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Optimal reactive power dispatch in a large power
system with AC – DC and FACTS controllers
D. Thukaram and G. Yesuratnam
Abstract: With the increased loading of existing power system, the problem of voltage stability
and voltage collapse has become a major concern in power system planning and operation. The
dependence of the system voltage profile on reactive power distribution forms the basis for reactive
power optimisation. The technique attempts to utilises fully the reactive power sources in the
system to improve the voltage profile and also to meet the reactive power requirements at the
AC – DC terminals to facilitate the smooth operation of DC links. The method involves successive
solution of steady-state power flows and optimisation of reactive power control variables with
unified power flow controllers using linear programming technique. The proposed method has
been tested on a real life equivalent 96-bus AC and a two terminal DC system.
1 Introduction However, the operator can use various control devices
like on load tap changers, generator excitations,
The fast development of power electronics based on new Switchable Var Compensators (SVC) and also FACTS
and powerful semiconductor devices has led to innovative controllers like Static Var Compensators, UPFCs to
technologies such as high-voltage DC transmission restore the system to normal conditions. These control vari-
(HVDC) and flexible AC transmission system (FACTS), ables are optimised for the purpose of improving voltage
which can be applied in transmission and distribution profile of the system. In an AC – DC power system, these
systems. The technical and economical benefits of these control variables have to be optimised in a co-ordinated
technologies represent an alternative to the application in manner taking into account of reactive power requirements
AC systems. Deregulation in the power industry and at the DC terminals.
opening of the market to deliver of cheaper energy to the Thukaram et al. [10] have given a method for
customers is creating additional requirements for the oper- co-ordinated optimum allocation of reactive power in
ation of power systems. HVDC and FACTS offer major AC – DC power system with an objective of enhancement
advantages in meeting these requirements. of steady-state voltage stability based on L-index. In this,
FACTS, based on power electronics, has been developed an algorithm is proposed to optimise the reactive power
to improve the performance of long-distance AC trans- control variables using linear programming technique. The
mission [1, 2]. Later, the technology has been extended to objective of reactive power optimisation is to minimise
the devices which can also control power flow [3, 4]. the sum of the squares of the L-indices of all the load
Excellent operating experiences are available worldwide buses of the system. However, the amount of complexity
and also FACTS technology became mature and reliable. and computational effort involved is very much high with
The market of FACTS and HVDC equipments for load-flow this objective. Hence, to overcome this, another objective
control is expected to develop faster in the future, as a result of minimisation of the sum-squared voltage deviations of
of the liberalisation and deregulation in the power industry. the load buses has been given in [11]. The algorithm
Considerable work has been reported in the literature given in [10] did not consider any FACTS controllers. It
with regard to integrated AC – DC system performance gives satisfactory results under peak load conditions, but
evaluation, notably for load-flow and stability studies [5 – it may not give satisfactory results under contingencies
9]. There is very limited work in the area of reactive like line outages. Hence, the algorithm proposed in [10]
power control in AC – DC systems [10]. Even though DC has been improved in this paper using the different objective
transmission lines carry no reactive power, real power given in [11] and FACTS controllers to improve the per-
flow into the converters is accompanied by some reactive formance of the system under normal and network
power flow because of the phase control. The considerations contingencies.
in the operation of a DC transmission system are to satisfy The most comprehensive device emanated from the
the need for reactive power at the terminals, to maintain FACTS initiative is the UPFC. The UPFC regulates the
good voltage profile and to improve voltage stability. In a active and reactive power control as well as adaptive to
day-to-day operation, it may be beyond the operator’s voltage magnitude control simultaneously or any combination
scope to take any control decision during emergencies. of them. Controlling the power flows in the network, under
normal and network contingencies, help to reduce flows in
# The Institution of Engineering and Technology 2008
heavily loaded lines, to reduce system power loss and to
doi:10.1049/iet-gtd:20070163
improve stability and performance of the system [12, 13].
Sawhney and Jeyasurya [14] present the application of
Paper first received 12th January and in revised form 10th July 2007
UPFC to improve the transfer capability of a power system.
The authors are with the Department of Electrical Engineering, Indian Institute
of Science, Bangalore 560012, India This paper is mainly concerned with the development of a
E-mail: dtram@ee.iisc.ernet.in, dtram_2001@yahoo.com
method for co-ordinated optimum allocation of reactive
IET Gener. Transm. Distrib., 2008, 2, (1), pp. 71 – 81 71
power in AC – DC power systems using FACTS controller L-index is computed as
UPFC, with an objective of minimisation of the sum of
Xg
Vi
the squares of the voltage deviations of all the load buses
[11]. The influence of UPFC on the system performance L j ¼ 1 À Fji (1)
i¼1
Vj
under contingency conditions has been discussed for a real-
life equivalent 96-bus AC and a two terminal DC system. where j ¼ g þ 1, . . . , n and all the terms within the sigma on
the RHS of (1) are complex quantities. The values Fji are
2 Static voltage stability analysis obtained from the Y-bus matrix as follows
! ! !
