Comparison of PI and PR Current Controllers applied ...

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Abstract- This paper analyzes differences between ap and dq reference frames regarding the control of two-level VSC-HVDC current loop and dc-link voltage ...
Comparison of PI and PR Current Controllers applied on Two-Level VSC-HVDC Transmission System Alisa Manoloiu1, Heverton A. Pereira2,5, Remus Teodorescu3, Massimo Bongiorno4, Mircea Eremia1, Selenio R. SilvaS I

University "Politehnica" of Bucharest, Romania, [email protected] Federal University of Vic;:osa, Brazil, heverton.pereira@ufv. br 3 Aalborg University, Denmark, [email protected] 4 Chalmers University of Technology, Sweden, [email protected] 5 Federal University of Minas Gerais, Brazil, [email protected] 2

Abstract- This paper analyzes differences between

ap

and dq

reference frames regarding the control of two-level VSC-HVDC

can expand the PI controller bandwidth but, unfortunately, push the systems towards their stability limits [3].

current loop and dc-link voltage outer loop. In the first part, voltage

feedforward

effect

is

considered

with

PI

and

PR

controllers. In the second part, the feedforward effect is removed

R

and the PR gains are tuned to keep the dynamic performance.

L

Also, the power feed forward is removed and the outer loop PI controller is tuned in order to maintain the system dynamic performance. The paper is completed with simulation results, which highlight the advantages of using PR controller.

Index Terms- Current control, PI Control, PR control, VSC­

(a)

HVDe.

INTRODUCTION

Voltage source converters (VSCs) have been widely used in power systems, for distributed generation, high voltage direct current transmission (HVDC) and back-to-back inverter drives. This technology can provide auxiliary functions as voltage regulation and harmonic compensation that have been also required for many grid codes. Depending on the penetration levels of decentralized generation and grid parameters, it is noticed that stability problems can appear due to large droop gains and demanded power changes [1], [2]. Thus, HVDC-VSCs should have a good current control design in order to be robust against grid disturbances, besides helping the AC grid to mitigate disturbances. Most controllers with sinusoidal reference tracking have complex computational requirements or have high parametric sensitivity. On the other hand, simple linear proportional integral (PI) controllers have drawbacks as error in steady-state and the need to decouple phase dependency in three phase systems [3]. In this manner, resonant controllers have become a widely employed option in several different applications [4]. The design of PR controllers is usually performed by Bode diagrams and phase-margin criterion, or using Nyquist diagram [5]. Many works compare PI and PR controllers [3], [5], [6] based on performance. PI controllers performance can be improved with addition of a grid voltage feedforward path that

Figure I. Electric diagram of VSC·HVDC (a) and control digram with inner and outer loop (b).

This work proposes the use of PR controllers tuned without voltage feedforward path with similar performance to a PR controller with feedforward path. This control strategy without voltage feedforward is an alternative for connecting to weak ac grids, since the feedforward affects system stability performance [7], [8]. The VSC-HVDC transmission system studied in this work is presented in Fig. 1 (a), and the control diagram with inner and outer loops is represented in Fig. I (b). Feedforward effect is analyzed in two frames: synchronous dq, Fig. 2(a), and stationary ajJ, Fig. 2(b), for inner and outer loop, respectively. METHODOLOGY

The aims of this paper is to compare the inner loop control characteristics in both synchronous dq frame and stationary ajJ frame regarding the impact of the voltage feedforward path. The inner loop structures in dq and ajJ reference frames are shown in Fig. 2 (a) and (b), respectively. In Fig. 2(a) it is necessary to add a phase-locked loop (PLL) for grid voltage

phase tracking. The current loop performance is analyzed using the transfer functions given by (1)-(4), for dq and afJ reference frame, respectively. !.E. f*d

!.E.

ra

-Gpf sL+R-Gpf

(1)

-GpR sL+R-GpR

(2)

d

C pf CP R

=

=

kpd +!l s (J. kt

S'cos!p-w'sin!p

S2+W2

(3)

(4)

200

--

-

-,

--,

--

150 100 50

========--

-----

--

-----

-50 90 45 -

$

Ii

0 -45 -90 -135

� 10

'

'

f

10

--Ijl«" I

--ldIId*

PM=90 J[PM=89.(

10

'

Frequency (Hz)

Where



100

"

·50 90·· 45 �

�

0.4

0.54

0.2

-- PI with I.Oltage FF

50 �=======:::::

0.56

0.6

0.62

-- PR with \Oltage FF

-- PR without \Oltage FF

oL--�--��==c===�====�-� 0.4 0.6 0.7 0.8 0.9 0.5

-- PR withvoltage FF PR without voltage FF

TIme(s)

--irrproved

Figure 9. Outer loop response due to a step in

·45 PM=89.1

·90

"

PM=89.8

10'

