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Steady-state analysis of PV supplied separately excited DC motor fed from IDB converter
Solar Energy Materials & Solar Cells 71 (2002) 493–510
Steady-state analysis of PV supplied separately excited DC motor fed from IDB converter Tomonobu Senjyu*, Mummadi Veerachary, Katsumi Uezato Department of Electrical and Electronics Engineering, Faculty of Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami, Okinawa 903-0213, Japan Received 12 March 2001; accepted 14 June 2001
Abstract Interleaved dual boost converter is capable of extracting more amount of power from the photovoltaic source than the conventional boost converter. Power extraction capabilities of the conventional boost and interleaved dual boost converters from the photovoltaic array are verified through experimental studies. As an application the effectiveness of this interleaved dual boost converter for PV supplied separately excited DC motor is studied through simulation. Extensive studies are made by formulating the mathematical models for photovoltaic source, interleaved dual boost converter, DC motor and load. Steady-state performance of the motor coupled to centrifugal pump load is analyzed for maximum power, gross mechanical energy operations. From the simulation studies, it is found that the motor performance is improved with gross mechanical energy output operation as compared to maximum power operation of solar cell array. Furthermore, the use of interleaved dual boost converter reduces the ripple content both in the source and load waveforms, thus resulting in reduced filtering requirements and improved photovoltaic array performance. r 2002 Elsevier Science B.V. All rights reserved. Keywords: DC motor; Interleaved dual boost converter; Maximum power operation; Solar cell array
1. Introduction The rapid trend of industrialization of nations and increased interest in environmental issues led, recently, to the exploration of the use of renewable forms such as solar energy. Photovoltaic (PV) generation is gaining increased importance as a renewable source due to its advantages like absence of fuel cost, little *Corresponding author. Tel.: +81-98-895-8686; fax: +81-98-895-8708. E-mail address: [email protected] (T. Senjyu). 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 1 0 2 - 7
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Nomenclature C Ce D DP1 ; DP2 Eb Ig Im ; I0m J La L1 ; L2 Pg Pm Pmc Ra r1 ; r2 S1 ; S2 TL ; Te Vg Vm V0m V0 o Z Zm
filter capacitance flux coefficient duty ratio of the converter diodes of individual boost cells Back EMF SCA current SCA, motor current at maximum power operation moment of inertia armature circuit inductance Inductances of individual boost cells SCA power output maximum power of SCA armature copper losses armature circuit resistance inductor series resistances switches of individual boost cells load, electromagnetic torque SCA voltage SCA voltage at maximum power operation motor armature voltage at maximum power operation load voltage motor speed efficiency of the DC–DC converter Efficiency of the motor
maintenance, no noise and wear due to absence of moving parts, etc. In particular, PV systems are rapidly expanding and have increasing roles in electric power technologies, providing more secure power sources to the pumping systems, where it is not economically viable to connect the existing grid supply. Optimum operation [1] of a combined system of solar cell array (SCA) and a DC shunt motor is achieved by means of a switching procedure of the SCA modules, direct current transformers as well as controlling the motor fluxes for maximum mechanical energy output. Performance of DC motors supplied from PV sources have been analyzed [2–6]. These studies reveal that the DC shunt motor powered by solar cells has an inferior performance and a separately excited DC motor [7] driving a centrifugal pump is the best drive as far as better matching of the PV generator is concerned. In the direct coupled PV supplied systems, the power delivered by the SCA is usually less than the maximum power it can supply. For proper utilization of SCA an intermediate DC– DC converter between SCA and load is required. By controlling the converter duty ratio it is possible to move the operating point towards the maximum power point [8,9].
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To improve the energy conversion performance of the PV system, it is desirable to minimize the long-term system losses by using high-efficiency converters with maximum power point controllers. The main features of these high performance of converters are: (i) the converter input current has very small ripple, (ii) converter efficiency should be high even at lower solar insolations. Interleaved converters [10] belongs to these category and are promising because of the following advantages: (i) ripple cancellation both in the input and output waveforms to maximum extent (ii) lower value of ripple amplitude, high ripple frequency in the resulting input and output waveforms (iii) efficiency of the parallel connected converter system can be improved if a proper number of converters in the system are activated. In particular with reference to PV systems, if the PV power decreases to low level due to changes in physical conditions, such as low insolation on the solar array, only few active converters may be sufficient for power transfer. On the other hand, when the power transfer increases beyond the maximum limit of the activated converters, an additional converter is put on to share the power transfer from the source. Thus, each converter can be operated at an optimal power level to improve the conversion efficiency. Further, parallel connection of converters has many desirable properties such as reduced device stresses, fault tolerance for the system, flexibility in the system design, etc. In this paper, the performance analysis of PV supplied DC motor driving a centrifugal pump load fed from an interleaved dual boost (IDB) converter is discussed. The comparative performance analysis is made for two cases: (i) when the PV array is operating at maximum power (MP) point, (ii) when the combined system operates at gross mechanical energy (GME) output. The organization of the paper is as follows. In Section 2, we present the development of mathematical models for the individual models like PV generator, DC motor, centrifugal pump load and IDB converter. Section 3 deals with the maximum power and gross mechanical energy operations of SCA with IDB converter. Experimental and simulation studies are discussed in Section 4. Conclusions follow in the final section of this paper.
2. Mathematical model of the system The combined system mainly consists of solar cell array, DC–DC converter, DC motor coupled to centrifugal pump as shown in Fig. 1. The DC–DC converter is an IDB converter. The analysis of the system is carried out under the following assumptions: (i) Switching elements of the converter are assumed to be ideal, i.e. forward voltage drops and ON-state resistances of the switches are neglected. (ii) The equivalent series resistance of the capacitance and stray capacitances are neglected. (iii) Passive components (R; L; C) are assumed to be linear, time-invariant and frequency-independent. (iv) The IDB converter cells are identical and operate in the continuous inductor current mode.