Voltage collapse is characterised by a slow variation in the IG Y GG Y GL V G
¼ (2)
system operating point, because of increase in the loads, in IL Y LG Y LL VL
such a way that the voltage magnitude gradually decreases
until a sharp accelerated change occurs. It has been where IG , IL and VG , VL represent currents and voltages at
observed that voltage magnitudes do not give a good indi- the generator nodes and load nodes. Rearranging (2) we get
cator of proximity to a voltage stability limit. Voltage col- ! ! !
lapse analysis involves both static and dynamic factors. VL Z LL F LG IL
¼ (3)
From a system operator’s viewpoint, a stressed (heavily IG K GL Y GG V G
loaded) system has to be carefully monitored and adequate  ÃÀ1  Ã
where FLG ¼ À YLL YLG are the required values. The
control action to be taken when the operating point L-indices for a given load condition are computed for all
approaches the limit of voltage stability. load busses.
In the day-to-day operation and control of power systems, For stability, the bound on the index Lj must not be vio-
these decisions require very fast computations in the energy lated (maximum limit, 1) for any of the nodes j. Hence, the
control centre. As dynamic computations are time consum- global indicator L describing the stability of the complete
ing (CPU time), the static aspects of voltage stability are subsystem is given by the maximum of Lj for all j (load
of great importance to system security and stability buses). An L-index value away from 1 and close to zero
assessment. Many voltage stability and voltage collapse indicates an improved system security. For a given
prediction methods have been presented [8, 15, 16]. This network, as the load/generation increases, the voltage mag-
section gives a brief outline of two methods used for nitude and angles change, and for near maximum power
static voltage stability analysis. transfer condition, the voltage stability index Lj values for
load buses tend to close to 1, indicating that the system is
2.1 Minimum singular value close to voltage collapse. The stability margin is obtained
as the distance of L from a unit value, that is (1 2 L).
Some researchers [15] have proposed minimum singular
value (MSV) of the load flow jacobian as a measure of
voltage stability. The singularity of the power flow jacobian 3 Approach
matrix as an indicator of steady-state stability is used, where
the sign of the determinant of jacobian matrix J determines This paper is mainly concerned with the development of a
whether or not the studied operating point is stable. method for co-ordinated optimum allocation of reactive
Singularity of the power flow jacobian matrix corresponds power in AC – DC power systems using FACTS controllers,
to that jacobian matrix for which the inverse does not with an objective of minimisation of sum of the squares of
exist and thus there is an infinite sensitivity in the solution the voltage deviations [11]. An algorithm is proposed for
to small perturbations in the parameter values. The MSV optimisation of reactive power control variables using
is used to indicate the distance between the studied operat- linear programming.
ing point and the steady-state voltage stability limit. At the The major blocks in the approach adopted are shown in
point of voltage collapse, no physically meaningful load Fig. 1. At the beginning of the reactive power optimisation
flow solution is possible as the load flow jacobian in AC – DC power systems, a satisfactory initial operating
becomes singular. At this point, the MSV becomes zero.
Hence, the distance of the MSV from zero at an operating
point is a measure of proximity to voltage collapse. The
point where the MSV equals to zero is called a static bifur-
cation point of the power system.
2.2 Voltage stability index L
Kessel and Glavitsch [16] have proposed static voltage
stability index L based on normal load flow solution. The
authors have shown that the value of L must lie within a
unit circle, with a range L ¼ 0 (no load on the system) to
L ¼ 1 (static voltage stability limit). The value of L is
computed for each load bus in the system.
Consider a system where n is total number of busses, with
1, 2, . . . , g generator busses (g), g þ 1, g þ 2, . . . , g þ s
SVC busses (s), g þ s þ 1, . . . , n the remaining busses
(r ¼ n 2 g 2 s) and t is number of OLTC (on load tap chan-
ging) transformers.
A load flow result is obtained for a given system operat-
ing condition, which is otherwise available from the output
of an on-line state estimator. Using the load flow results, the Fig. 1 Major computational blocks of the proposed approach
72 IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008
condition for the DC system is selected based on the control where Rc is commutation resistance, a is the transformer tap
strategies, viz., constant power control, constant current setting and a the firing angle. Neglecting the losses in the
control and constant voltage control applicable at the DC converter and its transformer and equating the expression
terminals. for powers on the AC and DC sides, the equation for
A solution for DC system is first obtained in block 2 and power factor angle (c 2 j) is given by
then the voltage, active and reactive power requirements at
the DC terminals are computed. Defining these require- V dc ¼ aV ac cosðc À jÞ (6)
ments at the AC side of the converter – inverter transfor-
mers, an AC power flow solution with UPFC is obtained and for the reactive power flowing from the AC bus into the
in block 3. Now the terminal transformer taps are computed converter terminal is
and their range checked for the satisfactory solution of the
Qdc ¼ Pac tanðc À jÞ (7)
AC – DC system in block 4. If the transformers tap change
is not satisfactory or the voltage profile has to be improved where c is the alternating voltage angle and j is the alternat-
further, reactive power optimisation for the AC system as ing current angle.
