Active and reactive power control schemes for distributedgeneration systems under voltage dipsCitation for published version (APA):Wang, F., Duarte, J. L., & Hendrix, M. A. M. (2009). Active and reactive power control schemes for distributedgeneration systems under voltage dips. In Proceedings IEEE Energy Conversion Congress and Exposition(ECCE 2009), 20-24 September 2009, San Jose, California (pp. 3564-3571). Institute of Electrical andElectronics Engineers. https://doi.org/10.1109/ECCE.2009.5316564

DOI:10.1109/ECCE.2009.5316564

Document status and date:Published: 01/01/2009

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Active and Reactive Power Control Schemes forDistributed Generation Systems Under Voltage Dips

Fei Wang, Jorge L. Duarte and Marcel A. M. HendrixDepartment of Electrical EngineeringEindhoven University of Technology

5600 MB Eindhoven, The NetherlandsEmail: f.wang@tue.nl

Abstract—During voltage dips continuous power deliveryfrom distributed generation systems to the grid is desirablefor the purpose of grid support. In order to facilitate thecontrol of distributed generation systems adapted to the ex-pected change of grid requirements, generalized power controlschemes based on symmetric-sequence components are proposedin this paper for inverter-based distributed generation, aiming atmanipulating the delivered instantaneous power under voltagedips. It is shown that active power and reactive power canbe independently controlled with two individually adaptableparameters. By changing these parameters, the relative ampli-tudes of oscillating power can be smoothly regulated, as wellas the peak values of three-phase grid currents. As a result,the power control of grid-side inverters becomes quite flexible.Furthermore, two strategies for simultaneous active and reactivepower control are proposed that preserves adaptive controlla-bility. Finally, the proposed schemes are verified experimentally.

I. INTRODUCTION

Voltage dips, usually caused by remote grid faults in thepower system, are short-duration decreases in rms voltage.Most voltage dips are due to unbalanced faults, while bal-anced voltage dips are relatively rare in practice [1] [2].Conventionally, a distributed generation (DG) system wouldbe required to disconnect from the grid when voltage dipsand to reconnect to the grid when faults are cleared. However,this requirement is changing. With the increasing applicationof renewable energy sources, more and more DG systemsactively deliver electricity into the grid. In particular, windpower generation becomes an important electricity source inmany countries. Consequently, in order to maintain activepower delivery and reactive power support to the grid, gridcodes now require wind energy systems to ride throughvoltage dips without interruption [3] [4]. For the futurescenario of a grid with significant DG penetration, it isnecessary to investigate the ride-through control of windturbine systems and other DG systems as well. Disregardingvarious upstream distributed sources and their controls, thecontrol of DG inverters will be focused on in this paper.

Concerning the control of DG inverters under voltagedips, especially unbalanced situations, two aspects shouldbe noticed. Firstly, fast system dynamics and good referencetracking are necessary. Controllers must be able to deal with

all the symmetric-sequence components and to have fastfeedback signals for closed-loop control. Secondly, in case ofunbalanced voltage dips, the generation of reference currentsis important. Because this paper focuses on the second aspect,the control structure of such inverters will be presented in thepart of experimental verification.

Under unbalanced voltage dips, current reference gener-ation is constrained by trade-offs. Considering the power-electronics converter constraints, a constant dc-link voltage isdesirable [5] and [6]. However, a constant dc bus is achievedat the cost of unbalanced grid currents, and this results ina decrease of maximum deliverable power. In [7], a powerreducing scheme is used to confine the current during a gridfault. On the other hand, the effects of the grid currents on thepower system side should also be taken into account whenassigning reference currents for DG inverters. As presentedin [8][9], several specific strategies are possible in orderto get different power quality levels at the grid connectionpoint in terms of instantaneous power oscillation and currentdistortion. One of the methods in [8], which is based oninstantaneous power theory [10], obtains zero instantaneouspower oscillation but generates distorted grid currents dueto asymmetry of grid voltages. Other methods in [8] lead tosinusoidal output currents. These strategies show flexible con-trol possibilities of DG systems under grid faults. However,they only cope with specific cases. Therefore, starting fromthe ideas in [8], a generalized strategy on reference currentgeneration is carried out in the following.

