single-stage boost inverter (SSBI) is presented in this paper. In three-phase SSBI, the voltage regulation is achieved by adjusting the boost ratio. The SSBI has ...
Voltage Regulation in Single-Stage Boost Inverter for Stand-Alone Applications Akanksha Singh, Student Member, IEEE, Alireza A. Milani, Behrooz Mirafzal, Senior Member, IEEE Department of Electrical and Computer Engineering Kansas State University, Manhattan, KS 66506 Abstract— The voltage regulation for stand-alone three-phase single-stage boost inverter (SSBI) is presented in this paper. In three-phase SSBI, the voltage regulation is achieved by adjusting the boost ratio. The SSBI has been simulated for a wide range of input dc voltages and load levels. Moreover, the performance a 2kW 208/230V laboratory-scale three phase boost inverter is presented for both linear and non-linear loads. The voltage regulation is realized along with implementing the modified PPWM technique in which the charging time stays constant over each sector and staircase pattern is used for discharging states. Index Terms: single-stage boost inverter, phasor pulse width modulation, voltage regulation, total harmonic distortion.
I.
INTRODUCTION
Nowadays, renewable energy resources such as photovoltaic panels and wind turbines play an important role in the electric power generation system. Connecting these energy resources to the power grid will help reduce the dependency of the electric grid to the price and availability of fossil fuels. However, while the energy produced by them is in a form that cannot be directly connected to the power grid, power electronic interface circuits are required to convert their output to a compatible form with electric grid and local loads. Moreover, the dc voltage that the photovoltaic systems can produce is usually lower than the required value to generate the desired ac peak voltage. Therefore, the interface circuit should also be able to boost the voltage to the required level [1]-[3].
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In this paper the application of modified PPWM switching technique to a three-phase SSBI to achieve a voltage regulation of less than 5% and load current THD of less than 5% has been presented. In addition to introduction, this paper contains two sections. Section II discusses about the modified PPWM switching pattern developed and Section III gives the simulation and experimental results for the voltage regulation in a SSBI using the modified PPWM switching technique.
Output Circuit
Previously, some studies have been done on the application of using current source inverters as an interface circuit for renewable energy systems. In [4], the necessity of “shoot through” state has been emphasized in order to boost the input dc voltage to a required peak to peak ac voltage. In the circuit experiments, a large inductor of 100 and a switching frequency of 1.2 have been used and the results show a maximum boost of 3.3 for the ratio of rms line to line voltage to the dc source voltage. In [5], a transformerless three-phase current source inverter has been presented which can be used to provide an output voltage of several hundred volts when its input is connected to a photovoltaic module. In [5], space vector modulation (SVM) has been applied to the phase currents of the current source inverter which calculates the duty cycles of the switching
states depending on a reference current vector. The switching frequency used in [5] is a relatively high, 25 . Moreover, a PI controller has been used in order to control the dc link current. With the descriptions above, the total harmonic distortion (THD) of the load current is about 4.5%. In [6], the concept of one cycle control (OCC) has been proposed and then, this concept and also the conventional PWM method have been used with a current source inverter for grid connection application. In [6], the dc inductance value has been kept low, i.e., 0.55 to reduce the size, weight and power dissipation of the inductor. It has been mentioned that using the OCC control method will simplify the control circuit which, will make the system response faster. However, a switching frequency of 40 has been used in [6] which is relatively high for renewable energy conversion systems. Application of the OCC method to an inverter prototype in [6] gives a THD of less than 5%.
Single Stage Boost Inverter Fig. 1. Power circuit of a three-phase single-stage boost inverter.
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PPWM has been formulated based on the phasor quantities, and not the space-vectors. Thus, there are three states as results of the three time-intervals in each switching cycle. Considering sector I from Table I, the staes can be described as follows:
TABLE I
SECTORS AND SWITCHING STATES [7] Sector
(I)
(II)
(III)
(IV)
0
(V)
(VI)
0
0
0
0
0
0
0
0
0
0
(1) State- : The charging time-interval, , in which two and (refer Fig. 2.), are switches in Leg-A, i.e. closed and the dc-link inductor is being charged. Fig. 3(a). shows the equivalent circuit of the converter during equals . this state. Thus, voltage across inductor
0
(2) The first discharging state 1: In the first discharging , the inductor current is directed into time-interval, phases A and B. During this period of time, the upper , and the lower switch of Leg-B, , switch of Leg-A, of the inverter are closed. Fig. 3(b). shows the equivalent circuit of the SSBI during this state. The voltage across equals . the (3) The second discharging state 2: the second discharging , in which the inductor current is time-interval, directed into phases A and C. During this period of time, the upper switch of Leg-A and the lower switch of Leg-C of the inverter are closed. Fig. 3(c). shows the equivalent circuit of the SSBI during the second discharging state. The voltage across for this state equals .