explained in Section 5 is carried out in block 5 with suitable A practical operating scheme for a DC system using local
terminal conditions. At this stage, a check for the AC – DC terminal controls is to have the DC system voltage deter-
system satisfactory condition is performed in block 6. If the mined at one terminal and the other terminals are provided
solution is still not satisfactory, modifications in the initial with scheduled power or current settings. To keep the reac-
conditions of the DC system are made with suitable tive power consumption of the converter and the losses low,
changes in the firing angles as shown in block 7 and the pro- the firing angles should be small. However, to maintain
cesses in blocks 2 – 7 are repeated. Finally, the nearest prac- phase control and reliable commutation, a minimum
tical possible tap settings are selected for the transformers at control angle should be maintained.
the AC – DC terminal and the final AC – DC power-flow
solution is obtained in block 8. The proposed method has
been tested on an equivalent 96-bus AC and a two-terminal 4.2 UPFC equivalent circuit
DC system.
The UPFC equivalent circuit for a steady-state model as
shown in Fig. 3 has been used in the evaluation of system
4 Description of model performance.
The equivalent circuit consists of two ideal voltage
4.1 Converter representation sources
A general AC – DC terminal and its equivalent circuit is VcR ¼ VcR (cos ucR þ j sin ucR )
shown in Fig. 2. The basic equations describing the conver- (8)
VvR ¼ VvR (cos uvR þ j sin uvR )
ter with its firing angle, tap controls and the DC network are
summarised based on the per-unit system selected as where VvR and uvR are the controllable magnitude (VvR min
follows. VvR VvR max) and angle (0 uvR 2p) of the parallel
AC system base quantities voltage source. The magnitude of VcR and angle ucR of the
series voltage source are controlled between limits
Pac ¼ three-phase power
base (VcR min VcR VcR max) and angle (0 ucR 2p), respect-
ac
Vbase ¼ Line pto-line RMS value
– ffiffiffi ively [17].
ac ac
Ibase ¼ Pac / 3 Vbase
base
DC system base quantities 4.3 Load model
pffiffiffi
Pdc ¼ Pac ; Vbase ¼ Kb Vbase ; Ibase
base base
dc ac dc ac
¼ ( 3=Kb )Ibase A composite load model, a combination of the ZIP models
p (ZIP load is a combination of constant-impedance, constant-
where Kb ¼ (3 2/p) nb and nb is the number of series 2 current and constant-power load ingredients) and an expo-
connected bridges in a terminal. nential model are considered. Active and reactive power
The direct voltage and power at the converter are loads are modelled as a function of voltage at the bus.
given by The functions considered are
V dc ¼ aV ac cosðaÞ À Rc I dc (4)
Pactual ¼ Pnominal (A0 þ A1 V þ A2 V 2 þ A3 V ep )
Li Loi (9)
Pdc ¼ V dc I dc (5)
Qactual ¼ Qnominal (R0 þ R1 V þ R2 V 2 þ R3 V eq )
Li Loi (10)
Fig. 2 Equivalent circuit of DC terminal Fig. 3 UPFC equivalent circuit
IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008 73
where A0 , R0 , A1 , R1 , A2 , R2 , A3 , R3 denote the portion of from the DC system solution and values of V ac from the
total load proportional to constant power, constant impe- AC system solution, the tap settings of the converter trans-
dance, constant current and exponential of voltages with formers are determined. If the tap settings violate
ep, eq given values. the limits, modifications such as a change in scheduled
voltage V dc at the voltage-controlled DC terminal, a
change in control angle a and optimisation of the reactive
4.4 AC –DC power-flow solution method power schedule in the AC system to obtain improved
values of V ac at the AC – DC terminals are done, and
Considering a DC system, where m represents the total the procedure to obtain AC – DC system solution are
number of DC terminals, p represents the number of term- repeated.
inals with constant power control, c represents the number
of terminals with constant current control and,
m ¼ ( p þ c þ 1) the terminal with voltage control. 5 Description of the reactive power optimisation
It is assumed that 1, 2, . . . , p are the constant power problem
control terminals, p þ 1, p þ 2, . . . , p þ c are the constant
current control terminals and m the voltage controlled term- Minimisation of voltage deviations of all the load buses in a
inal. The algebraic sum of the direct currents flowing into system forms the basis for the reactive power optimisation
the DC network must be zero and therefore problem. The model uses linearised sensitivity relationships
X
m to define the problem. The constraints are the linearised
dc
Ik ¼ 0 (11) network performance equations relating to control and
k¼1 dependent variables and the limits on the control variables.