-- PR with IOltage FF

PART II: OUTER Loop PERFORMANCE

The controller dynamics considering outer loop is analyzed in this section. The outer loop controls the square dc-link voltage, as shown in Fig. 2. There is a PI controller in the outer loop, and two topologies for inner loop controllers, such as presented in the previous case. The control gains in all study cases with outer loop control are shown in Table IV. TABLE IV Outer loop control parameters Gain Controller kp ki Case I - v�; step response PI, -94.2 -38.5 Ph 8.4 10"" 0.01 PR 45.4 10000 227. 4 PR without voltageFF 50000 Case IT - without voltage feedforward PR 818 100 PR without voltage FF 100 13.6W Case III - without power feedforward Ph without power FF 0.013 0.16 PR without power FF 45.4 10000

0.05 ::i

.9, N " "0

0

>

-0.05 -0.1

0.49

First, a step response in vi; is analyzed. Fig. 9 shows that a controller tuned to work without feedforward has similar performance to PI controller. The better performance of PR without feedforward is explained because voltage feedforward does not affect the vi; step response.

controller without voltage feedforward

The perturbation rejection performance is studied by a step response in the grid voltage. The PR controller was tuned to improve the performance, as shown in Table IV. Fig. 10 shows the dynamic behavior of Vic due to a perturbation in the grid voltage. Both controllers have similar dynamic performance.

0.5

0.51

0.52

0.53

0.54

TimA(�)

0.55

0.56

0.57

0.58

Figure 10. Dynamic behavior ofV�cdue to step in the grid voltage

An important characteristic is the improvement in the outer loop response due to the new controllers tuning. Fig. 11 shows a step in vi;, and now the PR The PR controller has similar dynamic behavior to the PI controller due to a step change in vi;, as seen in Fig. 11.

0.8

PR

-- PR without IOltage FF

0.1

Figure 8. Bode plot comparison between PR with feedforward and tuned PR without feedforward. -

-- PI with IOltage FF

10' Frequency (Hz)

RESULTS

v�;

"

0.15

-135 10'

A. PR

0.56

�

:f .g

1.f",-----�---�-==rI 1.09

0.6

>

0.4 0.2

0.55

0.57

-- PI with \Oltage FF

-- PR with \Oltage FF

-- PR without \Oltage FF

oL-__�__L-__L-__L-__L-_� 0.4 0.6 0.7 0.8 0.9 0.5 TIme(s)

Figure I I. Outer loop response due to a step in

vj;

The controllers were tuned to improve the dynamic system performance, both during disturbances and reference variation.

Thus, it is possible to eliminate the voltage feedforward measurements and keeping the system characteristics B. Ph

controller without power feedforward

Other feedforward term that influences the system dynamic is the dc-link power injection, as shown in Fig. 2. In this case, the PR controller tuning has a small influence in the control capacity of rejecting a disturbance.

0.8

1.05

.e, 0 6 NU . -0 >

The solution adopted in this work was to tune the PI controller in the outer loop, improving the dynamic response and consequently improving the system dynamic. Table IV shows the new gains for Pb.

0.95 '--'-----'--�---' 0.5 0.55 0.6 0.65 0.7

0.4

0.2

-- PI with power FF

-- PR with power FF

-- PR without power FF

o L--�--���=====c====�-�

Fig. 12 shows the dynamic behavior of VJc due to a perturbation in the power injected in the dc bus. In this study case, a step of 100 MW was performed. The tuning in the Ph control gains affect vJc step response as shown in Fig. 13. 0.02

1.1

�

0.4

0.5

0.6

0.7

0.8

0.9

TIme(s)

Figure 13. Outer loop response due to a step in PL

Heverton A. Pereira would like to thank CNPq (Conselho Nacional de Desenvolvimento Cientifico e TecnoI6gico), FAPEMIG (Fundayao de Amparo a Pesquisa do estado de Minas Gerais) and CAPES (Coordenayao de Aperfeiyoamento de Pessoal de Nivel Superior) for their assistance and fmancial support.

-0.02

NU � -0.06

REFERENCES [I]

-0.08 -- PI with pOVY'er FF

-0.1

-- PR with power

FF

-- PR without power

FF

-0.12 L--�-��-�-'==========='< 0.4 0.5 0.6 0.7 0.8 0.9 TIme(s)

Figure 12. Dynamic behavior ofV�cdue to power injected in the dc bus CONCLUSION

In this paper it was analyzed the control impact in two level VSC using o./J and dq reference frames. With a proper tuning of PR and PI controllers, they can control the system with the same dynamic performances, but PR has better performances in rejecting the voltage grid disturbances. Feedforward effect was studied and it was observed that PR can work without voltage feedforward with better results than PI controller. The proportional gain for the PR controller was modified in order to improve the system response without relying on voltage feedforward path. Thus, the stability performance was kept as in case with voltage feedforward. Furthermore, another advantage of avoiding grid voltage feedforward terms in HVDC transmission systems is the unpractical realization of this measurement in long distances lines. ACKNOWLEDGMENT

The work has been cofounded by the Sectoral Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRUI15911.5/S/132397.

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