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Converter Rating Powers of Unified Power Flow Controller
N. Dizdarevic, S. Tesnjak, Member, IEEE, and G. Andersson, Fellow, IEEE
Abstract - Converter loadings of Unified Power Flow Controller (UPFC) within alleviation of voltage stability problem represents main concern of this paper. The UPFC is analysed as the device, which provides voltage support and/or co-ordinating power flow control action. Voltage stability problem is viewed from longer-term time domain response of a dynamic load model with non-linear recovery. First, the optimal rating algorithm is addressed from a viewpoint of series power flow control as an initial estimate of the UPFC converter ratings. Then, further thorough analysis is employed should other operational aspects (e.g. damping and voltage support) be concerned. Computational procedure reveals a necessity to increase converter rating powers within dynamic voltage collapse scenario. Index Terms - FACTS, UPFC, voltage stability and collapse
I. INTRODUCTION
Voltage stability problem with voltage collapse as its final consequence is an emerging phenomenon in power system planning and operation. The increase in utilisation of existing elements may get the system operating closer to voltage stability boundaries with increased voltage collapse risk. Since the rapid development of power electronics has made it possible to design power electronic equipment of high rating for high voltage systems, the voltage stability problem resulting from transmission system may be improved by use of the FACTS-controllers. To provide adequate support, the controllers should have proper nominal ratings.
This paper is solely concerned with system wise aspects of the UPFC. In order to deal with the voltage stability problem, the solution with the UPFC provides voltage support and/or co-ordinated control actions. Dynamic simulation is used as the most important assessment tool [1]-[3]. Load behaviour and an over-excitation limiter (OEL) are denoted as the main driving forces of the voltage collapse.
The UPFC injection model [4] is included in the overall multi-machine system model. The impact of the UPFC on alleviation of voltage stability problem is generally investigated from combined dynamic and static aspects in [5]. For illustrational purposes, only dynamic aspect is retained here. The control system of the injection model is used to point out possible benefits within voltage stability problem.
This work is supported by the Ministry of Science and Technology - Republic of Croatia under Grant 036016, and by the Swedish Institute.
N. Dizdarevic is with the Energy Institute “Hrvoje Pozar”, Zagreb, Croatia (e-mail: [email protected]).
S. Tesnjak is with the Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia (e-mail: [email protected]).
G. Andersson is with the Federal Institute of Technology (ETH), Zurich, Switzerland (e-mail: [email protected]).
During time-domain simulations, active and reactive power of the UPFC converters are evaluated and checked against stated thermal limitations. Operation of the UPFC demands proper power rating of the series and shunt branches. The ratings should enable the UPFC carrying out pre-defined regulation tasks without becoming overloaded.
II. SYSTEM MODELLING
The benefits of the UPFC and its injection model are explored by analysing 6-machine, 400 kV test system (Fig. 1). It is inspired by the one often used in CIGRÉ reports [6]. Loads are either of the static ZIP type or the dynamic one with non-linear recovery. Dynamic loads are applied at buses 19 and 20. The UPFC is located in the line 26, which initially connects buses 19 and 20 with dynamic loads. In voltage collapse scenario, these loads are shown to have the largest contribution to instability due to their dynamics. The UPFC is located nearby to solve voltage stability problem.
Dynamics of synchronous generator is represented by appropriate transient model [7]. The sub-transient effects are neglected. The synchronous generators are equipped with excitation system, OEL and speed governor–turbine system. The systems are modelled in a rather simple way, [1] and [5].
The aggregate first-order non-linear recovery type of the dynamic load model is introduced in the voltage collapse scenario. As seen down from HV bus, it is aimed to represent load recovery process. This load model expresses load dynamics in terms of its steady state and transient characteristics, [5] and [8]. The steady state characteristic of the load dynamics is expressed by constant active/reactive load power, whereas the transient one by constant impedance.
Fig. 1. Multi-machine test system
III. THE UPFC MODEL
The UPFC can provide simultaneous control of all basic power system parameters (voltage, impedance and phase angle) and dynamic system compensation. The controller can fulfil functions of reactive shunt compensation, series compensation and phase shifting meeting multiple control objectives. From a functional perspective, the objectives are met by applying boosting transformer injected voltage and exciting transformer reactive current (Fig. 2). The injected voltage is inserted by using series transformer. Its output value is added to the network bus voltage from the shunt side, and is controllable both in magnitude and angle. The reactive current is drawn or supplied by using shunt transformer.