Then, the model selected for the reactive power optimis-
The direct voltages at terminals other than the voltage
ation uses linearised sensitivity relationships to define
controlled terminal are given by
the optimisation problem. The objective is to minimise
[Vbus ] ¼ [Rbus ][Ibus ] þ [Vm ] (12) the sum of the squares of the voltage deviations of all the
load buses for the system [11] is given by
where
[Vbus ]t ¼ [V1 , V2 , . . . , Vp , Vpþ1 , . . . , Vpþc ]
dc dc dc dc dc X
n
ye¼ (Vjdesired À Vjactual )2
t dc dc dc dc dc
[Ibus ] ¼ [I1 , I2 , . . . , Ip , Ipþ1 , . . . , Ipþc ] j¼gþ1
dc dc dc dc dc
[Vm ]t ¼ [Vm1 , Vm2 , . . . , Vmp , Vmpþ1 , . . . , Vmpþc ] where Vdesired is the desired value of the voltage magnitude
j
at the jth load bus. Vdesired is usually set to be 1.0 pu.
j
The control variables are
[Rbus] is the bus resistance matrix of the DC network with
voltage controlled terminal as reference † The transformer tap settings (DT )
dc
Vm is the scheduled voltage at the voltage controlled † The generator excitation settings (DV )
terminal † The SVC settings (DQ)
dc dc
Ipþ1 , . . . , Ipþc are the scheduled currents at the controlled
terminals These variables have their upper and lower limits.
dc dc
I1 , . . . , Ip are computed currents at the power controlled Changes in these variables affect the distribution of the
terminals (I dc ¼ P dc/V dc) reactive power and therefore change the reactive power at
generators, the voltage profile and thus the voltage stability
Using an iterative technique, the solution to (12) is of the system.
obtained for the values of direct currents, voltages and The dependent variables are (i) the reactive power
powers at all the DC terminals. For the terminals with outputs of the generators (DQ) and (ii) the voltage magni-
power control, and current control it is common practice tude of the buses other than the generator buses (DV ).
to co-ordinate the tap control with phase control, so that These variables also have their upper and lower limits. In
the terminal will operate at some direct voltage below its mathematical form, the problem is expressed as
own minimum firing (ignition or extinction) angle charac-
teristic to avoid frequent mode shifts from occurring with
normal alternative voltage fluctuations. Thus, the direct Minimise ne ¼ Cx (14)
voltage equation for the terminals with power control and Subject to b min
b ¼ Sx bmax
(15)
current control is modified as
min max
and x x x (16)
V dc ¼ M[aV ac cos a À Rc I dc ] (13)
where M is a coefficient typical of 0.97 for 3% voltage where C is the row matrix of the linearised objective func-
margin. Substituting the values of a, Rc , V dc, I dc and M, tion sensitivity coefficients, S the linearised sensitivity
the values of aV ac for all the terminals are obtained from matrix relating the dependent and control variables, b the
(4) and (12). Substituting the values of aV ac into (6), the column matrix of linearised dependent variables, x the
power factor angles (c 2 j) at all the terminals are obtained. column matrix of the linearised control variables, bmax
The active and reactive powers flowing from the AC bus to and bmin the column matrices of the linearised upper and
the converter terminals are computed from (5) and (7), lower limits on the dependent variables and xmax and xmin
respectively. Now the AC power-flow solution is obtained are the column matrices of linearised upper and lower
with the defined values of P, Q at the AC – DC terminals. limits on the control variables.
This solution provides the voltage conditions at all the AC The linear programming technique is now applied to the
buses. Knowing the values of aV ac, that is, the product of above problems to determine the optimal settings of the
converter station transformer tap and AC-bus voltage control variables.