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Fig. 1. Functional block diagram of the system.
(v) The switches ðS1 ; S2 Þ operate in an interleaved fashion. (vi) Constant mechanical losses are assumed in the DC motor. Mathematical models for individual components are developed in the following sections. 2.1. PV generator model The PV generator is formed by the combination of many PV cells connected in series and parallel fashion to provide the desired value of output voltage and current. This PV generator exhibits a non-linear insolation dependent v–i characteristic, mathematically expressed for the PV array [2] consisting of Ns cells in series and Np cells in parallel as Np Iph Ig Ns Ns Vg ¼ Ig Rs þ ; ð1Þ ln 1 þ Np L N p I0 where Rs is the cell series resistance, L ¼ ðq=AKT Þ; q the electric charge, A the Completion factor, K the Boltzmann constant, and T is the Absolute temperature. Fig. 2 shows the output (Vg –Ig ; Pg –Ig ) characteristics of the SCA, with solar insolation as a parameter. In this figure Ig ; Vg ; Pg are the output current, voltage and power of the SCA, respectively. From Fig. 2 it is seen that the maximum power point of the SCA is changing with solar insolation. The v–i characteristic of the PV generator used in the simulation studies (cell parameters are given in Table 1) is Vg ¼ 0:2Ig þ 7:88 lnf1:0 þ 4:748ð20:8Kins Ig Þg;
ð2Þ
where Kins is percentage of insolation. 2.2. Model of the DC motor When the separately excited DC motor is supplied from the PV supply through an intermediate IDB converter, the motor voltage and torque equations under steady state are V 0 ¼ E b þ R a I0 ;
ð3Þ
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Fig. 2. Vg –Ig and Pg –Ig characteristics of SCA.
Table 1 SCA parameters 0:05 O 13:7572 V1 0:0081 A 108 26
Rs L Iog Ns Np
Te ¼ Ce I0 ;
ð4Þ
Eb ¼ Ce o:
ð5Þ
Motor armature copper loss expression is given by Pmc ¼ Ra I02 : Efficiency of the motor is V0 I0 : Zm ¼ ðV0 I0 LossesÞ
ð6Þ
ð7Þ
For given values of SCA power ðPg Þ and converter efficiency (Z), the motor input power can be written as ZPg ¼ Eb I0 þ I02 Ra :
ð8Þ
The above equation can be rearranged as Ra I02 þ Eb I0 ZPg ¼ 0:
ð9Þ
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From the above equation, the solution for armature current is ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ZPg Eb Eb 2 : þ I0 ¼ þ 2Ra 2Ra Ra
ð10Þ
2.3. Model of the centrifugal pump load Pumps may be volumetric or centrifugal types having different head - vs - flow characteristics. In these studies, a centrifugal pump load having speed–torque characteristic including friction torque [2] given by TL ¼ C1 þ B1 o þ A1 o1:8 Nm
ð11Þ
is considered. 2.4. State-space modeling of the IDB converter The intermediate DC–DC converter (IDB converter) produces a chopped output DC voltage and controls the average DC voltage applied to the motor. Further, the converter continuously matches the output characteristic of the PV generator to the input characteristic of the motor, so that maximum power is extracted from the SCA. The steady-state voltage and current relations of the IDB converter operating in continuous current mode are derived using state-space analysis in the following lines. The IDB converter consists of two boost cells in parallel as shown in Fig. 3. It is assumed that the two parallel converter cells operate in the continuous inductor current mode and the two switches ðS1 ; S2 Þ operate in an interleaved fashion. Under this condition four different modes are possible in one cycle of operation. The corresponding operating modes are as follows: Mode 1: 0otpd1 T the switches S1 ; Dp2 are conducting Mode 2: d1 Totpðd1 þ d2 ÞT the switches Dp1 ; Dp2 are conducting
Fig. 3. Interleaved dual boost converter.
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Mode 3: ðd1 þ d2 ÞTotpðd1 þ d2 þ d3 ÞT the switches S2 ; Dp1 are conducting Mode 4: ðd1 þ d2 þ d3 ÞTotpT the switches Dp2 ; Dp1 are conducting. The equations describing these four different modes of operation respectively are (see appendix for detailed equations) X’1 ¼ ½A1 ½X þ ½B1 ½U ;
ð12Þ
X’2 ¼ ½A2 ½X þ ½B2 ½U ;
ð13Þ
X’3 ¼ ½A3 ½X þ ½B3 ½U ;
ð14Þ
X’4 ¼ ½A4 ½X þ ½B4 ½U :
ð15Þ
Taking the average of the above four state models results in the following average state-space model: X’ ¼ ½A ½X þ ½B ½U ;
ð16Þ