Fig. 2. The UPFC device circuit arrangement
Functional structure of the UPFC results with appropriate
electric circuit arrangement [4]. The series converter AC output voltage is injected in series with the line (Fig. 3). It exchanges only active power with shunt converter. Reactance xS is the one seen from terminals of the series transformer.
Fig. 3. The UPFC electric circuit arrangement
The UPFC injection model is derived enabling three
parameters to be simultaneously controlled, [4]-[5]. They are the shunt reactive power Qconv1, and the magnitude r and angle γ of the injected series voltage SV . Besides constant series branch susceptance bS, included in the system bus admittance matrix, the bus power injections of the UPFC PSi, QSi, PSj, and QSj are embedded in the model (Fig. 4). If there is a control objective to be achieved, the bus power injections are modified through changes of parameters r, γ, and Qconv1. Control system of the injection model is proposed in de-coupled single-input single-output proportional-integral form. It governs the system to a pre-defined operating point by set-point changes [5]. Selection of input/output signals depends on the predetermined control mode. The shunt side could be controlled only in the voltage mode, Vi↔Qconv1, emphasising that Qconv1 represents reactive power loading of the shunt converter. The series side could be controlled through the r⇔γ pair in several different modes.
Fig. 4. The UPFC injection model with control system
IV. CONVERTER RATING POWERS
The UPFC shunt and series converters mutually exchange
only active power, whereas reactive one is controlled independently at both sides. Concerning apparent power of the shunt 1convS and series 2convS converter, it is defined as
21 convconv PP = (1)
controlledtlyindependenQandQ convconv 21 (2) The active power of the shunt converter Pconv1 could be
computed from the apparent power 2convS , given as
( )[ ]( )( )[ ]222
2
*2
coscos
sinsin'
iSiSijjiS
iSijjiS
Sjij
iijSconv
VbrVrbVVrbj
VrbVVrbjxVVeVrIVS
−−+Θ+
+++Θ−=
=−==
γγ
γγ
γ
(3)
If device losses are neglected, the active power requirement is equal for both converters
( ) ( ) γγθ sinsinRe 2*21 iSijjiSijSconvconv VrbVVrbIVPP ++−=== (4)
Thereby, the minimum nominal rating power Sconv1n of the shunt converter is given as a maximum active power demanded by the injected series voltage source
( )γ,max 11 rPS convnconv = . (5) Since the rating MVA capacity is not always fully utilised,
there usually remains some capacity available for producing reactive power Qconv1 and controlling voltage magnitude Vi
12 cos conviSSi QVrbQ +−= γ (6)
During the simulation, maximum available reactive power capacity max Qconv1 is given as
),(max 21
211 γrPSQ convnconvconv −= (7)
Maximum reactive power capacity is less or equal to the minimum nominal rating power of the shunt converter. If the active power loading level is larger than zero, the controllable voltage range becomes VLOW≤Vi≤VUPP due to decreased reactive power capability (Fig. 5).
Fig. 5. Maximum reactive power capacity of shunt converter
However, in the model it is supposed that the thermal
limits are set due to the total current flow through the shunt converter instead of the power flow. Reactive current Iconv1q poses limits with transient overload capability.
Operation of the UPFC demands proper power rating of the series and shunt branches. The ratings should enable operation without overloading. Therefore, the algorithm for optimal rating of the UPFC [4] is employed here to give an initial estimate on minimum nominal dimensioning, which satisfies pre-defined series power flow objective (Fig. 6). The value given by max Pconv1 is considered to be minimal criteria for dimensioning shunt converter rating power, whereas the power SS represents series converter rating power as a function of the maximum magnitude rmax.
Fig. 6. Algorithm for optimal rating of the UPFC
The algorithm is based on a steady state load flow procedure. The series branch is rated according to the series power flow objective, whereas the shunt one just satisfies active power demand. If a damping of electromechanical oscillations is of concern, then the series branch could be rated with larger magnitude rmax and power Sconv2n. If the voltage stability problem is of concern, the shunt branch could be rated with larger power Sconv1n. It increases voltage support capability by providing larger maximum value of Qconv1. Described algorithm serves as an initial estimation of the UPFC dimensioning, followed by further thorough analysis when the other operational aspects are of concern.
