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Título:Co pariso of PI a d PR curre t co trollers applied o t o-le el VSC-HVDC tra s issio systeAutores:MANOLOIU, ALISA ; PEREIRA, HEVERTON A. ; TEODORESCU, REMUS ; BONGIORNO, MASSIMO ; EREMIA,MIRCEA ; SILVA, SELENIO R.Pu li ado em:

5 IEEE Ei dho e Po erTechData da pu li ação:

5Citação para a versão pu li ada:MANOLOIU, ALISA ; PEREIRA, HEVERTON A. ; TEODORESCU, REMUS ; BONGIORNO, MASSIMO ; EREMIA,MIRCEA ; SILVA, SELENIO R. Co pariso of PI a d PR curre t co trollers applied o t o-le el VSC-HVDCtra s issio syste . I : 5 IEEE Ei dho e Po erTech, 5, Ei dho e . 5 IEEE Ei dho ePo erTech, 5. p. .

Comparison of PI and PR Current Controllers applied

on Two-Level VSC-HVDC Transmission System Alisa Manoloiu1, Heverton A. Pereira2,5, Remus Teodorescu3, Massimo Bongiono4, Mircea Eremia1, Selenio R. SilvaS

I University "Politehnica" of Bucharest, Romania, alisa.manoloiu@gmail.com 2 Federal University of Vi:osa, Brazil, heverton.pereira@ufv.br 3 Aalborg University, Denmark, ret@et.aau.dk 4 Chalmers University of Technology, Sweden, massimo.bongiorno@chalmers.se 5 Federal University of Minas Gerais, Brazil, selenios@dee.uing.br

Abstrat- This paper analyzes differences between ap and dq reference frames regarding the control of two-level VSC-HVDC

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

voltage feedforward effect is considered with PI and PR

controllers. In the second part, the feed forward efect is removed

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

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 Ters- Current control, PI Control, PR control, VSC­

HVDe.

INTRODUCTION

Voltage source converters (VSCs) have been widely used in power systems, for distributed generation, high voltage direct curent transmission (HVDC) and back-to-back inverter drives. This technology can provide auxiliary unctions 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 curent 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 eror 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 feedforwrd path that

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

(a)

R L

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

This work proposes the use of PR controllers tuned without voltage feedforwrd path with similar performance to a PR controller with feedforward path. This control strategy without voltage feedforwrd is an altenative for connecting to weak ac grids, since the feedforwrd afects 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 efect is analyzed in two rames: synchronous dq, Fig. 2(a), and stationary aJ, 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 rame and stationary aJ rame regarding the impact of the voltage feedforward path. The inner loop structures in dq and aJ reference rames 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 unctions given by (1 )-(4), for dq and J reference rame, respectively.

. -Gpf f* d sL+R-Gpf

. -GpR ra sL+R-GpR

d Cpf = kd +l

p s

CPR = k. S'cosp-w'sinp t S2+W2

(1)

(2)

(3)

(4)

Where p is an additional degree of reedom that allows to add a phase lead at the considered requency ).

v" • +

(b)

Figure 2. VSC control - inner and outer loop: (a) dq reference frame; (b) .J reference rame.

In Fig. 2 (b), the blocks FJ and Fz stand for the relations between curent in a� rame and active/reactive powers. They result rom the Laplace transformation in a� voltages:

F = # __ s_ and F = # __

W_ 1 3V (S2+W2) 2 3V (S2+W2)'

The PI controller is tuned using the methodology proposed in [9], and the PR controller is tuned to have a similar performance, using [4]. Fig. 3 shows the open loop Bode diagram for dq and J reference rame. It can be observed that the systems have the same phase margin for both PI and PR controllers.

