a comprehensive approach to classify reactive power consumption in transmission...

7/28/2019 A Comprehensive Approach to Classify Reactive Power Consumption in Transmission Technologies-351-Hohn

1/6

International Conference on Renewable Energies and Power Quality (ICREPQ13)

Bilbao (Spain), 20th to 22th March, 2013exxtux Xxz tw cx dt| ]t(RE&PQJ)

ISSN 2172-038 X, No.11, March 2013

A comprehensive approach to classify reactive power consumption in transmission

technologies

S. Hhn, A. Semerow and M. Luther

Chair of Electrical Energy Systems

University of Erlangen-NurembergKonrad-Zuse-Strae 3-5 91052 Erlangen (Germany)

Phone number: +49 9131 85 23453,E-mail: [email protected], [email protected], [email protected]

Abstract. Reactive power consumption is an essential featureof any electrical equipment applied in electrical power systems.

To accomplish its main task, i.e. the transfer of active power, anelectrical device interacts with the system it is connected to. A

common aim is to reduce the reactive power flow on theterminals of the equipment to a minimum. Therefore its

necessary to compensate the reactive power consumption bymeans of adequate measures. This cant be reached without

precise investigation on the sources of reactive power emergence.This paper investigates the physical phenomena underlying the

reactive power behavior of HVAC and HVDC transmissiontechnologies. After having introduced a common mathematicaldefinition of active, apparent and reactive power, reactive power

is categorized and the concept is applied to analyze theaforementioned technologies.

Key words

HVDC, HVAC, reactive power, power quality, convertertechnology

1. IntroductionThe increasing infeed of electrical energy obtained throughrenewable energy sources like wind, water and sun leads tothe progressing geographical decoupling of generation andload [1]. Where fossil power plants are built in closevicinity to heavy load centers, the site of wind turbines,

hydroelectric and solar (thermal) power stations is defined

by natural location factors [1]. As it is crucial forachieving the changeover to a renewable driven energysystem, a growing demand for the transmission of electricenergy over long distances is arising worldwide. However,there are different technologies to achieve these purposes.For a specific task of transmission its not obvious whichof these potential possibilities is the most suitable.

Amongst others, reactive power consumption is a criterionto handle the comparison of transmission technologies.Reactive power has been a subject of scientific controversyfor several decades [2]. As a contribution to this subject,this paper uses a common mathematical classification [3]to assemble all physical phenomena, which contribute to

the reactive power consumption of the three availabletechnologies for bulk power transmission. In contrast toother publications, where phase difference is assumed to

be the only root for reactive power [4], a holistic approach

towards reactive power demand of transmission

technologies is conducted in this paper. A general

investigation on the functional chains concerning reactivepower of the involved electrical equipment gives a finehint to take appropriate steps in the process of achievingbalanced reactive power consumption.

2. Definition and classification of reactivepower

Starting from the introduction of the terms active,

apparent and reactive power, different classes of reactivepower are derived from the common mathematicdefinition to lay the foundations for the analyses on thetransmission technologies.

A. Active, apparent and reactive power

Active power is time-dependent without loss ofgenerality. Its defined as the derivative with respect oftime of electric energy, which is the product of voltageand current:

electricd

d

Wt u t i t

t

(1)

It is characteristic for symmetric three-phase AC systems,thatp(t) is constant.For periodic systems active powerPis the mean value of

time-dependent active powerp(t):

0

0

21d

2

t

tP p t t

(2)

Apparent power of a periodic system is obtained bymultiplying the RMS values of voltage and current [3]:

0 0

0 0

RMS RMS

2 22 21 1d t d t

2 2

t t

t t

S U I

u t i t

(3)

The physical analogy of the mathematic definitiondescribes apparent power as the maximum effectivepower that could be transferred for a defined utilizationof electrical equipment [3]. The relation between activeand apparent power is given by the power factor:

P

S (4)


2/6

All effects that reduce this power factor are embraced bythe term of reactive power. Hence, it is determined asfollows:

2 2Q S P (5)

While reactive power is often simplified to theconsequence of a phase difference between current andvoltage, figure 1 shows all four categories, as they describe

a separate physical phenomenon and possess an ownmathematical derivation. These classes of reactive powerare introduced in the next section.

