quantative analyis

8/12/2019 quantative analyis

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Coordinated Control of FACTS Devices basedon Optimal Power Flow

G. Glanzmann,Student Member IEEE, G. Andersson, Fellow IEEE

Abstract Flexible AC Transmission Systems (FACTS) are anoption to mitigate the problem of overloaded lines due toincreased electric power transmission by controlling power flowsand voltages. To avoid mutual influences among several devicesplaced in the same grid, a coordinated control is indispensable. Inthis paper, a supervisory controller based on Optimal PowerFlow (OPF) with multiple objectives is derived in order to avoidcongestion, provide secure transmission and minimize activepower losses. The contributions of SVC, TCSC and TCPST inthis coordinated control and the achieved improvementscompared with the case where no FACTS devices are in

operation are demonstrated. Index Terms Congestion Management, Coordinated Control,

FACTS, Optimal Power Flow, Power Systems

I. I NTRODUCTION R ANSMISSION lines in congested areas are often drivenclose to or even beyond their limits in order to satisfy the

increased electric power consumption and trades. Thus, secureoperation and reliable supply is endangered by the higher risksfor faulted lines. But the construction of additional powerlines is often difficult for environmental, economical and political reasons. This is where the technology of FACTS provides a significant opportunity [1-3].

The numerous publications in the field of FACTS in the lastfew years show the growing interest and need for thesedevices. Topics are the optimal placement, the value ofFACTS in the liberalized power market, the development ofnew devices and the control strategy.

FACTS devices are able to influence power flows andvoltages to different degrees depending on the type of thedevice. The focus in this paper lies on the Static VarCompensator (SVC), the Thyristor-Controlled SeriesCompensator (TCSC) and the Thyristor-Controlled PhaseShifting Transformer (TCPST).

Typically, the devices are divided into three categories:shunt-connected, series-connected and a combination of both.The SVC belongs to the shunt-connected devices and is sincelong in operation in various places. Conceptually, it is a

variable shunt reactance which injects or absorbs reactive power in order to control the voltage at a given bus. BothTCSC and TCPST are series-connected devices. The TCSCmainly controls the active power in a line by adapting the linereactance. This type of device is in operation at a few places but is still in the stage of development. The principle of aTCPST is very similar to a conventional phase angle regulato(PAR). A voltage in quadrature to the primary bus voltage isincorporated introducing a phase shift to control thetransmission angle. The difference compared with the PAR is

that the mechanical tap changer is replaced by a thyristor-controlled equivalent allowing for faster control [4].

This work is financially supported by ABB Switzerland.G. Glanzmann is PhD student at the Power Systems Laboratory of the

Swiss Federal Institute of Technology, 8092-Zurich, Switzerland (e-mail:[email protected])

G. Andersson is Professor at the Power Systems Laboratory of the SwissFederal Institute of Technology, 8092-Zurich, Switzerland (e-mail:[email protected])

In order to investigate the effects of FACTS devices insteady-state, appropriate models are needed capturing theinfluences of the devices on power flows and voltages.Various models for SVC, TCSC and TCPST are conceivableand applied in different studies. In Sect. II, the modeling ofFACTS devices used in this paper and how they areincorporated into the power flow calculations are described.

The influences of FACTS devices are not confined to one bus or line. Changing the voltage at a certain bus or the poweflow on a line also modifies the power flow in the surroundinggrid. If a FACTS device is placed in the vicinity of another,mutual influences may arise which could vitiate the positiveimpacts of a single device. Coordination is needed todetermine the variables such that detrimental actions are prevented. Additionally, measures in other parts of the gridhave to be taken into account such that it is avoided thatdistant lines become overloaded or that voltages at other buseare driven to unacceptable values. Both can be achieved by asupervisory controller based on Optimal Power Flow (OPF[5] with multiple objectives which determines the optimalsteady-state settings of the FACTS devices. Thus, in Sect. III,the applied OPF problem formulation is derived.