The efect of perturbation arising rom the grid is modelled using Fig. 2, and through the transfer unctions given by (5) and (6). (7), (8) and (9) re the transfer unctions that show the perturbation effect in the dc voltage outer loop, with a generic inner loop in dq rame.

fd _ 1-H�F VB sL+R-PR (5)

200 -

150

100

50 ===--

-50 90 45 0

-$ -45 i � -90 -135

10 '

-, -

--- -

f 10'

Frequency (z)

-, -

---

I-Ijl«" -ldIId*

PM=90 J[PM=89.(

10'

Figure 3. Bode plot of open loop PR and PI controllers in a VSC with current control.

L _ 1-H�F VB sL+R-Pf,

2 2'PI,'PI2 Vde _ sC(sL+R) va� �

2 �(HV -1) vde = sCCsL+R) FF VB den2

2 -..+�(HP -1) v de sC sCCsL+ R) F F -=

den3

(6)

(7)

(8)

(9)

Where the transfer unctions H�F and H;F re feedforwrd paths that represent low pass ilter measurements and den], denz and den3 are given by:

den1 = 1 + 2'Pf,'Pf2 + � (10) sC(sL+R) sL+R

den2 = 1 + 3'Vd (W -1) +� (11) sC(sL+R) FF sL+R

den3 = 1 - . + 2'Pf, (W -1) + � (12) sC sC(sL+R) FF sL+R

ESULTS - PART I: INNER Loop PERFORMANCE

Grid System parameters used in the inner loop simulations are shown in Table I.

TABLE I Grid parameters Parameter Value

Reactor inductance 24.53 mH Reactor resistance 0.062 Grid voltage 170 kV Grid frequency 50 Hz DC Capacitor 17.78 .lF DC Voltage +/- 150 kV

The cut requencies for voltage in dq and aJ reference rame and for power are presented in Table II.

TABLE 11 Cut requencies Cut requency [Hz]

Voltage feedforward in dq 250 Voltage feedforward in .J 300 Power feedforward 1500

A. PI and PR controller performances In this section, the impact of voltage feedforward is

analyzed in PI and PR controllers for a step change in grid voltage, as illustrated in Fig. 4. The analysis shows similar performance characteristics when the system is modelled in aJ or dq with feedforward and a better performance in aJ when the system works without feedforward.

0.025 � 0.02 -0

0.015 -- IjVg With Voltage feedfoward

la

lVg without Voltage feedfoward

v 0.01 -- IdlVg With Voltage feedfoward

� -- IdlVg without Voltage eedoward

. 0.005 E : � -.--

·0.005

·0.01

·0.015 Q5 Q� Q� O� Q� Q� Q� O� Q� Q� M ime(s)

Figure 4. Feedforward efect during disturbance in the grid voltage.

Fig. 5(a) shows the response of the close loop system when a step variation is made in the current reference for PI and PR controllers. Both controllers have similar performance regarding time to track the references, as observed in Fig. 5(b).

, 0.5 0 � . O-� E « ·0.5

·1-L_�� 0.49 0.495 0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54

(a) 0.8 1-111:1:

-- I�II�* 0.6 g w 0.4

0.2

o � �

0.49 0.495 0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 ime(s) (b)

Figure 5. Control in .J and dq frames (a) step response; (b) settling time error.

PI and PR curent loop controllers have the gains presented in Table III. The PR controller that substitutes the voltage feedforward efect is tuned differently, with higher proportional and integral gains.

TABLE III Inner loop control parameters

Controller Gain

kp ki PII 38.5 94.2 PR 45.4 10000 PR without voltage FF 227.4 50000

B. PR controller without voltage feed forward In order to design a controller for the case without voltage

feed forward, the proportional gain was chosen to maintain the stability and to get a good steady state phase and amplitude error.

PR controller without feedforward was tuned to provide similar overshooting than a PR with feedforward during grid disturbances, as shown in Fig. 6. The PR proportional gain, kp, was selected as a unction of the reactor prameters - reactance and resistance, and the sampling time [4].

-- PR with ,Itage FF PR without oltage FF 0.01 -- Improed PR without oltage FF

·0.01

.0.02 .---___ � ___ -'� ___ -__ -' 0.5 0.55 0.6

ime(s)

0.65 0.7

Figure 6. Comparison between PR structures during voltage disturbance.