Figure 1: categorization of reactive power [3]

B. Reactive power due to phase differenceBy the reason of its outstanding relevance oninterconnected systems is this class of reactive power oftenequated with being reactive power itself. Electrical

equipment, load and generation are analyzed regardingtheir influence on the phase difference. The balance ofreactive power locally affects the voltage level of a gridnode and globally maintains voltage stability of a powersystem.The sinusoidal signals of voltage and current are given:

cos , cosu iu t t i t t (6)The instantaneous power according to (1) is:

j -j j -j1 1e e e e

2 2

1cos 2 cos

2

u u i it t t t

u i u i

p t

p t t

(7)

The active power as the mean value over a period is:

2

0

2

0

1cos 2 cos d

2 2

1sin 2 cos

4 2

cos 2 cos4 2

u i u i

u i u i

u i u i

P t t

P t t

P

(8)

The apparent power of the signal is determined by (3):

2 22 2

2 2

0 0

22 2

2

0

2 2 2

2

0

cos d cos d2 2

1 1sin 2

4 2 2

1 1sin 2

2 2 4 2

u i

u

i

S t t t t

S t t

t t

(9)The comparison of the results for active power (8) andapparent power (9) reveals their relation with regards tothe phase difference:

cos cosu iP S S (10)

In consequence, the reactive power due to phasedifference can be stated as follows:

2 2 2 2

2 2cos 1 cos sin4 4 2

Q S

(11)

In consideration of equations (10) and (11) the definitionof the complex powerSis self-evident:

jS P Q (12)

Furthermore complex power is the product of complexvoltage and the complex conjugate current:

*S U I (13)

C. Reactive power due to distortionIndividual components of electrical power systems lead

to a non-linear relation between voltage and current.These effects create higher harmonics, which interfere

the fundamental frequency of the time-dependent signals.Power electronic switched devices and saturated powertransformers are the most frequent sources of harmonicdistortion in electric power systems.

Any electric signal can be depicted through the Fourierexpansion:

cos ,nn

v t A n t n

(14)

For the determination of active and apparent poweraccording to equations (2) and (3) its necessary to usethe Fourier series of each signal. Voltage and current ofdifferent harmonics dont contribute to the active power:

2

0

2

0

cos cos d2

sin sin

2 2 2

sin 2 sin 2

2 2 2

0 ,

m nmn

m nmn

m nmn

mn

P m t n t t

m n t m n t P

m n m n

m n m n P

m n m n

P m n m

(15)

However, form=n a contribution does exist:

2

0

2

0

cos cos d

2sin 21

2 2 4 2 2

m mmm

m m m m m m

P m t m t t

m t t

m

(16)

The apparent power for any arbitrary combination ofharmonics is:

2 22 2

0 0

2

0

2

0

cos d cos d2

1 1sin 2

2 2 4

1 1sin 2

2 4 2 2

m nmn

m nmn

m n m n

S m t t n t t

S t m t

m

t n t

n

(17)

Thus higher harmonics of a signal have the sameinfluence on the apparent power like the fundamentalcomponents (see equation (2)).


3/6

As per its definition in equation (5), reactive poweremerges unequivocally due to harmonic distortion.

D. Reactive power due to volatile load-flowLoads usually dont have time-constant active power

consumption. They rather fluctuate in a pretty slowmanner. This fact influences the power factor [3], which isproved by use of a simple example shown in Figure 2.