V. NUMERICAL RESULTS A. Initial Rating Powers of the UPFC Converters
Initial rating procedure concerns system without any dynamics based on steady state load flow computation. According to the algorithm (Fig. 6), the results concerning rmax, SS, and maxPconv1 are stably obtained for the range of rmax between 0.01 pu and 0.22 pu (Fig. 7). The powers correspond to range between 3 MVA and 112 MVA. Larger values of rmax increase discrepancy between them due to appearance of series side reactive power. For rmax = 0.15 pu, the powers SS and maxPconv1 are equal to 64.9 MVA and 60.5 MW, respectively. That value of rmax is usually estimated to be acceptable for voltage/power flow control purposes.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25
Rat
ing
Pow
ers
S_s
and
max
P_c
onv1
(pu
)
Additional Voltage Magnitude r (pu)
S_s (pu)
max P_conv1 (pu)
Fig. 7. Rating powers with respect to maximum magnitude
Later on, approximate rating of 65 MVA at rmax = 0.15 pu
is questioned due to a necessity of the UPFC’s participation in operations other than series power flow regulation. Subsequent repetitions of voltage/power flow control, oscillations damping, and voltage stability support led to a conclusion that Sconv1n and Sconv2n should be equal to 185 MVA for rmax = 0.15 pu. Power Sconv1n is increased due to voltage control, whereas Sconv2n due to damping control. This makes nominal ratings nearly 3 times larger than initial ones.
Steady state approach is compared to dynamic one, which includes system dynamics and rotational change of injected series voltage (r=0.15 pu and γ=[0°: 360°]. The UPFC shunt part is inactive in reactive power support.
Results from dynamic load flow approach (Figs. 8-9) show that series converter apparent power has a maximum value of 65 MVA, whereas the shunt one is 60 MVA. Obtained values closely match those computed for the rmax equal to 0.15 pu (Fig. 7). Within the series converter, reactive power Qconv2 exists in a significant amount. It keeps the apparent power Sconv2 at higher values when the active power Pconv2 passes through zero. At the shunt side, the apparent power Sconv1 is equal to the absolute value of the active power Pconv1. The active powers of both converters are equal. Initial reactive loading of the shunt converter does not impact significantly the maximum loading of the series converter.
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 50 100 150 200 250 300 350
Shu
nt C
onve
rter
Pow
ers
(pu)
gamma (deg)
S_conv1
P_conv1
Q_conv1
Fig. 8. Shunt converter powers with respect to the angle γ
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 50 100 150 200 250 300 350
Ser
ies
Con
vert
er P
ower
s (p
u)
gamma (deg)
S_conv2
P_conv2
Q_conv2
Fig. 9. Series converter powers with respect to the angle γ
B. Shunt-side Voltage Control Impact to Rating Powers
Having the UPFC series part inactive, the voltage control of the shunt part is applied solely. Time domain simulations showed that if the power ratings Sconv1n and Sconv2n would be set at 65 MVA, then with no-slope control characteristic the shunt magnitude Vi could be freely controlled in rather small range of ±0.010 pu. Since it is estimated that the voltage control range of ±0.025 pu suits voltage criterion better than the range ±0.010 pu, the rating power of the UPFC shunt converter is increased to 185 MVA, or roughly 3 times larger.
Control and system characteristics are evaluated in Vi = f (Qconv1) and Vi = f (Iconv1q) domains (Figs. 10-11, respectively).
The impact of the slope setting (0, 5 and 10%) is analysed. It is seen that within allowed limits of the current Iconv1q (±1 pu on converter base), the voltage magnitude Vi is controlled depending on the slope setting. At the limits, the current Iconv1q becomes constant, whereas the reactive power Qconv1 linearly changed due to changes of the voltage magnitude Vi.
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Bus
Vol
tage
Mag
nitu
de V
_i (
pu)
Shunt-part Reactive Power Q_conv1 (pu)
lower max.
upper max.
system characteristic
control characteristics
0%5%
10%
capacitive inductive
steady-state
Fig. 10. Control and system characteristics in Vi = f(Qconv1) domain
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
-1.5 -1 -0.5 0 0.5 1 1.5
Bus
Vol
tage
Mag
nitu
de V
_i (
pu)
Shunt-part Reactive Current I_conv1q (pu)
lower max.
upper max.
system characteristic
control characteristics
0%5%
10%
capacitive inductive
steady-state
Fig. 11. Control and system characteristics in Vi = f(Iconv1q) domain
C. Damping Control Impact to Rating Powers
Based on transient energy function, the UPFC injection model enables damping of electromechanical oscillations by simultaneous three-parameter control, [5] and [9]. Within damping control, dimensioning procedure is addressed from a viewpoint of the UPFC series side. A three-phase short circuit appears at the line 17 closely to the bus 15 (Fig. 1), being cleared after 220 ms by line outage. The disturbance initiates electromechanical oscillations between generators.