where A ¼ A1 d1 þ A2 d2 þ A3 d3 þ A4 d4 ; B ¼ B1 d1 þ B2 d2 þ B3 d3 þ B4 d4 ; and d1 þ d2 þ d3 þ d4 ¼ 1: The corresponding A and B matrices are 2 r 3 L11 ðd1 þ d2 þ d3 þ d4 Þ 0 ðd2 þdL31þd4 Þ 6 7 ½A ¼ 6 0 Lr22 ðd1 þ d2 þ d3 þ d4 Þ ðd1 þdL22þd4 Þ 7 4 5; ðd2 þd3 þd4 Þ ðd1 þd2 þd4 Þ ðd1 þd2 þd3 þd4 Þ C C RC 2 ðd1 þd2 þd3 þd4 Þ 3 2 3 0 " # i1 L1 6 ðd þd þd 7 Vg 6 7 þd Þ 1 2 3 4 7; ½X ¼ 4 i2 5; ½U ¼ ½B ¼ 6 : 0 4 5 L2 0 3 þd4 Þ v0 0 ðd1 þd2 þd C Assuming identical branches ðr1 ¼ r2 ¼ r; L1 ¼ L2 ¼ LÞ results d4 ¼ d2 ; d3 ¼ d1 ; and d1 þ d2 ¼ 0:5: With these assumptions the simplified matrices A and B are 2 2rðd þd Þ 3 2 2ðd þd Þ 3 2Þ 1L 2 1L 2 0 ðd1 þ2d 0 L 6 6 2ðd þd Þ 7 7 2Þ 7 1 2 6 7: ½A ¼ 6 0 2rðd1Lþd2 Þ ðd1 þ2d 0 4 5; ½B ¼ 4 L 5 L ðd1 þ2d2 Þ ðd1 þ2d2 Þ 2ðd1 þd2 Þ 2ðd1 þd2 Þ 0 C C RC C The steady-state behavior can be obtained from the following expression: 2 3 Vg 2 3 2 rþ2Rð1DÞ I1 6 7 Vg 7 6 7 6 ½Xss ¼ ½A 1 ½B ½U ¼ 4 I2 5 ¼ 6 rþ2Rð1DÞ 2 7; 4 5 2RVg ð1DÞ V0 rþ2Rð1DÞ2
ð17Þ
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where d1 ¼ D; d2 ¼ 0:5 D: From the above equations, the steady-state voltage gain of the IDB converter is V0 2Rð1 DÞ ¼ : ð18Þ Vg r þ 2Rð1 DÞ2 Using power balance, the current expression is obtained as I0 ¼
Zðr þ 2Rð1 DÞ2 ÞIg : 2RVg ð1 DÞ
ð19Þ
3. SCA operation with IDB converter 3.1. Maximum power operation of SCA For maximum utilization of SCA, a power converter is introduced in between SCA and motor. The duty ratio of the converter is changed accordingly to match the SCA output characteristic to the input characteristic of the motor. The equivalent circuit of the combined system is shown in Fig. 4. When the SCA is operating at maximum power point, the power absorbed by the motor load is equal to converter efficiency times power delivered by the SCA, i.e. Pmt ¼ ZVm Im ¼ V0m I0m ;
ð20Þ ð21Þ
where Vm ; Im are the SCA voltage, current, respectively, at maximum power point, V0m ; I0m are the motor armature voltage, current, respectively, at maximum power point of SCA. From the motor armature equivalent circuit (Fig. 4) V0m ¼ Eb þ Ra I0m :
ð22Þ
Transforming the above equation to SCA side using Eqs. (18) and (19), we have 2Rð1 DÞVm ðr þ 2Rð1 DÞ2 ÞZRa Im : ¼ Eb þ 2 2RVg ð1 DÞ r þ 2Rð1 DÞ
ð23Þ
Neglecting the parasitic resistance of the converter and solving the above equation for the duty ratio ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 ffi Eb Eb Pm D¼1þ : ð24Þ þ þ 2ZRa Im 2ZRa Im ZRa Im2 For a given SCA maximum power ðPm Þ; the motor armature current, obtained by using Eq. (10), is given as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eb Eb 2 ZPm ð25Þ þ I0m ¼ þ 2Ra 2Ra Ra where Eb is given by Eq. (5). It is seen that from the Eq. (24) that the converter duty ratio (D) depends on the motor back emf, which in turn depends on motor load.
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Fig. 4. Equivalent circuit of combined system.
When the DC motor is coupled to the centrifugal pump load (Eq. (11)) for a given SCA maximum power ðPm Þ; the back emf is obtained by solving (Te ¼ TL ) Eqs. (4), (11), and (25). Once back emf is calculated corresponding to Pm ; the duty ratio of the converter is obtained from Eq. (24). 3.2. Maximum daily gross mechanical energy operation For a given value of flux coefficient of the DC machine, it is not possible to make the SCA and motor to operate at maximum power points ðVm ; Im ; Pm Þ at all solar insolations [5]. This is because the motor v–i characteristics are dependent on the motor flux coefficient, and copper losses. In such cases, the system is made to operate at a point ðVmn ; Imn ; Pnm Þ of gross mechanical energy output per day for a given daily solar insolation curve. At this operating point, Vmn > Vm ; Imn oIm : This operating point can be computed from the maximum power point of SCA using the following relations [5]: Vmn ¼ Imn ¼
ð2Ra þ 89:8Im0:873 ÞVm ; ðRa þ 89:8Im0:873 Þ
ð89:8Im0:127 Þ : ðRa þ 89:8Im0:873 Þ
ð26Þ
ð27Þ
For the DC motor under consideration, the optimal parameter Ce ¼ 0:6626 makes the combined system to operate at the maximum gross mechanical energy output. Taking this optimal parameter ðCe Þ; the back emf is obtained by solving (Te ¼ TL ) Eqs. (4), (11), and (25). Once back emf is calculated corresponding to Pnm ; the duty ratio of the converter is obtained from the following equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u u Eb 2 E Pnm b n t : ð28Þ D ¼1þ þ þ 2 2ZRa Imn 2ZRa Imn ZRa Im*
4. Experimental results and discussions Experimental prototype PV supplied IDB converter system has been constructed for the present investigations. Extensive experimental studies are carried out to find the effectiveness of the IDB converter over conventional boost converter for PV
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applications. For illustration, experimental results are presented at one particular solar insolation. The instantaneous variation of converter input voltage, current and power oscillograms for both converters (boost and IDB) are shown in Figs. 5–7. From Fig. 6, it can be seen that the current waveform with IDB converter exhibits
Fig. 5. Experimental converter input voltage waveforms.
Fig. 6. Experimental converter input current waveforms.