The resulting objective function includes several

components such as minimizing active power losses, avoidingoverloaded lines and keeping bus voltages within anacceptable range and close to their reference values. Aspecific type of FACTS device is able to influence a certain parameter in the grid which is related to a particular part of theobjective function. For instance, the SVC injects or absorbsreactive power which is strongly coupled to the voltageTCSC and TCPST on the other hand control active powerflow. Therefore, Sect. IV investigates the relations betweendevices and their effects on the different parts of the objectivefunction.

T


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Section V illustrates the improvements of the derivedcoordinated control. In simulations, the performance of thecontroller with an SVC plus a TCSC and with an SVC plus aTCPST is compared with the case where no FACTS devicesare in operation. It is shown that overloaded lines are relieved,the voltage profile is improved and the power losses aredecreased, leading to the conclusions given in Sect. VI.

II. MODELING OFFACTS DEVICES Several ways of modeling FACTS devices are proposed in

the literature. In [6], the power injection method is presentedwhere the characteristics of the devices are reproduced by power injections. Another option is to model SVC and TCSCas variable reactances, whose values depend on the firingangle of the thyristors, [7], [8] and TCPST as a variablevoltage source [9]. This second possibility is applied in this paper in order to simplify the integration into the OPFformulation.

A. SVCA possible structure of the SVC is given in Fig. 1. It is a

shunt-connected device composed of several modules built ofa fixed capacitance in parallel with a thyristor controlledreactor. Each of these modules corresponds to a variablesusceptance. The equivalent susceptance Beq is determined bythe firing angle of the thyristors which is defined as thedelay angle measured from the peak of the capacitor voltageto the firing instant. The fundamental frequency equivalentneglecting the harmonics of the current results in [1]

( )eq L C B B B = + (1)

where

1 2 sin(2 )( ) 1 , L C B B L

C = =

(2)

C

L

C C

L L

Fig. 1. Structure of an SVC

The graph for Beq as a function of is given in Fig. 2. Theminimal and maximal values for the firing angle are 0 and90, respectively, resulting in a minimal value Bmin and amaximal value Bmax for the equivalent susceptance of eachmodule. At the resonance angle where

( ) L res C B B = (3)

the equivalent susceptance is zero. But this resonance is not a problem here because this simply corresponds to a module

which is not connected to the bus.

90

Bmaxunavailable

Bmin

res

unavailable

0

Beq

Fig. 2. Equivalent susceptance Beq in function of the firing angle

The total susceptance of the SVC is composed of the parallel equivalent susceptances of the modules, eachcontrolled separately. Thus, the SVC can be modeled as ashunt-connected variable susceptance BSVC (Fig. 3) with alower bound BSVC and an upper bound B SVC [7]. In the powerflow equations this is accounted for by including the reactive

power2

SVC k SVC Q V B= (4)

into the reactive power balance at busk subject to

SVC SVC SVC B B B . (5)

This range normally includes positive as well as negativevalues.

k V k

jBSVC

Fig. 3. Model of the SVC

B. TCSCSimilar to the SVC, the TCSC consists of several modules

built of a fixed capacitance in parallel with a thyristorcontrolled inductor. But here, the modules are connected inseries as shown in Fig. 4 [10].

C

L

C

L

C

L Fig. 4. Structure of a TCSC

Therefore, the equivalent reactance X eq of each individualmodule is considered which is determined by the firing angleof the thyristors by


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1( )( )eq L C

X B B

=+

(6)

where B L( ) and BC are given in(2). The graph of this function is shown in Fig. 5. Apparently, a

discontinuity exists at the resonance angle determined by(3). As it is unacceptable to introduce an infinite reactance inseries to the transmission line, the firing angle has to be kept adistance from the resonance point. A minimal value X min and a maximal value X max result for the equivalent reactance.Additionally, the minimal and maximal values for the firingangle are again 0 and 90. This yields an unavailable band between X lb and X ub [8].

For the total reactance value of the TCSC, the equivalentreactances of the modules are added. As each module iscontrolled separately, the unavailable band around zero can becovered [10]. Thus, the TCSC is modeled as variablereactance X TCSC with a lower bound X TCSC and an upper bound X TCSC connected in series with a line.

