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Phase Shifting Transformers: Principles andApplications
Jody Verboomen,Member IEEE, Dirk Van Hertem,Member IEEE, Pieter H. Schavemaker,Wil L. Kling, Member IEEE, Ronnie Belmans,Fellow IEEE
Abstract— The purpose of this paper is to give a short overviewof existing technologies regarding phase shifting transformers(PST’s). A classification is made based on the symmetrical orasymmetrical and on the direct or indirect character of thePST. As a case-study, the PST’s in Meeden, The Netherlandsare studied more profoundly. Furthermore, a model is developedon a real-time digital simulator (RTDS) in order to demonstratethe capabilities of the PST.
Index Terms— Phase Shifting Transformer, Power Flow Con-trol, Real Time Digital Simulator
I. I NTRODUCTION
In the recent past, the operation of a transmission grid wasrelatively straightforward. The grid was designed to supplyelectricity to the country in which it was built and to supportneighbouring countries in times of need. There was no needfor large capacities at the border, because most of the energywas supplied by powerplants within the country itself.
The deregulation of the electricity market, however, has ledto major changes. The transmission grid is used as a transportmedium between producer A and consumer B, not necessarilylocated in the same country. A and B have concealed a contractin which is stated that A produces a certain amount of energyand that B buys this energy. Hence, the contractual path of theelectricity is straight from A to B. The physical path, however,is a group of parallel paths, some of which lead throughcountries that are not involved in the contract. In this manner,uncontrolled power flows can occur in the transmission systemof a country and overload its lines.
Another problem that can occur is the uneven loading ofparallel transmission lines. The distribution of the power flowbetween two parallel lines is dictated by their impedances [1].The line with the smallest reactance carries the largest partof the load. In most situations, one of the two lines will beoperating well below its nominal rating because otherwise theparallel line would be overloaded.
In the two problems stated above, active power flow needs tobe controlled. The phase shifting transformer (PST) does justthat. Several countries have already installed or are planning toinstall PST’s [2], [3], [4]. Although the technology is relatively
J.Verboomen, P.H.Schavemaker and W.L.Kling are with the ElectricalPower Systems Group of the Delft University of Technology, Mekelweg4, 2628 CD Delft, The Netherlands, Email: [email protected],[email protected], [email protected]
W.L.Kling is also with the Power Systems Laboratory of the EindhovenUniversity of Technology, The Netherlands and Tennet bv, The Netherlands
D.Van Hertem and R.Belmans are with the ELECTA research group of theK.U.Leuven,Belgium
old, the PST proves to be a valuable means of control. Inthe following paragraphs, the principles of this device areexplained.
II. PRINCIPLES OF OPERATION
-2
-1,5
-1
-0,5
0
0,5
1
0 0,5 1 1,5 2 2,5 3 3,5��������(rad)
P,Q (pu)
Q
P
Fig. 1. Active and reactive power over a transmission line as a function ofδ
The active and reactive power transported over a transmis-sion line is given by the following equations:
P =|Us||Ur|
XLsin δ (1)
Q =|Us||Ur|
XL
(cos δ − |Ur|
|Us|
)(2)
These equations are plotted as a function ofδ in Fig. 1,with the voltages and the line reactance equal to 1 pu.
The active power is proportional to the voltages on thesending and the receiving side and to the sine of the electricalangle between both sides; it is also inversely proportional tothe line reactance. Altering the active power can be doneby altering the voltages, but this has a bigger influence onthe reactive power, so this method is not very effective.The total line reactance can be lowered by placing a seriescapacitor in order to compensate for the inductance of the line.Besides the increased power flow, an additional advantage ofthis method is that oscillations can be damped by switchingthe capacitor at appropriate times. Some Flexible AlternatingCurrent Transmission Systems (FACTS) can alter the total lineimpedance very dynamically [5], [6], [7].
The method discussed in this paper is the method of alteringthe electrical angle, as showed in Fig. 2.
