06360962

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A Novel Control Strategy for Load Converter of

Renewable Energy under Unbalanced Loading

Shaoru Zhang

1) College of Physics Science and Information

Engineering, Hebei Normal University, [email protected]

Fang Lin Luo, Senior Member IEEE

School of EEE

Nanyang Technological UniversitySingapore

[email protected]

Abstract —In this paper, a novel control strategy for the load

converter supplying the unbalanced AC load in the renewable

energy resources system is presented. This novel control strategy

is implemented in the a-b-c coordinate, so reference-frame

transformation from a-b-c coordinate to d -q-0 rotating coordinate

and inverse transformation from d -q-0 rotating coordinate to a-b-

c coordinate are not required which decreases the controller

operation time comparing with conventional d -q-0 controller. The

control algorithm results in balanced and sinusoidal load voltages

under unbalanced AC loading. The unbalanced load is

characterized in both the a-b-c and d -q-0 coordinates. Also, the

mathematical model of the load converter in both a-b-c and d -q-0

coordinates is derived by using the average large signal model.

Then, two control strategies for the load converter are presented.

The first one uses the conventional d -q-0 controller to ensure the

voltage and current regulation. The second one is this novel

proposed control strategy based on the power conservation

theory. The two control strategies have been applied to the

reference voltages generation of the load converter. The

performance of the load converter with these two control

strategies is compared with each other. Simulation and

experimental results show the validity and capability of the novel

proposed control strategy.

Keywords-load converter; renewable energy; unbalanced load;

mathematical model; power conservation theory; reference voltages

I. I NTRODUCTION

With the consumption of energy, it is necessary to exploitand utilize the renewable energy resource, such as solar power,tidal power, and geothermal power and so on [1-3]. Renewableenergy resources are attractive options for loads supplying in places where a connection to the utility network is eitherimpossible or unduly expensive [4]. Unbalanced AC loadingcould be occurred by different current levels among phases orsame current levels but with different phase shift, or both. Theunbalanced loading results in unbalanced voltage, poor powerfactor, power losses and other power quality disturbances.

The DC/AC load converter should deliver constant balanced AC voltage magnitude and frequency. In order toachieve this purpose, some control strategies for load converterhave been proposed [5-7]. The load converter controller hasused conventional d -q-0 rotating frame [8], space vectormodulation [9] and simple V - f voltage regulator schemes [10-11]. In conventional d -q-0 controller, the compensation of the

unbalanced voltage has been used current and voltageregulation in a d -q-0 reference frame rotating at thefundamental frequency. However, the voltage and current givesrise to 2 voltage and current ripples in the d -q channels. The 0channel is similarly affected by the disturbance at . As aresult, the performances of conventional d -q-0 control strategyare insufficient [12-14]. All the existing simple V - f voltageregulator schemes are unable to deal with the zero sequencecomponent caused by unbalanced loads [10-11]. The space

vector modulation schemes are implemented in a two-dimensional space, and are therefore unable to deal with thezero sequence component caused by unbalanced load.

A novel control strategy is proposed based on the powerconservation theory in this paper. The real power consumed byload is supplied by the source, and then the reference voltagemagnitude can be obtained. This novel control strategy isimplemented in the a-b-c coordinate, so reference-frametransformation from a-b-c coordinate to d -q-0 rotatingcoordinate and inverse transformation from d -q-0 rotatingcoordinate to a-b-c coordinate are not required which decreasesthe controller operation time comparing with conventional d -q-0 controller. The proposed novel controller has been applied tothe reference voltages generation of the load converter. The

theoretical formulation of these controllers has been analyzedand developed. The simulation and experimental results showthat the load converter with the proposed controller can handlethe unbalanced load.