The allowed degree of compensation of the line reactance

gives rise to additional limitations. In accordance with [11],the compensation range is set to 20% inductive and 80%capacitive.

90

X max

X min

res unavailable

X eq

X ub

X lb

r e s o n a n c e

0

Fig. 5. Equivalent reactance X eq in function of the firing angle

According to Fig. 6a), the TCSC is incorporated into thetransmission line model by simply adding the variablereactance X TCSC to the line reactance X [11]. As the TCSCsare normally placed close to a bus, it would be more accurateto add the reactance there (Fig. 6b)). But this complicates thesituation by far and especially in cases of short lines, thedifferences in power flow calculations are marginal due tosmall shunt susceptances B. Therefore, this simplification is justified and the TCSC is incorporated into the load flowcalculations by setting the total line reactance to

tot TCSC X X X = + (7)

and accounting for the limitations by

( ) ( )max , 0.8 min ,0.2TCSC TCSC TCSC X X X X (8)

R+jX

jBk m

2 jB2

jX TCSC

a)

R+jX

jBk m

2 jB2

jX TCSC

b)

Fig. 6. TCSC modeled as series-connected reactance a) simplified b) exact

C. TCPSTThe structure of a TCPST is given in Fig. 7. The shunt

connected transformer draws power from the network and provides it to the series connected transformer in order tointroduce a voltage V T at the series branch. Compared toconventional phase shifting transformers, the mechanical tapchanger is replaced by a thyristor controlled equivalent [9]The purpose of the TCPST is to control the power flow byshifting the transmission angle.

series branch

parallel branch

V T

Fig. 7. Structure of a TCPST

The model used is given in Fig. 8 where the TCPSTcorresponds to a variable voltage source with a fixed angle of90 with respect to the primary voltage. The manipulatedvariable is the phase shift which is determined by themagnitude of the inserted voltage V T .

R+jX

jBV k

2

jB

2

V mV k

V T

V k V k

V T .

Fig. 8. Model of a TCPST

It is assumed that the device is lossless. Thus, therelationship between the primary and the secondary voltage is

'

'

( 90 )' k k k

k k T

j j jk k T

V V V

V e V e V e = +

= + (9)


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where the magnitude of the inserted voltage is determinedfrom the phase shift by

tanT k V V = . (10)

The range in which the angle may vary is dependent on thespecific device and has to be taken into account by

min max (11)

in the process of determining the appropriate phase shift.Here, this range is set to 20.

These models for SVC, TCSC and TCPST can now beapplied in optimal power flow calculations in order todetermine the optimal settings for the devices.

III. COORDINATEDCONTROL The controlled variable in case of TCSC and TCPST is the

active power flow and in case of the SVC the corresponding bus voltage. As these devices are controlled locally so far,they do not take into account their influences on other lines or buses [12]. Thus, a control action which is reasonable for theline or bus where the device is located might cause anotherline to be overloaded or voltages to take unacceptable values.Additionally, if devices are located close to each other theaction of one controller can lead to a counteraction of theother controller possibly resulting in a conflicting situation.For these reasons, coordination is necessary, especially whenthe number of devices increases and the distance among themdecreases.

First, it has to be decided which control technique isapplied. Investigations have been carried out on fuzzy control

[11], remote feedback control [12] or different optimizationstrategies [8], [13], [14]. In this paper, a controller based onoptimal power flow with multiple objectives is developed. Theadvantage of this approach is that not the reference valuessuch as active power flow or voltages but directly the settingsof the devices like firing angle or phase shift which fulfill bestthe objectives are determined. The power flows and thevoltages follow accordingly from these settings. Thus, mutualinfluences like in the case with local control are not a problemany more.