Fig. 2. Model of a transmission line with and without a PST
The PST is modeled as a reactance in series with a phaseshift. The power flow through the line is increased by addingan angleα to the existing angleδ. The phase shift is control-lable within certain limits. Equation 1 becomes:
P =|Us||Ur|
XL + XPSTsin(δ + α) (3)
The equation stated above can also be interpreted in anotherway: the same amount of active power can be transported overthe transmission line with a smaller value ofδ.
The graph of 3 is shifted by an amountα in comparison with1, as can be seen in Fig. 3. The maximum power decreasesby a factor XL
XL+XP STwhen using a PST.
0
0,2
0,4
0,6
0,8
1
1,2
0 0,5 1 1,5 2 2,5 3 3,5
� (rad)
P/Pm (pu)
P without PST
P with PST
����
Fig. 3. Active power as a function ofδ with and without a PST
The active power transported over the line is a non-linearfunction ofα. This is an important aspect when designing con-trollers for a PST, although in most cases they are controlledby human action.
III. T YPES OFPST’S
PST’s come in many different forms. They can be classifiedby these characteristics:
• Direct PST’s are based on one 3-phase core. The phaseshift is obtained by connecting the windings in an appro-priate manner.
• Indirect PST’s are based on a construction with 2 sep-arate transformers; one variable tap exciter to regulatethe amplitude of the quadrature voltage and one seriestransformer to inject the quadrature voltage in the rightphase.
• Asymmetrical PST’s create an output voltage with analtered phase angleand amplitudecompared to the inputvoltage.
• Symmetrical PST’s create an output voltage with analtered phase angle compared to the input voltage, butwith the same amplitude.
The combination of these characteristics results in 4 cat-egories of PST’s. Each category will be discussed in thefollowing paragraphs.
A. Direct, asymmetrical PST’s
Fig. 4. Direct, asymmetrical PST
Fig. 5. Phasor diagram of a direct, asymmetrical PST
Fig. 4 shows the configuration of a direct and asymmetricalPST. The input terminals areL1 to L3. The winding withvariable tap [8] that is connected to the input terminal ismagnetically coupled with the winding between the other twoterminals. In this manner, a quadrature voltage that can beregulated by means of the variable tap is added to the inputvoltage in order to obtain a phase shiftα. The direction ofthe phase shift can be changed by using the switches. Inthis manner, the power flow in the line can be increased ordecreased. The relation between the tap position and the angleα is non-linear and can be derived from the phasor diagram:
α = arctan|∆U1||UL1|
(4)
The relationship between the output voltage and the injectedquadrature voltage is given by:
|Us1| =|∆U1|sinα
(5)
Using 4, 5 becomes:
|Us1| =|∆U1|
sin(arctan |∆U1|
|UL1|
) (6)
The output voltage|Us1| is always larger than the input volt-age|UL1|. The fact that voltage levels are changed, influencesthe transmitted power over the line:
P =|Us1||Ur|
XL + XPSTsin(δ + α) (7)
Using 4 and 6, 7 can be rewritten as follows:
P =|Ur|
XL + XPST· |∆U1|
sin(arctan |∆U1|
|UL1|
) sin(
δ + arctan|∆U1||UL1|
)(8)
This can be rewritten as:
P =|Ur|
XL + XPST· (|UL1| sin δ + ∆U1 cos δ) (9)
The effects of an increasing angle and an increasing sec-ondary voltage combine in such a way that the result is a linearbehavior of the active power with respect to the quadraturevoltage. In theory, there is no maximum for P.
Equations 4 and 9 are plotted in Fig. 6 forδ = π6 , with |UL1|
and |Ur|XL+XP ST
equal to 1 pu. The curve ofα is relatively linearup to a value of about0, 6 rad or 34 ◦.
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5|�U1| (pu)
P (pu)
0
0,2
0,4
0,6
0,8
1
1,2� (rad)
P
����
Fig. 6. Relation between P,α and the quadrature voltage for a directasymmetrical PST withδ = π
6
B. Direct, symmetrical PST’s
With some modifications, the direct, asymmetrical PST canbe made symmetrical. An additional tap changer is needed,which raises the total cost of the device. The advantages arethat the voltage amplitudes remain unchanged and that themaximum attainable angles are much larger.