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Fig. 7. Experimental converter input power waveforms.
lower current ripple than with the conventional boost converter. This is because of the interleaved gating of the IDB converter. As a consequence of this reduced current ripple, a lower value of capacitor is sufficient to smooth the PV voltage fluctuations on the input side of the converter. The instantaneous converter input power (SCA power output) is recorded with boost and IDB converters in Fig. 7. It is evident that the average PV output power(Pacb oPaid ) is higher in case of PV supplied IDB converter. Experimental investigations are also made to find the variation of PV power output by changing the duty ratio of the converter. The results (Fig. 8) indicate that the IDB converter system is capable of extracting higher amount of power from the SCA for almost all the duty ratios except at higher duty ratios, where the power extraction is a little higher than the conventional boost converter. Furthermore, experimental observations are also made with reference to power extraction from the SCA when the converter (boost/IDB) operating frequency (5–50 kHz) is changed. These studies reveal that the IDB converter can still extract higher amount of power (Fig. 8) from the SCA with slightly increased switching losses. But, the increased switching losses in IDB converter will not have any effect on the converter input side. However, if the converter is operated at optimum switching frequency, we can minimize the switching losses and can improve the efficiency of the converter system (Fig. 9). In order to evaluate the suitability of the IDB converter to PV systems, it has been employed for PV supplied DC motor system. A 120 V; 9:2 A; 1500 rpm DC separately excited motor is considered in these studies. The parameters of the machine are given in Table 2. The motor performance is evaluated when (i) the SCA is operating at maximum power point, (ii) gross mechanical energy output operation.
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Fig. 8. Measured PV array output power variation with converter duty ratio.
Fig. 9. Measured PV array output power variation with converter frequency.
Based on the mathematical models developed in the preceding sections, the converter duty ratios are computed for the two cases mentioned at different solar insolations (1 p:u: ¼ 100% solar insolation ¼ 1000 W=m2 ) and the results are plotted in Fig. 10. The IDB converter duty ratio is figured out to be higher for the GME operation.
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Table 2 Motor parameters 120 V 9:2 A 1500 rpm 1:5 O 0:02 H 0.621 0:02367 kg m2 0.000390 0.002387 0.5
V I N Ra La Ce J A1 B1 C1
Fig. 10. Converter duty ratio variation with solar insolation.
From Fig. 11 it can be noticed that the armature voltage is higher for GME operation than the MP operation satisfying the relation Vmn > Vm : However, under such conditions the motor armature current (Fig. 12) decreases (Imn oIm ), which in turn decreases the copper losses as shown in Fig. 13. Furthermore, GME operation results improved motor efficiency because of reduced copper losses (Fig. 14). Variation of starting torque, torque magnification factors for GME operation as compared to maximum power operation [6] are computed and the results are plotted
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Fig. 11. Motor armature voltage variation with solar insolation.
Fig. 12. Motor armature current variation with solar insolation.
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Fig. 13. Armature copper losses variation with solar insolation.
Fig. 14. Motor efficiency variation with solar insolation.
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Fig. 15. Torque magnification, starting torque variation with solar insolation.
in Fig. 15. From these results it can be noticed that, the GME operation has little effect on these factors.
5. Conclusions Interleaved dual boost converter power extraction capability from the PV system was verified experimentally and found to be extracting a higher amount of power from the SCA as compared to conventional boost converter. The suitability of this IDB converter for PV supplied DC motor system driving a centrifugal pump load is studied through simulations. Steady-state simulation results indicate that the GME operation improves the motor performance over the MP operation. Furthermore, interleaved operation of IDB converter reduces ripple content both on source and load side, resulting in reduced filtering requirements and also improves the SCA performance.
Appendix Mode 1: Vg r1 i1 i’1 ¼ ; L1 L1
ðA:1Þ
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Vg r2 i2 v0 ; i’2 ¼ L2 L2 L2
ðA:2Þ
i2 v0 iL ; V’0 ¼ C RC C
ðA:3Þ
X’1 ¼ ½A1 ½X þ ½B1 ½U :
ðA:4Þ
Mode 2: Vg r1 i1 v0 ; i’1 ¼ L1 L1 L1
ðA:5Þ
Vg r2 i2 v0 i’2 ¼ ; L2 L2 L2
ðA:6Þ
ði1 þ i2 Þ v0 iL ; V’0 ¼ C RC C
ðA:7Þ
X’2 ¼ ½A2 ½X þ ½B2 ½U :
ðA:8Þ
Mode 3: Vg r1 i1 v0 i’1 ¼ ; L1 L1 L1
ðA:9Þ
Vg r2 i2 i’2 ¼ ; L2 L2
ðA:10Þ
i1 v0 iL ; V’0 ¼ C RC C
ðA:11Þ
X’3 ¼ ½A3 ½X þ ½B3 ½U :
ðA:12Þ
Mode 4: Vg r1 i1 v0 ; i’1 ¼ L1 L1 L1
ðA:13Þ
Vg r2 i2 v0 ; i’2 ¼ L2 L2 L2
ðA:14Þ
ði1 þ i2 Þ v0 iL ; V’0 ¼ C RC C
ðA:15Þ
X’4 ¼ ½A4 ½X þ ½B4 ½U :
ðA:16Þ
References [1] Z. Zinger, A. Braunstein, IEEE Trans. PAS 100 (1981) 1193. [2] J. Appelbaum, IEEE Trans. Energy Conversion 1 (1986) 17. [3] P.K. Koner, J.C. Joshi, K.L. Chopra, Int. J. Energy Res. 16 (1992) 301.
