Grid connected PV System with Load PowerCompensation Capability using Sliding Mode

Control

Gabriel A. Fogli, Pablo C. de S. Furtado, Pedro M. de Almeida, Pedro G. Barbosa and Janaına G. de OliveiraFederal University of Juiz de ForaElectrical Engineering Program

Juiz de Fora, MG, Brazil 36036-330Email: gabriel.fogli@engenharia.ufjf.br

Abstract—This paper presents the modelling and design stepsfor a grid connected Photovoltaic System using a single-stagethree-phase Voltage Sourced Converter. As the PV array is di-rectly connected to the DC bus, a Maximum Power Point Trackingalgorithm provides the reference voltage for an outer DC voltagecontrol loop. The interface converter is controlled using a directpower sliding mode control without any synchronization circuit.This is possible because the converter’s control is done in thestationary reference frame. Besides the active power injection, thissystem is able to compensate the reactive and harmonics powerconsumed by the loads. For the pattern switching, space vectormodulation is used to generate constant switching frequency.Simulation results are presented to validate the proposed systemduring the active power injection and load compensation.

I. INTRODUCTION

Recently, the use of renewable energy connected to electricgrid is experiencing dramatic growth [1]– [2]. Photovoltaicsystem is a typical representative of such sources and it is com-monly connected to the distribution network, thus becomingDistributed Generators (DG). These alternative sources areemerging to produce highly reliable and good quality electricalpower. Hence, DG are becoming part of strategic plans formost countries to address current challenges associated withenergy management [3].

The connection of DG is generally done by power elec-tronic converters, which process the generated power. Fur-thermore, static converters are important elements in energyprocessing systems, such as high-voltage DC (HVDC) trans-mission, static VAR compensator (SVC), universal power flowcontrol (UPFC), uninterruptible power supply (UPS), andindustrial process control with variable frequency drives forimproving productivity and quality of products [4].

Many advantages can be related to the use of such conver-ters, such as sinusoidal line current with controllable powerfactor, high-quality DC voltage with small filter capacitor,and the capability of independent active and reactive powercontrol with bidirectional power flow [5]. One of the mostused converters is the Voltage Sourced Converter (VSC) andit is regularly used to transfer power from DC system to ACsystem or make back-to-back connection to AC systems [2].

At present, a significant attention is paid to control of gridconnected VSCs. Several typical control methods are listedin [2]. In general, the classic VSC control strategies can be

divided as Voltage Oriented Control (VOC) and Virtual FluxOriented Control (FOC). A combination of methods and strate-gies results in diverse control concepts, such as: synchronousVOC with conventional PI controllers, stationary VOC withProportional Resonant controllers, synchronous VFOC with PIcontrollers, Direct Power Control (DPC), Virtual Flux DPC.

Controls based on synchronously rotating frame have thedrawbacks that the performance highly relies on the complete-ness of current decoupling, the accurate tuning of controllerparameters and the connected grid voltage conditions [6]. Instationary frame, is possible to eliminate instantaneous powererror without a synchronization circuit.

In order to compensate harmonic power, it is necessary acontrol structure able to follow sinusoidal signals. Therefore,conventional PI controllers can not track such references withzero steady-state error. A solution to solve this issue, is use theSliding Mode Control (SMC). Grid connected VSC is a Vari-able Structure System (VSS), consequently a natural candidate[2]. The dominant role in VSS theory is played by slidingmodes, and the core idea of designing VSS control algorithmsconsists of enforcing this type of motion in some manifoldsin system state spaces [7]. The SMC, based on the VSS, is aneffective and high-frequency switching control for nonlinearsystems with uncertainties [8] [9]. Its main features are: simpleimplementation, disturbance rejection, strong robustness andfast response [10]. On the other hand, the controlled state mayexhibit undesired chattering [6]– [11].