The relation between the quadrature voltage and the angleαis still non-linear and can be derived from the phasor diagram(Fig. 8):
α = 2arcsin|∆U1|2|UL1|
(10)
Fig. 7. Direct, symmetrical PST
Fig. 8. Phasor diagram of a direct, symmetrical PST
Using 10, the transferred active power becomes:
P =|UL1||Ur|
XL + XPSTsin
(δ + 2 arcsin
|∆U1||2UL1|
)(11)
Equations 10 and 11 are plotted in Fig. 9 withUL1 and|Ur|
XL+XP STequal to1 pu. The quasi-linear range of theα-curve
has doubled in comparison with Fig. 6.An alternative implementation of a direct and symmetrical
PST is depicted in Fig. 10. The resulting phasor diagram(Fig. 11) has a hexagonal shape. An important advantage ofthis implementation is that only one tap variable transformeris needed per phase. A disadvantage is the need for additionalimpedances to protect the tap changers when the phase shift isset to zero, because in that case, short circuit currents occur.
C. Indirect, asymmetrical PST’s
The indirect, asymmetrical PST consists of an exciter anda series transformer. Depending on the rating of the system,these two transformers are housed in separate tanks or in asingle tank. The two-tank system has the advantage of easiertransport.
Fig. 12 shows the configuration of the system. The phasordiagram is exactly the same as the one depicted in Fig. 5.
0
0,2
0,4
0,6
0,8
1
1,2
0 0,5 1 1,5 2 2,5|�U1| (pu)
P (pu)
0
0,5
1
1,5
2
2,5
3
3,5 � (rad)
����
P
Fig. 9. Relation between P,α and the quadrature voltage for a directsymmetrical PST withδ = π
6
Fig. 10. Direct, symmetrical PST with hexagonal winding connection
D. Indirect, symmetrical PST’s
The indirect, asymmetrical PST can be made symmetricalby splitting the series winding in two halves and tapping thevoltage for the exciter from the middle. Fig. 13 shows thisconfiguration. The phasor diagram is the same as the one inFig. 8.
IV. CASE-STUDY: THE PST’S OFMEEDEN
The Netherlands has five interconnectors with its neighbor-ing countries Belgium and Germany (Fig. 14). The southernregion is much denser populated compared to the northernpart. As a consequence, import of power causes a heavyloading of the southern interconnectors, especially on the lineMaasbracht-Rommerskirchen/Siersdorf, compared to a lowloading of the most northern interconnector Meeden-Diele. Inorder to maintain n-1 security, the import capacity had to belimited. The Dutch Transmission System Operator (TSO) Ten-neT, studied various solutions to solve this problem. Additionaltransmission lines didn’t offer instant relief, as such projectswould take much too long because of negotiations with otherTSO’s and procedures to obtain all necessary permits. A bettersolution was to install a phase-shifter in an appropriate locationin the transmission grid [9], [10]. The device shouldn’t beplaced in the Maasbracht interconnector with Germany, asthis would only shift the import to the Belgian border, notaffecting the Meeden interconnector. Locating the PST inMeeden would offer the possibility to increase the import in
Fig. 11. Phasor diagram of a direct, symmetrical PST with hexagonal windingconnection
Fig. 12. Indirect, asymmetrical PST
the northern part of the country, distributing the loading ofthe interconnectors more equally. In reality, two PST’s arerequired because the interconnector consists of two circuits.
In the year 2000, TenneT ordered the PST’s with SmitTransformers. The most important design parameters are givenin Table I.
The chosen type of PST is a symmetrical, indirect config-uration (Fig. 13). The series transformer and the exciter canbe constructed as two separate 3-phase transformers. This isthe two-tank design. The problem with this design is the factthat the connections between the two tanks are at the highestvoltage level.
It is also possible to group the series transformer andexciter per phase, resulting in a three-tank design. Moreinterconnections are needed, but they are on a lower voltage
TABLE I
MAIN DESIGN PARAMETERS OF THEMEEDEN PST’S
3 phase through rating 1000 MVAApplicable standards IECType of cooling ONANType of regulation SymmetricalNumber of steps +/- 16 stepsNo-load phase angle 37.2 degreesLoad phase angle at 1000 MVA 30 degreesShort circuit impedance <12% at 1000 MVANominal voltage 380 kV
Fig. 13. Indirect, symmetrical PST
Fig. 14. Interconnectors of The Netherlands
level. This configuration has been adopted for the MeedenPST’s.