This paper proposes generalized and independent activeand reactive power control strategies based on symmetric-sequence components and shows explicitly the contributionsof symmetrical sequences to instantaneous power under un-balanced voltage dips. The proposed strategy enables DGinverters to be optimally designed. Furthermore, two strate-gies for simultaneous active and reactive power control areproposed that preserves the adaptive controllability.

II. INSTANTANEOUS POWER CALCULATION

To investigate power control strategy, the instantaneouspower theory [10] [11] is revisited in this section. Then in-stantaneous power calculation based on symmetric sequences

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is developed, and the notation for the reference current designin the next sections is defined.

A. Instantaneous Power Theory

For a three-phase DG system, instantaneous active powerand reactive power at the grid connection point are given by,respectively,

p = v · i = vaia + vbib + vcic, (1)

q = v⊥ · i = 1√3[(va − vb)ic + (vb − vc)ia + (vc − va)ib],

with v⊥ = 1√3

⎡⎣ 0 1 −1

−1 0 11 −1 0

⎤⎦v,

(2)where v =

[va vb vc

]T, i =

[ia ib ic

]T, bold

symbols represent vectors, and the operator “·” denotes thedot product of vectors. Note that the subscript “⊥” is usedto represent a vector derived from the matrix transformationin (2), although vectors v⊥ and v are orthogonal only whenthe three-phase components in vector v are balanced.

B. Symmetric-sequence Based Instantaneous Power

Symmetric-sequence transformation is a proven way todecompose unbalanced multi-phase quantities [12]. Conse-quently, instantaneous quantities for unbalanced a-b-c volt-ages are represented by

v = v+ + v− + v0, (3)

where v+,−,0 =[

v+,−,0a v+,−,0

b v+,−,0c

]T, and sub-

scripts ”+”, ”-”, and ”0” denote positive, negative, and zerosequences, respectively.

Similarly, current quantities can also be represented interms of symmetric sequences, i.e.

i = i+ + i− + i0, (4)

where i+,−,0 =[

i+,−,0a i+,−,0

b i+,−,0c

]T. As a result,

the calculation of instantaneous power in (1) and (2) can berewritten as

p = v · i = (v+ + v− + v0) · (i+ + i− + i0), (5)

q = v⊥ · i = (v+⊥ + v−

⊥ + v0⊥) · (i+ + i− + i0). (6)

With respect to the definitions of the symmetric-sequencevector in (3), corresponding orthogonal vectors in (6) canbe derived by using the matrix transformation in (2). Notethat v+

⊥ lags v+ by 900, v−⊥ leads v− by 900, and v0

⊥ isalways equal to zero. Because the dot products between i0

and positive-sequence or negative-sequence voltage vectorsare also always zero (due to symmetry of the components inv+ and v−), equation (5) and (6) can be simplified by

p = v · i = (v+ + v−) · (i+ + i−) + v0 · i0, (7)

q = v⊥ · i = (v+⊥ + v−

⊥) · (i+ + i−). (8)

v�

iq�

i p�

i�

v�

iq�

i p�

i�

v�

�

v�

�

Fig. 1. Decomposition of currents for independent PQ control.

Because the calculation of instantaneous power and currentreferences is carried out in terms of vectors, it can also beused in other reference frames, simply by substituting thevectors in the a-b-c frames with vectors derived in otherframes, for example, the stationary α-β-γ reference frame.

In next sections, current control based only on positive-sequence and negative-sequence components is investigated.Because zero-sequence voltages of unbalanced voltage dipsdo not exist in three-wire systems, nor can they propagateto the secondary side of star-ungrounded or delta connectedtransformers in four-wire systems, most case-studies onlyconsider positive and negative sequences. Even for unbal-anced systems with zero-sequence voltage, four-leg invertertopologies can eliminate zero-sequence current with appro-priate control. Simplifying assumptions we will use:

- Only positive-sequence and negative-sequence currentsare present;

- Only fundamental voltages exist, in practice they can beextracted out;

- The amplitude of the positive-sequence voltage is higherthan the negative sequence.

