Investigation of a unified power flow controller

T.Makombe and N.Jenkins

Abstract: Power flow in an AC transmission system depends on three basic parameters: transmission line impedance, voltage magnitude and phase angle. Maximum utilisation of the power system can be ensured by the control of these parameters in real-time. It is shown experimentally that a unified power flow controller (UPFC) can control each of the parameters either selectively or simultaneously in appropriate combinations. It is also shown that a UPFC can control independently the real and reactive power flow in a transmission circuit. Results from computer simulations and a hardware laboratory model are presented.

1 Introduction

The continuing rapid development of high-power semi- conductor technology now makes it possible to control electrical power systems by means of power electronic devices. These devices constitute an emerging technology called FACTS (flexible alternating current transmission sys- tems). FACTS technology has a number of benefits, such as greater power flow control, increased secure loading of existing transmission circuits, damping of power system oscillations, less environmental impact and, potentially, less cost than most alternative techniques of transmission syc tem reinforcement [I].

The UPFC is the most versatile of the FACTS devices. The usual form of this device consists of two voltage source inverters with a common DC link, as shown in Fig. 1. The inverter at the input end of the UPFC is connected in shunt to the AC power system. and the inverter at the output end of the UPFC is connected in series with the AC transmis- sion circuit. The UPFC can control the transmission circuit parameters singly, or simultaneously in appropriate comhi- nations, at its series-connected output end, while independ- ently providing reactive power support to the transmission line at its shunt-connected input end. Furthermore, the W F C can independently control real and reactive power flow along the transmission line at its output end, while providing reactive power support to the transmission line at fts input end.

It has been shown [ 2 4 that it is possible to independ- ently control real and reactive power flow at the W F C input circuit by regulating the DC-link capacitor voltage and varying both the phase angle and the modulation index of the input inverter. In this paper, the real and reac- tive power flow at the UPFC input circuit is controlled independently by keeping the modulation index of the input inverter constant and controlling only its phase angle. The DC-link capacitor voltage is unregulated. This tech-

0 IEE, 1999 IEE Proceedings online no. 19990037 DOL 10.1049hp-gtd19Y90037 Paper first received 22nd July 1997 and in revised form 11th March 1998 The authorj are with the Manchester Centre for Electrical Energy, UMIST, PO Box 88, Manchester, M60 100, UK

400

nique is common in STATCOMs and has the advantages that the control of the UPFC input inverter is greatly Si- plified and its switching losses reduced.

A mathematical model of a vector-controlled UPFC has been derived and a vector control system developed for each of the W F C operational modes identifed. Computer simulations and experimental implementation of a UPFC verity the performance of the vector control strategy. Two- level inverters were used for the UPFC. A pulse-width modulation technique was used to switch the inverters. Insulated gate bipolar transistors (IGBTs) were used as the switching elements in the inverters.

2

In this section, we deal with the mathematical analysis and modelling of a vector-controlled UPFC, based on previous analysis of a STATCOM [5]. The use of vectors simplifies the analysis and control of a UPFC connected to a sym- metrical three-phase AC network. Vector control has long been used in electrical machine analysis [6] and is now being applied more widely to electrical power system analy- sis and control [5, 71. In this analysis, instantaneous three- phase variables are converted to vectors with orthogonal d- axis and q-axis components in a synchronously rotating d-q axes system.

A simplified three-phase representation of a WFC-con- trolled transmission circuit is as shown in Fig. 1. The inductance at the UPFC input represents the leakage reac- tance of the power transformer used, and the resistance represents the inverter and transformer conduction losses. The series-connected transformer is assumed to be ideal. The transmission line is represented as a lumped series inductance and series resistance to represent transmission line losses. The inverters are regarded simply as lossless power transformers that convert DC power to AC power. The internal structures of the inverters have not been con- sidered.

It is convenient to define a per-unit system as follows: i = ?libnre, v = vrIvbaser e = e'les,,, Q,, = vhsJibme, x = ubaSJl

Vector analysis and control of UPFC

ahsea xc = I~~base%me> I' = waba.w

2.1 Analysis of UPFC input circuit Referring to Fig. 1 the W F C input circuit equations can be written in per-unit as

IEE Yroc.-Gener. Transm. Dirbib., Yo/. 146, No. 4. hr /y I999

Fig.1

0 0 -TLWDRIl

S.

