05278765 - Compensation of Load Unbalance, Reactive Power and Harmonic Distortion by Cooperative...

7/28/2019 05278765 - Compensation of Load Unbalance, Reactive Power and Harmonic Distortion by Cooperative Operation

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COMPENSATION OF LOAD UNBALANCE, REACTIVE POWER AND

HARMONIC DISTORTION BY COOPERATIVE OPERATION OF

DISTRIBUTED COMPENSATORS

Paolo Tenti, Daniela TrombettiDEPARTMENT OF INFORMATION ENGINEERING,

UNIVERSITY OF PADOVA

Via Gradenigo 6/B 35131 Padova Italy

Tel. +39-049-827.7503, Fax +39-049-827.7699

[email protected], [email protected]

www.dei.unipd.it

Elisabetta Tedeschi, Paolo Mattavelli

DEPARTMENT OF MANAGEMENT AND MECHANICAL INNOVATION,

UNIVERSITY OF PADOVA

Stradella S. Nicola, 3 36100 Vicenza Italy

[email protected], [email protected]

www.gest.unipd.it

Keywords

Reactive compensation, Unbalance compensation, Harmonic compensation, Static VAR

compensators, Active power filters.

Abstract

Distribution grids are increasingly populated by a variety of renewable energy sources, which create

new opportunities in terms of efficient use of energy and can also help to improve power quality. In

fact, they are connected to the grid by means of Power Switching Interfaces (PSI) which are capable

to control power flow and waveform of absorbed currents as well. They can therefore contribute to

power balance and compensation of asymmetry and distortion together with other compensation units,

e.g., passive filters, SVC (Static VAR Compensators) and APF (Active Power Filters). Of course,

effective use of such distributed compensation capability requires cooperative operation of

compensators and propersharingof compensation duties.

This paper shows that distributed compensation of load unbalance, reactive power and harmonic

distortion can be achieved by a cooperative control approach. Energy efficiency and power quality canbe managed as a whole at a system level, by taking full advantage of the distributed compensation

capability.

Introduction

Although unbalance, reactive and harmonic compensation has been the subject of several

contributions [1-10], based on approaches in the time [6-10] and frequency [2-5] domain, the problem

is still open and becomes increasingly difficult and intriguing. In fact, reference is usually made to

grids fed by power sources of large capacity, which impress sinusoidal and symmetrical voltages at the

Point of Common Coupling(PCC). Nowadays, however, this is not generally true, since proliferation

of small power sources and distorting loads may cause the grid to appear as a weak power source,characterized by non-negligible impedance, voltage asymmetry and distortion.


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In order to fully exploit the available energy sources while providing good power quality there is a

need to compensate for load unbalance, distortion and reactive power. This is particularly important in

smart grids, where renewable energy sources of different type (wind mills, PV panels, fuel cells,

micro-turbines) coexist and must be utilized in the most efficient way.

Different kinds of compensation units (passive filters, stationary compensators, SVC, APF, PSI) can

provide the required compensation capability. However, with the standard approach, each unit is

designed and controlled independently to suit specific local needs. If they have to cooperate to

improve globalefficiency and power quality, a cooperative control approach [17-19, 21] is needed,

which dynamically shares the compensation effort among the various units without affecting their

local duty.

This paper presents a theoretical background to systematically approach the problem of cooperative

control of distributed compensators. The approach is validated in a significant test case, which shows

that cooperative control performs effectively under stationary and dynamic conditions and is capable

to fully exploit every type of compensator.

Power-based control approach

When dealing with remote controlof distributed compensation units, a basic problem relates to the

need to exchange compensation information between units which are connected to different network

ports, supplied by voltages of different amplitude and phase, in a situation where the distribution grid

is substantially unknown. This sets a fundamental difference compared to the usual local control

approach, which holds when the compensation unit is connected at the load terminals, or at PCC, and

shares the voltage supply with the load to be compensated. In this case the compensation command is

fed to the compensator as a current reference, and compensation is performed by current control.

Instead, for remote control we need conservative control variables, which allow encoding,

transmission and decoding of the compensation commands at different network ports, irrespective of

voltage amplitude, phase and waveform. Here we propose to adopt, as remote control variable, the

instantaneous complex power, which is defined, for any set of periodic voltages and currents measured

at a generic network port, by:s = p+ j q = u i = u + j

u( ) i = un in + j

un in( )

n=1

N

(1)

where u and i are the vectors of the N-phase voltages and currents and symbol means scalarproduct. The sum is extended to all phase conductors, including neutral wire, and the voltage reference

is selected to give un

n=1

N

= 0 . Termp is instantaneous real power, while q is instantaneous imaginary

power. Voltage is normalized voltage integral, defined by:

un =

1

2fn n( ), where: n = un dt0t , n = 1

T

n dt

0

T

(2)

In (2)fis line frequency and Tis line period. Voltageun

is therefore the unbiased integral of voltage

un divided by angular line frequency.