III. STRATEGIES FOR INDEPENDENT P&Q CONTROL

In order to separately analyze the contribution of currentsto independent active and reactive power control, sequencecurrents i+,− can be decoupled into two orthogonal quanti-ties, i.e. i+,−

p and i+,−q , as depicted in Fig. 1. The subscript

“p” represents active power related quantities, and “q” reac-tive power related quantities.

A. Reactive Power Control

For reactive power control, only i+q and i−q are present,which are defined in phase with v+

⊥ and v−⊥, respectively, in

order to generate reactive power only. Rewriting (7) and (8)in terms of i+q and i−q , we obtain

p = v+ · i−q + v− · i+q︸ ︷︷ ︸p̃2ω

, (9)

q = v+⊥ · i+q︸ ︷︷ ︸Q+

+v−⊥ · i−q︸ ︷︷ ︸Q−

+v−⊥ · i+q + v+

⊥ · i−q︸ ︷︷ ︸q̃2ω

, (10)

where Q+ and Q− denote the constant reactive powerintroduced by positive and negative sequences, respectively,

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p̃2ω is oscillating active power, and q̃2ω oscillating reactivepower. It can be found that the two terms of p̃2ω are in-phasequantities oscillating at twice the fundamental frequency. Asimilar property can be found for the two terms of q̃2ω .

Because oscillating active power can reflect a variation onthe DC-link voltage, and high DC voltage variation may causeover-voltage problems, output distortion, or even controlinstability, it is desirable to eliminate p̃2ω. On the other hand,the oscillating reactive power q̃2ω also causes power lossesand operating current rise, and therefore it is advantageous tomitigate q̃2ω as well. A trade-off between p̃2ω and q̃2ω is notstraightforward and depends on practical requirements. In thefollowing, strategies to achieve controllable oscillating activeand reactive power are derived from two considerations.

1) Controllable oscillating reactive power:For given reactive power Q, the first two terms of (10) are

deigned to meet

Q = v+⊥ · i+q + v−

⊥ · i−q . (11)

Since the two terms of q̃2ω in (10) are in-phase quantitiesthat add to each other, it is expected that these two terms cancompensate each other. By setting intentionally

v+⊥ · i−q = −kqv−

⊥ · i+q , 0 ≤ kq ≤ 1, (12)

after some manipulations the negative-sequence current i−q isderived from (12) as

i−q =−kqv+

⊥ · i+q∥∥v+⊥

∥∥2 v−⊥. (13)

where∥∥v+

⊥∥∥2

= ‖v+‖2 = v+ · v+, operator “|| · ||” meansthe norm of a vector.

Substituting (13) into (11), and using∥∥v+,−

⊥∥∥2

=‖v+,−‖2, we obtain

Q∥∥v+

∥∥2 = (∥∥v+

∥∥2 − kq

∥∥v−∥∥2)(v+⊥ · i+q

). (14)

Then, based on (13) and (14), currents i+q and i−q can becalculated as

i+q =Q

‖v+‖2 − kq ‖v−‖2 v+⊥, (15)

i−q =−kqQ

‖v+‖2 − kq ‖v−‖2 v−⊥. (16)

Finally, the total current reference is the sum of i+q and i−q ,that is

i∗q =Q

‖v+‖2 − kq ‖v−‖2 (v+⊥ − kqv−

⊥), 0 ≤ kq ≤ 1. (17)

2) Controllable oscillating active power:Instead of compensating the oscillating reactive power in

(10), we can similarly control the oscillating active power in(9). For this purpose negative-sequence currents are imposedto meet

v+ · i−q = −kqv− · i+q , 0 ≤ kq ≤ 1. (18)

By considering equation v+ · i− = v+⊥ · i−⊥ (because v+⊥

lags v+ by 900 and i−⊥ leads i− by 900), the left side of (18)can be rewritten as

v+ · i−q = v+⊥ · i−q⊥ = −kqv− · i+q , (19)

where i−q⊥ denotes the orthogonal vector of i−q according to(2). Then, it follows that

i−q⊥ =kqv+

⊥ · i+q‖v+‖2 v−. (20)

Hence the negative-sequence current i−q follows directlyfrom (20) as

i−q =−kqv+

⊥ · i+q‖v+‖2 v−

⊥. (21)

