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Dynamic behavior of a single-phase self-excited induction generator using a three-phase machine feeding single-phase dynamic load
Electrical Power and Energy Systems 47 (2013) 1–12
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Dynamic behavior of a single-phase self-excited induction generator using a three-phase machine feeding single-phase dynamic load S.N. Mahato a,⇑, S.P. Singh b, M.P. Sharma c a
Department of Electrical Engineering, National Institute of Technology, Durgapur 713 209, India Department of Electrical Engineering, Indian Institute of Technology, Roorkee 247 667, India c Alternate Hydro Energy Centre, Indian Institute of Technology, Roorkee 247 667, India b
a r t i c l e
i n f o
Article history: Received 29 June 2012 Received in revised form 25 October 2012 Accepted 27 October 2012
Keywords: Damping resistance Dynamic load Eigenvalue analysis Self-excited induction generator Single-phase power generation Transient analysis
a b s t r a c t This paper is motivated to analyze the transient behavior of a single-phase self-excited induction generator (SEIG) using a three-phase machine due to switching of single-phase dynamic load like induction motors. The generator consists of a three-phase star connected induction machine excited with threecapacitors and a single-phase induction motor (IM) load. The developed dynamic models of the SEIG and the motor are based on stationary reference frame d–q axes theory incorporating the effect of cross-saturation in the magnetic circuit of the machine and the equations of excitation capacitors are described by three-phase abc model. The system suffers from heavy transients during switching of induction motor and becomes unstable. These problems may be due to resonance caused by series capacitors and the inductive motor load. The use of damping resistors across one series capacitor is proposed to damp out the starting transients for the stable operation. The motor can be started up successfully using the damping resistor. The variation of the damping resistance with the increase in load on the motor after successful starting to maintain constant terminal voltage has been presented. The eigenvalue technique is also employed to examine the transient conditions in the studied SEIG-IM system. The simulated and experimental results are presented for both the unsuccessful and successful starting of the motor. These results are in close agreement with each other, which show the effectiveness of the approach. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The induction machines are increasingly being used as small capacity generators for isolated applications because of their distinct advantages like simplicity, low cost, ruggedness, little maintenance, absence of DC excitation. In remote and rural areas, the population is sparsely distributed and the electric loads are usually of single-phase types. In such cases, the single-phase power supply is preferred over three-phase one in order to make the distribution system simple and cost effective. Single-phase induction motor can be operated as SEIG [1], but limited to relatively small power outputs. For power ratings above 3 kW, three-phase machines being cheaper, more readily available with higher efficiency than equivalent sized single-phase machine, may be used for single-phase power generation. The single-phase induction motors used for different home appliances, constitute a major part of the domestic loads. However, a very little information on the operation of the SEIG feeding single-phase dynamic load has been reported. The steady-state analysis of three-phase SEIG feeding static load [2–5] has been reported. With C-2C configuration [2], almost ⇑ Corresponding author. Tel.: +91 9734734024; fax: +91 343 2547375. E-mail address: [email protected] (S.N. Mahato). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.10.067
balanced operation of three-phase delta connected SEIG feeding single-phase load is obtained at partial power output. However, the scheme is suitable only for constant power application. The steady-state performance of a single-phase self-regulated SEIG using a three-phase machine has been analyzed by Chan and Lai [3] using symmetrical component theory. A self-regulated self-excited single-phase induction generator using a three-phase machine was reported by Fukami et al. [4] by including series compensation capacitances for improved voltage regulation, but phase unbalance was a problem and the output power was small compared to the three-phase rating of the machine. An approach employing genetic algorithm for the analysis of single-phase operation of three-phase self-excited induction generator has been presented by Kumaresan [5]. Murthy et al. [6] have presented the dynamic and steady-state performance of a stand-alone SEIG feeding single-phase and three-phase loads with digitally controlled electronic load controller. The methodologies to use a three-phase SEIG for providing single-phase power using appropriate renewable energy sources with suitable prime-movers have been explored in [7]. The dynamic analysis of a self-excited induction generator (SEIG) considering the iron losses in the model that is both simple and accurate, has been carried out by Basic et al. [8]. Rahimi and Parniani [9] have investigated the effects of system and controller
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Nomenclature Cp, Cs Cm Rs, Rr
capacitances start/run capacitor of the motor per phase stator and rotor (referred to stator) resistances of the SEIG Rdsm, Rqsm resistance of stator main and auxiliary winding of the motor Rdrm, Rqrm rotor main and auxiliary winding resistance referred to stator winding Xls, Xlr per phase stator and rotor (referred to stator) leakage reactances of the SEIG Lls, Llr per phase stator and rotor (referred to stator) leakage inductances of the SEIG Lldsm, Llqsm stator main and auxiliary winding leakage inductances of the motor Lldrm, Llqrm rotor main and auxiliary winding leakage inductances referred to stator of the motor Lm magnetizing inductance of the SEIG Lmd, Lmq d-axis and q-axis magnetizing inductance of the SEIG considering cross-magnetization Lmdm, Lmqm d, q components of the magnetizing inductance of the motor Ldqm, Lqdm cross-saturation inductances of the motor