510 [4] [5] [6] [7] [8] [9] [10]
T. Senjyu et al. / Solar Energy Materials & Solar Cells 71 (2002) 493–510 C.L. Putta Swamy, B. Singh, B.P. Singh, J. Solar Energy Materials and Solar Cells 36 (1995) 187. M.M. Saied, IEEE Trans. Energy Conversion 3 (1988) 465. M. Veerachary, J. Solar Energy Materials & Solar Cells 61 (2000) 365. J. Appelbaum, S. Singer, M.S. Sarma, Electric Mach. Power Systems 20 (1992) 173. S.M. Alghuwainem, IEEE Trans. Energy Conversion 7 (1992) 267. K. Siri, V.A. Caliskan, C.Q. Lee, IEE Proc.-G 140 (1993) 106. Roberto Giral, Luis Martinez-Salamero, Sigmond Singer, IEEE Trans. Power Electron. 14 (1999) 643.
Steady-state analysis of PV supplied separately excited DC motor fed from IDB converter Tomonobu Senjyu*, Mummadi Veerachary, Katsumi Uezato Department of Electrical and Electronics Engineering, Faculty of Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami, Okinawa 903-0213, Japan Received 12 March 2001; accepted 14 June 2001
Abstract Interleaved dual boost converter is capable of extracting more amount of power from the photovoltaic source than the conventional boost converter. Power extraction capabilities of the conventional boost and interleaved dual boost converters from the photovoltaic array are verified through experimental studies. As an application the effectiveness of this interleaved dual boost converter for PV supplied separately excited DC motor is studied through simulation. Extensive studies are made by formulating the mathematical models for photovoltaic source, interleaved dual boost converter, DC motor and load. Steady-state performance of the motor coupled to centrifugal pump load is analyzed for maximum power, gross mechanical energy operations. From the simulation studies, it is found that the motor performance is improved with gross mechanical energy output operation as compared to maximum power operation of solar cell array. Furthermore, the use of interleaved dual boost converter reduces the ripple content both in the source and load waveforms, thus resulting in reduced filtering requirements and improved photovoltaic array performance. r 2002 Elsevier Science B.V. All rights reserved. Keywords: DC motor; Interleaved dual boost converter; Maximum power operation; Solar cell array
1. Introduction The rapid trend of industrialization of nations and increased interest in environmental issues led, recently, to the exploration of the use of renewable forms such as solar energy. Photovoltaic (PV) generation is gaining increased importance as a renewable source due to its advantages like absence of fuel cost, little *Corresponding author. Tel.: +81-98-895-8686; fax: +81-98-895-8708. E-mail address: [email protected] (T. Senjyu). 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 1 0 2 - 7
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Nomenclature C Ce D DP1 ; DP2 Eb Ig Im ; I0m J La L1 ; L2 Pg Pm Pmc Ra r1 ; r2 S1 ; S2 TL ; Te Vg Vm V0m V0 o Z Zm
filter capacitance flux coefficient duty ratio of the converter diodes of individual boost cells Back EMF SCA current SCA, motor current at maximum power operation moment of inertia armature circuit inductance Inductances of individual boost cells SCA power output maximum power of SCA armature copper losses armature circuit resistance inductor series resistances switches of individual boost cells load, electromagnetic torque SCA voltage SCA voltage at maximum power operation motor armature voltage at maximum power operation load voltage motor speed efficiency of the DC–DC converter Efficiency of the motor
maintenance, no noise and wear due to absence of moving parts, etc. In particular, PV systems are rapidly expanding and have increasing roles in electric power technologies, providing more secure power sources to the pumping systems, where it is not economically viable to connect the existing grid supply. Optimum operation [1] of a combined system of solar cell array (SCA) and a DC shunt motor is achieved by means of a switching procedure of the SCA modules, direct current transformers as well as controlling the motor fluxes for maximum mechanical energy output. Performance of DC motors supplied from PV sources have been analyzed [2–6]. These studies reveal that the DC shunt motor powered by solar cells has an inferior performance and a separately excited DC motor [7] driving a centrifugal pump is the best drive as far as better matching of the PV generator is concerned. In the direct coupled PV supplied systems, the power delivered by the SCA is usually less than the maximum power it can supply. For proper utilization of SCA an intermediate DC– DC converter between SCA and load is required. By controlling the converter duty ratio it is possible to move the operating point towards the maximum power point [8,9].
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To improve the energy conversion performance of the PV system, it is desirable to minimize the long-term system losses by using high-efficiency converters with maximum power point controllers. The main features of these high performance of converters are: (i) the converter input current has very small ripple, (ii) converter efficiency should be high even at lower solar insolations. Interleaved converters [10] belongs to these category and are promising because of the following advantages: (i) ripple cancellation both in the input and output waveforms to maximum extent (ii) lower value of ripple amplitude, high ripple frequency in the resulting input and output waveforms (iii) efficiency of the parallel connected converter system can be improved if a proper number of converters in the system are activated. In particular with reference to PV systems, if the PV power decreases to low level due to changes in physical conditions, such as low insolation on the solar array, only few active converters may be sufficient for power transfer. On the other hand, when the power transfer increases beyond the maximum limit of the activated converters, an additional converter is put on to share the power transfer from the source. Thus, each converter can be operated at an optimal power level to improve the conversion efficiency. Further, parallel connection of converters has many desirable properties such as reduced device stresses, fault tolerance for the system, flexibility in the system design, etc. In this paper, the performance analysis of PV supplied DC motor driving a centrifugal pump load fed from an interleaved dual boost (IDB) converter is discussed. The comparative performance analysis is made for two cases: (i) when the PV array is operating at maximum power (MP) point, (ii) when the combined system operates at gross mechanical energy (GME) output. The organization of the paper is as follows. In Section 2, we present the development of mathematical models for the individual models like PV generator, DC motor, centrifugal pump load and IDB converter. Section 3 deals with the maximum power and gross mechanical energy operations of SCA with IDB converter. Experimental and simulation studies are discussed in Section 4. Conclusions follow in the final section of this paper.