Solving (21) and (11), the positive-sequence current andnegative-sequence current are derived as

i+q =Q

‖v+‖2 + kq ‖v−‖2 v+⊥, (22)

i−q =kqQ

‖v+‖2 + kq ‖v−‖2 v−⊥. (23)

Again, the total current reference is the sum of i+q and i−q ,that is,

i∗q =Q

‖v+‖2 + kq ‖v−‖2 (v+⊥ + kqv−

⊥), 0 ≤ kq ≤ 1. (24)

3) Merging strategies 1) and 2):Simple analysis reveals that (17) and (24) can be put

together as

i∗q =Q

‖v+‖2 + kq ‖v−‖2 (v+⊥ + kqv−

⊥), −1 ≤ kq ≤ 1.

(25)Further, by substituting (25) into (9) and (10), it follows that

p =Q(1 − kq)

(v+⊥ · v−)

‖v+‖2 + kq ‖v−‖2 , (26)

q = Q +Q(1 + kq)

(v+⊥ · v−

⊥)

‖v+‖2 + kq ‖v−‖2 . (27)

It can be seen that the variant terms of (26) and (27), i.e.oscillating active power and reactive power, are controlledby the coefficient kq. These two parts of oscillating powerare orthogonal and equal in maximum amplitude. Simula-tion results are obtained in Fig. 2 by sweeping parameterkq. It is illustrated that either oscillating active power or

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(a)

(b)

(c)

(d)

Vab

c (v

)Ia

bc (

A)

p (k

W),

q (

Var

)kq

p

q

Fig. 2. Simulation results of the proposed reactive power control with Q = 10kVar, P = 0, where voltages of phase A and B dip to 70% at t=0.255s, (a)phase voltages, (b) injected currents, (c) instantaneous p, q, and (d) adjustable coefficient kq sweeping from -1 to 1.

oscillating reactive power can be controlled and even canbe eliminated at the two extremes of the kp curve. Thiscontrollable characteristic allows to enhance system controlflexibility and facilitates system optimization. It is pointed outthat the strategies proposed in [9] namely positive-negative-sequence compensation (PNSC), average active-reactive con-trol (AARC), and balanced positive-sequence (BPS) areequivalent to the results of the proposed strategy when kq

equals -1, 1, and 0, respectively.

B. Active Power Control

For given power P , the current reference for active powercontrol can be derived similarly, as calculated by

i∗p =P

‖v+‖2 + kp ‖v−‖2 (v++kpv−), −1 ≤ kp ≤ 1, (28)

where kp is the adjustable coefficient for active power control.Detailed derivation of (28) is presented in [13], as well as theapplicability for optimization based on this strategy.

IV. STRATEGIES FOR COMBINED P&Q CONTROL

As already mentioned, some grid codes also require DGsystems to contribute with reactive power [3]. For example,with respect to the amplitude drop of voltages, DG systemshaving agreements with grid operators are expected to deliverboth active power and reactive power during grid faults.Hence the reference currents for this case, named i∗pq , canbe derived by adding (25) and (28), as expressed by

i∗pq = i∗p + i∗q =P

‖v+‖2 + kp ‖v−‖2 (v+ + kpv−)

+Q

‖v+‖2 + kq ‖v−‖2 (v+⊥ + kqv−⊥ ), (29)

with −1 ≤ kp ≤ 1,−1 ≤ kq ≤ 1.It can be seen that there are infinite combinations for (29)

with independent coefficients kp and kq . This also implicatesthat the linear controllability benefiting from previous inde-pendent control strategies does not really exist. In order topreserve the controllability, two joint strategies are proposedto simplify (29) by linking the two coefficients.