parameters and operating conditions on the dynamic and transient behavior of wind turbines with doubly-fed induction generators. The application of the model predictive control approach to control the voltage and frequency of a stand-alone wind generation system consisting of a wind turbine which drives an induction generator feeding an isolated load, has been investigated by Kassem [10]. A sliding mode control associated to the field oriented control of a dual-stator induction generator based wind energy conversion systems has been reported in [11]. The study on the transient performance of SEIG under unbalanced conditions is very much scarce. Shilpakar et al. [12] have studied the transient performance of three-phase SEIG supplying single-phase load with C-2C configuration of excitation. However, the voltage regulation is large and the de-excitation of the generator occurs for short-circuit fault at load terminals. Wang and Deng [13] have specified the transient performance of the induction generator under unbalanced excitation capacitor using an approach based on three-phase induction machine model to derive the dynamic equations of an isolated SEIG under unbalanced conditions. Jain et al. [14] have presented the generalized dynamic model of a delta connected three-phase self-excited induction generator under unbalanced operating conditions. The analysis was done considering the effect of main and cross flux saturation for load perturbation, three-phase and line-to-line short-circuit, opening of one capacitor, two capacitors and a single line at the capacitor bank, opening of single-phase load, two-phase load and a single line at load. But all the above analyses deal with static load. The study of the performance of SEIG feeding IM load is of importance, because these loads cause voltage dip and inrush current when put into operation. Sridhar et al. [15] reported a method to predict the steady-state behavior of a SEIG supplying an IM. The steady-state analysis and control of a wind-driven stand-alone SEIG feeding a three-phase induction motor was presented by Alghuwainem [16]. Singh et al. [17] identified the unstable behavior of shortshunt SEIG-IM configuration during the starting of the induction motor load and proposed damping resistors across series capacitors to obtain the stable operation. Transient analysis of SEIG feeding dynamic load is reported in [18,19]. But three-phase SEIG-IM system has been considered in all the above reported works [15–19]. The
Im, ILm
magnetizing current of the SEIG and the motor respectively ids, iqs d-axis and q-axis components of stator currents of the SEIG idr, iqr d-axis and q-axis components of rotor currents (referred to stator) of the SEIG idsm, iqsm main and auxiliary winding currents of the motor idrm, iqrm d, q components of rotor currents (referred to stator) of the motor isa, isb, isc stator phase currents in a, b, c phases of the SEIG current through capacitance Cp icp vsa, vsb, vsc stator voltages of a, b, c phases of the SEIG vds, vqs d-axis and q-axis components of stator voltages of the SEIG vdsm, vqsm voltage across main and auxiliary winding of the motor vmc, VL voltages across the start/run capacitor of the motor and output of the generator respectively xr, xrm rotor speed of the SEIG and the motor respectively Tshaftm shaft load torque Rb damping resistance
transient behavior of a single-phase SEIG with electronic load controller during the starting of a single-phase induction motor has been investigated by Singh et al. [20]. Hence, it is observed that the analysis of SEIG feeding single-phase dynamic load is inadequate. The single-phase induction motors are widely used in household applications. Considering the importance of single-phase induction motor in domestic use, further investigation is very much required for the single-phase SEIG feeding dynamic load. Further, the single-phase supply requirement is in the order of 230–240 V. The voltage ratings of normally available three-phase induction machines are 415 V. The output in the range of 230– 240 V is available by using a three-phase, 415 V, star connected induction machine with suitable connection. Moreover, considering the advantages of single-phase distribution system in remote and rural areas, this paper deals with the dynamic behavior of a single-phase SEIG using a three-phase star connected induction machine during the switching of induction motor load. The dynamic model of the SEIG and the motor have been developed in d–q axes stationary reference frame incorporating the effect of cross-saturation and the equations of the excitation capacitors are described by three-phase abc model. The machine performances are computed by solving the non-linear first order differential equations of the developed dynamic model using famous fourth-order Runge–Kutta numerical technique of integration. The transient behavior of the system has also been analyzed with eigenvalue analysis. Experimental results have been compared with the simulated results to validate the developed model.
2. Dynamic modeling The schematic diagrams of the SEIG without damping resistance and also the SEIG including damping resistance and the motor load are shown in Figs. 1a and 1b respectively. The generator consists of a three-phase star connected induction machine with three capacitors, Cp and two Cs’s, and a single-phase induction motor. Two capacitors (Cs’s) are connected in series with the two phases of the stator winding and one (Cp) is connected in parallel with the motor load.
