Modeling and Control of a Cascaded NPC/H-Bridge Inverter with LCL Filter in PV- Grid Application

T. Wanjekeche *, D.V.Nicolae * * Department of Electrical Engineering

Tshwane University of Technology Pretoria, South Africa

Email: Wanjekeche@yahoo.com, nicolaedv@tut.ac.za

A.A.Jimoh Department of Electrical Engineering Tshwane University of Technology

Pretoria, South Africa Email: JimohAA@tut.ac.za

Abstract— The output voltage and current of renewable energy sources such as Photo- voltaic are not controlled. Consequently PV- Grid interface system is employed condition output voltage and current into the grid. This call for efficient and well designed control strategies to ensure reliability, stability and quality power output. This paper proposes nine- level cascaded NPC/H-bridge inverter as the PV- Grid interface. Cascaded NPC/H-Bridge inverter is modeled and a control law for realizing nine- level output with reduced harmonic content is developed. Modeling is easily achieved by considering the whole inverter as having four cascaded three level legs, two positive and two negative. Then a mathematical model is formulated for LCL filters assuming that the resistances associated with the inductances have negligible effect on the system steady state variables. Finally a control technique is developed for the whole system and its robustness tested by carrying out several simulations tests in MATLAB under different operating conditions.

Keywords- Cascaded NPC/H-Bridge; LCL filter; PWM inverter; PV – grid interface;

I. INTRODUCTION Grid connected PV systems are nowadays recognized for

their clean power generation, the main objective of grid connected PV system is to maximize power generation and injection to the grid but at the same time ensuring reliability, stability and quality power output. This calls for innovative but also more reliable, stable and cost effective power converters for interfacing PV modules to the grid [1]- [2].

Multilevel inverter is an effective solution for increasing power and reducing harmonics content of an ac waveform. This is because multilevel inverter has several advantages over the conventional two level inverters such as high voltage rating based on conventional power switches, better output voltage waveform which is close to sine wave with reduced harmonic content and less dv/dt, and finally higher output power is easily achieved [3] – [5].

Based on these advantages various circuits and topologies and modulation strategies have been reported for better utilization of multilevel voltage source inverters. Multilevel topologies are classified into three categories, namely; the NPC inverter [6], The Flying Capacitor (FC) [7] and the cascaded inverters with separate voltage sources (also called H-bridge converters) [8]. A cascade multilevel inverter is a

special kind of multilevel inverter built to synthesize a desired AC voltage from several levels of DC voltages [9].

Various switching strategies have been developed to fit diverse topologies and applications. For PWM control methods the study is focused on harmonic elimination PWM modulation, multicarrier SPWM control, carrier phase shifted SPWM, and space vector modulation [10]-[12].

Cascaded multilevel inverter have been the subject of research in the last several years, where the DC levels were considered to be identical in that all of them were batteries, solar cells, ultra capacitors, etc. Their limitation is several isolated DC sources for PV application which makes it more expensive and for diode clamped there is problem of capacitor voltage balancing especially for voltage levels beyond five.

Based on the above disadvantages the two topologies are combined to realize a hybrid topology called NPC/H-Bridge inverter [13], but still past research has also concentrated on realizing a five level NPC/H-Bridge inverter without cascading the bridge [14]; this fails to address the principle of realizing a general cascaded n- level NPC/H-Bridge.

This paper discusses the design of the control system for a nine- level cascaded NPC/H-bridge inverter interfaced with the grid through an LCL filter. The system will be descried and analyzed using mathematical models; secondly development of new and improved Phase shifted PWM technique will be formulated and tested on the model. Finally a control scheme will be designed and its robustness tested using simulation.

II. DESCRIPTION OF THE MAIN STAGES OF A NINE LEVEL CASCADED NPC/H-BRIDGE MULTILEVEL INVERTER

The model scheme of the Cascaded NPC/H-Bridge inverter for PV- Grid application is as shown in fig. 1. The system consist of two PV arrays of same current and voltage ratings, the nine level cascaded NPC/H-bridge inverter, the LCL filter and AC grid represented by a sinusoidal voltage source. The area of interest to be discussed in this paper is the modeling of the inverter, the LCL filter and the effect of the output voltage of the inverter on the grid voltage and current. The building block of the proposed topology consists of two identical NPC cascaded cells. The inverter phase voltage Van is the sum of the two cascaded cells, i.e.,

978-1-4244-7398-4/10/$26.00 ©2010 IEEE IPEC 2010334

+ _

+_ +

Fig. 1. Scheme of cascaded NPC/H-bridge inverter based PV- Grid interface.