The UPFC damping control depends mostly on the rmax value. It influences series converter apparent power Sconv2, whose maximum value gives an estimate of its nominal rating power Sconv2n. Series converter should be adequately dimensioned to enable damping control without overloading.
Impact of rmax is analysed by employing two values: 0.15 pu and 0.25 pu. Responses of the rotor angle difference (Fig. 12) show that the UPFC damping control is more effective with larger rmax, especially in the initial large oscillations
period. Responses of series converter apparent power Sconv2 (Fig. 13) shows that by increasing rmax a larger peak of Sconv2 appears. For rmax=0.25 pu, that peak is nearly 185 MVA, whereas for rmax=0.15 pu, it is 120 MVA. Different values of rmax cause just minor changes of the shunt converter loading.
-120
-100
-80
-60
-40
-20
0
20
40
10 12 14 16 18 20
Rot
or A
ngle
Diff
eren
ce G
EN
6-G
EN
5 (d
eg)
Time (s)
r_max = 0.25 pu
r_max = 0.15 pu
Fig. 12. Rotor angle difference (δGEN6-δGEN5) with respect to rmax
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
10 12 14 16 18 20
Ser
ies
Con
vert
er A
ppar
ent P
ower
S_c
onv2
(pu
)
Time (s)
r_max = 0.25 pu
r_max = 0.15 pu
Fig. 13. Series converter apparent power Sconv2 with respect to rmax
D. Rating Powers in Voltage Collapse Scenario
Rating powers are checked during voltage collapse scenario based on a slow dynamics initiated by previous disturbance. Restoration of dynamic loads causes generators 5 and 6 being OEL restricted, which induces the collapse.
In order to avoid the collapse, the UPFC voltage support is applied at several time instants. Two-parameter support is first activated. Step changes are applied to the referent values of the shunt and series bus voltage magnitudes of the UPFC. The support is activated by switching on the regulation modes Vi↔Qconv1 and Vj↔r through equal step changes in their references set at 0.95 pu. The UPFC bus voltage magnitudes become equalised in the final part of each successful case (Fig. 14). Upon establishing stable operating point by two-parameter voltage control, at t=750 s the third-parameter control (LF, angle γ) is activated as well. Keeping the UPFC bus voltage magnitudes constant, the series active power flow is changed from -1.7 pu to -2.5 pu (γ=93°). This is applied to increase minimum singular value and decrease power loss [5].
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500 600 700 800 900 1000
Bus
Vol
tage
Mag
nitu
des
V_i
and
V_
j (pu
)
Time (s)
successful
initial
unsuccessful
LF control
Fig. 14. The UPFC bus voltage magnitudes Vi and Vj
With rating powers (Sconv1n, Sconv2n)=185 MVA, the
converters are operated within limits (Figs. 15-16). Exceptions appear only in damping period when shunt converter is allowed to be 35% shortly overloaded. Without LF control, shunt converter is loaded more heavily than the series one. Difference appears due to a fact that magnitude Vi is controlled at the shunt side while the series one just adds injected voltage source to its magnitude.
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500 600 700 800 900 1000
Shu
nt C
onve
rter
App
aren
t Pow
er S
_con
v1 (
pu)
Time (s)
successful
initial
unsuccessful
with LF control
w/o LF control
3ph short-circuit35% overload
Fig. 15. The UPFC shunt converter apparent power Sconv1
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600 700 800 900 1000
Ser
ies
Con
vert
er A
ppar
ent P
ower
S_c
onv2
(pu
)
Time (s)
successful
unsuccessful
with LF control
w/o LF control
3ph short-circuit
Fig. 16. The UPFC series converter apparent power Sconv2
Powers Sconv1 and Sconv2 are decomposed into active and reactive power parts, Qconv1, Pconv2, and Qconv2 (Figs. 17-19). Loadings without LF control are higher with small active power demand. With LF control, reactive power loading is decreased. Responses of Pconv2 show that a very low active power demand exists without LF control when the shunt converter is loaded dominantly with reactive power. With LF control, active power arises, but Qconv1 still has a larger
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500 600 700 800 900 1000
UP
FC
Con
trol
Var
iabl
e Q
_con
v1 (
pu)
Time (s)
successful
initial
unsuccessful
with LF control
w/o LF control
3ph short-circuit35% overload
Fig. 17. Shunt converter reactive power Qconv1
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500 600 700 800 900 1000
Act
ive
Pow
er o
f Ser
ies
Con
vert
er P
_con
v2 (
pu)
Time (s)
successful
initial
unsuccessful
with LF control
w/o LF control
3ph short-circuit
Fig. 18. Series converter active power Pconv2
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 100 200 300 400 500 600 700 800 900 1000
Rea
ctiv
e P
ower
of S
erie
s C
onve
rter
Q_c
onv2
(pu
)
Time (s)
successful
initial
unsuccessful
with LF control
w/o LF control
3ph short-circuit
Fig. 19. Series converter reactive power Qconv2
portion in Sconv1. Responses of Qconv2 denote low loading level in cases without LF control. With LF control, not only Pconv2 is increased, but Qconv2 as well. Change of series active power flow requires increase in reactive power if voltage magnitudes at both sides should be kept constant and equalised.