Figure 2: Fluctuation of a DC-load

Active and apparent power for the given load curve are

determined in (18) and (19):

2 1 2

11 2

0 02 2

1 2 11 1 2 1 2 1 2

2 2 2

1 1d d d

1

T T T

TP t t t

T T

T T TP T T T

T T T

(18)

2 2

2 1 2

1

2 2

0 02

22 2

1 20 0

2

2 2 2 2

2 1 1 2 2 1 1 1 2 2 1

2 2

1d d

1d d d

T T

T T T

T

S t t T

t t t T

T T T T T T T

T T

(19)

The corresponding reactive power can be determined withthe general equation (5).

E. Reactive power due to non-symmetric operationIn addition to the aforementioned three categories another

reactive power class has to be considered for three-phaseAC-systems. A three-phase system is called symmetricwhen all time-dependent phase values have identicalmagnitude and frequency in each phase and the phasedifference between all three phases is equal to 120 degrees.Whenever electrical equipment impacts symmetry,

additional reactive power is to be applied.A single phase load shall be examined towards reactive

power:

Figure 3: single-phase load

The ohmic resistance is connected between the phases R

and T. Therefore the active power at the load is:

2 2

2

0 0

22 2

0

1 3d cos d

2 2 6

3 1 1 3sin 2

2 2 4 3 2

RT R

P u t i t t t t

t t

R R

(20)

Apparent power of a three-phase system is defined as

follows [3]:2 2 2 2 2 2

,RMS ,RMS ,RMS ,RMS ,RMS ,RMSR S T R S TS U U U I I I

(21)Assuming pure sinusoidal voltages and currents itspossible to determine the apparent power throughequation (9):

22 23 3

2 2R

S

R (22)

The power factor of the examined non-symmetricoperation is:

1

0.7072

P

S (23)

3. Reactive power consumption oftransmission technologies

After having introduced the specific reactive powerphenomena, this chapter aims at investigating theirinfluence on HVDC and HVAC transmissiontechnologies. AC-connections basically comprisetransmission line and two power transformers at bothends of the line. The behavior of a HVDC applicationregarding reactive power consumption is largely identical

to the behavior of the converter stations. This paperaddresses both topologies, classic HVDC with linecommutated converters using thyristor valves (LCC) andHVDC with voltage sourced converters (VSC) usingIGBT modules.To simplify the comprehension of the following chapters,

a 6-pulse converter bridge is depicted in figure 4.

Figure 4: converter with diode valves

A. Phase difference on HVAC transmissionTo analyze the effect of a three-phase AC-transmissionline, figure 5 shows the equivalent circuit of the positive

sequence with an ohmic loadR(1) at its end.

Figure 5: Equivalent positive sequence circuit of a transmissionline


4/6

As it contains a capacitive and an inductive component itsobvious, that there wont be any phase difference ifinductance and capacity would neutralize each other. As

reactive power is the imaginary part of complex power Sthe reactive power consumption of these two components

can be stated:

* * 2

1 1Im Im jCC C CC CQ U I U C U C U (24) * * 2(1) (1)Im Im jL L LLL LQ U I L I I L I (25)

QC depends on the voltage magnitude, which remainswithin a well-defined tolerance range for all undisturbedoperating points. QL, however, varies in dependency on thetransmitted power. The summation of the two factors

reveals an operating point, where the line neither producesnor absorbs reactive power.

! !

1 1 1or Im || 0C LQ Q X C R (26)

When equation (26) is satisfied, the line is operated with

natural powerPnat. Figure 6 shows the reactive powerconsumption of a 380kV transmission line. Its typical per-unit-length parameters were adopted from [5].

0 0.5 1 1.5 2 2.51

0

1

2

3

4

S / Pnat

MVar/km

Figure 6: reactive power consumption of a transmission line

Its obvious, that the transmission line consumes reactivepower when operated above natural power and has a

capacitive behavior when charged lower than the naturalload. The task of compensation strategies is to operate thetransmission line as close as possible to its natural load.That minimizes the reactive power production orconsumption, respectively. To reach this target for a widerange of operating points, reactive-power compensationdevices control the surge impedance by switching

capacitive and inductive elements. The use of powerelectronics has accelerated the controller velocity and has

provided continuous step control.