( )10201

⋅+= VVan

V

Using appropriate switching technique, five different voltage outputs (+2Vdc, +Vdc, 0, -Vdc and –2Vdc) are generated on the ac terminal of the cascaded model.

A. Control Technique For a nine level cascaded NPC/H-bridge inverter eight power switches are controlled to supply sinusoidal output voltage with low current harmonic and low Total Harmonic Distortion (THD). Because of the modularity of the topology, one cell is used for analysis.

To prevent the top and bottom power switched in each inverter leg from conducting at the same time, the constraints of power switches can be expressed as

( )2142

131

⎪⎭

⎪⎬

⎫

=+

=+

iSiS

andiSiS

Where i = 1, 2.

Let T1 = S11 & S12

T2 = S13 & S13

T3 = S21 & S22 T4 = S23 & S24

The four valid expressions are given by;

( )30

12&111

1 ⎪⎩

⎪⎨⎧

=otherwise

ONareSSbothifT

( )40

14&131

2 ⎪⎩

⎪⎨⎧

=otherwise

ONareSSbothifT

)5(0

22&2113 ⎪⎩

⎪⎨⎧

=otherwise

ONareSSbothifT

( )60

24&231

4 ⎪⎩

⎪⎨⎧

=otherwise

ONareSSbothifT

The equivalent switching function in each NPC – leg is;

( )7

1211120

111

⎪⎪

⎩

⎪⎪

⎨

⎧

=−=

==

TifSif

Tif

aK

)8(1411220

131

⎪⎪⎩

⎪⎪⎨

⎧

=−=

==

TifSifTif

bK

For the control technique stated above, the voltage levels for the two legs of one of the leg is given by equations (9) and (10) [15]. Equation (9) is for one leg of the cell

)9(221

121

dcVaKaKdcVaK

aKaV ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−

+=

Similarly for the second leg the expression is given by;

)10(221

121

dcVbKbKdcVbK

bKbV ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−

+=

And finally the voltage output for a nine level cascaded NPC/H-Bridge inverter is given as;

( ) ( ) )11(212

2221201 dcVdcVbKaK

dcVdcVbKaKV −−++

−=

Assuming that Vdc1 = Vdc2 = Vdc3 = Vdc4 = Vdc, the

switching states are as shown in table 2. For a nine level cascaded NPC/h-bridge inverter, there are

22 valid switching states though tow of the switching states are short circuits and thus cannot compensate the DC capacitor as current do not pass through either of the four DC- link capacitors.

335

TABLE 2 SWITCHING SCHEME FOR ONE PHASE LEG OF A NINE LEVEL

CASCADED NPC/H- BRIDGE INVERTER

B. Proposed Hybrid PWM Control An improved strategy for realizing nine level output is

proposed in this paper. The paper uses the principle of decomposition where each leg is treated independently and gives a three level output. Positive and negative legs are connected together back to back and they share the same voltage source E as shown in fig. 2 and the nine level output with reduced harmonic content is as shown in fig.3. The proposed hybrid technique is the combination of carrier phase shifted PWM and PD. In each cell carriers vcr1 and vcr2 in phase but vertically disposed and modulating wave phase shifted by π are used. Finally a nine- level PWM output is achieved by using the same two carriers but phase shifted by π/4 and modulating wave phase shifted by π. The switching states for one phase leg of a nine- level NPC/H-bridge inverter is shown in table 2, as can be seen there several redundant states which can be utilized in DC voltage balance, this is not within the scope of this paper.

The control strategy has two advantages as compared to multicarrier PWM approach. First for an N-level cascaded NPC/H-bridge PWM inverter, we can use a switching frequency of 4N times less to achieve the same spectrum as multicarrier approach,

Secondly the multicarrier PWM approach requires 8 carriers to achieve nine level output, but the proposed control strategy requires only one carrier phase shifted by (n-1)π/4 where n is the number of series connected NPC/H-Bridge inverter.