II. SYSTEM DESCRIPTION

The diagram of DC isolated distribution system withunbalanced AC load is shown in Figure 1. This could be themodel for a small off-grid distribution system. In Figure 1, theunbalanced AC load is connected to the DC bus via a three phase three-leg DC/AC load converter with neutral clampedDC capacitors. This topology is characterized by theconnection of the neutral point of the load to the midpoint ofthis DC/AC converter. As a result, the phase voltage can becontrolled independently. The battery may be sized to cover theload consumed power for different operating conditions, whilethe DC/DC converter provides the power balancing in DC bus.The DC voltage regulator of DC/DC converter can adjust theDC bus voltage, V dc , in the acceptable voltage range. Therenewable energy units can inject DC power to the DC bus.

Supported by Educational Commission of Hebei Province, China(2009141); National Natural Science Foundation of China(60974063) and PhD Foundationof Hebei Normal University(L2008B04).

1506978-1-4577-2119-9/12/$26.00 c2011 IEEE

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Figure 1. Diagram of DC isolated distribution system with unbalanced AC load

III. U NBALANCED LOAD IN BOTH A-B-C A ND D-Q-0

COORDINATES

An unbalanced load could produce negative and zerosequence currents. In Figure 1, the unbalanced AC load should be supplied by balanced sinusoidal voltages:

( )

( )

( )

°+

°=

120t sinV

120-t sinV

t sinV

v

v

v

lm

lm

lm

lc

lb

la

ω

ω

ω

(1)

where V lm is the peak value of load voltages and is thefundamental angular frequency. If the load is linear and

unbalanced (i.e., Rla Rlb R lc and/or X la X lb X lc ), theamplitudes and phase shifts are different in each phase currentand the neutral current will flow between the neutral of the loadside and source side. The three-phase currents are expressed bythe following equation:

( )

( )

( )

−°+

−°=

clcm

blbm

alam

lc

lb

la

120t sin I

120-t sin I

-t sin I

i

i

i

θ ω

θ ω

θ ω

(2)

Using phasor representation, a three phase unbalanced loadcurrents can be expressed by symmetrical components of thefundamental positive sequence (ila,p , ilb,p and ilc,p) rotatingcounterclockwise with angular frequency, , negative sequence

(ila,n , ilb,n and ilc,n) rotating clockwise with the same angularfrequency, and zero sequence ( ila,0 , ilb,0 and ilc,0 ), as follows:

++

++

++

=

lc,0nlc, plc,

lb,0nlb, plb,

la,0nla, pla,

lc

lb

la

iii

iii

iii

i

i

i (3)

The load currents can be transformed into the d -q-0synchronous reference frame, as follow:

++

++

++

=

=

l0,0nl0, pl0,

lq,0nlq, plq,

ld,0nld, pld,

lc

lb

la

0dq

l0

lq

ld

iii

iii

iii

i

i

i

T

i

i

i (4)

where the coordinate transformation matrix, T dq0 is expressed by the following equation:

( ) ( ) ( )

( ) ( ) ( )

°+−°−−−

°+°−

=

2

1

2

1

2

1120t sin120t sint sin

120t cos120t cost cos

3

2T

0dq ω ω ω

ω ω ω

After this transformation, the positive sequence d -q currents( ild,p , ilq,p ) appear as DC quantities (with = 0 ), the negativesequence d -q currents (ild,n , ilq,n ) appear as a ripple with theangular frequency of 2 [6-8]. The zero sequence currentappears as a disturbance in the 0 axes at . However, the positive, negative and zero sequences appear as DC signals intheir own synchronously rotating reference frames.