74 IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008
The control vector in incremental variables is defined as . . . k SVCs, (k ¼ t þ g þ s)
x ¼ [DT1 , . . . , DTt , DV1 , . . . , DVg , DQgþ1 , . . . , DQgþs ]T @ne X
n
¼ 2(Vjdesired À Vjactual )(ÀS jm ) (22)
(17) @Tm j¼gþ1
and the dependent vector in incremental variables as
where m ¼ 1, 2, . . . , t for calculating the objective function
h iT
sensitivities with respect to transformer taps, and Sjm is cor-
b ¼ DQ1 , . . . , DQg , DVgþ1 , . . . , DVgþsþ1 , . . . , DVn
responding elements in (21)
(18)
@ne X
n
The upper and lower limits on both the control and ¼ 2(Vjdesired À Vjactual )(ÀS jm ) (23)
@Vm j¼gþ1
dependent variables in linearised form are expressed as
max max max
xmax ¼ [DT1 , . . . , DTtmax , DV1 , . . . , DVg , where m ¼ t þ 1, t þ 2, . . . , t þ g for calculating the objec-
tive function sensitivities with respect to generator exci-
DQmax , . . . , DQmax ]T
gþ1 gþs tations
min min min
xmin ¼ [DT1 , . . . , DTtmin , DV1 , . . . , DVg , @ne X
n
¼ 2(Vjdesired À Vjactual )(ÀS jm ) (24)
DQmin , . . . , DQmin ]T
gþ1 gþs
@Qm j¼gþ1
(19)
max max
bmax ¼ [DQmax , . . . , DQmax , DVgþ1 , . . . , DVgþs ,
1 g where m ¼ t þ g þ 1, . . . , k for calculating the objective
max
DVgþsþ1 , . . . , max
DVn ]T function sensitivities with respect to SVCs.
It is important to note that the cost coefficients of the
bmin ¼ [DQmin , . . . , DQmin , DVgþ1 , . . . , DVgþs ,
min min objective with respect to all controlling variables are
1 g
obtained from (22). In terms of cpu time for estimating
min min
DVgþsþ1 , . . . , DVn ]T the cost coefficients, objective used in this paper takes
only one-nineth of the time taken by the objective used in
where [10] per one iteration. Hence, the amount of complexity
and computational effort involved in estimating the cost
DT max ¼ T max À T act , DT min ¼ T min À T act coefficients is very much less incomparision with the objec-
tive used in [10].
DQmax ¼ Qmax À Qact , DQmin ¼ Qmin À Qact
DV max ¼ V max À V act , DV min ¼ V min À V act 5.3 Computational procedure
5.1 Computation of sensitivity matrix (S) This section presents the computational steps followed in
the program developed for the optimisation of reactive
The sensitivity matrix S relating the dependent and control power allocation in an AC –DC power system. In the day
variable is evaluated [11] in the following manner. to-day operation of the power systems, the following steps
Considering the fact that the reactive power injections at a are used to obtain the optimal reactive power allocation in
bus does not change for a small change in the phase angle the system for improvement of voltage profile.
of the bus voltage, the relation between the net reactive
Step 1:
power change at any node as a result of change in the trans-
former tap settings and the voltage magnitudes can be † Input the data relating to DC system
written as 1. Network
2 3 2. Power, current and voltage schedule at the terminals
2 3 2 3 DTt
DQg A1 A2 A3 A4 6 DV 7 3. Firing angle setting
6 7 6 g7 4. Converter transformer tap ranges.
4 DQS 5 ¼ 4 A5 A6 A7 A8 56 7 (20)
4 DVs 5 † Input data relating to AC system
DQr A9 A10 A11 A12
DVr 1. Network
2. Scheduled load and generation
Then, transferring all the control variables to the right- 3. Upper and lower limits and step-size for transformers tap
hand side and the dependent variables to the left-hand settings, generator excitation settings and SVC settings
side and rearranging, we set 4. Upper and lower limits on the generator reactive powers
2 3 2 3 and voltage magnitudes at buses other than the generator
DQg DTt buses.
6 7 6 7 † Form the network matrices.
4 DVS 5 ¼ [S]4 DVg 5 (21)
DVr DQs Step 2:
5.2 Computation of objective function Vdesired
P † Set the initial/modified values for scheduled firing angle
(Ve ¼ n desired
j¼g+1 (Vj 2 Vjactual) 2) sensitivities (C) a, voltage V dc, current I dc and power P dc for the converter
with respect to control variables terminals.
† Solve for the direct voltage and current at all the DC term-
Consider a system where k is the total number of control inals. Compute the values of aV ac, power factor angles c 2 j,
variables with 1, 2, . . . , t number of OLTC transformers, power factor, and active and reactive powers flowing from the
t þ 1, t þ 2, . . . , t þ g generator excitations and t þ g þ 1 AC bus into converters at all the AC–DC terminals.
IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008 75
† Find the equivalent active and reactive loadings at the detailed contingency/stability studies, it has been observed
AC terminals including the local reactive power compen- that, the placement of UPFC between these two buses gives
sation at the terminals. better results compared with other transmission lines for
most of the contingencies. Hence, this line has been selected
Step 3: for placement of UPFC. The rating of the UPFC is
100 MVA. The series converter is rated 100 MVA. The
† Perform the AC power flow with UPFC (or output of the shunt converter is also rated for 100 MVA.