This paper presents the direct active and reactive powermanagement using the Sliding Mode Control applied to a solarenergy system connected to a secondary distribution network.An single-stage VSC is used as interface to connect to grid,and the SMC is used to regulate the active and reactive powerin grid. Besides, possibility to load power compensation isadded to the system proposed.

After the Introduction Section, this paper is organized asfollows: Section II presents the proposed system, Section IIIshows the modelling of DC link and the grid connected,Section IV validates the used control by the simulations andSection V highlights the main paper conclusions.

978-1-4673-7553-5/15/$31.00 ©2015 IEEE 751

PWM

SVM

abcαβ

PV Array DC Link VSC system AC system

MPPT

Control scheme

PCC

Power controller(Sliding Mode Control)

i lLoads

mαβ

VDC

Ug,αβ

VDC

+ _

abcαβ

p* q*

PPVp Instantaneous

power

abcαβ

PPV PDC

pq

IPV IDC

gi R L VPCC VsCeq

g,αβi

l,αβi

isVg

Voltage controller

VDC*

APF

g

g

g g

Figure 1. Proposed system.

II. SYSTEM DESCRIPTION

The proposed system to connect the photovoltaic system toAC grid is shown in Fig. 1. There are just one stage of powerprocessing.

Despite all advantages of solar energy systems, the effi-ciency of energy conversion is currently low and the initialacquisition cost is high. So, the use of Maximum Power PointTracking (MPPT) becomes necessary to extract the maximumavailable power [12]. This paper uses the Incremental Con-ductance (IC) that is based on the fact that the power slopeof the PV is null at maximum power point (MPP) ( dPdV = 0),positive in the left and negative in the right [12] – [13]. TheIC method needs to monitor both PV voltage and current andit is not necessary to calculate the PV power [12].

The output variable of MPPT algorithm is a referencesignal for the voltage controller. This regulator is the outer loopof the power controller scheme. The voltage controller providesthe active power reference. Besides, the load power calculate,through the voltage in the point of common coupling (PCC)and the current loads, provides the reactive power reference.The active power portion is the sum of the active power of thePV cells.

Then, the SMC is used to control the active and reactivepowers. A synchronization circuit is not required, becausecontrol scheme is based on stationary reference frame. Theswitching pattern is defined through Space Vector Modula-tion (SVM) technique, as this modulation provides constantswitching frequency. VSC output terminals are connectedto distribution network through a first-order filter based oninductors bank.

III. MODELING OF GRID-CONNECTED DC/ACCONVERTERS

A. Power Controller

The concept of space vector is used in VSC mathematicalmodelling. Figure 2 shows the simplified equivalent circuitwithout voltage harmonics and switching currents from the

semiconductor devices. In the αβ frame, the grid-connectedVSC model becomes

Ugαβ = −RIgαβ − LdIgαβdt

+ Vgαβ , (1)

where I, U and V are the space vectors of current, VSC outputvoltage and grid voltage, respectively.

Vgαβ

LRigαβ

Ugαβ

Figure 2. Equivalent circuit of the grid connected DC/AC converter in thestationary frame.

For balanced three-phase system, the instantaneous active(pg) and reactive (qg) power, in the stationary reference frame,can be defined as [14]

pg =3

2(ugαigα + ugβigβ)

qg =3

2(ugβigα − ugαigβ)

. (2)

Neglecting the harmonics and considering a balanced networkit is possible to write the derivatives of the instantaneouspowers pg and qg given in (2) by

dpgdt

= − 3

2L[(u2

gα + u2gβ)− (ugαvgα + ugβvgβ)]−

−RLpg − ω qg

dqgdt

= − 3

2L[−(ugβvgα − ugαvgβ)] + ω pg −

R

Lqg

, (3)

where ω represents the grid angular fundamental frequency.It is the main expression for designing the power controlscheme in this paper.

752

B. DPC using SMC

The dominant role in VSS theory is played by SMC, andthe main idea is based on the design of discontinuous controlsignal that drives system operation states toward manifolds instate space [8]. These manifolds are chosen in such a waythe control system will have the desired behaviour as statesconverge to them. In this paper, an SMC scheme based onDPC concept for regulating active and reactive powers of gridconnected DC/AC converter is applied.