It can be demonstrated that voltage integralsun, like voltages u

n, comply with Kirchhoff Law, thus

both p and q comply with Tellegens Theorem and are conservative quantities. Accordingly, total

complex power sPCC

absorbed atPCCsums all power terms taken by each branch in the network.

The above consideration sets the basis for cooperative control of distributed compensators. In fact, the

compensation duty can be shared among the various units by giving a suitable complex power

command to each of them.

Note that averaging the instantaneous complex power over line period Tgives:

s = p + j q , where:p = P = u,i =

1

Tun in dt

n=1

N

0T

= Pnn=1

N

q=

Q=

u,i

=

1

T

un

in

dtn=1

N

0

T

=

Qnn=1

N

(3)


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In the above expression, chevrons .,. refer to internal product in the L2 space. Pis active power,

obtained by adding the active powers of each phase. Irrespective of voltage and current waveform, P

accounts for average power absorption at the given port. Similarly Q is reactive power and,

irrespective of voltage and current waveforms, accounts foraverage energy stored in the equivalent

passive network seen by the given port [17]. It was shown in [10] that (3) extends the reactive power

definition to the case of non-sinusoidal quantities. Observe that an inductorL, in fact, contributes toreactive power with term:

QL =L IL2= 2wL , where: IL = iL ,iL , wL =

1

T

1

2L

0

T

iL2dt (4.a)

Similarly, a capacitorCcontributes to reactive power with term:

QC = CUC2= 2wC, where: UC = uC,uC , wC =

1

T

1

2C

0

T

uC2dt (4.b)

Such expressions show that reactive power is proportional to average energy stored in capacitors and

inductors irrespective of voltage and current waveforms. All power terms defined by (1) and (3) are

therefore related to physical quantities. Moreover, they can be measured and processed in the time

domain.

Principle of distributed compensation

For compensation purposes, we identify three types of network ports:

Supply ports, where energy sources inject power into the network. Energy sources are normallyrepresented as voltage supplies and thepower quality issue at these ports is related to the quality

of absorbed currents. They should be purely resistive and symmetrical, so as to provide unity

power factor and effective energy source utilization.

Let e be the port voltages, the currents can be split into orthogonal terms:

i = ia+ i

r+ i

u+ i

v(5)

The meaning of the current terms is the following.

Active currents ia

are the minimum currents needed to convey active power P provided by the

source. They can be expressed as:

ia=G

ee , where: G

e=

e,i

e,e=

P

En

2

n=1

N

(5.a)

Ge

is equivalent port conductance and En

is rms value of voltage en.

Reactive currents are the minimum currents needed to convey reactive power Q provided by

the source. They can be expressed as:

ir=B

e

e , where: B =

e ,ie ,

e=

QEn

2

n=1

N

(5.b)

Be is equivalent port susceptance and

En is rms value of normalized voltage integralen .

Unbalance currents iu

are due to asymmetrical network behavior. They can be expressed as a

function of active and reactive power absorbed by each phase ( n =1 N) as:

iun = Gn Ge( )en + Bn Be( )en =

Pn

En2

P

En2

n=1

N

en +

QnEn

2

QEn

2

n=1

N

enk

(5.c)

These currents vanish only if the equivalent conductance and susceptance are the same in all

phases (Gn= G

e, B

n= B

e).

Void currents are the remaining current terms. They do not convey active or reactive power and

account forgenerated current harmonics (harmonic terms which exist in currents but not in

voltages) and scattered currents (current terms which reflect a different network behavior at

different harmonics) [17].


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A high power factor requires that reactive, unbalance and void currents are suppressed or reduced

below an acceptable level. Since reactive currents depend on reactive power, they can be

eliminated by compensating the reactive power by proper control of SVC units. Elimination of

unbalance currents requires control of active and reactive power distribution among the phases,

and this can also be done by SVC units, according to the Steinmetz approach [1]. Finally,

suppression of void currents requires control of the instantaneous current waveforms, which can

be obtained by proper control of switching compensators (APF, PSI).

At supply ports the power quality is measured by local quality indexes, i.e., the unbalance factor

(ratio between negative and positive sequence rms currents) and the power factor(ratio between

active power and apparent power).