A. Joint Strategy with Same-Sign Coefficients

By setting kp = kq = kpq in (29), reference currentcalculations are simplified and rewritten as

i∗pq =S

‖v+‖2 + kpq ‖v−‖2 R(ϕ)(v+ + kpqv−), (30)

where S is the apparent power with P = S cosϕ, Q =S sin ϕ, and ϕ the power factor angle. Since the α-β referenceframe is used in the experiments, it can be derived that

R(ϕ) =[

cosϕ sin ϕ− sinϕ cosϕ

]. (31)

Note that R(ϕ) will be different in the a-b-c reference frame.On the basis of (30), the resulting currents and oscillating

powers can now be predicted and adaptively adjusted. To helpunderstanding, a vector diagram representing voltage andcurrent trajectories and the relationship between oscillatingpower are plotted with kpq as an adjustable parameter underan unbalanced voltage dip, where ϕ = 300.

As shown in Fig. 3(a), when kpq changes from 1 to -1,the length of current vectors changes and reaches a minimumvalue at kpq = 0. In Fig. 3(b), the amplitudes of the oscillatingpowers also vary with the change of kpq , which can bepredicted by substituting (30) into (7) and (8). Note that whenϕ is not 00 or 900, i.e. active power and reactive power are

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α

β

ω

Pre-fault Current

Pre-faultvoltage

Unbalanced Voltage dips

1pqk = −

0pqk =0.5pqk =

0.5pqk = −1pqk =

0

ω

Currents trajectories

2p ω

2q ω

0

1pqk = −

1pqk =

0pqk =0.4pqk =

0.4pqk = −

pk

qk

-1 1

1

-1

(a) (b) (c)

Fig. 3. Graphic representation of (a) grid voltage and current trajectories before and after unbalanced voltage dips in the stationary frame, and (b) relationshipbetween oscillating active power p̃2ω and reactive power q̃2ω with kpq as an adjustable parameter under the joint strategy of (c), where kp = kq = kpq .

α

β

ω

1pqk = −

0pqk =

0.5pqk =

0.5pqk = −

1pqk =

0

ω

1pqk = −

1pqk =

0pqk =

0

0.4pqk = −

0.4pqk =

2p ω%

2q ω%

pk

qk

-1 1

1

-1

(a) (b) (c)

Fig. 4. Graphic representation of (a) grid voltage and current trajectories before and after unbalanced voltage dips in the stationary frame, and (b) relationshipbetween oscillating active power p̃2ω and reactive power q̃2ω with kpq as an adjustable parameter under the joint strategy of (c), where kp = −kq = kpq .

not zero, p̃2ω or q̃2ω cannot be eliminated since either activepower or reactive power delivery will introduce oscillatingpower at the two extremes of kpq .

B. Joint Strategy with Opposing-Sign Coefficients

By setting kp = −kq = kpq in (29), the reference currentis represented by

i∗pq =S cosϕ

‖v+‖2 + kpq ‖v−‖2 (v+ + kpqv−)

+S sin ϕ

‖v+‖2 − kpq ‖v−‖2 (v+⊥ − kpqv−⊥ ). (32)

Illustrative plots are drawn in Fig. 4. It can be seenfrom (32) that this joint strategy actually requiring twice thecomputation time of joint strategy A. Fortunately, zero p̃2ω

or q̃2ω can be achieved at the two extremes of kpq , as shownin Fig. 4 (b). Similar to joint strategy A, when shifting kpq

towards zero the length of current vectors decreases and thecurrent trajectory tends to be a circle.

Therefore it can be summarized that the simple adaptivecontrollability of independent power control is preserved inthe two joint strategies above. This enables DG systems to

be optimized under unbalanced voltage dips, e.g. the outputpower maximization, and the limitation of oscillating activepower / reactive power.

V. EXPERIMENTAL RESULTS

To verify the proposed strategy, experiments are carriedout on a laboratory experimental system constructed from afour-leg inverter that is connected to the grid through LCLfilters, as shown in Fig. 5. The system parameters are listed inTable I. By using a four-leg inverter, zero-sequence currentscan be eliminated when the grid has zero-sequence voltages.For the cases where the zero-sequence voltage of unbalancedgrid dips is isolated by transformers, a three-leg inverter canbe applied. A 15kVA three-phase programmable AC powersource (SPITZENBERGER+ SPIES DM 15000/PAS) is usedto emulate the unbalanced utility grid, and the distributedsource is implemented by a dc power supply. The controlleris designed on a dSPACE DS1104 setup by using Matlab /Simulink.