state estimation) to obtain the values of voltage deviations
of all load buses. Find the tap settings of all the
converter station transformers and check for the satisfactory 6.1 Case 1: line outage 27 – 28
range of the converter transformer tap settings. If yes, go to
step 6. With this contingency, for a peak load condition, the power
flow results for this case show a low-voltage profile in the
Step 4: system with the voltages of about 48 buses not being
within acceptable limits (0.95– 1.05 pu). There are 13 gen-
† Compute the column vectors bmax, bmin, xmax, xmin and erators exceeding the maximum Q limits and no generator Q
modify the column vectors xmax and xmin to reasonably is exceeding the minimum limit. As indicated in Table 2,
small ranges. Compute the sensitivity matrix S, the row the MSV before optimisation is 0.20491. The minimum
vector C of the objective function. Solve the optimisation 55.
voltage is 0.732 pu at bus number P The sum of squares
problem using the linear programming technique and of voltage stability L-indices L 2 is 7.2002. The
obtain the AC power-flow solution. sum-squared voltage deviation of all the load buses y e is
† Find the tap settings of all the converter station transfor- 0.64807. Initially, the proposed algorithm for reactive
mers and check for the satisfactory range of the converter power optimisation has been applied to improve the situ-
transformer tap settings. If yes, go to step 6. ation without using any UPFC. Then, the results are
obtained by placing the UPFC on the line connecting
Step 5: buses 39 and 86. The step-size taken for both the regulating
transformers and the generators excitations is 0.0125 pu.
† Find the suitable modified settings for the DC scheduled The total number of SVC buses selected for the compen-
voltages and scheduled firing angles and go to step 2. sation is about 30. Initially, the compensation at the selected
places is assumed to be zero. After three iterations of the
Step 6: VAr optimisation, the voltages at all the buses have been
brought within the satisfactory operable limits (0.95–
† Set the converter station transformer tap settings to the 1.05 pu). After the optimisation, the minimum voltage has
nearest practical possible settings. Compute the modified been improved to 0.978 with UPFC and to 0.959 without
converter control (ignition or excitation) angles a. UPFC and the sum of square of voltage stability L-indices
P 2
Compute the modified power factor, active and reactive L is reduced to 4.4566 without UPFC where as
powers flowing from the AC bus into converters at all the this value is only 2.5366 with UPFC. The MSV after
terminals. optimisation is 0.26788 and the sum-squared voltage devi-
ations of all the load buses is improved to 0.03488. The cor-
Step 7: responding values are 0.28193 and 0.03408 with UPFC. All
these results indicate that there is an improvement in
† Perform the AC power-flow solution with the optimum voltage stability margin with the given optimisation algor-
settings of the reactive power control variables. Check for ithm. The improvement is much better in the presence of
satisfactory limits on the dependent variables, voltage UPFC. The transmission loss of the system also reduced
profile and voltage stability L-indices. If no, go to step 2. from 491.96 (initial value) to 382.44 MW without UPFC
and to 363.56 MW with UPFC as indicated in Table 2.
Step 8: After optimisation, all the generators reactive power
outputs Q are not brought within the limits, still some of
† AC/DC system final results. the generators Q were exceeding the maximum limits (gen-
erator 6, 12 and 17 highlighted in Table 3), if there is no
6 System studies FACTS controller. Where as with the presence of UPFC,
the reactive power outputs of all the generators have been
An AC – DC system of two-terminal DC and 96 AC buses, brought within their limits during optimisation as indicated
typical of Indian grid equivalent system including the in Table 3. The summarised results, initial and after optim-
voltage levels of 220 and 400 kV as shown in Fig. 4a has isation (with and without UPFC), for the given system are
been considered for this study. The corresponding single indicated in Tables 2 and 3. The load bus voltage profiles
line diagram is shown in Fig. 4b. There are 20 generators and voltage stability indices before and after optimisation
in the system connected at buses 1 –13, 15– 19, 95 and (with and without UPFCs) are shown in Fig. 5a and b,
96. The AC – DC converter stations are connected at buses respectively. In this case, the DC terminal at bus 32 is con-
29 and 32. The DC system data is given in Table 1. There sidered as receiving end power control.