Load ports, where power quality is related to stability andpurity of the voltage waveform. Thisrequires the compensation system to perform voltage support, to keep stable and symmetrical the

voltage supply in every operating condition, and harmonic suppression, to improve quality of the

voltage waveform in presence of distorting loads. The first task can be done by SVCunits, the

second byAPFandPSI.

Local quality indexes, describing the network performance at load ports, are voltage THD (Total

Harmonic Distortion) and asymmetry factor (ratio between negative and positive sequence rmsvoltages). Otherpower quality indexes, e.g., flicker, voltage sags, micro-interruptions, should also

be considered.

Compensation ports, where the compensators inject suitable current waveforms to provide thedesired compensation. Power quality is not an issue at these ports. Rather the compensation

effectiveness, describing the network response to a compensation command, should be

characterized.

Note that local quality indexes mentioned above do not provide exhaustive description of network

operation. Global performance indexes should also be considered, e.g., transmission efficiency (ratio

between transmission losses and active power flow) and power flow control efficiency (global

utilization rate of power sources, weighted according to energy production cost), so as to optimize thenetwork performance both in terms of efficiency and economics.

Since optimizing all local and global quality indexes at the same time is impossible, the problem can

be approached by making reference to suitable cost factors, which weight properly the various goals

and drive the system toward aglobal optimization. As a first step in this direction, we will analyze the

capabilities of various compensation units and derive a general approach to optimize the system

behavior atPCCby making use of cooperative control of distributed compensators.

Power capability and control of compensators

Compensators can be classified in three main categories:

Stationary compensators, which include fixed capacitor or inductor banks and passive filters.They contribute to compensation with a fixed amount of reactive power and/or filtering capability.

In practice, operation is influenced by surrounding network and, under certain circumstances, such

units can generate voltage ringing or over-currents, which may cause detrimental effects. Here

such compensators will be considered as network elements, since they cannot be controlled.

Quasi-stationary compensators, which include every kind of SVC, in particular TCR (ThyristorControlled Reactors) and TSC (Thyristor Switched Capacitors). While both TCR and TSC

contribute to reactive power control, respectively with positive and negative amounts, in our

approach the unbalance compensation will be demanded to TCR only. Although reference is made

to TSCand TCR, STATCOMunits are inherently considered too, because they provide a similar

compensation capability by low-frequency operation of switching power converters.


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Dynamic compensators, which includeAPFandPSI, provide harmonic suppression and can alsocontribute to reactive power control and unbalance compensation. As a whole, they are classified

as SPC(Switching Power Compensators) because of their capability to control current waveforms

by high-frequency modulation of power switches.

Compensation capability and control criteria of each type of compensator will be analyzed hereafter.

Thyristor-Switched Capacitors

TSC include multiple banks of delta-connected capacitors, which can be inserted or disconnected by

controlling thyristor switches. Thus, they provide step regulation of capacitive power from zero to

rated VA capability. Control is simply done by assigning a suitable reactive power command to each

unit. In the following we assume that TSCunits are operated symmetrically, to avoid amplification of

asymmetry in presence of voltage distortion.

Thyristor-Controlled Reactors

Recall first that reactive and unbalance compensation can be performed, under sinusoidal conditions,by means of the Steinmetz circuit [1], which includes only reactive elements. In presence of

asymmetrical and distorted voltages, we still apply the Steinmetz method by making reference to the

fundamental positive-sequence components up

of actual voltages u . The effect of voltage asymmetry,

distortion and phase control of thyristor switches is then corrected by proper control ofSPCunits.

Lets consider a TCR made up of three delta-connected inductors controlled by bidirectional thyristor

switches. Phase control of thyristor switches provides independent and continuous regulation of the

equivalent susceptance of each branch from zero to rated value.

Let B12,B23,B31 be the phase-to-phase susceptances and up

the fundamental positive-sequence supply

voltages. Compensation of reactive power requires the TCR to absorb suitable positive-sequence

fundamental currents ip, while compensation of load unbalance requires absorption of suitable

negative-sequence fundamental currents in

. These sequence components are [20]:ip= B

12+B

23+B

31( )up

(6)

in= B

12

u2

p

u1

p

u3

p

B23

u1

p

u3

p

u2

p

B31

u3

p

u2

p

u1

p

(7)

Equation (7) shows that currents in

do not change if B12,B23,B31 are increased by the same amount.