OR Reverse blocking IGBT
Herein, sector.
Fig. 2. Topology of a three-phase SSBI.
II. MODIFIED PHASOR PULSE WIDTH MODULATION SWITCHING PATTERN
and
can be identified from Table I based on the
Accordingly, one can write the following expressions.
The SVPWM based switching pattern for a three-phase single-stage boost inverter, also known as Phasor Pulse Width Modulation (PPWM) has been developed in [7]. In each switching cycle, , there are three time-intervals; one timeinterval for charging the dc-link inductor, , and two timeintervals for injecting current into two different phases, . In other words, the six main switching states, and two and zeros, with three switches conducting at any given instant in conventional space vector PWM (SVPWM) techniques, are modified to six states with only two switches conducting at any given instant, as well as three charging states in PPWM for current source single-stage boost inverter. Notice that
From the voltage – second balance law in a switching converter at steady state, the following can be written: V
V
2
⟶
⟶
(a)
0
This yields
⟶
:0
1
:
:
(c) (b) Fig. 3. Equivalent circuit of the SSBI during (a) state C: charging time interval, (b) state D1: first discharging time interval and, (c) state D2: second discharging time interval.
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Sap Sector
6 0
San
1 0
Sbp
1 0
Sbn
1 0
Scp
1 0
Scn
1 0
1 0
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
0
5
10
15 20 tim me (msec)
25
30
35
dspaace
L -Filter
dc--link indductor
Booost invverter
Resisstive load
Cac
Fig. 4. Switching pattern obtained frrom using modifieed phasor pulse width modulation. Fig. 5. 22kW 208/230V thrree-phase single-sttage boost inverterr setup.
D Dividing (2) by
gives us thee following:
3
⁄ , ⁄ , and w where coorresponding duty d ratios, i.e., 1
4
H Herein, the objjective is to calculate, c appproach is to determine . Then n from equation n (4) 1
⁄ , are the
, , and . One O /3 3 and 5
The switching pattern p thus pro oduced is not sy ymmetric in so ome seectors. This is because of lo ow resolution of the processsor w which leads to dropping of th he narrow pulses which furtther leeads to unsymm metrical switch hing pattern in different secto ors. These unsymmeetrical switchin ng patterns willl increase the to otal haarmonic distorttion (THD) of the t output currrent signal. Thus, in order to solve thiss problem, a modified m version n of PP PWM method is developed which w guaranteees the symmeetric coondition in th he switching pattern. p In thiis method, ev very sw witching cycle is discretized and described d by a preseleccted nuumber of points, therefore, in nstead of havin ng time durations foor charging and d discharging states, s these tim mes are presen nted ass number of po oints. In modiffied PPWM meethod, the num mber off points for th he charging sttate, , is callculated and kept k coonstant over each e sector. Meanwhile, M the discharging tiime inntervals are discretized. The number n of poin nts associated with w thhe charging statte is found by multiplying m bo oost ratio, to the tootal number of points, , and taking thee integer part of o it ass can be seen n in (6). Wh here is callculated by after coomparing the desired line-to o-line voltage rms value to the m measured line-to o-line rms voltaage value. 6 The rest of th he points are be divided between b the two t diischarging statees. In the previious approach of PPWM, as one o off the discharrging times is i increasing, , the otther diischarging time is decreasing g, , thereforre, the numberr of
points associated with these disscharging timees can be approxim mated by sym mmetrically inncreasing and decreasing steps. Iff the number off steps is assum med to be (the length of each step is degrees), tthe amplitude oof steps can be founnd by using (7) and (8).. The switchiing pattern developped by applyiing the discreetized approacch and for and resppectively, is increasinng and decreeasing of shown iin Fig. 3 . Thiss figure showss the symmetriic switching pattern developed ussing the modiified phasor ppulse width modulattion for two poower cycles. Equation (9) has been used to makee sure that thee summation oof and is and equal too . 1: 1: 1 7
;
1
;
1
1: 1:
1 8 9
The control index iin modified PP PWM is the chharging duty for ratio . The relationnship between modulation inndex originall PPWM and boost ratio foor modified PPW WM can be as obtainedd by linearizinng (5) and takinng average valuue of as ccan be seen inn (11). Thereefore, one cann write the followinng expressionss. 3
1
1 3
3
10
11
Thiss newly develooped switching pattern was im mplemented in the vooltage regulatiion of the threee-phase single--stage boost inverterr, and findinggs are presennted in the subsequent sectionss.
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200
200 VLL (V)
400
VLL (V)
400
0
0
-200 0
20
40
60
80
-400
100
4
4
2
2 IL (A)
IL (A)
-400
-200
0 -2 -4
0
20
40
60
80
100
0
20
40 60 time (msec)
80
100
0 -2
0
20
40 60 time (msec)
80
-4
100
(a)
(b)
Fig. 6. (a) Simulated three phase line voltages and currents of SSBI. (THD = 3.1%) (b) Measured three phase voltage and current waveforms of the prototype three - phase SSBI. (THD = 3.9%) – simulation and experimental results.