Each one-phase unit consists of:
• A single-phase series transformer, rated at 213 MVA• A single-phase exciter with two tap-changers, rated at 202
MVA• Two current control transformers to distribute the current
equally between the two tap-changers.
The scheme of a unit is drawn in Fig. 15. The seriestransformer consists of two smaller transformers of 133 kVprimary and 70 kV secondary each. The exciter is constructedout of two parallel transformers with variable tap. The primarywinding is rated at 208 kV and the secondary winding at 38.5kV. The secondary windings are connected in series, resultingin a rated regulating voltage of 77 kV.
Fig. 15. A one-phase unit of a Meeden PST
V. SIMULATION ON A REAL-TIME DIGITAL SIMULATOR
Fig. 16. The configuration used for the RTDS simulation
A Real-Time Digital Simulator (RTDS) is used to demon-strate the use of a symmetrical, indirect PST. The configurationis shown in Fig. 16. Two transmission lines connect an idealgenerator with a load. The lines are identical, except for thelength. The shortest transmission line (line A) is loaded moreheavily than the longer one. A PST can distribute the loadmore equally. Fig. 17 shows the results of the simulation.The active power flow is shifted from line A to line B asthe magnitude of the phase shift angleα increases. It is evenpossible to load line B more heavily than line A ifα isincreased beyond17 degrees.
VI. CONCLUSIONS
Phase shifting transformers exist in different forms. Theasymmetrical version is relatively simple compared to thesymmetrical PST but changes the voltage amplitude. Theindirect configuration offers an easier modular design, but theoverall cost is higher than the direct version. A PST is auseful means of control of active power flow, as is provedby hands-on experience obtained from the Meeden PST’s inThe Netherlands. A simulation in a real-time digital simulator(RTDS) illustrates the ability to regulate the active powertransmitted over a line.
0
100
200
300
400
500
600
-25 -20 -15 -10 -5 0� (deg)
P (MW)
PA (MW)
PB (MW)
equilibrium at -17º
Fig. 17. The results of the RTDS simulation
ACKNOWLEDGMENT
This research at the TU Delft has been performed within theframework of the research program ’intelligent power systemsthat is supported financially by SenterNovem. SenterNovemis an agency of the Dutch ministry of Economic Affairs.
The research performed at the KU Leuven is financiallysupported by the Belgian ‘Fonds voor WetenschappelijkOnderzoek (F.W.O.)-Vlaanderen’. Dirk Van Hertem isa doctoral research assistant of the F.W.O.-Vlaanderen.
REFERENCES
[1] IEEE Power Engineering Society, “C57.135 : IEEE Guide for theApplication, Specification, and Testing of Phase-Shifting Transformers,”May 2002.
[2] P. Bresestiet al., “Application of Phase Shifting Transformers for asecure and efficient operation of the interconnection corridors,” inIEEEPower Engineering Society General Meeting, 2004, pp. 1192–1197.
[3] R. M. G. Castro, F. M. R. Batista, and J. M. M. Medeiros Pinto, “Appli-cation of FACTS in the Portuguese Transmission System : Investigationon the Use of Phase-Shift Transformers,” inIEEE Porto PowerTech2001,Porto, 2001.
[4] J. Bladow and A. Montoya, “Experiences with Parallel EHV ShiftingTransformers,”IEEE Transactions on Power Delivery, vol. 6, no. 3, pp.1096–1100, July 1991.
[5] P. Moore and P. Ashmole, “Flexible AC transmission systems part 4 :Advanced FACTS controllers,”Power Engineering Journal, pp. 95–100,April 1998.
[6] R. Grunbaum, M. Noroozian, and B. Thorvaldsson, “FACTS - powerfulsystems for flexible power transmission,”ABB Review, vol. 5, pp. 4–17,1999.