S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
p½i ¼ ½L1 1 f½m ½R1 ½i xr ½G1 ½ig
3
ð2Þ
Also, from Figs. 1a and 1b, the following equations can be written:
Fig. 1a. Connection diagram of the single-phase self-excited induction generator.
pmcp ¼
1 icp Cp
ð3Þ
pmbcs ¼
1 isb Cs
ð4Þ
pmccs ¼
1 isc Cs
ð5Þ
icp ¼ isa iL
ð6Þ
msb þ mbcs mccs msc ¼ 0
ð7Þ
and,
msa þ mcp mbcs msb ¼ 0
ð8Þ
where vsa, vsb and vsc are voltages across stator phases A, B and C respectively, and vcp, vbcs and vccs are voltages across capacitances Cp, Cs of phase B and Cs of phase C respectively and p = (d/dt) is a time derivative operator. When the damping resistance Rb is connected across the series capacitor of phase B, as shown in Fig. 1b, the Eq. (4) is modified as:
pmbcs ¼
1 mbcs isb Cs Rb
ð9Þ
Expressing the stator phase variables of Eqs. (7) and (8) in terms of d–q variables, we get, Fig. 1b. Connection diagram of the single-phase self-excited induction generator including damping resistance.
mds ¼
mbcs þ mccs 2mcp 3
ð10Þ
and, 2.1. Modeling of the SEIG
mqs ¼ The dynamic model of the three-phase squirrel cage induction generator is developed by using stationary d–q axes reference frame and the relevant volt-ampere equations are as:
½m ¼ ½R1 ½i þ ½L1 p½i þ xr ½G1 ½i
ð1Þ
The matrices of Eq. (1) are defined as:
½m ¼ ½mds
mqs mdr mqr T ; ½i ¼ ½ids iqs idr iqr T
2
Lls þ Lmd
Ldq
Lmd
Ldq
Ldq
Lls þ Lmq
Ldq
Lmq
Lmd
Ldq
Llr þ Lmd
Ldq
Ldq
Lmq
Ldq
Llr þ Lmq
6 6 ½L1 ¼ 6 4 2
0 6 0 6 ½G1 ¼ 6 4 0 Lm
0 0
0 0
Lm
0
0
Llr þ Lm
7 7 7 5
dLm imd imq ; djIm j jIm j
7 7 7 Llr Lm 5
Te ¼
imd imq
and Lmq ¼ Lm þ Ldq
2 pxr P
ð12Þ
where the developed electromagnetic torque of the SEIG is expressed as:
0
Lmd ¼ Lm þ Ldq
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffi 2 2 imd þ imq 2;
T shaft ¼ T e þ J
Here, suffixes d, q refer to d and q axis (in stationary reference frame), and s and r refer to stator and rotor. The equations of Ldq, Lmd and Lmq are given as:
Ldq ¼
ð11Þ
where imd = ids + idr and imq = iqs + iqr are direct and quadrature axes components of the magnetizing current. The magnetizing inductance is calculated from the magnetizing characteristics between Lm and im. The torque balance equation of SEIG is defined as:
3
3
0 0
pffiffiffi 3
where vds and vqs are d-axis and q-axis components of stator voltages respectively. Since, the magnetization characteristics of the SEIG are non-linear due to saturation, the magnetizing inductance depends on the instantaneous value of the magnetizing current. The magnetizing current must be calculated at each step of the integration as:
im ¼ ½R1 ¼ diag½Rs Rs Rr Rr
mbcs mccs
imq : imd
From the Eq. (1), the current derivative can be expressed as:
3P Lm ðidr iqs iqr ids Þ 4
ð13Þ
The shaft torque, Tshaft of prime-mover and speed is represented by a linear curve given as:
T shaft ¼ k1 k2 xr where Tshaft is the shaft torque which shows the drooping characteristic of prime-mover and k1 and k2 are constants. J is the moment of
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inertia of the induction machine including the machine (primemover) coupled on its shaft. From Eq. (12), we get,
2 pxrm Pm
ð18Þ
From Eq. (18), the speed derivative may be defined as:
P ðT shaft T e Þ 2J
pxr ¼
T e m ¼ T shaftm þ J m
ð14Þ pxrm ¼
The differential Eqs. (2)–(5) and (14) describe the dynamic model for the prediction of transient performance of the three-phase SEIG for single-phase power generation.
Pm ðT e m T shaftm Þ 2J m
ð19Þ
Hence, Eqs. (16), (17), and (19) represent the dynamic model of the single-phase induction motor.