2. Mathematical model of the system The combined system mainly consists of solar cell array, DC–DC converter, DC motor coupled to centrifugal pump as shown in Fig. 1. The DC–DC converter is an IDB converter. The analysis of the system is carried out under the following assumptions: (i) Switching elements of the converter are assumed to be ideal, i.e. forward voltage drops and ON-state resistances of the switches are neglected. (ii) The equivalent series resistance of the capacitance and stray capacitances are neglected. (iii) Passive components (R; L; C) are assumed to be linear, time-invariant and frequency-independent. (iv) The IDB converter cells are identical and operate in the continuous inductor current mode.
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Fig. 1. Functional block diagram of the system.
(v) The switches ðS1 ; S2 Þ operate in an interleaved fashion. (vi) Constant mechanical losses are assumed in the DC motor. Mathematical models for individual components are developed in the following sections. 2.1. PV generator model The PV generator is formed by the combination of many PV cells connected in series and parallel fashion to provide the desired value of output voltage and current. This PV generator exhibits a non-linear insolation dependent v–i characteristic, mathematically expressed for the PV array [2] consisting of Ns cells in series and Np cells in parallel as Np Iph Ig Ns Ns Vg ¼ Ig Rs þ ; ð1Þ ln 1 þ Np L N p I0 where Rs is the cell series resistance, L ¼ ðq=AKT Þ; q the electric charge, A the Completion factor, K the Boltzmann constant, and T is the Absolute temperature. Fig. 2 shows the output (Vg –Ig ; Pg –Ig ) characteristics of the SCA, with solar insolation as a parameter. In this figure Ig ; Vg ; Pg are the output current, voltage and power of the SCA, respectively. From Fig. 2 it is seen that the maximum power point of the SCA is changing with solar insolation. The v–i characteristic of the PV generator used in the simulation studies (cell parameters are given in Table 1) is Vg ¼ 0:2Ig þ 7:88 lnf1:0 þ 4:748ð20:8Kins Ig Þg;
ð2Þ
where Kins is percentage of insolation. 2.2. Model of the DC motor When the separately excited DC motor is supplied from the PV supply through an intermediate IDB converter, the motor voltage and torque equations under steady state are V 0 ¼ E b þ R a I0 ;
ð3Þ
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Fig. 2. Vg –Ig and Pg –Ig characteristics of SCA.
Table 1 SCA parameters 0:05 O 13:7572 V1 0:0081 A 108 26
Rs L Iog Ns Np
Te ¼ Ce I0 ;
ð4Þ
Eb ¼ Ce o:
ð5Þ
Motor armature copper loss expression is given by Pmc ¼ Ra I02 : Efficiency of the motor is V0 I0 : Zm ¼ ðV0 I0 LossesÞ
ð6Þ
ð7Þ
For given values of SCA power ðPg Þ and converter efficiency (Z), the motor input power can be written as ZPg ¼ Eb I0 þ I02 Ra :
ð8Þ
The above equation can be rearranged as Ra I02 þ Eb I0 ZPg ¼ 0:
ð9Þ
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From the above equation, the solution for armature current is ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ZPg Eb Eb 2 : þ I0 ¼ þ 2Ra 2Ra Ra
ð10Þ
2.3. Model of the centrifugal pump load Pumps may be volumetric or centrifugal types having different head - vs - flow characteristics. In these studies, a centrifugal pump load having speed–torque characteristic including friction torque [2] given by TL ¼ C1 þ B1 o þ A1 o1:8 Nm
ð11Þ
is considered. 2.4. State-space modeling of the IDB converter The intermediate DC–DC converter (IDB converter) produces a chopped output DC voltage and controls the average DC voltage applied to the motor. Further, the converter continuously matches the output characteristic of the PV generator to the input characteristic of the motor, so that maximum power is extracted from the SCA. The steady-state voltage and current relations of the IDB converter operating in continuous current mode are derived using state-space analysis in the following lines. The IDB converter consists of two boost cells in parallel as shown in Fig. 3. It is assumed that the two parallel converter cells operate in the continuous inductor current mode and the two switches ðS1 ; S2 Þ operate in an interleaved fashion. Under this condition four different modes are possible in one cycle of operation. The corresponding operating modes are as follows: Mode 1: 0otpd1 T the switches S1 ; Dp2 are conducting Mode 2: d1 Totpðd1 þ d2 ÞT the switches Dp1 ; Dp2 are conducting
Fig. 3. Interleaved dual boost converter.