The control objectives for DC/AC converters are to slidethe trajectories. For this purpose, the sliding surface is set as

S = [SP SQ]T . (4)

The switching surfaces are in the integrals forms to maintainthe enhanced transient response and minimize the steady-stateerror. [11].

SP = eP (t) +KP

∫ t

0

ep(τ)dτeP (0)

SQ = eQ(t) +KQ

∫ t

0

eQ(τ)dτeQ(0)

, (5)

where eP = p∗g − pg and eQ = q∗g − qg are the errors betweenthe references and the actual values of active and reactivepowers, respectively. The gains KP and KQ are positiveconstants that define the system convergence time.

When SP and SQ are null, it represents the precisetracking of converter active and reactive powers. Accordingto switching surfaces, when S = dS

dt = 0, gives

dePdt

= −KP eP (t)

deQdt

= −KQeQ(t)

. (6)

Power systems will converge asymptotically to the originwith time constants of 1

KPand 1

KQ, respectively. The motion

projections of the systems (2) and (3) on S subspace are

dSPdt

=dePdt

+KP eP (t) = −dpgdt

+KP (p∗g − pg)

dSQdt

=deQdt

+KQeQ(t) = −dqgdt

+KQ(q∗g − qg). (7)

Substituting (3) into (7) leads to

dS

dt= F + DVg, (8)

whereF = [FP Fq]

T Vg = [vgα vgβ ]TFP =

3

2L(u2gα + u2

gβ) +R

Lpg + ωqg +KP (p∗g − pg)

FQ =R

Lqg − ωqg +KQ(q∗g − qg)

(9)

D = − 3

2L

[ugα ugβ

ugβ −ugα

].

In SMC, a Lyapunov approach is used on the control lawthat will drive the state orbit. The quadratic Lyapunov functionis selected as

W = 0.5 STS ≥ 0, (10)

and the time derivative of W

dW

dt= ST

dS

dt= ST (F + DVg). (11)

The time derivative of W is definitely negative with S 6= 0.Therefore, the following control law is selected

Vg = −D−1

[FPFQ

]+

[KP1 sgn(SP )KQ1 sgn(SQ)

], (12)

where KP1 and KQ1 are the positive control gains andsgn(SP ) and sgn(SQ) are switch functions for active andreactive powers, respectively. The DPC strategy using SMCis depicted in Fig. 3. The active power reference is dependentof output signal voltage controller and the active power filter(APF). Reactive power reference depends on output signalof APF. The power controller generates voltage reference ofSVM.

abcαβ

VSC

GridVcc

RL

SVMvgβvgα**

Instantaneous Power (2)

Ug,αβg,αβi

Vg calculation based on (9)

and (12)

g g

p*q*

Ug,αβ

g,abci g,abcU

p q

Figure 3. Schematic diagram of the DPC using SMC.

C. DC Voltage Controller

The active power of PV cells (PPV ) can be consideredequal to the sum of the active power of capacitor terminals(PCeq ) and the VSC active power output (pg). Thus, therelation of active power on this system can be written as:

PPV =1

2Ceq

d(V 2DC)

dt+ pg. (13)

Note that (13) is not linear [15]. Thus, using the Laplacetransform and linearizing, it can be written:

753

MPPT ( )2. + _ -1 C(s) +

_VDC eV

APF

PVp**VDC

IDC

C(s)V P sC

|

eq

2 VDC2ΔΔ p

p

Figure 4. Voltage Controller.

(PPV +∆PPV ) =1

2Ceqs(V

2DC+∆V 2

DC)+(Pg+∆pg). (14)

Considering that the grid voltage does not fluctuate, thelinear relation to small disturbance in the quadratic value ofthe voltage over the DC bus is expressed as:

∆V 2DC

∆pg= − 2

sCeq. (15)

In Figure 4 is shown the voltage controller scheme. Thiscontroller is composed by outer loop compensator Cv(s) toregulate the DC voltage and by inner loop CP (s) to controlthe active and reactive powers. The PAPF is the active powerload to compensation.