2.2. Modeling of the single-phase induction motor 3. Experimental set-up The circuit diagram of a single-phase induction motor is shown in Fig. 2. The dynamic model has been developed in d–q axis stationary reference frame. The voltage-current equations can be written as:
½mm ¼ ½R2 ½iL þ ½L2 p½iL þ xrm ½G2 ½iL
ð15Þ
The matrices of Eq. (15) are defined as:
½mm ¼ ½mdsm
mqsm mdrm mqrm T ; ½iL ¼ ½idsm iqsm idrm iqrm T
½R2 ¼ diag½Rdsm Rqsm Rdrm Rqrm 2
Lldsm þ Lmdm
6 6 ½L2 ¼ 6 4
Ldqm
Lmdm
Ldqm
Lqdm
Llqsm þ Lmqm
Lqdm
Lmqm
Lmdm
Ldqm
Lldrm þ Lmdm
Ldqm
Lqdm
Lmqm
Lqdm
Llqrm þ Lmqm
2
0
0
0
6 6 ½G2 ¼ 6 4
0 0
0 L mqm a
0 0
aLmdm
0
aðLldrm þ Lmdm Þ
0
3
0
7 7
3
4. Experimental procedure
7 7 7 5
ðL þL Þ7 lqrm a mqm 5
0
From the Eq. (15), the current derivative can be expressed as:
p½iL ¼ ½L2 1 f½mm ½R2 ½iL xrm ½G2 ½iL g
ð16Þ
In order to use the correct value of magnetizing inductance, the amplitude of the magnetizing current space vector is evaluated at each step of computation as:
iLm
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2 2 ¼ iLmd þ iLmq = 2
where iLmd = idsm + idrm and iLmq = iqsm + iqrm are direct and quadrature axes components of the magnetizing current space vector. The derivative of the voltage across the capacitor connected in series with the auxiliary winding is defined as:
pmmc ¼
1 iqsm Cm
ð17Þ
The equation of the mechanical motion is given by,
In the laboratory test rig, a three-phase star-connected squirrel cage induction machine, coupled to a separately excited DC motor, which operates as the prime-mover, has been used for experimentation. One single-phase induction motor is used as a dynamic load. The parameters of both the induction machines are obtained by conducting DC resistance test and block rotor test. The magnetization characteristics of the induction machines under test are achieved using synchronous speed test. All these are given in Appendix A.
Initially, the SEIG is excited at no-load condition and the voltages are built-up in the stator windings. After successful voltage build-up, the single-phase induction motor i.e., the dynamic load is suddenly switched onto the terminals of the generator. The voltage and the current waveforms of Phase-A of the SEIG and the main winding of the single-phase induction motor are recorded with Fluke-43B Power Quality Analyzer. The observations are discussed in the next section. In some cases, the values of the capacitors Cp and/or Cs are changed at the time of switching of the motor load. While performing the experimentation with damping resistance, it is connected across the series capacitor Cs of phase-B at the time of switching of the dynamic load. The waveforms are recorded using the same instrument. 5. Results and discussion The simulated performance and experimental results are presented for starting of the induction motor load with different values of capacitors and also with and without damping resistances. The experimental results are compared with the simulated results to validate the developed mathematical model. From the steadystate model of the generator, it has been found that to obtain a voltage of 235 V at no-load, the required capacitances are Cp = Cs = 44 lF. The performance of the SEIG has been studied during switching of the induction motor load for different cases as follows:
Fig. 2. Circuit diagram of the single-phase induction motor.
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5.1. Without damping resistance
300 250
Vsa (volt)
Wrm (rad/sec.)
The generator is initially excited at no-load with Cp = Cs = 44 lF and there is voltage build-up of the SEIG. Keeping the values of the capacitors unchanged when the single-phase motor load is switched onto the SEIG terminals, the inrush transients are obtained in both the generator and motor currents. The motor cannot be started-up successfully and highly oscillatory behavior of sustained nature due to resonance problem of series capacitors and the motor load being inductive in nature is observed. Figs. 3–5 show such oscillatory waveforms of the voltage and current of the phase A of the generator, main winding of the motor and the motor speed respectively. The starting of the single-phase motor without any load has been attempted by changing the capacitances Cp and/or Cs. Initially, the SEIG is excited with Cp = Cs = 44 lF at no-load and after voltage build-up, the dynamic load is switched onto the terminals of the generator. The values of Cp and/or Cs are changed at the instant of switching of the motor load. With different variations of Cp and Cs at the instant of switching of the motor, attempts have been made to start the motor successfully but without result. It is found that the sustained oscillations are present in all these cases and the system becomes unstable. The reason for such type of oscillations is the resonance because of the series capacitors and the inductive dynamic load. These results have been listed in Table 1, which shows the different cases when the generator is excited at no-load with Cp = Cs = 44 lF and the values of Cp and/or Cs are changed at the instant of switching of the motor. It is found that sustained oscillations are present in all the cases. Hence, simply by changing
200 150 100 50 0 -50 1.6
1.8
2
2.2
2.4
2.6
2.8
3
Table 1 Summary of results of starting of the motor without damping resistance. Sl. no.
1 2 3 4 5 6 7
Values of Cp and Cs before switching on the motor
Values of Cp and Cs after switching on the motor
Cp (lF)
Cs (lF)
Cp (lF)
Cs (lF)
44 44 44 44 44 44 44
44 44 44 44 44 44 44
44 44 44 SO 30 SO 30
44 80 30 44 44 80 30
Remarks
Sustained Sustained Sustained Sustained Sustained Sustained Sustained
200 0 -200 1 .8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
Isa (amp.)
time (sec.) 20 10 0 -10 -20 1 .6
1 .8
2
2.2
2.4
2.6
2.8
time (sec.) simulated
experimental
Vmw (volt)
Fig. 3. Voltage and current waveforms of phase A of the SEIG during switching of the motor load with constant Cp and Cs.