are 20 generators, 18 tap regulating transformers and 95
transmission lines in the system. About 30 buses are con-
sidered as SVC buses. The system has about 12345.8 MW 6.2 Case 2: line outage 37 – 38
and 6410.0 MVAr peak load. Results obtained for the two
contingencies have been presented. The 400 kV line con- With this contingency, for a peak load condition, the power
necting between buses 39 and 86 is selected for the place- flow results for this case show a low voltage profile in the
ment of UPFC. The bus 39 has got more number of system with the voltages of about 46 buses not being
connections with other 400 kV buses. From a separate within acceptable limits (0.95 – 1.05 pu). There are 13
76 IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008
Fig. 4 Typical Indian grid system
a AC – DC system of two-terminal DC and 96 AC buses
b Single line diagram of 96 bus Indian system
IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008 77
Table 1: DC system data Table 2: System performance parameters with line
outage 27–28 controller settings
Sending end Receiving end
Initial values Without UPFC With UPFC
transformer secondary, kV 219.0 216.0
MVA rating 465.0 460.0 Ploss, MW 491.96 382.44 363.56
xc , pu 0.1900 0.1900 MSV 0.20491 0.26788 0.28193
P 2
tap max, pu 1.10 1.10. L 7.2002 4.4566 2.5376
tap min, pu 0.90 0.90 Vmin 0.732 (at bus 55) 0.959 0.978
tap step, pu 0.0125 0.0125 ye 0.64807 0.03488 0.03408
P specified, MW 1540.0 1500.0
commutating resistance, pu 0.00535 0.00541
Rdc line, pu 0.00137 and without UPFC), for the given system are indicated in
Tables 4 and 5. The load bus voltage profiles and voltage
stability indices before and after optimisation (with and
without UPFCs) are shown in Fig. 6a and b, respectively.
generators exceeding the maximum Q limits and no genera-
tor Q is exceeding the minimum limit. Initially, the pro-
posed algorithm for reactive power optimisation has been 6.3 Convergent features of the proposed
applied to improve the situation without using any UPFC. algorithm
As indicated in Table 4, the minimum voltage is 0.766 pu
In the present study, we desire to control the buses voltage
at bus number 55. After five iterations of the VAr optimis-
deviation within +5% of the nominal voltage (1.0 pu). As
ation, the voltages at all the buses have been brought within
shown in Fig. 7a, all the voltage violations are alleviated
the satisfactory operable limits (0.95 –1.05 pu) and the
in only three iterations for the line outage of 27 – 28 (case
minimum voltage has been improved to 0.951 pu without
1) and its optimum objective value is 0.03408. Similarly,
UPFC and to 0.975 pu with UPFC. The sum of square of
P 2 all the voltage violations are alleviated in only five iter-
voltage stability L-indices L is reduced to 4.5659
ations for the line outage of 37– 28 (case 2) and its
(without UPFC) from the initial 6.6658, where as this
optimum objective value is 0.02763. From these graphs, it
reduced value is 2.8812 with UPFC. The MSV after optim-
is clear that the proposed algorithm converges very
isation is 0.27354 and the sum-squared voltage deviations
smoothly and achieves the global optimal solution in a
of all the load buses y e is improved to 0.04287 without
very short computing time because the cost coefficients of
UPFC. The corresponding improved values with UPFC
the proposed objective with respect to all controlling vari-
are 0.28345 and 0.02763. All these results indicate that
ables are obtained from (22). In terms of cpu time for esti-
there is an improvement in voltage stability margin with
mating the cost coefficients, objective used in this paper
the given optimisation algorithm. The improvement is
takes only one-nineth of the time taken by the objective
much better with the presence of UPFC. The transmission
used in the [10] per one iteration for the system considered.
loss of the system also reduced from 439.57 (initial value)
Hence, the proposed algorithm is very much suitable for
to 368.58 MW without UPFC, where as this reduced
on-line application in an energy control centre.
value is only 356.38 MW with UPFC as indicated in
Table 4. However, after optimisation, all the generators
reactive power outputs Q are not brought within the limits, 6.4 Case 3: Congestion management
still some of the generators Q were exceeding maximum
limits (generators 6 and 12 highlighted in Table 5). The Existence of transmission system constraints dictates the
summarised results, initial and after optimisation (with finite amount of power that can be transferred between
Table 3: Reactive power output of some critical generators with line outage 27–28
Generation bus no. Reactive power output
Initial values Without UPFC With UPFC QGmax limit, mvar
6 450.92 219.6 177.5 206.0
9 491.54 311.0 223.4 330.0
10 317.72 149.0 132.0 248.0
11 64.72 27.4 19.0 30.0
12 239.04 145.5 82.5 135.0
13 179.90 80.4 16.8 96.0
15 133.68 72.3 29.3 99.0
16 247.58 102.3 96.0 160.0
17 187.11 89.7 45.5 80.0
18 739.88 361.4 435.2 586.0
19 410.74 282.8 204.2 297.0
95 186.92 119.6 56.9 120.0
96 533.89 395.6 388.6 469.0
78 IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008
Table 4: System performance parameters with line
outage 37–38 controller settings
Initial values Without UPFC With UPFC
Ploss, MW 439.57 368.58 356.38
MSV 0.23562 0.27354 0.28345
P 2
L 6.6658 4.5659 2.8812
Vmin 0.766 at 55 0.951 0.975
ye 0.47147 0.04287 0.02763
presence of such network or transmission limitation is
referred to as congestion. Congestion in a transmission
system, whether in vertically integrated or unbundled elec-
tric systems, cannot be tolerated except briefly, since this
may cause cascade outages with uncontrolled loss of load.