B. Phase difference on HVDC transmissionAs there are different processes influencing reactive powerperformance on LCC and VSC technology, they are

discussed separately.Two distinct phenomena result in a phase delay of the DC-

current and thus contribute to the inductive behavior ofrectifier and inverter. To expose their basic schemes, theinfluences of commutation and converter control areisolated from other effects and examined in highlysimplified examples.

For the examination of commutation these simplificationsare a rectangular phase currents and sinusoidal phase-to-phase voltages. The resulting current of phase S under

neglect of commutation (left) and for an angle of overlapequal to 30 (right) are depicted in figure 7.

0 60 120 180 240 300 3601

0.5

0

0.5

1

t

= 0

uRS

uST

uTR

iS

uRS

uST

uTR

ud

0 60 120 180 240 300 3601

0.5

0

0.5

1

t

= 30

uRS

uST

uTR

iS

uRS

uST

uTR

ud

Figure 7: influence of commutation on the phase difference

It can be easily derived from the trend of the phasecurrent, that the phase difference due to commutation

Kom is /2. As is a function of the firing angle and theshort-circuit impedance there are rather small chances to

counteract the origin of the phase difference due tocommutation.The controllability of a classic HVDC interconnection byadjusting the fire impulses of the thyristor valves is paidby the disadvantage of increasing the reactive power

consumption. The longer the impulses are delayed, thehigher gets the phase difference in the rectifier mode.Considering the inverter, however, the higher theextinction angle gets, the higher is the reactive powerconsumption. These phenomena are illustrated in figure8.

0 60 120 180 240 300 3601

0.5

0

0.5

1

t

= 0

uRS

uST

uTR

iS

uRS

uST

uTR

ud

0 60 120 180 240 300 3601

0.5

0

0.5

1

t

= 30

uRS

uST

uTR

iS

uRS

uST

uTR

ud

0 60 120 180 240 300 3601

0.5

0

0.5

1

t

= 90

uRS

uST

uTR

iS

uRS

uST

uTR

ud

0 60 120 180 240 300 3601

0.5

0

0.5

1

t

= 150

uRS

uST

uTR

iS

uRS

uST

uTR

ud

Figure 8: influence of fire impulse control on phase difference

The impact of the additional phase difference due to thecontrol activity on the reactive power consumption canbe stated in dependency of fundamental frequencyapparent powerS1:

1Control 1,eff 1,eff Im sinQ S U I (27)The locus of reactive power consumption due tocontrollability, as shown in figure 9, comprises active andreactive power as a function of the firing angle [6].The converter has an inductive behavior in all operatingpoints. Involving the tap changers of the converter

transformers as control variables gives rise to a degree offreedom, which can be used to optimize the HVDCcontrol towards reactive power consumption.


5/6

Figure 9: P-/Q-locus of a classic HVDC scheme [6]

For VSC topology, the rectifier ordinarily works as anuncontrolled diode bridge, whereas the inverter can setmagnitude and phase of the output voltage independentlyby means of space vector modulation. Thus, the inverter

can absorb or inject reactive power. The range of operationis provided by a manufacturer (figure 10).

Figure 10: P-/Q-controllability of a VSC HVDC system, adopted

from [7]

There are some additional topics that are not addressed inthis paper. For instance the transformers as ohmic-inductive components and the influences of a possible DC-inductor contribute to the overall phase delay of the

current.

C. Distortion on HVAC linesFor distortion analyses, AC transmission lines could berather treated as passive elements that dont create higher

harmonics. However, a line transfers signal harmonics and

thus has impact on the signal spectrum. The complexpropagation constant comprises of the attenuationconstant and the phase constant .

j ' j ' ' j C 'R L G (28)

Both constants are in general frequency-dependent. Fortypical values of a 380kV transmission line, attenuation

and phase difference are depicted in figure 11. Thefundamental frequency and very low harmonics up to thefifth are less damped than higher harmonics, where aconstant behavior can be stated. The phase constant is alinear function of frequency. In conclusion, theobservations for harmonics higher than the fifth are

consistent with the Heaviside condition of a distortion-freeline [8].