IV. LOAD CONVERTER UNDER U NBALANCED LOADING

CONDITIONS

The load converter has Insulated Gate Bipolar Transistor(IGBT) switches and has been controlled by Pulse-WidthModulation (PWM) voltage controller. Assuming the switchingfrequency is much higher than the fundamental frequency ofthe AC signals, therefore all voltage and current ripples arenegligible and the averaging technique can be used to modelthe load converter as shown in Figure 2. The average largesignal modeling provides the most efficient way to study thesystem stability, subsystem interactions and controllers performance in load converter [14]. The equations describingload converter voltages and currents in the circuit model can beexpressed by the following equation:

+

+

=

fc

fb

fa

f

f

f

fc

fb

fa

f

f

f

lc

lb

la

fc

fb

fa

i

i

i

dt

d

L00

0 L0

00 L

i

i

i

R00

0 R0

00 R

v

vv

v

v

v (5)

where v fa , v fb and v fc are line to neutral three phase outputvoltages of the load converter. i fa , i fb and i fc are three phaseoutput currents of the load converter. vla , vlb and vlc are line toneutral three phase voltages of the AC loads. The voltagesequation can be presented in the d-q-0 reference frame, asfollows:

−

+

+

+

=

f0

fq

fd

f

f

f0

fq

fd

f

f

f

f0

fq

fd

f

f

f

l0

lq

ld

f0

fq

fd

i

i

i

000

00 L

0 L0

i

i

i

dt

d

L00

0 L0

00 L

i

i

i

R00

0 R0

00 R

v

v

v

v

v

v

ω

ω (6)

As it can be seen from the equation (6), the d and q channelsare coupled by L f iq and L f id terms, but the 0-channel iscompletely decoupled from the d and q channels.

Figure 2. Average large signal model of load converter

V. CONVENTIONAL CONTROL STRATEGY

The circuit configuration and conventional control scheme based on d -q-0 coordinate for load converter has been depictedin Figure 3. The load converter can be controlled by the V - f control strategy, which regulates the voltage and the frequencyof AC load. It is clear that:

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) 1507

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des

ld v

des

lqv

des

0l v

ref

ld i ref

lqi

ref

0l i

ref

fd v ref

fqv ref

0 f v

ref

fav

ref

fbv

ref

fcv

Figure 3. Control strategy of load converter based on d -q-0 controller

a) The frequency () can be obtained by Phase Lock Loop(PLL) using desirable frequency (e.g., 50 Hz).

b) The load phase voltages (vla, vlb and vlc) can be detected andtransformed to the d -q-0 synchronously rotating referenceframe, using following equations:

=

lc

lb

la

0dq

l0

lq

ld

v

v

v

T

v

v

v

(7)

It is obvious that the load phase voltage should be adjustedto the balanced and sinusoidal voltage with constant amplitudeand frequency. Therefore the desired load voltage in the d -q-0reference frame has only the following values:

=

0

3

20.4

0

v

v

v

des

des

des

l0

lq

ld (8)

The reference load currents in the d -q-0 coordinate are:

( )( )( )

−

−

−

=

des

l0

des

lq

des

ld

ref

ref

ref

l0

lq

ld

l0

lq

ld

vv PI

vv PI

vv PI

i

i

i (9)

In Figure 3, the reference load currents are compared withthe measured output current of load converter, in the d -q-0coordinate ( i fd , i fq and i f0 ).

=

fc

fb

fa

0dq

f0

fq

fd

i

i

i

T

i

i

i (10)

The output signals of the PI controller can be expressed by theequation (11).

( )( )( )

−

+

+

=

0

i L

i L

i-i PI

i-i PI

i-i PI

v

v

v

i

i

i

fd f

fq f

f0

ref

fq

ref

fd

ref

l0

lq

ld

ref

ref

ref

l0

lq

ld

f0

fq

fd

ω

ω (11)

The reference output voltages for the load converter aretransformed to the a-b-c coordinate by using inversesynchronously rotating reference frame, i.e.:

=

ref

ref

ref

abc

ref

ref

ref

f0

fq

fd

fc

fb

fa

v

v

v

T

v

v

v (12)

where,

( ) ( )( ) ( )

( ) ( )

°+−°+

°−−°−

−

=

1120t sin120t cos

1120t sin120t cos

1t sint cos

T abc

ω ω

ω ω

ω ω

Then, the available voltages in the a-b-c coordinate arecompared with the triangular wave provided by PWM voltagecontrol module. Therefore, the output provides a suitableswitching pattern for the load converter.