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
Isa (amp.)
time (sec.) 20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
time (sec) simulated
2.8
3.4
Fig. 5. Simulated waveform of the motor speed during switching on with constant Cp and Cs.
400
-400 1 .6
3.2
time (sec.)
experimental
Fig. 4. Voltage and current waveforms of main winding of the single-phase motor during switching on with constant Cp and Cs.
oscillation oscillation oscillation oscillation oscillation oscillation oscillation
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To examine the different transient conditions due to switching of IM load, eigenvalue technique has also been employed. Table 2 gives the eigenvalues for the conditions when the SEIG is at noload, at the moment of connection of the IM load and after starting of the IM with Cp = Cs = 44 lF without using damping resistance. From the second column, it is found that the third complex-conjugated eigenvalue pair (i.e., 0.03 ± j 313.27) is very close to the imaginary axis and one eigenvalue is at the origin when the IM load is not connected. Hence, at no-load, the SEIG can maintain sustained self-excitation to generate voltage. The third column lists the eigenvalue results at the moment of connecting the IM load to SEIG. The fifth complex conjugated eigenvalue pair (i.e., 9.2 ± j 299.7) have positive real parts. This signifies the condition of self-excitation of the SEIG feeding IM load and means that when the IM load is connected to the SEIG terminals, the SEIG has the ability to start the IM load. The eigenvalues listed in the fourth column of Table 2 are obtained after starting of the IM load. It is found
Table 2 Eigenvalues for Cp = Cs = 44 lF without damping resistance. Eigenvalues
Without IM load Cp = 44 lF, Cs = 44 lF
1 2 3 4 5 6 7
With IM load and without damping resistance (Cp = 44 lF and Cs = 44 lF)
132.30 ± j 878.98 96.58 ± j 878.25 0.03 ± j 313.27 0.0 – – –
At the moment of connection
After starting of the IM load
150.0 ± j 114.4 ± j 162.9 ± j 161.8 ± j 9.2 ± j 16.0 13.1
150.5 ± j 114.4 ± j 167.4 ± j 175.8 ± j 9.1 ± j 4.5 ± j
1449.4 877.8 470.1 291.3 299.7
1448.5 877.8 467.2 313.9 300.0 141.7
the values of the capacitors at the instant of switching of the motor, it is not possible to start it successfully.
Table 3 Eigenvalues for different values of capacitances without damping resistance. Eigenvalues
Vsa (volt)
1 2 3 4 5 6
Without IM load
With IM load and without damping resistance (after starting of the IM load)
Cp = 44, Cs = 44 (lF)
Cp = 80, Cs = 44 (lF)
Cp = 30, Cs = 44 (lF)
Cp = 44, Cs = 80 (lF)
Cp = 44, Cs = 30 (lF)
Cp = 80, Cs = 80 (lF)
Cp = 30, Cs = 30 (lF)
132.30 ± j 878.98 96.58 ± j 878.25 0.03 ± j 313.27 0.0 – –
151.8 ± j 114.3 ± j 171.3 ± j 171.6 ± j 8.7 ± j 5.7 ± j
150.0 ± j 114.4 ± j 166.0 ± j 177.5 ± j 9.3 ± j 4.1 ± j
152.0 ± j 120.8 ± j 188.5 ± j 148.3 ± j 8.4 ± j 6.8 ± j
148.8 ± j 112.2 ± j 156.5 ± j 184.9 ± j 4.5 ± j 3.5 ± j
154.9 ± j 120.6 ± j 187.7 ± j 147.7 ± j 8.7 ± j 7.7 ± j
148.9 ± j 112.3 ± j 154.2 ± j 186.8 ± j 4.6 8 ± j 3.0 ± j
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
1096.8 878.1 467.0 306.6 300.5 140.9
2.6
2.8
1740.5 877.7 467.4 316.7 299.8 142.0
3
3.2
3.4
3.6
3
3.2
3.4
3.6
1436.8 647.3 400.9 287.2 283.8 139.1
1461.7 1065.8 539.8 320.6 307.8 142.4
1080.2 647.5 402.8 280.4 285.1 138.2
time (sec.) 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
2.8
time (sec.)
experimental
simulated Fig. 6. Voltage and current waveforms of phase A of the SEIG during switching on of the motor load with damping resistance.
Vmw (volt)
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
time (sec.) Imw (amp.)
Isa (amp.)
20
20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
2.8
time (sec.) simulated
experimental
Fig. 7. Voltage and current waveforms of the main winding of the motor during switching on with damping resistance.
1750.9 1065.7 542.0 323.1 307.8 142.7
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S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
400
Wrm (rad/sec.)