III. MODELING OF THE LCL FILTER The output voltage generated by the inverter has high-

frequency harmonics due to the switching of the power semiconductor devices. In order to inject clean energy into the grid, these harmonics has to be reduced. The model uses an

LCL filter. When compared with other topologies (i.e L or LC filter, the LCL filter has the advantage of providing better decoupling between the filter and grid impedance (reducing the dependence on grid parameters) and a lower ripple current stress across the grid inductance (since the current ripple is reduced by the capacitance, the impedance at the grid side suffers less stress when compared with the LC topology). The selection of the type of inductors and capacitors is a compromise between performance, size and cost [16]. The values of the filter are shown in table 3. For the three phase inverter side the LCL filter is composed of three inductances Lf1-x and three capacitors star- connected.Rf1-x is the on- state resistance of the IGBT.The grid branch of the filter includes the coupling impedance Lf2 and Rf2. The filter for a balanced system is shown in fig. 4

Fig.2. Simulation model for a nine level NPC/H-Bridge consisting of four decomposed 3- level leg

(a)

(b)

Fig. 3. (a) Waveform and (b) Spectrum for a nine- level cascaded NPC/H-Bridge inverter phase voltage (fm=50HZ, fsw,dev=500HZ, mf=40, ma=0.9)

336

TABLE 3

LCL COMPONENT PARAMETER

Symbol Parameter Value

Lf1 Inverter side inductance 0.45 mH

Rf1 intern resistance of Lf2, inverter side inductance 10mΩ

C Filter capacitance 9.4μF

Lf2 Grid side inductance 0.5mH

Rf2 intern resistance of Lf2, grid side inductance 1mΩ

Rd Damping resistor in series with C(not shown) 1.6Ω

Rf1 Rf2 Lf2 Lf1

C Vs

If Is

Ic

Vi

Fig. 4. LCL filter

From the mathematical expression for the filter whish is not included here because of space limitation the grid current to inverter voltage transfer function is given by

)12(

21)2121(

1

)1221(221(3

1

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

+++++

+

+++

+

=

fRfRfLfLCfRfRS

CdR

CfRfLfRfLSCfLfLS

CdR

iVsi

Neglecting the effect of Rf1 and Rf2, equation (12) is simplified to;

)13(21()21(221(3

1

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

++++

+

= fLfLSCdRfLfLSCfLfLS

CdR

iVsi

With equation (13) the bode plot is plotted and can be seen in fig. 5

IV CONTROL SCHEME In [17], using the developed small signal model of the cascaded NPC/H-Bridge inverter shown in fig. 6, the complete control diagram in synchronous rotating d- q frame is shown in fig. 7. For the grid current control, there are two main control loops, isq for the reactive power control and isd for the active power control. The tuning for the compensators is only made for one loop assuming that both of them have the same dynamics. Cross – axis decoupling terms and feed forward terms are used to decouple the grid voltage from the output of the controllers [18]. Open loop transfer function for a current controller is

composed of PI + Delay + Saturation representing also the limit of the inverter [-30, 88] + LCL transfer function. The resultant transfer function is discretized using zero- order hold at sampling frequency of 10 kHz. Tuning of the PI gain is done using Tustin a tool provided by MATLAB. With proper tuning a gain Kp = 2.75 is obtained and fig. 8 shows the root locus of current controller

-150

-100

-50

0

50

Mag

nitude (dB)

103

104

105

106

-270

-225

-180

-135

-90

Pha

se (de

g)

Bode Diagram

Frequency (rad/sec) Fig.5 Bode diagram of the LCL filter

3V1

3V2

R/3

+ -

+ -

-

+

-

+

3V1

3V2

R/3

3V1

3V2

R/3

+ -

+ -

+ -

+ -

+ -

+ -

11~ VD d

11~VD d

22~VD d

22~ VD d

22~ VD q

22~VD q

11~ VD q

11~VD q

+ -

+ -

fdifL ~,1ω

fqifL ~,1ω sqifL ~

,2ω

sdifL ~,2ω

sdi~

sqi~

fqi~

fdi~

cdi~

cqi~

cdV~

cqV~

cqVC~ω

cdVC~ω

sdV~

sqV~

1fR 2fR 2fL

1fR 2fR 2fL

1fL

1fLqIqdqiqDdIdddidD

qIqdqiqDdIdddidD

qIqdqiqDdIdddidD

,25~~

,25,25~~

,25

,24~~

,2424~~

,24

,23~~

,2323~~

,23

++++

++++

+++

qIqNdqiqNDdIdNddidND

qIqNdqiqNDdIdNddiNdD

qIqNdqiqNDdIdNddiNdD

,5~~

,5,5~~

,5

,4~~

,44~~

,4

,3~~

,33~~

,3

++++

++++

+++

qIqdqiqDdIdddidD

qIqdqiqDdIdddidD

qIqdqiqDdIdddidD

,15~~

,15,15~~

,15

,14~~

,1414~~

,14

,13~~

,1313~~

,13

++++

++++

+++

Fig. 6 Small signal model of the NPC/H-bridge inverter based PV-Grid interface in dq co-ordinate