Using a PI controller, the closed-loop transfer function canbe expressed for the quadratic value of DC voltage

∆V 2DC

∆V 2∗DC

=

2kp,vs

Ceq+

2ki,vCeq

s2 +2kp,vs

Ceq+

2ki,vCeq

. (16)

Comparing (16) with the canonical form

H(s) =2ξωns+ ω2

n

s2 + 2ξωns+ ω2n

, the gains of PI controller

can be determined as:

kp,v = Ceqξωn

ki,v =Ceqω

2n

2

(17)

where the parameter ξ is the damping ratio, ω is the undampednatural frequency and Ceq is the DC-bus capacitance.

D. Load Power Compensation

In [14] the concept of instantaneous power theory validfor steady and transient states is presented. There are norestrictions for voltage and current waveform to its application,and this theory can be applied for both three or four wiresystems. The application of this theory should employ theClarke transformation for voltage and current. In this referenceframe, zero-sequence components are separated. Also, notethat zero-sequence is always null in three-phase three-wiresystem.

Measuring load currents and PCC voltage, the active andreactive power consuming by the load can be divided as:

pload = pload + pload

qload = qload + qload(18)

where the superscript ’ ¯ ’ and ’ ˜ ’ represent average andoscillatory power components.

Active Power Filter must compensate the average imagi-nary power (qload), the real power oscillators (pload and qload).Figure 5 illustrates the power calculation procedure.

In this paper the active power reference (P ∗) is provided byPV cells and oscillatory load powers. Reactive power reference(Q∗) is the negative of load reactive power. The separationbetween average and oscillatory power is done by digital lowpass filter.

p∗ = PPV − pload

q∗ = qload + qload. (19)

Instantaneous power

ii

uu

l,αl,β

αβ

il,a

il,cil,b

a

cb

u

uu

abcαβ

abcαβ

p

q_

q ~q

load

load

load

load

LPF

LPF +_

~pload+_

Figure 5. Extraction of power reference for load compensation.

IV. SIMULATION RESULTS

This section presents simulation results of the proposedDPC strategy based on SMC for grid connected VSC inorder to validate the control scheme performance. Computersimulation has been done using PSIM Simulation Software toverify the results.

The characteristics of BPSX120 module are used for thePV array in this work. This PV module provides 120 Wof rated maximum power with 33.7 V . These characteristicscorrespond to test conditions of 1 kW/m2 irradiation and25C ambient temperature [16]. The PV array is composed oftwelve series-connected modules forming each string. A totalof ten strings are connected in parallel. This PV array providestheoretical 14.4 kW at MPP. Simulation parameters are listedin Table I.

Table I. SYSTEM PARAMETERS.Description Value

Line-to-line voltage of grid (rms) 220 VFrequency of voltage 60 HzInductance of the output filter 1.2 mHResistance of the output filter 0.33 ΩDC link voltage 250 VSwitching frequency 21 kHzSampling frequency 21 kHz

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PI voltage controller and SMC parameters are listed inTable II.

Table II. CONTROLLER PARAMETERS.Description Value

Damping ratio (ξ) 1Undamped natural frequency (ω) 188.5 rad/sProportional gain (kp,v) 0.88 W/VIntegral gain (ki,v) 83.5 W.s/VSMC positive gains (KP , KQ) 10000SMC control gains (KP1, KQ1) 15000

In order to validate the proposed system, active and reactivepowers references are changed during simulations. Activepower injection and load compensation features are tested bothseparately and simultaneously.