300 200 100 0 -100 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
time (sec.) Fig. 8. Simulated waveform of the motor speed during switching on with damping resistance.
Vsb (V)
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
Isb (A)
20 10 0 -10 -20 1.6
Time (Sec.) simulated
experimental
Vsc (V)
Fig. 9. Voltage and current waveforms of phase B of the SEIG during switching on of the motor load with damping resistance.
400 200 0 -200
Isc (A)
-400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
20 10 0 -10 -20 1.6
Time (Sec.) simulated
experimental
Fig. 10. Voltage and current waveforms of phase C of the SEIG during switching on of the motor load with damping resistance.
Fig. 11a. Measured THD of the voltage and current of the main winding of the motor after successful starting.
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5.2. With damping resistance The starting of the motor load has been attempted by inserting the damping resistances across the capacitor of either phase B or phase C of the SEIG. It has been found that successful starting of the motor load is not possible by connecting damping resistance across the capacitor of phase C, but is possible if the damping resistance is connected across the capacitor of phase B. The generator is initially excited at no-load with Cp = Cs = 44 lF. After successful build-up of voltage, the motor is switched onto the terminals of the SEIG. Simultaneously the suitable value of damping resistance is connected across the capacitor of phase B of the generator. It is observed that the starting oscillations are damped out and the motor load is started-up successfully. In this case, the resonance problem is solved by using the damping resistance. The selection procedure of the damping resistance for successful starting of the motor at no-load and to maintain the rated terminal voltage while increasing the load on the motor after successful starting, is given in Appendix B. The voltage and current waveforms of stator phase A of the generator, main winding of the motor and the speed of the motor during starting of the motor with capacitances Cp = Cs = 44 lF and damping resistance Rb = 28 X which is connected across the capacitor of phase B of the generator at the time of switching of the motor are given in Figs. 6–8 respectively. It is found that the motor is started up successfully using the damping resistance. Also, the voltage and current waveforms of stator phases B and C of the generator during starting of the motor including damping resistance are shown in Figs. 9 and 10 respectively. Both the voltages and the currents are reduced slightly. The measured THD of the voltage and current of the main winding and few cycles of the main winding voltage and current of the motor at steady-state after successful starting with Cp = Cs = 44 lF are given in Figs. 11a and 11b respectively. It is observed that the harmonics content in the voltage and current of main winding of the motor are very low, which indicates the good quality of power supplied to the motor. Table 4 gives the eigenvalue results for successful starting of the motor with damping resistance. In the third column, the complex conjugated eigenvalues (0.2 ± j 296.9) are located in the right half of complex plane at the moment of connection of the IM load to the SEIG terminals. It means that the SEIG has the capability to start the motor. In the fourth column, it is found that one complex conjugated eigenvalue pair (0.0 ± j 305.1) lie on imaginary axis and all the other eigenvalues have negative real parts. Hence, according to the view point of system dynamic stability, the SEIG-IM system is stable at steady-state condition with damping resistance and
Fig. 11b. Main winding voltage and current waveforms of the motor at steady-state after successful starting.
Table 4 Eigenvalues for Cp = 44 lF and Cs = 44 lF with damping resistance. Eigenvalues
Without IM load Cp = 44 lF Cs = 44 lF
1 2 3 4 5 6 7
132.30 ± j 878.98 96.58 ± j 878.25 0.03 ± j 313.27 0.0 – – –
With IM load including damping resistance (Cp = 44 lF and Cs = 44 lF) At the moment of connection
Under steadystate condition
152.6 ± j 186.5 ± j 205.4 ± j 178.0 ± j 0.2 ± j 15.3 13.1
215.2 ± j 141.0 ± j 291.7 ± j 402.4 ± j 16.3 ± j 0.0 ± j
1449.3 870.7 489.3 289.7 296.9
2135.6 1120.7 709.8 467.6 268.1 305.1
that there are two eigenvalue pairs (i.e., 9.1 ± j 300.0 and 4.5 ± j 141.7) having positive real parts which indicates that the system is unstable after starting of the IM. Similarly, Table 3 lists the eigenvalues of the SEIG-IM system after starting of the IM when the values of Cp and/or Cs are either reduced or increased at the time switching of the motor load. The second column is same as the second column of Table 2, because of the same conditions. It is found that the fifth and sixth eigenvalue pairs of all the other columns of Table 3 have positive real parts indicating the unstable system after connecting the motor load for those values of capacitances. Hence, the eigenvalue analysis confirms the unsuccessful starting and the unstable behavior of the SEIG-IM system without any damping resistance.
Vmw (volt)
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
2.8
3
3.2
3.4
3.6
time (sec.) Imw (amp.)
20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
time (sec.)
experimental
simulated Fig. 12. Voltage and current waveforms of the main winding of the motor during switching on with high value of damping resistance.
9
Vmw (volt)
S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
Imw (amp.)
time (sec.) 20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
2.8
experimental
time (sec.) simulated
Fig. 13. Voltage and current waveforms of the main winding of the motor during switching on with low value of damping resistance.