For the formulation of an optimal power flow problem,three elements have to be defined: the objective function

f (x,u), the equality constraints g(x,u) and the inequality

constraints h (x,u) yieldingmin

subject to( , )( , ) 0( , ) 0

f =

x u

g x u

h x u

(12)

where the vector x contains the voltages and angles of all buses and u the set values for the devices and the slackvariables used to define soft constraints:

1

1

;

SVC

TCSC n

PST

slack

n

V

V

u

= =

x u (13)

As opposed to the equality and inequality constraints whichare mostly determined by the system, the objective function isnot given a priori but has to be specified such that it reflectsthe intended objectives. In the following, the equality andinequality constraints as well as the objective function arediscussed.

g(x,u): power flow : The equality constraints result from the

power flow equations including the power injections by SVCs, the modifications of the line reactances byTCSCs and the phase shifts of the TCPSTs.

h(x,u): FACTS devices : The equations (5), (8) and (11)which define the limitations for the settings of theFACTS have to be hold.

transmission lines: Lines should not be loaded tomore than 90% or, if this is not achievable, at leastshould not exceed the transfer capacities. This isdefined using soft constraints in order to avoid anunfeasible system. For each linei, the inequalities

max

max

0.9 , 0, 0

i i i

i i i

S S

S S i

i

+ +

(14)

result, where S i is the apparent power flow on linei and S imax the corresponding capacity limit. The slackvariables i and i are only non-zero if the originalconstraints are violated. They are penalized in theobjective function such that the controller has astrong incentive to set them to zero whereas the penalization ofi is much severer than oni.

buses : Unacceptable bus voltages should be avoided,i.e. their values should lie within a certain range. Thisis also defined as soft constraints

, 0 j

ref lim j jV V V j + (15)

where V j is the bus voltage at bus j, V jref is thecorresponding reference value andV lim is the allowedrange of acceptable voltage values.

f (x,u): resolve congestions : This is done by keeping the

loading of the lines below 90% or at least byavoiding overloading. Thus, the penalization of theslack variables used in (14) to define soft constraintson the apparent power flows contributes to thisobjective.


5/8

improve security : If voltages exceed a certain rangeof acceptable values the security of the grid isendangered. Therefore, penalizing the slack variableused in (15) and keeping the voltage values as closeas possible to their references improves security.

minimize power losses : This simply is incorporated by summing the active power losses and penalizingthem in the objective function.

Thus, the complete objective function is the sum of theseobjectives each weighted with an appropriate factor

( )

1 2

2

3

( , ) lossi i ii

ref j j j

j

f a P b c

d V V e

= + + +

+ +

x u

(16)

The setting of the weightsa , b, c, d and e, which are atthe same time the control parameters, are dependent onthe importance of each objective. A summary of themeaning of all weights is given in Table I. As theincentive to avoid overloaded lines consequentially isgreater than to keep their loadings below 90%, the weightc will be larger than b. For the other parameters nogeneral statement is applicable.

It is of course possible to include other objectives inthe objective function. This will be the topic of futureresearch.

TABLEIOVERVIEW OF WEIGHTS IN THE OBJECTIVE FUNCTION

Weight Objectivea minimization of active power lossesb keeping line loadings below 90%c keeping line loadings below 100%d minimization of voltage deviations from referencese keeping bus voltages within acceptable limits

With g(x,u), h(x,u) and f (x,u) the problem is formulatedand can be given to an appropriate solver which is able tosolve an optimization problem with a nonlinear objectivefunction subject to nonlinear equality and inequalityconstraints. For the simulations in this paper, the MATLABfunction fmincon is used.

IV. A NALYSIS OF THEOBJECTIVEFUNCTION

The objective function (16) consists of three componentsThe first is the minimization of active power losses, thesecond accounts for keeping the line loadings below thetransfer capacities and the third concerns the bus voltages, i.ekeeping them close to their reference values and within anacceptable range. A given type of FACTS device is not able toinfluence all parts to the same extent. In simulations whereonly some control parameters in the objective function arenon-zero, it can be evaluated which device is mainlyresponsible for which part of the objectives.

The test grid for the simulations is shown in Fig. 9. The left part of this grid is basically a generation area and the right par

a load area. The considered combinations of FACTS devicesare given in Table II. In the first three combinations, only onesingle device is placed in the grid whereas in combinations 4and 5 two different devices are in operation at the same time.For these combinations the coordinated control derived in the preceding section with different parts of the objective functiontaken into account is applied.