VI. PROPOSED CONTROL STRATEGY

The objective of proposed control strategy for the loadconverter is providing high power quality, reliability andefficiency. In Figure 1, the output voltage of the load convertershould be balanced sinusoidal voltages:

( )

( )

( )

°+=

°=

=

120t sinV v

120-t sinV v

t sinV v

m fc

m fb

m fa

ω

ω

ω

(13)

where V m is the peak value of the output voltages. These balanced sinusoidal voltages are reference voltage. Theunbalanced AC load results in unbalanced current. Theunbalanced output currents of load converter can be expressed by

( )

( )( )

−°+

−°=

fccm

fbbm

faam

fc

fb

fa

120t sin I 120-t sin I

-t sin I

ii

i

θ ω

θ ω

θ ω

(14)

where I am, I bm, I cm, are the a-phase, b-phase, and c-phase peakvalue of the output currents, respectively. According to thesymmetrical-component transformation for the three-phase rootmean square (rms) currents, the three-phase instantaneousunbalanced output currents of load converter can be expressed by symmetrical components of the fundamental positivesequence, negative sequence and zero sequence.

fk0 fkn fkp fk iiii ++= , K k ∈ (15)

In (15), K = {a, b, c}. p, n, and 0 stand for positive-, negative-,

and zero-sequence components, respectively. Since thecapacitor and inductor don’t consume real power and the real power consumed by the load over one period of time T must besupplied by the source, (16)–(18) must hold

l dc p p = (16)

dcdcdc I V p = (17)

1508 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

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∈

= T

0 K k

fk fk l dt iv

T

1 p , K k ∈ (18)

Substituting (13) and (15) into (18) yields the sum of the powerterms at the three sequential components, as given in (19)

0

l l l l p p p p ++=

−+ (19)

where

( ) ( ) ( ) ( ) ( ) ( ) °+°++°°+=+

T

0 cmmbmmamml 120t sin I 120t sinV 120-t sin I 120-t sinV t sin I t sinV

T

1 p ω ω ω ω ω ω

( ) ( )

°−−

++= 120 sin I I

2T

1

2

I I I V

cmbm

cmbmam

m

(20)

and

0 p p 0

l l ==

− (21)

Each power term in (21) is determined based on the orthogonaltheorem for a periodic sinusoidal function. Then, (18) becomes

( ) ( )

°−−

++==

+ 120 sin I I 2T

1

2

I I I V p p

cmbm

cmbmam

ml l

(22)

By (16), (17) and (22), the desired output voltage magnitude ofload converter is determined as

( ) ( )°−−++

=

120 sin I I 2T

1

2

I I I

I V V

cmbm

cmbmam

dcdc

m

(23)

The frequency () can be obtained by Phase Lock Loop(PLL). Substitution (23) into (13), the reference output voltagesof load converter can be determined. The proposed controlstrategy scheme of load converter is shown in Figure 4. Thereference voltages in the a-b-c coordinate are compared withthe triangular wave provided by PWM voltage control module.Therefore, the output provides a suitable switching pattern forthe load converter.

Figure 4. The proposed control strategy of load converter

VII. SIMULATION R ESULTS

The system shown in Figure 1 has been modeled andsimulated by MATLAB software in order to analyse and

compare the performance of the load converter with the twocontrol strategies.

In this simulation, the DC distribution supplies theunbalanced resistive-inductive load by star connection. Thesystem parameters chosen for the simulation of Figure 1 arelisted in Table 1, which is loaded with 50 kW. The renewableenergy units generate 55 kW. The batteries bank, which

ensures the power balance of the system, has a rated capacity of285Ah.