Li 0 0

(vsa - e<.)

x [ !:::] + [ - (vsb - e < b ) ] E y

- Z P q C

(1) Consider the vectorial transformation of variables from three-phase quantities to the synchronously rotating d-q plane defmed by the following equations, in which the ref- erence vector, and therefore the d-axis, is defined by the sending-end busbar voltage set v,, v, and v,:

where

1 cos(6') cos (0 -4) cos (6' + f ) -sin (0 - F) - sin (6' +?)

1 - 1 - fi fi

( 2 )

and

In the synchronously rotating reference frame, eqn. 1 can be written as

--TaWb .. )ut d - [ ( i p + jiq)e3ut] = -(ip + p o ) e dt 2,

+c, (I(v8)l - (ezd + j e i , ) ) e j W t

( 5 )

W b

where w = d8ldt. Now

d d t

+ j w ( i p + j i q ) e j w t ( 6 )

Substituting eqn. 6 in eqn. 5 and simplifying gives

d i p .d iq - -TiWbase x+3--- z p + w i ,

d t Xi

IEE Proc.-Cener. Trunrni. Dlstrib.. Yo/. 146, No. 4, July 1999

(7) 401

[A Equating real and imaginary parts:

Eqn. 8 is a mathematical model of the UPFC input circuit in per-unit notation in the synchronously rotating d-q refer- ence frame. The reactive current component iq is assumed to be either capacitive or inductive, with a variable magni- tude (0 5 iq L i,,,,) that is independent of the terminal volt- age. The real current component i, is due to any real power that may he drawn by the shunt section of the power flow controller.

Neglecting the input inverter voltage harmonics, the fol- lowing equations can be written relating the amplitudes of the voltage vector components at the input inverter AC- side terminals to the capacitor voltage on the common DC link:

e i d = miv, cos a( (9)

(10) ei, = miv, sin ai

where ai is the phase angle difference between the input inverter AC voltage vector ei and the line voltage vector v,. The factor mi is the modulation index of the input inverter.

2.2 Analysis of DC-link circuit The instantaneous powers at the AC and DC terminals of the input and output inverters, respectively, are equal if the inverters are assumed to be lossless. This gives two power balance equations in per-unit: v& = eij + ei& and v& = eo& + eoqiou. The DC-link circuit can 6e descnhed by the per-unit equation

2,3 Analysis of UPFC output circuit For the output inverter, the AC-side equations are (for an ideal series transformer of turns ratio of n : 1) [ ne;,, ne&b] = [ $ 1 and [::;I = [

ne;,, e m nibc

These output cwcuit equations can be transformed in the same way as the input circuit equations from the three- phase AC form to the per-unit vector form in the synchro- nously rotating d-q plane as follows:

Neglecting the output inverter voltage harmonia, the fol- lowing equations can be written relating the injected com- ponent magnitudes ed and e, to the DC-link voltage:

e d = m,v, cos cyo and e, = move sin cy,

where a, is the angle between e,, and v,, and m, is the modulation index of the output inverter.

2,4 Analysis of transinission circuit In terms of the instantaneous variables shown in Fig. 1, the transmission circuit equations can be written in per-unit as follows:

402

0

= /

0 0

(11) 1 -(vas + edqa - urd

-(us, + e+ - vrc) f [ %(Vsb + e d q b - W y b )

Eqn. 11 can be transformed in the same manner as eqn. 1 to the synchronously rotating d-q axes reference frame as follows:

5, --w

?(vs + ed - wu,d)

Eqn. 12 is a mathematical model of a simplified UPFC- controlled transmission circuit in per-unit notation in the synchronously rotating d-q reference frame.

3 Control objectives using series voltage source

Control of transmission circuit parameters and transmitta- ble real and reactive power flow is achieved by adding the voltage vector e,, to the input terminal voltage vector v,, as shown in Fig. 2d. Vector e,, is defined to have no angular restrictions (0 h arg(e4) h 2 4 and a variable magnitude (0 5 ledql L By appropriate control of e, the unified power flow controller can be used to accompish different control objectives by means of its series voltage source, and the shunt element provides reactive power support to the AC system hy means of iu. The input inverter draws i, from the AC system and supplies the real power require- ments of the output inverter via the DC link. The injected vector e& consists of the following components: e, = e,, + e,,,, for terminal voltage magnitude control, e, = exd + e,, for series compensation, e6 = ea + e& for phase angle con- trol, and e& = eqd + e for real and reactive power control. It has been shown previously [8, 91 that a number of modes of operation may be identified.

pq.

Fig.2 , Vector dwgrmnr i lhrmhg operation of UPFC n executing terminal voltage regulation only b erecutmg lerminal voltage rcgulafion and series line compensation e executing terminal voltige regul~tion and phase angle ~ontr01 d executing control of real and reactive tran~mittable power

3. I Series element inactive (mode I ) In mode 1, the series element of the UPFC is inactive (edq). The UPFC is thus equivalent to a STATCOM in this mode of operation.