VI. CONCLUSIONS
The UPFC is analysed as the device, which provides voltage support and/or co-ordinating power flow control action. Voltage stability problem is viewed from longer-term time domain response of a dynamic load model. Converter loadings within alleviation of voltage collapse is concerned. First, the rating algorithm is addressed from a viewpoint of series power flow control as an initial estimate. Then, the analysis is employed with additional operational aspects (damping/voltage support). Computational procedure reveals a necessity to increase converter ratings within dynamic voltage collapse scenario in comparison with the ones obtained from series power flow regulation solely.
VII. REFERENCES [1] P. Kundur, Power system stability and control, EPRI McGraw-Hill,
ISBN 0-07-035958-X, 1994 [2] C. Taylor, Power system voltage stability, EPRI McGraw-Hill, ISBN 0-
07-063184-0, 1994 [3] T. Van Cutsem and C. Vournas, Voltage stability of electric power
systems, Kluwer Academic Publishers, ISBN 0-7923-8139-4, 1998 [4] M. Noroozian, L. Ängquist, M. Ghandhari, and G. Andersson, “Use of UPFC for
optimal power flow control,” IEEE Trans. Power Delivery, vol. 17, no. 4, pp. 1629-1634, Oct. 1997
[5] N. Dizdarevic, “Unified Power Flow Controller in Alleviation of Voltage Stability Problem,” Ph.D. dissertation, Faculty of Electrical Engineering and Computing, Univ. Zagreb, Zagreb, Croatia, 2001.
[6] CIGRÉ TF 38-01-06, “Load flow control in high voltage power systems using FACTS controllers,” Tech. Rep., 1996
[7] P. Anderson and A. Fouad, Power system control and stability, IEEE Press, Revised Printing, ISBN 0-7803-1029-2, 1994
[8] D. Hill, “Nonlinear dynamic load models with recovery for voltage stability studies,” IEEE Trans. Power Systems, vol. 8, no. 1, pp. 166-176, Feb. 1993
[9] M. Ghandhari, “Control Lyapunov Functions: a control strategy for damping of power oscillations in large power systems,” Ph.D. dissertation, Electric Power Systems, Royal Institute of Technology, Stockholm, Sweden, 2000.
VIII. BIOGRAPHIES
Nijaz Dizdarevic received his B.S., M.S., and Ph.D. degrees from Univ. Zagreb, Croatia, in 1990, 1994, and 2001, respectively. From 1991 till 2001 he was with the Dept. Power Systems at the same Faculty. During 1996 and 1997 he was at the KTH Stockholm, Sweden. Since 2002 he is with the Energy Institute “Hrvoje Pozar”, Zagreb, working on power system stability.
Sejid Tesnjak received his B.S., M.S., and Ph.D. degrees from Univ. Zagreb, Croatia, in 1972, 1977, and 1984, respectively. Since 1972 he has been with the Dept. Power Systems at the same Faculty where currently works as a Professor in system dynamics.
Göran Andersson (M’86, SM’91, F’97) received his Civ.Ing. and Ph.D. degrees from Lund Institute of Technology, Sweden in 1975 and 1980, respectively. Since 1986 till 2000 he was a Professor at the KTH Stockholm, Sweden. Since 2000 he is a Full Professor at the ETH Zurich, Switzerland. He is a Member of the Royal Swedish Academy of Engineering Sciences and the Royal Swedish Academy of Sciences.