Stator phase currents (amp)
5 4
Isa Isb Isc
3 2 1 0 200
300
400
500
600
700
Motor load (watt) Fig. 14. Experimentally obtained variation of stator phase currents with increase of load on the motor after successful starting.
thus, the eigenvalue results confirm the simulated and the experimental results. Figs. 12 and 13 indicate the effect of damping resistances on starting of the motor load. It is found that if higher value of damping resistance (say, Rb = 50 X) is used keeping the values of the capacitors unchanged, there is sustained oscillation (shown in Fig. 12) and with the lower value of the damping resistance (say, Rb = 10 X), the voltage of the generator collapses (shown in Fig. 13). Actually, for very low value of the damping resistance,
the damping effect becomes very high and the voltage of the SEIG collapses. Hence, for successful starting of the motor, proper value of damping resistance should be chosen. It is seen that after successful starting of the motor without any load, if the damping resistance is increased, the oscillation occurs. Hence, the damping resistances should be kept in the circuit while the motor is at noload. Fig. 14 shows the experimentally obtained variations of stator phase currents with increase of load on the motor after successful starting with proper value of damping resistance. It is found that the motor draws 200 W from the generator at no-load. The currents in both A and C phases increase while in phase B, it decreases with increase of load on the motor. After successful starting of the motor with Cp = Cs = 44 lF and damping resistance Rb = 28 X, the output voltage of the generator becomes 230 V. Now, if the load on the motor is gradually increased, the output voltage reduces. To keep the output voltage constant at this value, either the capacitances have to be increased if damping resistance is kept unchanged, or the damping resistance has to be changed keeping the capacitors’ values fixed. Fig. 15 shows the variation of the damping resistance with increase in load on the motor to maintain terminal voltage constant after successful starting with Cp = Cs = 44 lF which are kept unchanged. It is found that the value of the damping resistance is reduced with increase in load on the motor to keep the terminal voltage of the SEIG at constant value. The theoretical and the experimental values are very close to each other indicating the effectiveness of this approach. There will be small amount of power loss in the damping resistance. The variation of power loss in the damping resistance with increase in load on the motor keeping constant terminal voltage is shown in Fig. 16.
30 simulated 25
experimental values
Rb (ohm)
20 15 10 5 0
0
100
200
300
400
500
600
700
Motor load (watt) Fig. 15. Variation of damping resistance with the increase in load on the motor keeping capacitances unchanged.
S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
Power loss in Rb (watt)
10
80 60 40 20 0 200
250
300
350
400
450
500
550
600
650
700
Motor load (watt) Fig. 16. Power loss in the damping resistance with increase in load on the motor.
Fig. B1. Flow chart for determination of damping resistance.
It is seen that the power loss in the damping resistance when the motor is at no-load is 80 W i.e., 3.6% of the three-phase rating of the SEIG and decreases with increase in load on the motor. Since, the current in phase B of the SEIG decreases with increase of load, the voltage across the capacitance of phase B i.e., the voltage across the damping resistance reduces, and hence, the power loss in the
damping resistance also reduces with increase in load on the motor. From the figure, it is observed that the power loss is 10 W when the motor load is 700 W i.e., the power loss becomes 0.45% of the three-phase rating of the machine, which is negligible. Hence, though the damping resistance always remains in the circuit, the power loss in it is very small.
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Lmqm
6. Conclusions The transient behavior of a single-phase SEIG using three-phase machine feeding single-phase dynamic load is presented. It is found that the motor cannot be started up successfully while switched onto the SEIG terminals directly, and sustained oscillation is observed. Attempts have been made for successful starting of the motor by changing the values of the capacitors, but without result. Successful starting of the motor load is only possible with the damping resistance connected across the capacitor of phase B of the SEIG. The motor at no-load can be started-up successfully if the damping resistance is chosen properly. During starting, the lower value of damping resistance results into voltage collapse, while the higher value results in sustained oscillations. With the increase in motor load after successful starting, either the capacitances may be increased or the damping resistance may be changed (i.e., Rb is reduced) to maintain the constant terminal voltage. An algorithm has been developed for selection of damping resistance for successful starting of the motor and to maintain the terminal voltage constant while loading the motor. Moreover, the harmonics contents in the voltage and current of the main