3.2 Terminal voltage regulation only (mode 2) The first control objective using the series element is termi- nal voltage regulation or control only. This is achieved by

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keeping the angle of ed, zero with respect to the reference vector:

e, = k,u, (13) k,, is a scalar quantity and v, is a unit vector in the direo tion of v,. Thus, only the magnitude of v, is changed with respect to v,, as illustrated in Fig. 2u. The magnitudes of the d-q axes components of e,,, in this mode of operation can be expressed as

ed = emd = k m

eq = emY = 0

(14)

(15)

3.3 Terminal voltage regulation and series line compensation (mode 31 In this mode of operation, e(,, consists of e,, the series com- pensation component which either leads or lags the line current vector ii by 90", and e,,,, the terminal voltage regula- tion component orthogonal to e, in the two-dimensional vector space, as shown in Fig. 2b. Voltage e,y presents a capacitive or inductive virtual reactance to the line accord- ing to whether e, lags or leads it When inserting an induc- tive virtual reactance, e, = kJji,), and when inserting a capacitive virtual reactance, ei = kx(jii), where k, is a sca- lar quantity andj,, is a unit vector perpendicular to ir. The terminal voltage regulation component is expressed as e,n = k& The magnitudes of the d-q axes components of ed, in this mode of operation can be expressed as

(16)

(17)

e d = e z d + emd = -k, sin ail + k , cos ail

e, = ezq + emq = k, cos azl + k , sin ail

3.4 Terminal voltage and phase-angle regulation (mode 4J In this mode of operation, e,, consists of e6, the phase angle regulation component, and e,,, the terminal voltage regulation component, as shown in Fig. 2c. In this case, e,, is added in phase with v, to achieve the required terminal voltage magnitude. Vector e, is then injected to obtain the required phase angle. Vector e,,, can he expressed as e, = k,v,, as in mode 2. Vector e6 is given as [8] e6 = 2/v, + e,l/sin(kd2)lexplj(-~2 + kd2)], where kd is in rad. The direc- tion and magnitude of e6 ensure that the resultant terminal voltage v, = v, + e, + e6 has the same magnitude as vs + e",, hut leads or lags v, by k,. The magnitudes of the d-q axes components of e , , in this mode of operation can be expressed as

e d = ead+e,d = --2Iv,+e,Isin- ' I ($) +km (18)

eq = ehq + e,, = Iv, + e,l sin k6 (19)

3.5 Real and reactive power control (mode 5) The final control objective is the control of transmittable real and reactive power. In this mode of operation the UPFC is fully operational as a power flow control device. By considering Fig. 2d, it can he seen that the transmission line 'sees' the voltage v, + ed,, ,as the effective sending-end voltage. By independently varymg the magnitude and angle of e,,,, the UPFC acts as a general controller for transmitta- ble real and reactive power between the sending and receiv- ing ends. Assuming the practical situation that xl >> ri, eqn. 12 gives the steady-state line current components as

i i , Wbnbr (eq - W?, ) / (WZI ) (20)

IEE Pm.-Ger,er. Tmnsm. Disfrib.. Vol. 146, Nu. 4, Juiy 1999

i l q = -Wbase(Us f e d - % d ) / ( W Z l ) (21) The real and reactive transmittable powers in per-unit are given, respectively, by

P = usWliase(eq - U 7 , ) / ( W Z 1 ) (22 )

q = U, [-wase(~. + ed - ~ ~ d ) / ( ~ x t ) ] (23) Eqn. 22 shows that p depends on e,, and eqn. 23 shows that q depends on e& Real power can therefore be control- led primarily hy modulating the quadrature component of e,,, e,, and reactive power can be controlled primarily by modulating the in-phase component of ed,, ed. It is possible to define feedback loops and PI compensation for the inde- pendent control o f p and q as follows:

4 UPFC control system

4.1 Control of real and reactive current components at UPFC input The real and reactive current components, 'p and i,, in the UPFC input circuit can be controlled by operating the input inverter appropriately in order to obtain the required components eid and eiq in the mathematical model of eqn. 8. Assuming the practical situation that xi >> ri, eqn. X gives the steady-state input circuit current components as 'p = -whseeid(uxi) and iq = ubme(-vS + eiJ/(uxi). Therefore, the vector eid can be regulated in phase with v, in order to control the reactive current component iq, and the vector e, can he regulated in quadrature to v, to control the real cur- rent component $. The factor mi in eqns. 9 and 10 is kept constant. The angle ai between ei and v, is then vaned to achieve real power transfer to or from the DC-link circuit, and so establish the required value of the DC-link capacitor voltage v,. The required values of eid and eiq are thereby obtained.