[7] R. Grunbaum, R. Sharma, and J. P. Charpentier, “Improving the effi-ciency and quality of AC transmission systems,” ABB Power Systems- Joint World Bank, Tech. Rep., March 2000.
[8] A. Kramer and J. Ruff, “Transformers for Phase Angle Regulation Con-sidering the Selection of On-Load Tap-Changers,”IEEE Transactionson Power Delivery, vol. 13, no. 2, pp. 518–525, April 1998.
[9] W. L. Kling et al., “Phase shifting transformers installed in the Nether-lands in order to increase available international transmission capacity,”in CIGRE Session 2004 - C2-207, 2004.
[10] C. J. G. Spoorenberg, B. F. van Hulst, and H. F. Reijnders, “Specificaspects of design and testing of a phase shifting transformer,” inXIIIthInternational Symposium on High Voltage Engineering, 2003.
BIOGRAPHIES
Jody Verboomen obtained his M.Eng. in Electron-ical Engineering from Group T Technical School inLeuven, Belgium in 2001. He obtained his M.Sc.in Electrical Engineering from the Catholic Uni-versity of Leuven (KUL), Belgium in 2004. He iscurrently working towards a Ph.D. on the applicationof FACTS in transmission systems in the ElectricalPower System (EPS) laboratory of the Delft Univer-sity of Technology, The Netherlands.
Dirk Van Hertem graduated as a M.Eng. in 2001from the KHK, Geel/Belgium and as a M.Sc.in Electrical Engineering from the K.U.L./LeuvenBelgium in 2003. From 2003 he has been work-ing towards a Ph.D. in the ELECTA researchgroup, department of Electrical Engineering of theK.U.Leuven, Belgium. From October 2004, he is aresearch assistant for the F.W.O.-Vl. In 2001, hismasters thesis received the ‘V.I.K. award’ and in2004, he received the ‘K.B.V.E. R&D award’ for hissecond masters thesis. His special fields of interest
are power system control and optimization.
Pieter H. Schavemaker obtained his M.Sc. inElectrical Engineering from the Delft University ofTechnology in 1994 and he obtained his Ph.D. inElectrical Engineering from the Delft University ofTechnology in 2002. Since 1996 he has been withthe Power Systems Laboratory where he is currentlyAssistant Professor. His main research interests in-clude power system transients and power systemcalculations.
Wil L. Kling received his M.S-degree in electricalengineering from the Technical University of Eind-hoven in 1978. Since 1993 he has been a (part-time) professor with the Department of ElectricalEngineering at Delft University of Technology, inthe field of Power Systems Engineering. In addition,he is with the Operations department of TenneT (theDutch Transmission System Operator). Since 1999,he has also been a part-time professor at the TUEindhoven. His area of interest is related to planningand operations of power systems. He is the project
leader of the research programme ’Intelligent Power Systems’, sponsored bySenter, an agency of the Dutch Ministry of Economic Affairs. Prof. Klingis involved in scientific organizations such as CIGRE and the IEEE. AsNetherlands’ representative, he is a member of its Administrative Council.Furthermore, he is involved in several international working groups in thefield of network planning and system studies, within UCTE, Eurelectric andother bodies.
Ronnie Belmansreceived the M.S. degree in elec-trical engineering in 1979, the Ph.D. in 1984, andthe Special Doctorate in 1989 from the K.U.Leuven,Belgium and the Habilitierung from the RWTH,Aachen, Germany, in 1993. Currently, he is fullprofessor with K.U.Leuven, teaching electrical ma-chines and variable speed drives. He is appointedvisiting professor at Imperial College in London.He is also President of UIE. He was with theLaboratory for Electrical Machines of the RWTH,Aachen, Germany (Von Humboldt Fellow, Oct.’88-
Sept.’89). Oct.’89-Sept.’90, he was visiting associate professor at Mc MasterUniversity, Hamilton, Ont., Canada. During the academic year 1995-1996 heoccupied the Chair at the London University, offered by the Anglo-BelgianSociety. Dr. Belmans is a fellow of both the IEEE and the IEE (UnitedKingdom). He is the chairman of the board of Elia, the Belgian transmissiongrid operator.