Gain modiications does not afect the overshoot dynamic in terms of curent step response, as seen in Fig. 7. Voltage feedforward should be avoided in weak grids since instability problems are possible to occur [10]. In this case, a system without feedforward has superior damping and tracking performance than a system with feedforwrd.

" -,

0 E i E :

-- la

reerence

1.5 -- la

response - PR with Oltage FF -- l

a - improed PR without oltage FF

0.5

0

·0.5

·1

0,498 0.5 0.502 0.504 0.506 0.508 0.51 0.512 0.514 0.516 0.518 ime(s)

Figure 7. Comparison between step response of PR structures.

Fig. 8 shows the open loop Bode diagrams for Ia/ I� for PR with feedforward and improved PR without feedforward. In both cases, the system has similar phase margin and cut-of requency. Thus, removing feedforwrd path with a new PR tuning can keep the system dynamic and eliminate the grid voltage measurement.

150 ii � 100 : � 50 �=====::: "

·50 90· 45

� � ·45

·90 -135 10'

- R with voltage FF

-irproved R without voltage FF

10' 10' Frequency (z)

PM=89.1"

PM=89.8"

Figure 8. Bode plot comparison between PR with feed forward and tuned PR without feed forward.

RESULTS - PART II: OUTER Loop PERFONCE

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

Controller Gain

kp ki

Case I - v�; step response PI, -38.5 -94.2 Ph 8.4 10"" 0.01 PR 45.4 10000 PR without voltageFF 227.4 50000

Case IT - without voltage feedforward PR 818 100 PR without voltage FF 13.6W 100

Case III - without power feedforwrd Ph without power FF 0.013 0.16 PR without power FF 45.4 10000

First, a step response in vi; is analyzed. Fig. 9 shows that a PR 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.

A. PR controller without voltage feed forward 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.

1.1--=' 0.8 � , 0 6 , .

0 > 0.4 0.54 0.56 0.56 0.6 0.62

0.2 - PI with Oltage FF - PR with Oltage FF - PR without Oltage FF o--�--��===�==�-� 0.4

0.15

0.1

0.05 i ,

0.5 0.6 0.7 TIme(s)

0.8 0.9

Figure 9. Outer loop response due to a step in v�;

-PI with Oltage FF -PR with Oltage FF - PR without Oltage FF

N 0 "

0 >

-0.05

-0.1

0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 TimA(�)

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 � f 0.6 g >

0.4

0.2

1.---=I 1.09

0.55 0.57 - PI with Oltage FF - PR with Oltage FF - PR without Oltage FF

o-__ � __ -__ -__ -__ -_� 0.4 0.5 0.6 0.7 TIme(s)

0.8 0.9

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 feedforwrd measurements and keeping the system characteristics

B. Ph controller without power feedforward Other feedforward term that inluences the system dynamic

is the dc-link power injection, as shown in Fig. 2. n this case, the PR controller tuning has a small inluence in the control capacity of rejecting a disturbance.

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.

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 afect vJc step response as shown in Fig. 13.

0.02

-0.02

NU � -0.06 -0.08 -0.1 - PI with pOer FF

- PR with power FF - PR without power FF -0.12 L--�-��-�-========< 0.4 0.5 0.6 0.7

TIme(s)

0.8 0.9

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 .J and dq reference rames. 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.

Feedforwrd efect was studied and it was observed that PR can work without voltage feedforwrd with better results than PI controller. The proportional gain for the PR controller was modiied in order to improve the system response without relying on voltage feedforwrd 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.

0.8 1.1 � , 0 6 NU .

1.05

0 > 0.4 0.95 --------'

0.5 0.55 0.6 0.65 0.7

0.2 - PI with power FF - PR with power FF - PR without power FF o --�--���==c==�-�

0.4 0.5 0.6 0.7 Ime(s)

0.8 0.9

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

Heverton A. Pereira would like to thank CNPq (Conselho Nacional de Desenvolvimento Cientiico 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 nd fmancial support.

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