loop and 3-phose to rotatino D-Q I oxis transfirmotion I

In this control strategy, therefore, the capacitor voltage is not regulated, hut varies with the operational conditions. Fig. 3 shows a block diagram of the control system for the UPFC input circuit. The output of the PI compensation block is the angle a,. The vector phase-locked loop ensures synchronous operation of the input inverter by providing the transformation angle 8. The input inverter fVing angle is given by pi = ai + 8. The three-phase to d-q axes trans- formation is as defined by eqns. 2, 3 and 4.

403

"0 j mode

6

Fig.4 Cmtrolsf trmmiwion c i r a i r p v m t e r s ondpuwn.

4.2 Control of transmission circuit parameters and power Fig. 4 shows a block diagram for the control of terminal voltage magnitude, series reactance, phase angle and real and reactive power using PI controllers. The closed loops force the output inverter to produce the AC voltage which corresponds to the appropriate combination of control sig- nals, as determined by eqns. 26 and 27, and the truth table for the combination of control signals shown in Fig. 4

e d & f = Gmemd + Gzezd f G 6 e 6 d f Gpqeqd (26)

eqRef = Gmem, + GA, f Gaes, + G,,e,, (27)

5 Computer simulation and experimental implementation of UPFC

Computer simulation and experimental implementation of a vector-controlled UPFC were carried out. The electro- magnetic transients simulation program, EMTDC, was employed for the computer simulation. Referring to Fig. 1, the parameters of the circuit used in both the experimental implementation and the computer simulation were as fol- lows: Li = 19mH, Ri = 0.652, C = 220pF, L1 = 58mH and RI = 0.652. The transformation ratio of the series-connected transformer was 21, with a leakage reactance of 0.738. The system base voltage and base current were 50 V,,, and 0.64 respectively. The sending end was connected to the laboratory supply and set at 1 per-unit using a var- iac. A phase-variable solid-state generator comprising a voltage-source inverter (VSI) and DC source constituted the receiving end, also set at 1 per-unit. The transmission angle was set at 27'. The VSIs in Fig. 1 were implemented in the experimental model using IGBT modules with inter- nal diodes. A programmed pulse-width modulation tech- nique [IO], implemented using a 68020 microprocessor, was used to switch the inverters and selectively eliminate three low-order non-triplen harmonics without generating triplen or even harmonics, or operating at an excessively high switching frequency. The UPFC was digitally controlled using a 33MHz 486 host processor and various electronic

404

interface circuits, such as current and voltage sensors and a multi-channel analogueidigital convertor. Inverter control data were transferred between the asynchronous 486 proc- essor and 68020 microprocessor systems using data latch circuits.

The experimental results were compromised by two fac- tors. First, the control loop time delay of the experimental controller was between 6ms and Sms, depending on the mode of operation. This delay was excessive and resulted in slow response and steady-state ripple. Secondly, the trans- formation of instantaneous three-phase variables to syn- chronously rotating d-q axes, described by eqns. 2, 3 and 4, requires that all variables are sampled at the same instant, i.e. in parallel. For this application, however, only a single, multi-channel analogue/digital convertor was used. This resulted in an 18" separation between the first and last s m - pling points and consequent errors in the computation of the d-y components.

Owing to the inadequate speed of the 486 host processor for this application, the 68020 microprocessor was synchro- nised with the AC system using a semi-digital phase-locked loop, based on the 4046 integrated circuit, driven by a volt- age signal from the sending-end busbar [Ill.

The calculation time step for computer simulations was lops, but the speed of response was slower than would be desirable in a practical installation owing to the rather sim- ple representation of the phase-locked loop and the control system filters [Ill.

Figs. 5 1 6 show the computer simulation and experimen- tal results for operation of the WFC in modes 1, 2, 3, 4 and 5. In all the modes of operation, it is seen that the sending-end busbar voltage is maintained at 1 per-unit by the reactive power support provided by the input inverter of the W F C . This demonstrates the independence of the input and output circuits of the UPFC. In modes 3 and 4, the series reactance and phase angle, respectively, are con- trolled independently of the terminal voltage. In mode 5, the transmittable real and reactive powers are controlled independently.