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Mode 3: ðd1 þ d2 ÞTotpðd1 þ d2 þ d3 ÞT the switches S2 ; Dp1 are conducting Mode 4: ðd1 þ d2 þ d3 ÞTotpT the switches Dp2 ; Dp1 are conducting. The equations describing these four different modes of operation respectively are (see appendix for detailed equations) X’1 ¼ ½A1 ½X þ ½B1 ½U ;
ð12Þ
X’2 ¼ ½A2 ½X þ ½B2 ½U ;
ð13Þ
X’3 ¼ ½A3 ½X þ ½B3 ½U ;
ð14Þ
X’4 ¼ ½A4 ½X þ ½B4 ½U :
ð15Þ
Taking the average of the above four state models results in the following average state-space model: X’ ¼ ½A ½X þ ½B ½U ;
ð16Þ
where A ¼ A1 d1 þ A2 d2 þ A3 d3 þ A4 d4 ; B ¼ B1 d1 þ B2 d2 þ B3 d3 þ B4 d4 ; and d1 þ d2 þ d3 þ d4 ¼ 1: The corresponding A and B matrices are 2 r 3 L11 ðd1 þ d2 þ d3 þ d4 Þ 0 ðd2 þdL31þd4 Þ 6 7 ½A ¼ 6 0 Lr22 ðd1 þ d2 þ d3 þ d4 Þ ðd1 þdL22þd4 Þ 7 4 5; ðd2 þd3 þd4 Þ ðd1 þd2 þd4 Þ ðd1 þd2 þd3 þd4 Þ C C RC 2 ðd1 þd2 þd3 þd4 Þ 3 2 3 0 " # i1 L1 6 ðd þd þd 7 Vg 6 7 þd Þ 1 2 3 4 7; ½X ¼ 4 i2 5; ½U ¼ ½B ¼ 6 : 0 4 5 L2 0 3 þd4 Þ v0 0 ðd1 þd2 þd C Assuming identical branches ðr1 ¼ r2 ¼ r; L1 ¼ L2 ¼ LÞ results d4 ¼ d2 ; d3 ¼ d1 ; and d1 þ d2 ¼ 0:5: With these assumptions the simplified matrices A and B are 2 2rðd þd Þ 3 2 2ðd þd Þ 3 2Þ 1L 2 1L 2 0 ðd1 þ2d 0 L 6 6 2ðd þd Þ 7 7 2Þ 7 1 2 6 7: ½A ¼ 6 0 2rðd1Lþd2 Þ ðd1 þ2d 0 4 5; ½B ¼ 4 L 5 L ðd1 þ2d2 Þ ðd1 þ2d2 Þ 2ðd1 þd2 Þ 2ðd1 þd2 Þ 0 C C RC C The steady-state behavior can be obtained from the following expression: 2 3 Vg 2 3 2 rþ2Rð1DÞ I1 6 7 Vg 7 6 7 6 ½Xss ¼ ½A 1 ½B ½U ¼ 4 I2 5 ¼ 6 rþ2Rð1DÞ 2 7; 4 5 2RVg ð1DÞ V0 rþ2Rð1DÞ2
ð17Þ
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where d1 ¼ D; d2 ¼ 0:5 D: From the above equations, the steady-state voltage gain of the IDB converter is V0 2Rð1 DÞ ¼ : ð18Þ Vg r þ 2Rð1 DÞ2 Using power balance, the current expression is obtained as I0 ¼
Zðr þ 2Rð1 DÞ2 ÞIg : 2RVg ð1 DÞ
ð19Þ
3. SCA operation with IDB converter 3.1. Maximum power operation of SCA For maximum utilization of SCA, a power converter is introduced in between SCA and motor. The duty ratio of the converter is changed accordingly to match the SCA output characteristic to the input characteristic of the motor. The equivalent circuit of the combined system is shown in Fig. 4. When the SCA is operating at maximum power point, the power absorbed by the motor load is equal to converter efficiency times power delivered by the SCA, i.e. Pmt ¼ ZVm Im ¼ V0m I0m ;
ð20Þ ð21Þ
where Vm ; Im are the SCA voltage, current, respectively, at maximum power point, V0m ; I0m are the motor armature voltage, current, respectively, at maximum power point of SCA. From the motor armature equivalent circuit (Fig. 4) V0m ¼ Eb þ Ra I0m :
ð22Þ
Transforming the above equation to SCA side using Eqs. (18) and (19), we have 2Rð1 DÞVm ðr þ 2Rð1 DÞ2 ÞZRa Im : ¼ Eb þ 2 2RVg ð1 DÞ r þ 2Rð1 DÞ
ð23Þ
Neglecting the parasitic resistance of the converter and solving the above equation for the duty ratio ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 ffi Eb Eb Pm D¼1þ : ð24Þ þ þ 2ZRa Im 2ZRa Im ZRa Im2 For a given SCA maximum power ðPm Þ; the motor armature current, obtained by using Eq. (10), is given as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eb Eb 2 ZPm ð25Þ þ I0m ¼ þ 2Ra 2Ra Ra where Eb is given by Eq. (5). It is seen that from the Eq. (24) that the converter duty ratio (D) depends on the motor back emf, which in turn depends on motor load.
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Fig. 4. Equivalent circuit of combined system.
When the DC motor is coupled to the centrifugal pump load (Eq. (11)) for a given SCA maximum power ðPm Þ; the back emf is obtained by solving (Te ¼ TL ) Eqs. (4), (11), and (25). Once back emf is calculated corresponding to Pm ; the duty ratio of the converter is obtained from Eq. (24). 3.2. Maximum daily gross mechanical energy operation For a given value of flux coefficient of the DC machine, it is not possible to make the SCA and motor to operate at maximum power points ðVm ; Im ; Pm Þ at all solar insolations [5]. This is because the motor v–i characteristics are dependent on the motor flux coefficient, and copper losses. In such cases, the system is made to operate at a point ðVmn ; Imn ; Pnm Þ of gross mechanical energy output per day for a given daily solar insolation curve. At this operating point, Vmn > Vm ; Imn oIm : This operating point can be computed from the maximum power point of SCA using the following relations [5]: Vmn ¼ Imn ¼
ð2Ra þ 89:8Im0:873 ÞVm ; ðRa þ 89:8Im0:873 Þ
ð89:8Im0:127 Þ : ðRa þ 89:8Im0:873 Þ
ð26Þ
ð27Þ
For the DC motor under consideration, the optimal parameter Ce ¼ 0:6626 makes the combined system to operate at the maximum gross mechanical energy output. Taking this optimal parameter ðCe Þ; the back emf is obtained by solving (Te ¼ TL ) Eqs. (4), (11), and (25). Once back emf is calculated corresponding to Pnm ; the duty ratio of the converter is obtained from the following equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u u Eb 2 E Pnm b n t : ð28Þ D ¼1þ þ þ 2 2ZRa Imn 2ZRa Imn ZRa Im*
4. Experimental results and discussions Experimental prototype PV supplied IDB converter system has been constructed for the present investigations. Extensive experimental studies are carried out to find the effectiveness of the IDB converter over conventional boost converter for PV
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applications. For illustration, experimental results are presented at one particular solar insolation. The instantaneous variation of converter input voltage, current and power oscillograms for both converters (boost and IDB) are shown in Figs. 5–7. From Fig. 6, it can be seen that the current waveform with IDB converter exhibits
Fig. 5. Experimental converter input voltage waveforms.