1 5 10 15 20 25 30 35 40 45 502.5252

2.5253

2.5254

x 105

number of harmonics

5 10 15 20 25 30 35 40 45 50

0

0.02

0.04

Figure 11: attenutation and phase constant of a 380kV line

Another point, which influences the harmonic spectrumof a transmission signal, is the non-linear hysteresis of

the ferrite core of a power transformer. The higher theutilization, the greater is the resulting distortion.

D. Distortion on HVDC systemsUnlike the HVAC transmission, the HVDC technology isa serious source of distortion. Different origins contribute

to the overall behavior. They are discussed in the chapter.Assuming a large inductor on the DC-side and a smallshort circuit inductivity, the phase currents can beconsidered to be rectangular. The Fourier analysis revealsa spectrum of a p-pulse converter with its characteristicharmonics n given in equation (30) [6]:

01,n k p k (29)In order to expose the influence of commutation on thephase current distortion, a trapezoidal signal with a linearcommutation is examined regarding its harmonics. Theharmonics up to the 40

thare plotted in figure 12. Its

evident, that the commutation reduces the harmonic

distortion of the phase current.

0 60 120 180 240 300 3601

0.5

0

0.5

1

uRS

uST

uTR

uRS

uST

uTR

iS

isn

0 60 120 180 240 300 3601

0,5

0

0,5

1

t

uRS

uST

uTR

uRS

uST

uTR

iS

isn

Figure 12: influence of commutation on phase currentharmonics

Filtering or control with regards to elimination of certainharmonics can compensate the reactive powerconsumption due to distortion of the phase current.

As the DC-voltage is not a pure DC-signal, the voltageripple of a classic HVDC connection is another principle

contributing to the overall reactive power consumption.Using the equivalent circuits for commutation and twoconducting valve mode [5] results in the equation for thecorresponding DC-voltages UDC,Kom and UDC,2Vv.

DC,Kom Kom

DC,2Vv 2Vv

3cos

2

3 cos

p

p

U t

U t

(30)

In equation (30) p is the magnitude of the voltage

source, the phase angles are given in table 1.


6/6

Table 1: angles for valve participations of a 6-pulse converter

valve participation 123 234 345 456 561 612

Kom -/3 -2 /3 - 2 /3 /3 0

valve participation 12 23 34 45 56 61

2Vv - /6 - /2 -5 /6 5 /6 /2 /6

The voltage drop due to commutation has impacts on themean value and the ripple of the DC-voltage. There aretwo factors influencing the severity of the impact: Thefiring angle and the angle of overlap . UDC for an entireperiod is shown in figure 13.

0 60 120 180 240 300 360

1,5

1

0.5

0

0,5

1

1,5

2

t

u

/

p

= 0, = 30

uRS

uST

uRT

uRS

uST

uRT

ud

udi06

0 60 120 180 240 300 360

1,5

1

0.5

0

0,5

1

1,5

2

t

u

/

p

= 30, = 30

uRS

uST

uRT

uRS

uST

uRT

ud

udi06

Figure 13: influence of commutation on DC-voltage ripple

Once more, the results show, that also regarding thedistortion on the DC side, the operating point should be asclose as possible to full power operation at a rectifier angle

close to zero and a minimal extinction angle at theinverter.With the voltage not being a pure DC-signal anymore, theinductive and capacitive elements of the transmission linecant be neglected further on.The VSC HVDC can significantly reduce the distortion onAC-terminals and DC-circuit by using several discrete

steps to form the AC-voltages at the inverter. This

multilevel approach is state-of-the-art for VSCconverters in power systems [9].