Thus, let:

B0

=B12+ B

23+ B

31

3 and

B12

'= B

12 B

0

B23

'= B

23

B0

B31

'= B

31 B

0

(8)

from (6) and (7) we easily obtain:

sp= u

p i

p= 3Bo u

p+ j

up( ) up = j9BoUp2 = jQp (9.a)

sn= u

p i

n=p

n+ j q

n p

n= 3 B

12

'u3

p u3

p+B

23

'u1

p u1

p+B

31

'u2

p u2

p( )qn= 3 B

12

' u3

p u3

p+B

23

' u1

p u1

p+B

31

' u2

p u2

p( )

(9.b)

The total instantaneous complex power absorbed by the TCR is therefore given by:

s = p+ j q = pn+ j Q

p+ q

n( ) (10)


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Considering that Qp is constant while pn

and qn

are alternate quantities, equation (10) sets the basis

forTSCcontrol. In fact, given TCR complex power reference srefSVC, the powerterms Qp , pn and qn

can easily be extracted by separation of dc and ac components, and susceptances B12,B23,B31 are then

derived by inversion of (9).

Let In be the rms value of currents i

nand S

n= 3U

PI

n be the unbalance power, it can be

demonstrated that compensation of currents in

corresponds to a reactive power absorption equal to

Sn . However, the reactive power compensation capability of the TCR is reduced by 3S

n .

Active Power Filters and Power Electronics Interfaces

PSC units (APF and SPI) are capable to provide every kind of compensation. However, they are

normally used to refine the action of stationary and quasi-stationary compensators by suppressing the

residual reactive, unbalance and harmonic terms. Each SPC receives a complex power command

srefSPC

= prefSPC

+ j qrefSPC and transforms it into a set of current references according to the equation:

i refSPC

=

prefSPC

w qrefSPC

w

(11.a)

where:

w =

w1

w2

w3

=

u2 u

3

u3 u

1

u1 u

2

=w1

w

2

w1w

2+ w

2

w

3

w

2w

3+ w

3

w1

w

3w1

3(11.b)

The reference current can therefore be evaluated, on instantaneous basis, from complex power

reference and line-to-line voltages. The compensation capability of an SPCis only limited by voltage

and current ratings, thus the instantaneous complex power must satisfy the condition:

s = p2+ q

2ASPC= 3Urat

Irat pk

2(12)

where Urat

is rated rms voltage and Irat pk is peak current capability of the SPC. Apparent power ASPC

is the ratedswitching power capability.

Implementation of cooperative control

As mentioned before, we assume that cooperative control aims at making proper use of distributed

compensation capability so as to optimize operation at the point of common coupling. At PCC, the

goal is therefore to absorb only active currents, the remaining current terms being suppressed by

cooperative operation of distributed compensators.

Fig. 1: General Network

Representation

The network is schematically represented in Fig.1, where

only PCC and connection ports of controllablecompensation units (TSC, TCR, SPC) are shown, the rest of

the network (power sources, transformers, transmission

lines, loads, stationary compensators) being included in

block . Every compensator, when switched on, informs the

central controller about its residual compensation capability,

which is the rated one less the part invested for local needs.

Based on the compensation needs atPCCand total available

compensation capability, the controller distributes the duty

among the various compensators so as to minimize a global

cost function, which takes into account the cost and

effectiveness of the compensation task performed by every

compensation unit.


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The proposed implementation of the central controller is shown in Fig.2. It features closed loop

control of input currents at PCCand feed-forward control of remote compensators. The controller is

designed to perform properly even in presence of non-negligible communication delays and slow

network response. In particular, the control bandwidth is chosen small enough to avoid instability.

Moreover, the instantaneous quantities handled by the controller are, in practice, frames of data which

are collected every half line cycle, processed and transmitted in the following half cycle and executed

in the next cycle. Consequently, control is characterized by at least one-cycle delay and the controller

is designed accordingly.

Fig. 2: Central Controller

The control operates as follows. First of all, currents ii

absorbed at PCC are processed to extract

active components ia, which are taken as input current references. Since full compensation is not

always possible, due to limited availability of reactive and switching power, current references ia

are

modified by non-compensable current terms inc

estimated by the controller.

Error signals i, generated by comparison of references with actual input currents i

i, are processed by

error amplifierA, which generates internal current references i

ref

.

The fundamental positive- and negative-sequence components i refp

and i refn

of references i ref are then

extracted and multiplied by positive-sequence complex voltage ep= e

p+ j

ep

to get instantaneous

complex power references (srefp = ep i refp , srefn = ep i refn ). These quantities are then fed to the SVCControl block which, based on reactive and unbalance compensation needs and available

compensation capability, computes actual SVCcurrent references ( iSVC

= i rp+ i u

n) and complex power

reference sSVC.

Power SharingblocksPSTSC

andPSTCR

split the compensation duty among the SVCunits, according to

their type and compensation capability, and send a proper complex power reference to each of them.

This reference is then executed according to a feed-forward control approach based on the theoretical

results given in the previous section.