TABLEIICONSIDERED COMBINATIONS OFFACTS DEVICES

Comb. Devices1 SVC at bus 72 TCSC in line 63 TCPST in line 64 SVC at bus 7, TCSC in line 65 SVC at bus 7, TCPST in line 6

3

4 5

1

2

3 8

7

66

5

2

1

4

8

7 10

9

2000 MW

300 MVar

slack

1200 MW200 MVar

800 MW200 MVar

1600 MW300 MVar

1500 MW250 MVar

1200 MW250 MVar

500 MW150 MVar

Fig. 9. 8-bus test grid with a generation area on the left and a load area on the right


6/8

In Table III, the obtained steady-state values for the SVCsusceptance BSVC (p.u.), the TCSC reactance BTCSC (p.u.) andthe TCPST phase shift PST are presented. In the secondcolumn, the components of the objective function which weretaken into account in each case are listed according to thenumbering in (16). The control parameters belonging to theother components are set to zero. The third column identifiesthe considered combination according to Table II. Thecolumns O1, O2 and O3 indicate the values of the differentobjectives

( )( )

( )( )2

1 (active power losses)

2 (line l

3 (bus voltages)

lossi

i

i ii

ref j j j

j

O a P

O b c

O d V V e

=

= +

= +

oadings) (17)

in the considered case and combination. The sum of thesevalues yields the total value of the objective function f (x,u ). In

the first row, the corresponding values for the base case whereno FACTS devices are in operation are given for comparison.

TABLEIIIOPTIMAL SETTINGS OFSVC, TCSC AND TCPST FOR DIFFERENT OBJECTIVES

Case Obj. Com. B SVC X TCSC PST O 1 O 2 O 3

Base - - - - - 84.03 84.31 111.67A 1 1

2345

0.754--

0.7500.754

--0.0148

--0.0021

-

--

-0.173-

-0.024

78.2983.6484.0278.2878.29

B 2 12345

0.686--

-0.0030.214

--0.0354

--0.0353

-

--

-3.918-

-3.566

66.250.000.000.000.00

C 3 12345

0.768--

0.7880.858

--0.0720

-0.0180

-

--

-1.378-

5.677

7.2244.34

110.717.046.71

D 1,2 12345

0.700--

0.6770.753

--0.0313

--0.0294

-

--

-3.918-

-3.142

78.3284.2986.2579.6279.81

66.260.000.000.000.00

E 1,3 12345

0.767--

0.7700.770

--0.0670

-0.0024

-

--

-1.090-

0.439

78.2993.5984.1678.3178.33

7.2246.68

110.747.197.16

F 2,3 12345

0.753--

0.7450.770

--0.0354

--0.0295

-

--

-3.918-

-3.140

66.450.000.000.000.00

7.2770.87

113.987.667.77

G 1,2,3 12345

0.754--

0.7390.769

--0.0354

--0.0295

-

--

-3.918-

-3.140

78.2984.7086.2579.6679.81

66.450.000.000.000.00

7.2670.87

113.987.677.77

In case A, the only objective is the minimization of active power losses. In all combinations, the SVC susceptance BSVC takes similar values independent of if a TCSC or a TCPST isturned on or not and columnO1 shows that where an SVC isin operation, the power losses are reduced by about 5.6%

compared with the base case. TCSC and TCPST in singleoperation do not manage to decrease the power lossessignificantly. From this, it can be concluded that theimprovements concerning power losses are mostly due to anSVC.

Case B only incorporates the objective to keep the lineloadings below 90% or at least below 100%. Here, thesituation is reversed to case A. Combinations where a TCSCor a TCPST is employed manage to bring all line loadings below 90% indicated byO2 equal to zero. The influence ofthe SVC on this objective is limited. In combinations 2 to 5,there exists more than one setting which brings all lineloadings below 90%. Therefore, the shown settings are just possible values among others to reach the minimal value ozero for the objective function.

Concerning case C where the bus voltages are to be keptclose to their reference values and within an acceptable rangeagain the SVC is the most effective device. The value forO3is brought to a minimum. The TCSC is able to reduce thisvalue, too, but the resulting reactance value hits the lower

limit. Additionally, the SVC in all combinations has similarsettings whereas for the TCSC and also for the TCPST thevalues differ considerably. Thus, SVC is the device which isresponsible for controlling the bus voltages.