A. Control Realization

The proposed controller is realized with a double-loopcurrent controller, which consists of an outer control loop

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P+R P

P+R

P+R

abci

i� i�

Labci

i�

i�

i�

* *0

abc

���

abc

���

PoCgav

gbv

gcv

gaZ

av

ai

gbZ

gcZ

gnZ

bv

cv

bi

ci

g

La

aC

Lai

ab

cn

bC cC

Lb

Lc

Ln

Lbi

Lci Distributed

sources

Lsa

Lsb

Lsc

abcv

1v���

1v���

Sequence

Detection

Filter

power

control

strategies

P

P

P

abcv abc

���

abc

���SPWM

dcV

dcC

abc

���

v��

Fig. 5. Circuit diagram and control structure of experimental four-leg inverter system.

TABLE ISYSTEM PARAMETERS

Description Symbol ValueOutput filtering inductor Lsa,b,c 2mHOutput filtering capacitor Ca,b,c 5μFOutput filtering inductor La,b,c 2mHNeutral filtering inductor Ln 0.67mH

DC-link voltage Vdc 750VDC-link capacitors Cdc 4400uF / 900Vdc

Switching frequency fsw 16kHzSystem rated power Srat 15kVA

Tested apparent power S 2500VA

with proportional-resonant (PR) controllers for eliminatingthe steady-state error of the delivered currents, and an innerinductor current control loop with simple proportional gain toimprove stability. In addition, a feed-forward loop from thegrid voltages is used to improve system response to voltagedisturbances.

The control for both positive-sequence and negative-sequence components would be much too complicated andcomputation-time consuming when conventional PI controlwith coordinate transformation is used. Furthermore, thesequence detection of feedback currents can be left out.Therefore, it is preferred to choose a PR controller in thestationary frame. A quasi-proportional-resonant controllerwith high gain at the fundamental frequency is used

Gi(s) = Kp +2Krωbrs

s2 + 2ωbrs + ω21

, (33)

where Kp is the proportional gain, Kr is the resonant gain,ω1 denotes the fundamental radian frequency, and ωbr theequivalent bandwidth of the resonant controller. A detaileddesign for the PR controller has been presented in [14], it isnot duplicated here. Through optimizing, the parameters usedin the experiment are Kp=2, Kr=100, and ωbr=10 rad/s.

Since the whole controller is designed in the stationaryframe, the sequence detection of grid voltages is also realized

Time (s)

Vabc

(V)

0 0.02 0.04 0.06 0.08 0.1-400

-300

-200

-100

0

100

200

300

400

Fig. 6. Emulated grid voltages to be faulty at t=0.03s, where phases A andB dip to 70%.

based on a stationary frame filter cell in the α−β frame [15].The basic filter cell can be easily implemented using a multi-state-variable structure. Besides, a high performance outputcan still be achieved under distorted grid voltages.

Concerning the power factor angle ϕ, two values are testedin the experiment. Firstly, a slightly modified approach isused here to calculate the angle ϕ according to the grid codein [3]. Specifically, the DG system should inject at least 2%of the rated current for each percent of the fundamental-sequence voltage dip. Therefore the desired angle ϕ iscalculated by

ϕ = sin−1

(2|V + − VN |

VN

), (34)

where VN is nominal voltage amplitude, and V + the positive-sequence voltage amplitude. Furthermore, it is also requiredin [3] that a reactive power output of at least 100% of therated current is possible when necessary. Hence also ϕ = 900

is assigned directly to test a complete power change fromactive power to reactive power.

Note that dc-link voltage control is not added here. Usually,

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I abc

(A)

Time (s)

p(W

),q

(Var

)

p

q

0 0.02 0.04 0.06 0.08 0.1

0 0.02 0.04 0.06 0.08 0.1

0

1000

2000

3000

-10

0

10

(a)

I abc

(A)

Time (s)

p(W

),q

(Var

)

p

q

0 0.02 0.04 0.06 0.08 0.1

0 0.02 0.04 0.06 0.08 0.1

0

1000

2000

3000

-10

0

10

(b)

I abc

(A)

Time (s)

p(W

),q

(Var

)

p

q

0 0.02 0.04 0.06 0.08 0.1

0 0.02 0.04 0.06 0.08 0.1

0

1000

2000

3000

-10

0

10

(c)

Fig. 7. Experimental results of the joint strategy A with kpq set to (a) 1, (b) 0, and (c) -1, where the waveforms from the top down are injected currentsand instantaneous power when ϕ = 230.