Thus, Fig. 6 (a) shows the system response for differentactive and reactive power references. Between 0.02 s and0.08 s, the VSC is only injecting active power from PV cells.In this period, power reference is approximately 13.3 kW .The overshoot in active power curve is consequence of the PIvoltage controller. At 0.08 s, the active power filter mode isactivated together with the injection mode. In addition to activepower injection, the VSC also compensates load reactive andoscillatory powers. At 0.14 s PV cells stop injecting and theVSC works as an APF. Figure 6 (b)-(c) present the trackingof references.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−5000

0

5000

10000

15000

20000

Act

ive

pow

er(W

) Rea

ctiv

e po

wer

(var

)

Time (s)

pg qg

(a)

0.06 0.07 0.08 0.09 0.1 0.11 0.12

1.2

1.4

1.6

1.8x 104

Act

ive

pow

er (W

)

Time (s)

pg p*

g

(b)

0.06 0.07 0.08 0.09 0.1 0.11 0.12−3000

−2000

−1000

0

1000

2000

3000

Rea

ctiv

e po

wer

(var

)

Time (s)

qg q*g

(c)

Figure 6. Power waveform: (a) Active (pg) and reactive (qg) provide byVSC. (b) Active power (pg) and active power reference (p∗g) (c) Reactivepower (qg) and reactive power reference (q∗g )

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2390

395

400

405

410

415

420

Vol

tage

(V)

Time (s)

VDC V*

DC

Figure 7. DC voltage and DC voltage reference signals.

Figure 7 shows the DC voltage response during the si-mulation. Because of the DC controller parameters there areovershoot of about 3 % and settling time of 45 ms. The DCvoltage reference is defined by the MPPT, but when the VSConly compensate the loads, the DC voltage is set to 404, 4 V .

Figure 8 (a)-(c) presents load, VSC and main current forone system phase. From 0.02 s to 0.08 s the VSC outputcurrent is highly sinusoidal. The total harmonic distortion ofthe grid current is smaller than 5 % as recommended by IEEEStd 929-2000. After 0.08 s, the total load and VSC currentsshould be considered for power quality analysis. The loadapparent power is about 1.48 kV A. Thus, when the VSC isworking like APF, grid current meet limits recommended byIEEE Std. 929-2000. After 0.14 s, it just compensates the load.In this operation mode, there is no available power from PVcells.

Figure 9 (a) presents the frequency spectrum of VSCcurrent between 0.02 s and 0.08 s, when there is just ac-tive power injection. While Fig. 9 (b) shows the frequencyspectrum of grid terminals during 0.14 s and 0.2 s. Notethat, in both cases the frequency spectrum is smaller thanrecommended limits for harmonic distortion.

V. CONCLUSION

This paper presented the DPC strategy using SMC for aVSC connected to grid. Design steps of voltage controller andDPC was detailed. The proposed system presented the capabi-lity of active power injection and the load power compensationwith satisfactory dynamics response under a sudden change ofactive and reactive power.

SMC was able to track adequately even oscillatory refe-rence signals. This characteristic is required in active powerfilters. Thus, SMC is a good choice for grid connected conver-ters applications. Space vector modulation allowed nonlinearcontrol implementation with constant pattern switching. Basedon results is possible to note that DPC using SMC was able totrack the references in different scenarios and to comply withthe recommended limits of power quality.

ACKNOWLEDGMENT

The authors would like to thank CAPES, CNPq andFAPEMIG for financial support.

755

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−100

−50

0

50

100C

urre

nt (A

)

Time (s)

(a)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−100

−50

0

50

100

Cur

rent

(A)

Time (s)

(b).

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2−100

−50

0

50

100

Cur

rent

(A)

Time (s)

(c)

Figure 8. Phase ”A” currents: (a) Load terminal.(b) Output VSC terminal.(C) Grid terminal.

5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

Cur

rent

(A)

Order(a)

5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

Cur

rent

(A)

Order(b)

Figure 9. Frequency spectrum: (a) VSC current during 0.02 s and 0.08 s(THD = 1.3 %).(b) Power electric system current during 0.14 s and 0.2 s(THD = 2.75 %).

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