The cost associated with necessary remedial measures to
relieve congestion can increase to a level that could
present a barrier in electricity trading. Therefore, congestion
management has been at the centre of debate over facilitat-
ing competition in electricity industry.
UPFC, by controlling the power flows in the network, can
help to reduce the flows in the heavily loaded lines, resulting
in an increased loadability, low system loss, and improved
stability of the network. The possibility of controlling
power flow in an electric power system without generation
rescheduling or topological changes can improve the system
performance considerably.
The 400-kV sub-station with bus 39 has got connection
with five other 400-kV substations. The UPFC is connected
between buses 39 and 86. The series power flow control
becomes important under some contingency conditions.
To illustrate the role of UPFC on congestion management,
Fig. 5 Bus voltage profile voltage stability of line outage 27 –28
the case study with the outage of the lines connecting the
a Bus voltage profile before and after optimisation with and without buses 27 and 28, 39 and 26, 39 and 35 has been considered.
FACTS controllers
b Voltage stability L-index profile before and after optimisation with With these contingencies, the line connecting the buses 39
and without FACTS controllers and 40 gets overloaded. Following these contingencies,
this line is loaded to 620.03 MVA (line limit is
500 MVA). By controlling the series-injected voltage of
two points on the electric grid. In practice, it may not be UPFC along with the optimisation of the control variables
possible to deliver all bilateral and multilateral contracts generator excitation settings, SVCs and OLTCs, the
in full and to supply all pool demand at least cost as it loading on the line 39– 40 has been brought down to
may lead to violation of operating constraints such as 475.75 MVA (95.2%) besides the overall improvement of
voltage limits and line over-loads (congestion). The voltage stability. Whereas without UPFC, there is an
Table 5: Reactive power output of some critical generators with line outage 37–38
Generators bus no. Reactive power output
Initial values Without UPFC With UPFC QGmax limit, mvar
6 386.3 232.4 176.0 206.0
9 453.6 258.4 257.3 330.0
10 296.8 189.1 227.7 248.0
11 61.8 26.3 24.5 30.0
12 210.7 154.3 90.4 135.0
13 170.9 69.3 57.1 96.0
15 114.2 78.0 98.9 99.0
16 226.6 82.0 90.0 160.0
17 163.5 48.9 33.4 80.0
18 649.2 454.6 424.3 586.0
19 375.9 222.8 212.2 297.0
95 175.4 115.5 61.8 120.0
96 482.9 398.8 402.3 469.0
IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008 79
Fig. 6 Bus voltage profile and voltage stability of line outage
37– 38 Fig. 7 Convergence of voltage deviations during optimisation
a Bus voltage profile before and after optimisation with and without a Case 1
FACTS controllers b Case 2
b Voltage stability L-index profile before and after optimisation with
and without FACTS controllers
7 Conclusions
improvement in voltage profile, but the congestion through
the line connecting the buses 39 and 40 has not been Power electronics equipment for power systems have been
relieved during optimisation as indicated in Table 6. The developed over the past three decades, starting with
summary of the results is indicated in Table 6. From these HVDC and extending later to FACTS. HVDC became a
results, it is very much clear that, in this case study, the technically and economically competitive technology to
UPFC is not only improves the voltage profile but also the AC transmission. It is used in important large-scale pro-
relieves the congestion on the line connected between jects transmitting power over long distances and to intercon-
buses 39 and 40 and hence the UPFC being utilised fully. nect power systems even in cases when AC interconnection
The UPFC can also be used to prevent power oscillations is technically not feasible. FACTS controllers, especially
and voltage swings followed by a contingency/disturbance. UPFCs, can essentially improve long-distance AC trans-
However, the scope of the present study is limited to the mission. It will be supported by the needs of the deregulated
steady-state operational studies. power systems.
An algorithm for optimum allocation of reactive power in
AC – DC system using FACTS devices, with an objective of
Table 6: Summary of results with contingencies improving the voltage profile of the system, has been pre-
sented. The developed algorithm has been tested on
Initial values Without UPFC With UPFC typical sample systems and on a practical real-life equival-
ent system of a 96-bus AC and a two-terminal DC system
Ploss, MW 536.91 388.05 379.82
with UPFC. The study results show that under contingency
MSV 0.16736 0.25173 0.25702 conditions, the installation of FACTS controllers has con-
P 2
L 8.3604 4.5378 3.2659 siderable impact on over all system voltage stability and
V39 0.833 0.952 0.997 on power loss minimisation. The proposed algorithm is
ye 0.94669 0.05465 0.03490 giving encouraging results for improving the operational
conditions of the system under normal and contingency con-
39– 40 loading, MVA 620.03 622.20 475.75
ditions. The objective used in reactive power optimisation
80 IET Gener. Transm. Distrib., Vol. 2, No. 1, January 2008
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