I abc

(A)

Time (s)

p(W

),q

(Var

)

p

q

0 0.02 0.04 0.06 0.08 0.1

0 0.02 0.04 0.06 0.08 0.1

0

1000

2000

3000

-10

0

10

(a)

I abc

(A)

Time (s)

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),q

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q

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bc

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Fig. 8. Experimental results of the joint strategy A with kpq set to (a) 1, (b) 0, and (c) -1, where the waveforms from the top down are injected currentsand instantaneous power when ϕ = 900.

a dc-link voltage control loop is included in the controlstructure, for instance, in a rectifier system [6] or for awind turbine inverter [7]. The dc bus in the experimentalsystem is only controlled by the dc power supply with aquite low bandwidth to maintain a stable dc bus in an averagesense. Since the experiment intends to investigate the effectsof the proposed strategy when choosing different kpq, it isconvenient to leave out the dc voltage control in order toonly observe the performance of the proposed strategy.

B. Experimental Results

By shifting the controllable parameter kpq, the system istested under unbalanced voltage dips with the joint strategies.In order to capture the transient reaction of the system, threesituations are intentionally tested for comparison at the startmoment voltage dips.

As shown in Fig. 6, grid voltages are emulated to be faultyat t = 0.03s where phases A and B dip to 70%. Consequently,the power factor angle ϕ derived in the control is 230 and thecorresponding results of joint strategy A are obtained in Fig.7. It can be seen that the reactive power support starts withinhalf a cycle after voltage dips. As analyzed in Section IV, theinstantaneous active power and reactive power always have

oscillating power ripples, and the injected grid currents getbalanced only when kpq gets near to zero. In case of ϕ equals900, the joint strategy A turns out to be a reactive powercontrol strategy as expressed by (25). Therefore, comparingwith the simulation results in Fig. 2 at the point of kq = -1,0 and 1, it can be seen that the results in Fig. 8 show thesame effects on the regulation of oscillating power ripple andreference current.

Under the same test conditions, experimental results arealso measured for joint strategy B. As shown in Fig. 9, zerooscillating reactive power and active power are achieved atkpq = 1 and -1, respectively. When kpq = 0, the results ofjoint strategy B are same as the results of joint strategy A,since both joint strategies only depend on positive-sequencecomponents in this case. The results with ϕ = 900 are givenin Fig. 10. Comparing with the results in Fig. 8 of jointstrategies A, it is easily found that both joint strategies turnout to be the same but needing an opposing sign of kpq .

VI. CONCLUSION

This paper proposes generalized strategies for independentactive and reactive power control of distributed generationinverters operating under unbalanced voltage dips. Using

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I abc

(A)

Time (s)

p(W

),q

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p

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0 0.02 0.04 0.06 0.08 0.1

0 0.02 0.04 0.06 0.08 0.1

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I abc

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Time (s)

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Time (s)

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Fig. 9. Experimental results of the joint strategy B with kpq set to (a) 1, (b) 0, and (c) -1, where the waveforms from the top down are injected currentsand instantaneous power when ϕ = 230.

I abc

(A)

Time (s)

p(W

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0 0.02 0.04 0.06 0.08 0.1

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(c)

Fig. 10. Experimental results of the joint strategy B with kpq set to (a) 1, (b) 0, and (c) -1, where the waveforms from the top down are injected currentsand instantaneous power when ϕ = 900.

derived formulas and graphic representations, the contribu-tions of symmetric-sequence components to the instantaneouspower and the interactions between symmetric sequenceswere explained in detail. Furthermore, for simultaneouslycontrolling active and reactive power, two joint strategiesare proposed that preserves the adaptive controllability. Theflexible adaptivity of the proposed strategy allows it to copewith multiple constraints and to be optimized in practical ap-plications. The performance of the proposed control strategiesis verified by experiments.

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