III.
SIMULATION AND EXPERIMENTAL RESULTS TABLE II SIMULINK MODEL AND CIRCUIT COMPONENT VALUES
In this paper, a three-phase single stage boost inverter with a modified PPWM switching strategy for voltage regulation in stand-alone applications is presented. In order to verify the open loop voltage regulation in a three – phase single – stage boost inverter, feeding different loads, it has been modeled and simulated in MATLAB/Simulink. The results obtained in simulation were also verified experimentally on a laboratory scale setup of three-phase single stage boost inverter shown in Fig. 5. The parameters of the developed set-up are summarized in Table II. The inverter switching signals are calculated and produced using dSPACE 1103, which operates at a sampling frequency of 86 .
Parameter
Value
50 – 80 volts 10mH
10μF & 20μF Resistive Load: 75 - 100Ω Inductive Load: 7.5mH
2.4kHz 41
1
Vdc = 50V Vdc = 65V
215 205 195 70
75
80
85
90
95
75
80
85
90
95
100
105
Vdc = 50V Vdc = 65V
0.6 0.4
0.4 70
205
0.8
Vdc = 50V Vdc = 65V
0.6
Vdc = 50V Vdc = 65V
215
195 70
105
D
D
0.8
100
225 VLLrms (V)
VLLrms (V)
225
1
75
80
85 90 Load (Ohms)
95
100
70
105
(a)
75
80
85 90 Load (Ohms)
95
100
105
(b)
Fig. 7. (a) Simulation result for voltage regulation and variation with change in load. (b) Experimental results for voltage regulation and with change in load – simulation and experimental results.
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variation
400
4
200 VLL (V)
THD (%)
5 3 2
Vdc = 50V Vdc = 65V
1 0 70
75
80
85
90
95
100
0 -200 -400 0
105
5
20
40
60
80
20
40 60 time (msec)
80
5
3 2
IL (A)
THD (%)
4
Vdc = 50V Vdc = 65V
1 0 70
75
80
85 90 Load (Ohms)
95
100
-5 0
105
Fig. 8. Phase current THD (%) variation with load.
Fig. 10. Output line voltage and current waveform of SSBI when connected to a rectifier and 150Ω load – experimental result.
The voltage regulation and output current THD of a laboratory scale three-phase single-stage boost inverter (SSBI) setup with varying load, varying input dc voltage have been presented in this section. Three-phase SSBI output with various loads have also been presented in this section. Fig. 6(a) shows the waveforms of line-to-line voltage and load current of the inverter obtained by simulation when connected to an R-L load of 70Ω and 7.5 . The of the load voltage is regulated to 208V and the load current is 3.1%. Fig. 5(b) shows experimentally obtained waveform of line-to-line voltage and load current of the three-phase SSBI connected to R-L load of 70Ω and 7.5 . The obtained line-to-line voltage is 208 load current 3.9% The simulation and experimental results for the voltage regulation can be seen in Fig 7. The load connected to the inverter here is R-L load and it was varied by varying R. Thus, 75 100Ω 7.5 . This comparison is 50 65 . The regulation in is less than for
VLL (V)
500
0
-500
0
20
40
60
80
100
4 IL (A)
2
5%. Fig 7(a) shows the results of voltage regulation obtained from simulation and the variation in to achieve the desired regulation for the above mentioned change in load. Fig. 7(b) shows experimentally obtained results for the same load variation. The simulated and experimental results for variation in load current for the variation in load can be seen in Fig. 8 (a) and (b) respectively. It can be observed from Fig. 8 that the load current never exceeds 5%, as required for the grid-tied and stand-alone applications. The SSBI line voltages and currents when feeding power to a three phase 0.33 , 240 induction motor (dynamic load) can be seen in Fig. 9. It can be noted from the waveforms that the motor was not balanced, whereas the of the line current was 4.7%. In this test, a dc voltage of 65 to feed the induction motor. Also, was boosted to 240 the three-phase SSBI output for a non-linear load can be seen in Fig. 10. This figure demonstrates inverter line voltages and load currents when the SSBI was connected to a three phase rectifier and the output of the rectifier connected to a resistive load of 150Ω. IV. CONCLUSION The objective of this paper was to apply the modified version of phasor pulse width modulation for the boost inverter in stand-alone applications. The laboratory-scale boost inverter prototype was tested for several input dc voltages and different linear and non-linear loads and the results verifying effectiveness of the switching pattern and capability of the voltage regulation have been presented in this paper.
0
V. REFERENCES
-2 -4
0
0
20
40 60 time (msec)
80
100
Fig. 9. Inverter line voltages and currents when connected to a three phase induction motor – experimental result.
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