IEE Proc.-Gorer. Trunrm. Disirib.. Vol. 146, No. 4, July 1999

I b

0.25 t -0.25

-0.5- 0 . L 0.8 1.2 1.6 2.0 2.1

tirne.s

1.11 ? a - ; 1.0 > 3

0.91 0

0.125

- 0 . 2 5 0 1 0.4 0.8 1.2 1.8 2.0 2.1

time.s

0

? 4 Y

b

-0.501-- c

Fi 6 UPFC made o/opwarion rerpone io siep c h g e s h experimn-

0 ' ' ' ' - ' ~ , ~~ b - - - - , , ~ ~ ~ ~ Cd

time scale = 2OOmddiu.

"Rd ~~

lui?&li.Y

.... .. ....

6 Conclusions

Computer simulation and experimental results have shown that a UPFC is a highly versatile FACTS device that can

IEE Proc.-Gener. Trmsm. Di.strib.. Vol. 146, No. 4, July 1999

9 p -0.125

control transmission circuit voltage, series reactance and phase angle singularly, or in appropriate combinations, at its series-connected output while maintaining reactive power support at its shunt-connected input. It can also per- form independent control of transmittable real and reactive power at its series-connected output while maintaining

405

0.71

l . L L

4 1.2-

L

? .. ;o 0.8-

0.6

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1 . 0 2 : i- I : - 2 "

I a 5 c 0 b ' a

0 . 7 r

a

l . L

2 1.2 - 0 1.0 B ,o 0.8

b

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Fig. 10 UPFCmde 3 of opwalzo~ m p o m to step h g o u1 xR# yo reg- ulated at I per-mu experunental results

c l

1.1 * a 1.2

* 1.0 B 1

Zo 0.8 0.6

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0.2 0 0 4 0.6 0.8 1.0 1.2 1.1 1.6 1.8 2.0 2.2 2.L

time,s

UPFC mude 4 ofopmtim, response to step changes k a,, vu r e p

>

c Fig. 11 lated a1 I permit: .+mulation result3

b 0 x ' ~ 0 VoRd c 0 vr 0 v.R./ A vc

0 0 8 06,<

35 t

0.1 o.61

406 TEE Prac.-Cmer. T P M . ~ Disirib.. Vol. 146. No. 4, Jut" I999

1.41 1 . 4 1

1.250-

0.125

1.2

1.0

0.8

0.6

0.L

0.2 0

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C

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IEE Proc.-Gener Trunrm Di.wib, Vol 146. No. 4, July 1999 407

reactive power support at its shunt-connected input. This has been achieved using a vector control strategy for the UPFC. The versatility of the UPFC means that an appro- priate operating mode for the device can be chosen to suit the requirements of the transmission circuit at the time. Both the hardware model and computer simulations had a speed of response considerably slower than would be desir- able in practice. Further work is in progress to investigate faster control circuits.

References

HINGORANI, N.G.: 'FACTS-flexible AC transmission system'. IEE 5th international conference an AC and DC irunsmission, London, 11K Scntemkr 1991

~~~~

ROUND, S.D., YU, Q., NORUM, L.E., and UNDELAND, T.M.: 'Performance of a unified power flow controller using a d-q-control system'. IEE conference on AC and DCpoiver transmission, London, UK, 29 April - 3 May 1996

LIU, J.Y., SONG, Y.H., and FOSS, A.M.: 'Di@taI simulation ofthe PWM UPFC Using EMTP. IEE conference on AC and DCpower trimsmission, London, UK, 29 April - 3 May 1996 LOMBARD, X., and THEROND, P.G.: 'Control of unified power flow controller: comparison of methods on the basis of a detailed numerical model'. IEEUPES Summer Meeting, Denver, Colorado, July 28-August 1 1996 SCHAUDER, C., and MEHTA, H.: 'Vector analysis and control of advanced static Var commnsators'. IEE Proc. C, 1993. 140. (4)

1990,37, (1) GYUGYI, L.: 'A unified power flow control concept far flexible AC transmission system'. IEE 5th international conference on AC rrnd DC trailsmis~ion, London, UK, September 1991 GYUGYI, L.: 'The unified power flow controller: a new approach to power transmission control', IEEE Trom., Power Deliv., 1995, 10, (2)

10 MAHESHWARI, A., and NGO, D.T.: 'Synthesis of sinstep pulsewidth modulated waveforms with selective harmonic elimination', IEEE Tram. Power Electron., 1993,8, (4)

I1 MAKOMBE, T 'An investigation of a unliied power flow controller'. PhD thesis, UMIST, UK, 1997

,

408 IEE Proc-Gener. Tronsn,. Diwib., Vol. 146, No. 4, July I999