Table 1 Simulation parameters

Parameters Values

Rated output load voltage 0230V la

∠= V

Rated output frequency f = 50 Hz

Rated DC bus voltage V dc = 750 V

Filter component L f = 3 mH, R f =0.1

AC Loads

Rla + jX la = 2.11 + j0.432

Rlb + jX lb = 2.65 + j0.812

Rlc + jX lc = 1.75 + j3.9

The simulation results in the case of load converter withconventional d -q-0 controllers were shown in Figures 5 and 6.The unbalanced load phase currents and the neutral currentwere shown in Figure 5. It was found that the load phasecurrents are not balanced due to the unbalanced AC load. Theload phase voltages were shown in Figure 6. It can be seenfrom Figure 6 that the balanced voltages are not provided for

the AC load while the load phase currents are not balanced.

Figure 5. Unbalanced load currents

Figure 6. Unbalanced load phase voltages

The simulation results for the load converter with the proposed control strategy were shown in Figures 7 and 8. Theload phase currents and the neutral current were shown inFigure 7. The load phase voltages were shown in Figure 8. Itwas found from Figures 7 and 8 that the load phase currents arenot balanced due to the unbalanced AC load, but the balancedvoltages are provided for the unbalanced AC load while theload phase currents are not balanced.

Figure 7. Load current with the proposed controller


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Figure 8. Balanced load voltage with the proposed controller

VIII. EXPERIMENTAL R ESULTS

For further verifying the effectivity of the proposedcontroller, based on Figure 4, the presented novel control

strategy for load converter has been implemented on alaboratory testing system. The system parameters chosen forthe experiment of Figure 1 are same as those used forsimulation in previous section.

The experimental results in the case of load converter withconventional d -q-0 controller were shown in Figures 9 and 10.The unbalanced load phase currents and the neutral currentwere shown in Figure 9. The load phase voltages were shownin Figure 10.

Figure 9. Unbalanced load currents

Figure 10. Unbalanced load phase voltages

The experimental results for the load converter with the proposed control strategy were shown in Figures 11 and 12.The load phase currents and the neutral current were shown inFigure 11. The load phase voltages were shown in Figure 12.

Figure 11. Load current with the proposed controller

Figure 12. Balanced load voltage with the proposed controller

The experimental results confirm efficacy of the proposedcontroller for load converter while the AC load is not balanced.From these experimental results, it can be seen that theconventional d -q-0 controller can not provide balancedvoltages for the AC load while the load phase currents are not balanced. But the proposed controller can provide balancedvoltages for the unbalanced AC load while the load phasecurrents are not balanced.

IX. CONCLUSION

In this paper, the control of the load converter underunbalanced loading conditions for renewable energy resourcessystem has been investigated, while the load converter model is presented and two different control strategies are compared.The first one uses the conventional d -q-0 frame rotatingcontroller to regulate the voltages and currents. The performances of this control strategy are insufficient. As aresult, in this paper the novel control strategy has beendeveloped. This strategy is based on the power conservationtheory. This novel control strategy is implemented in the a-b-ccoordinate, so reference-frame transformation from a-b-ccoordinate to d -q-0 rotating coordinate and inversetransformation from d -q-0 rotating coordinate to a-b-ccoordinate are not required which decreases the controlleroperation time comparing with conventional d -q-0 controller.The two control strategies have been applied to the referencevoltages generation of the load converter. The novel controlstrategy makes it possible to eliminate the disturbance of theoutput voltage caused by the unbalanced AC load. Simulationand experimental results show the effectiveness of the proposedcontrol strategy versus the conventional control strategy.

R EFERENCES

[1] C. A. Busada, H. G. Chiacchiarini and J. C. BaldaY,“ Synthesis ofSinusoidal Waveform References Synchronized With Periodic Signals,”

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[4] S. A. Daniel and N. A. Gounden, “A novel hybrid isolated generatingsystem based on PV fed inverter-assisted wind-driven inductiongenerators,” IEEE Trans. Energy Conversion, vol. 19, no. 2, pp. 416-422, Jun. 2004.