Fig. 6. Experimental converter input current waveforms.
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Fig. 7. Experimental converter input power waveforms.
lower current ripple than with the conventional boost converter. This is because of the interleaved gating of the IDB converter. As a consequence of this reduced current ripple, a lower value of capacitor is sufficient to smooth the PV voltage fluctuations on the input side of the converter. The instantaneous converter input power (SCA power output) is recorded with boost and IDB converters in Fig. 7. It is evident that the average PV output power(Pacb oPaid ) is higher in case of PV supplied IDB converter. Experimental investigations are also made to find the variation of PV power output by changing the duty ratio of the converter. The results (Fig. 8) indicate that the IDB converter system is capable of extracting higher amount of power from the SCA for almost all the duty ratios except at higher duty ratios, where the power extraction is a little higher than the conventional boost converter. Furthermore, experimental observations are also made with reference to power extraction from the SCA when the converter (boost/IDB) operating frequency (5–50 kHz) is changed. These studies reveal that the IDB converter can still extract higher amount of power (Fig. 8) from the SCA with slightly increased switching losses. But, the increased switching losses in IDB converter will not have any effect on the converter input side. However, if the converter is operated at optimum switching frequency, we can minimize the switching losses and can improve the efficiency of the converter system (Fig. 9). In order to evaluate the suitability of the IDB converter to PV systems, it has been employed for PV supplied DC motor system. A 120 V; 9:2 A; 1500 rpm DC separately excited motor is considered in these studies. The parameters of the machine are given in Table 2. The motor performance is evaluated when (i) the SCA is operating at maximum power point, (ii) gross mechanical energy output operation.
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Fig. 8. Measured PV array output power variation with converter duty ratio.
Fig. 9. Measured PV array output power variation with converter frequency.
Based on the mathematical models developed in the preceding sections, the converter duty ratios are computed for the two cases mentioned at different solar insolations (1 p:u: ¼ 100% solar insolation ¼ 1000 W=m2 ) and the results are plotted in Fig. 10. The IDB converter duty ratio is figured out to be higher for the GME operation.
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Table 2 Motor parameters 120 V 9:2 A 1500 rpm 1:5 O 0:02 H 0.621 0:02367 kg m2 0.000390 0.002387 0.5
V I N Ra La Ce J A1 B1 C1
Fig. 10. Converter duty ratio variation with solar insolation.
From Fig. 11 it can be noticed that the armature voltage is higher for GME operation than the MP operation satisfying the relation Vmn > Vm : However, under such conditions the motor armature current (Fig. 12) decreases (Imn oIm ), which in turn decreases the copper losses as shown in Fig. 13. Furthermore, GME operation results improved motor efficiency because of reduced copper losses (Fig. 14). Variation of starting torque, torque magnification factors for GME operation as compared to maximum power operation [6] are computed and the results are plotted
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Fig. 11. Motor armature voltage variation with solar insolation.
Fig. 12. Motor armature current variation with solar insolation.
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Fig. 13. Armature copper losses variation with solar insolation.
Fig. 14. Motor efficiency variation with solar insolation.
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Fig. 15. Torque magnification, starting torque variation with solar insolation.
in Fig. 15. From these results it can be noticed that, the GME operation has little effect on these factors.
5. Conclusions Interleaved dual boost converter power extraction capability from the PV system was verified experimentally and found to be extracting a higher amount of power from the SCA as compared to conventional boost converter. The suitability of this IDB converter for PV supplied DC motor system driving a centrifugal pump load is studied through simulations. Steady-state simulation results indicate that the GME operation improves the motor performance over the MP operation. Furthermore, interleaved operation of IDB converter reduces ripple content both on source and load side, resulting in reduced filtering requirements and also improves the SCA performance.
Appendix Mode 1: Vg r1 i1 i’1 ¼ ; L1 L1
ðA:1Þ
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Vg r2 i2 v0 ; i’2 ¼ L2 L2 L2
ðA:2Þ
i2 v0 iL ; V’0 ¼ C RC C
ðA:3Þ
X’1 ¼ ½A1 ½X þ ½B1 ½U :
ðA:4Þ
Mode 2: Vg r1 i1 v0 ; i’1 ¼ L1 L1 L1
ðA:5Þ
Vg r2 i2 v0 i’2 ¼ ; L2 L2 L2
ðA:6Þ
ði1 þ i2 Þ v0 iL ; V’0 ¼ C RC C
ðA:7Þ
X’2 ¼ ½A2 ½X þ ½B2 ½U :
ðA:8Þ
Mode 3: Vg r1 i1 v0 i’1 ¼ ; L1 L1 L1
ðA:9Þ
Vg r2 i2 i’2 ¼ ; L2 L2
ðA:10Þ
i1 v0 iL ; V’0 ¼ C RC C
ðA:11Þ
X’3 ¼ ½A3 ½X þ ½B3 ½U :
ðA:12Þ
Mode 4: Vg r1 i1 v0 ; i’1 ¼ L1 L1 L1
ðA:13Þ
Vg r2 i2 v0 ; i’2 ¼ L2 L2 L2
ðA:14Þ
ði1 þ i2 Þ v0 iL ; V’0 ¼ C RC C
ðA:15Þ
X’4 ¼ ½A4 ½X þ ½B4 ½U :
ðA:16Þ
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