In cases D to F where always two different objectives aretaken into account, the separation of the objectives becomeseven more apparent. The power losses are only reduced whenan SVC is in operation and also the voltage deviations take byfar the best values in these combinations. On the other handthe loadings are all brought below 90% only in combinationwhere a TCSC or a TCPST is employed.

Case G incorporates all objectives. When the SVC is thesingle device in operation, active power losses and voltagedeviations are reduced but loadings are still quite high. On theother hand, when a TCSC or a TCPST is the only device, lineloadings are optimally taken care of but power losses are evenincreased and the voltage deviations are still considerable. Incombinations where an SVC as well as a TCSC or a TCPSTare employed, a reduction in active power losses and involtage deviations are achieved and all line loadings are brought below 90%.

The conclusion is that the objectives can be divided into a part which is mainly controlled by SVC namely active powelosses and voltage deviations and a part corresponding to lineloadings which is controlled by TCSC and TCPST.

Combinations of an SVC and a TCSC or a TCPST thereforemanage to improve all objectives.

V. SIMULATIONR ESULTS For the following simulations, again the test grid in Fig. 9 is

used. The coordinated control described in Sect. III is appliedfor the combinations 4 and 5 given in Table II.

In Fig. 10, the line loadings, the power losses and thevoltage profile for combination 4, an SVC at bus 7 and aTCSC in line 6, is compared with the case where no FACTS


7/8


8/8

VI. CONCLUSION FACTS devices are a powerful tool to resolve congestions

and to improve security of the system. But an uncoordinatedutilization of such devices may result in conflicting situationswhich can endanger secure operation of the transmission grid.Thus, a coordinated control based on optimal power flow has been developed in this paper. The objective was to resolvecongestions, improve security and decrease active powerlosses.

The objective function was analyzed in simulations withdifferent combinations of FACTS devices. It wasdemonstrated that each device is able to influence certain partsof the objective function. SVCs are responsible for the partsdealing with the voltage and the active power losses andTCSCs as well as TCPST account for the part concerning lineloadings. Thus, a decoupling takes place which allows for astraightforward application of the various FACTS devices.

Finally, simulations showing the improvements of thederived control were presented: congestions were resolved,voltage profiles became more balanced and active power

losses were reduced. Additionally, it was demonstrated thatTCSC and TCPST have comparable effects concerning theconsidered objectives.

A more detailed comparison of TCSC and TCPST and theirsimultaneous use will be subject to future elaborations.Additionally, the derived control will be studied for largertransmission grids in order to investigate the performance in amore practical environment.

ACKNOWLEDGMENT The authors like to thank Mats Larsson, Alexandre Oudalov

and Petr Korba from ABB and Walter Sattinger from

ETRANS for stimulating discussions.

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technology of flexible AC transmission systems . New York: IEEE Press,2000.

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[3] Y.-H. Song, Flexible ac transmission systems (FACTS) . London: TheInstitution of Electrical Engineers, 1999.

[4] P. Moore and P. Ashmole, "Flexible AC transmission systems. III.Conventional FACTS controllers," Power Engineering Journal , vol. 11, pp. 177-183, 1997.

[5] J. Carpentier and A. Merlin, "Optimization methods in planning andoperation," International Journal of Electrical Power and EnergySystems , vol. 4, pp. 11-18, 1982.

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[9] S. Gerbex, R. Cherkaoui, and A. J. Germond, "Optimal location of multtype FACTS devices in a power system by means of genetic algorithms,

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[11] A. Oudalov, "Coordinated control of multiple FACTS devices in anelectric power system." Diss. EPF Lausanne, 2003, pp. 190.

[12] M. Larsson, C. Rehtanz, and D. Westermann, "Improvement of Cross border Trading Capabilities through Wide-area Control of FACTS,

presented at Bulk Power System Dynamics and Control VI, CortinD'Ampezzo, Italy, 2004.[13] S.-H. Song, J.-U. Lim, and S.-I. Moon, "Installation and operation o

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