[5] M. A. Nejad, S. Pierfederici, J. P. Martin and F. M. TabarS, “Study of anHybrid Current Controller Suitable for DC–DC or DC–ACApplications,” IEEE Trans. Energy Conversion, vol. 22, no. 6, pp. 2176-2186, Nov. 2007.

[6] Y. Xiao, H. N. Shah, R. Natarajan, E. J. Rymaszewski, T. P. Chow andR. J. GutmannM, “Integrated flip-chip flex-circuit packaging for powerelectronics applications,” IEEE Trans. Energy Conversion, vol. 19, no.

2, pp. 515-522, Mar. 2004.[7] C. M. Wang, “A novel single-stage full-bridge buck-boost inverter,”

IEEE Trans. Energy Conversion, vol. 19, no. 1, pp. 515-522, Jan. 2004.

[8] G.S. Thand, “Modeling, control and stability analysis of a PEBB basedDC DPS,” IEEE Trans. Power Delivery, vol. 14, no. 2, pp. 497-505,Apr. 1999.

[9] R. Zhang, “High Performance Power Converter System for Nonlinearand Unbalanced Load/Source,” PhD thesis, Electrical and ComputerEngineering, Blacksburg, Virginia, USA, 1998.

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[10] M. Saisho, T. Ise and K. Tsuji, “Configuration of DC loop type qualitycontrol center,” in Proceedings of the Power Conversion Conference,Osaka, Japan, pp. 434-439, 2002.

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BIOGRAPHIES

Shaoru Zhang received her B.S. degree in physics from Hebei Normal University, China, in1995, her M.E. degree in control theory andcontrol engineering from Hebei University ofTechnology, China, in 2005, and her Ph. D.degree in power electronics and drives fromTianjin University, China, in 2008. She studied asan exchange student in the School of Electricaland Electronic Engineering, NanyangTechnological University, 50 Nanyang Avenue,

Singapore. She is with Hebei Normal University,Shijiazhuang 050016, China.

She is with the Hebei Normal University; Shijiazhuang, China as anassociate professor.

Dr. Fang Lin Luo (IEEE M’84 – SM’95)received his Bachelor Sc. Degree, First Classwith Honours in Radio-Electronic Physicsfrom the Sichuan University, Chengdu,Sichuan, China and his Ph. D. Degree inElectrical Engineering and Computer Science(EE & CS) from Cambridge University,England, UK in 1986. He is with the School ofElectrical and Electronic Engineering, Nanyang Technological University (NTU), Nanyang Avenue, Singapore 639798, and alsowith the AnHui University of Technology,

AnHui 243002, China.

Dr. Luo was with the Chinese Automation Research Institute ofMetallurgy (CARIM), Beijing, China as a Senior Engineer after his graduationfrom Sichuan University. He was with the Entreprises Saunier Duval, Paris,France as a project engineer in 1981 - 1982. He was with Hocking NDT Ltd,Allen-Bradley IAP Ltd. and Simplatroll Ltd. in England as a Senior Engineerafter he received his Ph. D. Degree from Cambridge University.

He is a Senior Member of IEEE. He has published 8 teaching textbooksand 238 technical papers in IEEE-Transactions, IEE-Proceedings and otherinternational journals, and various International Conferences. His presentresearch interest is in the Digital Power Electronics and DC & AC motorDrives with Computerized Artificial Intelligent control (AIC) and DigitalSignal Processing (DSP), and DC/AC Inverters, AC/DC rectifiers, AC/AC &

DC/DC Converters.

Dr. Luo was the Chief Editor of the International journal <Power SupplyTechnologies and Applications> in 1998-2003. He is the International Editor ofthe International journal <Advanced Technology of Electrical Engineering andEnergy>. He is currently the Associate Editor of the IEEE Transactions on bothPower Electronics and Industrial Electronics. Dr. Luo was the GeneralChairman of the IEEE conference ICIEA’2006, 24-26 May 2006 in Singapore,and is the General Chairman of the ICIEA’2008, 3-5 June 2008 in Singapore.


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06360962