E. Volatile load-flowOriginally, the definition of reactive power due to volatileload-flow aimed at covering the effect of fluctuating load,

which often, especially in industrial applications, follow aslow, cyclic power consumption. For a renewable driven

power system, this definition must be extended to avolatile energy generation, which is characteristic for windand solar based infeed. In comparison to the analysis offluctuating load of a DC-system, performed in chapter 2, a

similar approach did not show any significant differences.These elementary calculations should be extended to real

configurations to estimate the outcome of this aspect.

F. Non-symmetric operationFor any electrical device its impossible to construct a totalsymmetric design with identical distances between phasesand equidistance to earth at the same time. Therefore acomplete symmetry cannot be reached. However, it can bereduced to a tolerable level.

The transposition of phases is a well-known measure tocompensate non-symmetric configuration of transmission

lines bridging long distances. Adequate transpositionschemes are described in literature [5], [8].As mentioned hereinbefore, a converter has two differentoperating states, commutation and two conducting valves

mode. For a DC-periodic view on the behavior, both ofthem seem to be non-symmetric states. For instance,while conducting of valves 1 and 2, the systemarrangement is abstractly seen similar to a load between

phases R and T according to figure 3. However, thedefining rules for symmetry are obtained for a whole AC-

period. A 120 phase difference between currents andvoltages as well as an identical magnitude of all phasevalues is kept for equidistant firing pulses.Its evident, that this prerequisite cant be valid forpractical operation. As there are fluctuations andoscillations, the control has to adjust firing and extinction

angels of the rectifier and the inverter permanently tomaintain a steady transmission. Therefore a converter

requires additional reactive power in consequence ofnon-equidistant firing impulses.

4. ConclusionA comprehensive approach to classify reactive power

consumption of different transmission technologies wasperformed. The emphasis within the comparison was puton HVAC and classical HVDC concepts. Nevertheless,wherever the VSC HVDC displayed different behavior, itwas highlighted separately.Based on the mathematical definition, reactive power iscategorized into four main classes, whereas lots of works

are only considering reactive power behavior regardinginfluences on the phase difference. This approach is the

basis for a holistic consideration of all physicalphenomena, which affect the particular categories. Thoseare briefly introduced and possible countermeasures arepresented.

This approach contributes to maintain the balance ofreactive power in operation and to reduce reactive power

consumption of individual components as well as ofentire transmission systems.

References

[1] J. Schlabbach, K. Rofalski, Power System Engineering,WILEY-VCH, Weinheim (2008),

[2] Wissenschaftlicher Ausschuss des VDE, Blindleistung,VDE-Verlag, Berlin (1963)[3] G. Herold, Elektrische Energieversorgung I, J. Schlembach

Fachverlag, Wildburgstetten (2005), 2nd Edition[4] D.A. Deib, H.W. Hill, Optimal Firing-Angle Control of

Cascaded HVDC converters for Minimum Reactive PowerDemand, Applied Power Electronics Conference andExposition, San Diego (1993)

[5] K. Heuck, K. Dettmann, D. Schulz, ElektrischeEnergieversogung, Vieweg + Teubner, Wiesbaden (2010), 8th

Edition[6] G. Herold, Elektrische Energieversorgung V, J. Schlembach

Fachverlag, Wildburgstetten (2009)[7] M. Davies et al., HVDC plus Basics and Principle ofOperation, http://www.energy.siemens.com/mx/pool/hq/power-

transmission/HVDC/HVDC_Plus_Basics_and_Principle.pdf,accessed on 22th October 2012[8] G. Herold, Elektrische Energieversorgung II, J. Schlembach

Fachverlag, Wildburgstetten (2008), 2nd Edition

[9] G. Gemmell, J. Dorn, D. Retzmann, D. Soerangr, Prospectsof Multilevel VSC Technologies for Power Transmission, IEEETransmission and Distribution Conference and Exposition

2008, Chicago

a comprehensive approach to classify reactive power consumption in transmission...

Documents