1abc

Step Iorder (pu)

Scope1

abc

Cos_Sindq0

S/Q TXi

abc

Cos_Sindq0

S/Q TX

dg0

Cos_Sin

abc

Q/S TX

Cos_Sin

PLL

Error Out

PI_rec_vd

Error Out

PI_rec_iq

Error Out

PI_rec_id

Error Out

PI_rec_i0

-K-

Ki1

-K-

Ki

0

Iso_ref

Vdc_ref

Isq_ref

em

em

3Vs-x

2is-x (pu)

1Vdc (pu)

Fig.7. Complete control diagram of the NPC/H-bridge inverter in synchronous d- q rotating reference frame

337

-2.5 -2 -1.5 -1 -0.5 0 0.5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

π/T

0.1π/T

0.2π/T

0.3π/T

0.4π/T0.5π/T

0.6π/T

0.7π/T

0.8π/T

0.9π/T

π/T

0.10.20.30.40.50.60.70.80.9

0.1π/T

0.2π/T

0.3π/T

0.4π/T0.5π/T

0.6π/T

0.7π/T

0.8π/T

0.9π/T

Root Locus

Real Axis

Imag

inar

y Axi

s

Fig.8. Root Locus of current controller

V SIMULATION ANALYSIS To check the validity of the design and analysis, MATLAB simulations using simulink is done on the model shown in fig. 9 with different DC voltages and loads. Using the LCL parameters given in table 3, other parameters needed are as follows; Vdc = 500V, P(kW) = 500 kW. Supply voltage (Vs) = 600 V, f= 60 Hz Sampling frequency = 2 kHz.

Fig.9. Complete simulation model of cascaded NPC/H-bridge inverter based PV- application

To check the robustness of the control scheme, when DC voltage from the PV source is changing, The DC bus voltage in increased at t= 0.05s as shown in fig. 10 (a), This increases the inverter output voltage making it larger than the grid voltage and thus reactive power is supplied to the network as shown in fig.10 (b).At t= 0.08s DC bus voltage is reduced as shown. This reduces inverter output voltage making it lower than grid voltage, thus the inverter absorbs reactive power from the network. However the DC voltage regains its 500 V after 1.5 cycles, the results shows excellent dynamic response of the system with sudden changes in PV source. The designed

PI controller forces the grid current to be in phase with the grid voltage after t= 0.08s as shown in fig. 10(c) This ensures that model operates at unity power factor. In fig. 10 (b), the effect of change on load on id, idref and iq, iqref is shown. It is clearly shown that all regain the values after the disturbance.

(a)

(b)

(c)

(d)

Fig.10. Transient simulation of (a) DC bus voltage (b) active and reactive power (c) Grid current and voltage (d) d-q Grid current and their references due to sudden change of DC voltage

P(kW)

Q(kVAr)

Grid current Grid voltage

id idref

iq iqref

338

Fig.11. Transient simulation of grid voltage and current due to sudden change of load. Fig. 11 shows the effect on change of load on the operation of the model. From fig. 10 (a), the inverter is operated at constant DC voltage at no load for the first three cycles, then at t = 0.025, an RL (100kW and 100 kVAr) load is switched on, it can be seen that the grid voltage is smoother after 0.025s because harmonics are filtered by the leakage reactance.

VI CONCLUSION

Advanced, well designed and properly controlled power converters are needed in order to facilitate the integration of renewable energy sources into the grid. This paper demonstrates with proper modeling of the converter, the operating characteristic and the control technique to be applied on the model can be easily found. The tuning of the PI controller and design of the LCL filter resulted in the robustness of the control scheme and proper tracking of the grid current reference. The improved phase shifted PWM Technique has proved that with proper phase shifting of the carrier signals, an improved voltage output with reduced harmonic content is achieved.

Detailed simulation results have demonstrated that the control scheme has fast dynamic response for generating or absorbing reactive power as demanded by the load. with varying DC voltages, the model’s parameters retains their original values in the shortest time possible, this shows that the control scheme applied on this model is a preferred choice for obtaining a sinusoidal voltage output with a varying DC source (photovoltaic cells).

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