286 – 1297, Dec. 2000.



Appendix Optimal distribution of the reactive power

In the control of the isolated system, two synchronous reference frames are considered. The first one is used in the DFIG control, which utilizes the MSC as the final control element, and is oriented to the stator flux vector. The second one is used in the control of the FEC and is oriented by considering the stator voltage vector. The variables associated with the DFIG are s dqi , r dqi ′ , and

s dqv (stator voltage represented in the stator flux vector oriented reference frame), whilst the ones associated with the FEC are L dqi , n dqi , C dqi , FEC dqi , n dqu (stator voltage represented in the stator voltage vector oriented reference frame). Fig. A.1 shows the schematic diagram of the isolated system and the positive direction of the previously mentioned currents.

MSC FEC

LZ

1Z 2ZcjX

si

Li ni

ri

DFIG

FECi Ci

Fig. A.1. Schematic diagram of the isolated system and its current flow.

In accordance with the used orientation, in the DFIG-MSC subsystem the q-component is associated with the active power, and the d-component with the reactive one. At the same time, in the FEC subsystem the opposite is valid. TABLE A.1 shows some of the powers in the system.

TABLE A.1. Some active and reactive powers in the isolated system.

DFIG Variables (in a reference frame oriented by the stator flux vector)

Voltage Current Active Power (per phase) Reactive Power (per phase)

s dq sv jV= s dq sd sqi i j i= + 12s s sqP V i= 1

2s s sdQ V i=

FEC Variables (in a reference frame oriented by the stator voltage vector)

Voltage Current Active Power (per phase) Reactive Power (per phase)

n dq su V= L dq Ld Lqi i j i= + 12L s LdP V i= 1

2L s LqQ V i= −

n dq su V= FEC dq FECd FECqi i j i= + 12FEC s FECdP V i= 1

2FEC s FECqQ V i= −

n dq su V= C dq Cqi j i= 0CP = 12C s CqQ V i= −

where: Vs is the stator voltage (controlled) amplitude.



Proposition 1. Suppose that the voltage drop in the stator resistance is negligible, which implies that the active and reactive powers in the stator and the rotor are decoupled. Consider the PI controllers designed in Section 5 for the entire system. If the set-point for the q-component of the FEC current vector is given by (8.1) then the cupper losses given by (8.2) are minimized.

* eFECq

e

ViR

= − (A.1)

1 2s rCuL r rP P P P P= + + + (A.2)

where: ( ) ( )21 2e s s rR r L M r r r′ ′= + + + (A.3)

( )( )1 2 1e s s rV I r I L M r r′ ′= − + (A.4)

1 Cq LqI i i= − (A.5)

( )2 1ms sI i L M I= − (A.6)

where: PCuL are the system cupper losses, Prs, Prr, P1, and P2 are the cupper losses in the resistances of the stator, the rotor, the wire connecting the MSC with the DFIG, and the wire in the inductor of the LC Filter, respectively.

Proof: From Fig. A.1. it is possible to obtain:

( )sd Lq FECq Cqi i i i= − − − (A.7)

It must be recalled that the DFIG stator voltage is indirectly controlled by regulating the magnetizing current. This is done by manipulating i'rd in a stator flux oriented reference frame and under the assumption that the voltage drop across the stator resistance is negligible. Because of this, once the desired stator voltage amplitude is known, it sets the corresponding magnetizing current, see (A.8), and the controller forces the relationship (A.9):

ms s e sdi V M Mω λ= = (A.8)

( ) ( )1 rd sd s sd ms s sdMi L i i L M iλ′ = − = − (A.9)

In TABLE A.1 it can be observed that isd is related with the stator reactive power, and in (A.7) the way it is affected by the load and the filter reactive currents. Furthermore, expression (A.9) specifies the effect of isd on i'rd, in which the magnetizing current is constant and determined by the desired stator voltage. On the other hand, for a constant load, the only possible variation in the amplitude of the isolated system currents would be produced by a controlled distribution in the reactive power, i.e. by an intentional variation in the reactive currents (because the active ones are constant in the supposed operating condition). This way, a strategy for dividing the reactive power could be proposed in order to minimize the cupper losses in the system. These cupper losses are given by: 2 2 2 21

1 2 1 22s rCuL r r s s r r r FECP P P P P i r i r i r i r⎡ ⎤′ ′ ′ ′= + + + = + + +⎣ ⎦ (A.10)

Additionally, from (A.7) we can obtain:

( ) 1

constant

sd FECq Lq Cq FECqi i i i i I= − − = + (A.11)

where: 1 Cq LqI i i= − (A.12)



Now, if (A.11) is substituted in (A.9) then (A.13) is obtained: ( ) ( ) ( ) 1 2rd ms s FECq s FECqi i L M i I I L M i′ = − ⋅ + = − (A.13)

where: ( )2 1ms sI i L M I= − (A.14)

By using expressions (A.11)-(A.14) the magnitude of the current vectors can be obtained: ( ) ( )22 2 2 2 2

1 1 12s sq FECq FECq FECq sqi i i I i I i i I= + + = + + + (A.15)

( )( ) ( ) ( ) ( )22 22 2 2 2 2 2 22r rq s FECq s FECq s FECq rqi i I L M i L M i I L M i i I′ ′ ′= + − = − + + (A.16)

2 2 2 FEC FECd FECqi i i= + (A.17)

Now, by substituting (A.15)-(A.17) in (A.10) the power losses expression can be rewritten in the form:

212CuL FECq FECqP A i B i C⎡ ⎤= ⋅ + ⋅ +⎣ ⎦ (A.18)

where: ( ) ( )21 2s s rA r L M r r r′ ′= + + + (A.19)

( )( )1 2 12 2s s rB I r I L M r r′ ′= − + (A.20)

( ) ( )( )2 2 2 2 21 2 1 2sq s rq r FECdC i I r i I r r i r′ ′ ′= + + + + + (A.21)

Finally, if the equation dPCuL/dt=0 is solved for iFECq, it can be shown that the minimum is obtained when:

2FECqBiA

= − (A.22)

which can be easily manipulated to obtain (A.1), and the proof is complete.

Emulation of an Isolated Wind Energy Conversion System: Experimental Results - Final Report

Documents

Transcript of Emulation of an Isolated Wind Energy Conversion System: Experimental Results - Final Report