Thecurrent references for the switching compensators ( i refSPC

) are computed by subtracting SVCcurrent

references iSVC

from i ref . Scalar multiplication of i refSPC

by complex voltages e = e+ je generates

complex power reference srefSPC, which is fed to the SPC Controlblock. This block, based on available

switching power, determines the actual SPC current references iSPC

and corresponding complex

power reference sSPC

. The Power Sharingblock receives power command sSPC

and splits it among

the SPCunits according to suitable duty-sharing criteria.

Non-compensable current terms are finally determined as i nc = i ref iSVC

iSPC

. They are fed back to

the input summation node to correct the input current references.


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Application example

Fig. 3: Simulated Network

As an example of cooperative control the network of

Fig.3 was simulated. It includes unbalance and distorting

loads, transmission lines, transformers and various

compensation units (fixed capacitor bank, TCR, TSC,APF) and is fed by distorted and asymmetrical voltages.

The central and local control units are implemented

according to the criteria given above. It is assumed that

the TSCand TCR are switched on at time t1 (0.2 s) and

the APFat time t2 (0.6 s). In time t3 (1 s) a sudden load

change (from single-phase resistive to single-phase

capacitive) is introduced, so as to show the dynamic

response.

Fig. 4: Voltages atPCC Fig. 5: Currents atPCCwithout compensation

Fig.4 shows the voltages at PCC. They exhibit considerable asymmetry (unbalance factor equal to

10%) and distortion (5th harmonic: 5.0%, 7th harmonic: 5.0%).

Fig.5 shows the currents at PCCwhen the compensation units are off. The high distortion is due not

only to the distorting load, but also to the capacitor bank located next to PCC. Current asymmetry is

due to load unbalance and voltage asymmetry.

Fig. 6: Currents atPCCwith SVCturned on Fig. 7: Currents atPCCwithAPFturned on


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Fig.6 shows the currents at PCC after time t1 when the SVC units (TCR and TSC) are turned on.

Although distorted, the currents are now reasonably balanced and in phase with the corresponding

voltages.

Fig.7 shows the currents at PCC after time t2, when also the APF is turned on. Within the control

bandwidth, the input currents now track the supply voltages with good accuracy.

Fig. 8: Time behavior of Power Factor Fig. 9: Time behavior of Unbalance Factor

Finally, Figs. 8 and 9 show the time behavior of the power factor (ratio between active and apparent

powers) and unbalance factor (ratio between negative and positive sequence components of the input

currents), both computed at PCC. Both values are averaged over a period of the line voltage. The

power factor is initially very low (0.58), due to unbalance, distortion and reactive current components.

The intervention of the SVC almost suppresses reactive and unbalance currents, thus the power factor

increases progressively to 0.96. A power factor close to unity is reached after intervention of the APF,

which removes the residual reactive and unbalance currents together with the void currents, including

those generated by SVCunits. The effect of load transient on this parameter is temporary and small.

The unbalance factor is initially high (0.28) due to load unbalance. The intervention of SVC units

reduces considerably the unbalance. When the APF is turned on the unbalance factor improves further;

in fact, the residual unbalance is only due to voltage asymmetry. The effect of the load transient on

this parameter is appreciable and derives from the inherent slow response of the controller.

Conclusion

A general approach to cooperative control of distributed compensation units was developed, which

allows simultaneous and effective use of every type of compensator (STATCOM, TCR, TSC, APF,

PSI). The theoretical background lies on the definition of instantaneous complex power, a

conservative quantity which allows remote control of compensators irrespective of phase shifts and

voltage changes introduced by transformers and voltage drops on transmission lines.

The characteristics of the various kinds of compensator were analyzed, both in terms of local

compensation capability (to suit surrounding network needs), and global compensation capability (tocooperate for improving system-level performance indexes). The compensation limits were also

discussed together with the response to complex power commands, so as to characterize the operating

properties of each compensation unit when controlled from remote by a central controller.

The proposed control approach was verified by simulation of a network including all typical

compensation elements (passive filters, SVC, APF), fed by non-sinusoidal and asymmetrical voltages

and loaded by unbalanced, distorting and time-varying loads. In spite of the difficult operating

environment, the cooperative operation of distributed compensators provides substantial reduction of

load unbalance, distortion and reactive power and fast adaptation to load changes as well.


10/10

References

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[17] P.Tenti, E.Tedeschi, P.Mattavelli, Compensation Techniques based on Reactive Power Conservation,Journal on Electrical Power Quality and Utilization, vol. XIII, n.1, 2007, pp.17-24.

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05278765 - Compensation of Load Unbalance, Reactive Power and Harmonic Distortion by Cooperative...

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