winding of the motor after successful starting with damping resistance are very small indicating the good quality of power supplied to the motor. The eigenvalue analysis confirms the simulated and experimental results. The experimental results show close agreement with the simulated results and thus the proposed model is validated. Hence, it is concluded that the single-phase induction motors, which are very common in domestic use, can be started-up successfully by using this scheme and with the proposed manner. Appendix A The specifications of the induction machines and the primemover characteristics are given below: A.1. Induction generator 2.2 kW, 3-phase, 4-pole, 50 Hz, 415 V, 4.5 A, star connected, 1440 rpm, Rs = 3.735 X, Rr = 2.91 X, Xls = 4.727 X, Xlr = 4.727 X. Base impedance = 53.24 X. Base speed = 1500 rpm, J = 0.0842 kg m2. The magnetizing inductance Lm is related to the magnetizing current in the following manner:
Lm
¼ 0:3177
for Im 6 0:75
¼ 0:3502 0:0349Im 0:0017I2m ¼ 0:17667
for 0:75 < Im 6 4:25 for Im > 4:25
A.2. Induction motor 1 hp, 230 V, 6 A, 4-poles, capacitor-start capacitor-run singlephase induction motor. Rdsm = 3.41 X, Rdrm = 4.37 X, Xldsm = Xldrm = 3.99 X, Rqsm = 11.22 X, Rqrm = 8.01 X, Xlqsm = Xlqrm = 6.433 X, Turns ratio, a = Nq/Nd = 1.4, and Cm = 100 lF for starting and 6.3 lF for running. The magnetization curves are modeled as given under based on test data: Main winding: Lmdm ¼ 0:3204 for ILm 6 1:22 ¼ 0:6692 þ 1:695ILm 0:9292I2Lm þ 0:168I3Lm for 1:22 < ILm 6 2:24 ¼ 0:4523 0:0476ILm þ 0:00164I2Lm ¼ 0:244
Auxiliary winding:
for 2:24 < ILm 6 5:32 for ILm > 5:32
¼ 0:662
for ILm 6 0:93
¼ 2:074 þ 7:066ILm 6:03I2Lm þ 1:713I3Lm
for 0:93 < ILm 6 1:32
¼ 0:6856 þ 0:0427ILm 0:0317I2Lm ¼ 0:6158
for 1:32 < ILm 6 2:29 for ILm > 2:29
A.3. Prime-mover characteristics
T shaft ¼ k1 k2 xr where k1 = 249.39 and k2 = 0.7875. Appendix B The selection procedure of the damping resistance for successful starting of the motor without load and to maintain the rated terminal voltage while increasing the load on the motor is shown in Fig. B1. In this flowchart, initially a small value of damping resistance has been chosen. For this small value of damping resistance, the generator voltage collapses at the time of switching on the motor load. This resistance is increased gradually such that for a particular value of this resistance, there is no voltage collapse and the motor is started up successfully. This value of the resistance is the damping resistance required to start the motor successfully at noload. It has been found that after successful starting of the motor, the output voltage increases with decrease in the value of the damping resistance. If the load on the motor is increased, the output voltage of the SEIG reduces. Hence, to maintain the terminal voltage constant at 230 V with increase in load on the motor, the damping resistance is reduced gradually. The value of the resistance corresponding to the terminal voltage of 230 V is the required damping resistance for that particular load. References [1] Murthy SS. A novel self-excited self-regulated single-phase induction generator Part 1: basic system and theory. IEEE Trans Energy Convers 1993;8:377–82. [2] Bhattacharya JL, Woodward JL. Excitation balancing of self-excited induction generator for maximum power output. IEE Proc, Gener, Transm Distrib 1988;135:88–97. [3] Chan TF, Lai LL. Steady-state analysis and performance of a single-phase selfregulated self-excited induction generator. IEE Proc, Gener, Transm Distrib 2002;149:233–41. [4] Fukami T, Kaburaki Y, Kawahara S, Miyamoto T. Performance analysis of a selfregulated self-excited single-phase induction generator using a three-phase machine. IEEE Trans Energy Convers 1999;14:622–7. [5] Kumaresan N. Analysis and control of three-phase self-excited induction generators supplying single-phase AC and DC loads. IEE Proc, Electr Power Appl 2005;152:739–47. [6] Murthy SS, Ramrathnam, Gayathri MSL, Naidu K, Siva U. A novel digital control technique of electronic load controller for SEIG based micro-hydel power generation. In: Proc of IEEE int conf on power electronics, drives and energy systems 2006 (PEDES ’06); 2006. [7] Murthy SS, Bhuvaneswari G, Gao S, Ahuja RK. Self-excited induction generator for renewable energy applications to supply single-phase loads in remote locations. In: Proc of IEEE int conf on sustainable energy technologies (ICSET); 2010. [8] Basic M, Vukadinovic D, Petrovic G. Dynamic and pole-zero analysis of selfexcited induction generator using a novel model with iron losses. Int J Electr Power Energy Syst 2012;42:105–18. [9] Rahimi M, Parniani M. Dynamic behavior analysis of doubly-fed induction generator wind turbines – the influence of rotor and speed controller parameters. Int J Electr Power Energy Syst 2010;32:464–77. [10] Kassem AM. Robust voltage control of a stand alone wind energy conversion system based on functional model predictive approach. Int J Electr Power Energy Syst 2012;41:124–32. [11] Amimeur H, Aouzellag D, Abdessemed R, Ghedamsi K. Sliding mode control of a dual-stator induction generator for wind energy conversion systems. Int J Electr Power Energy Syst 2012;42:60–70. [12] Shilpakar LB, Singh B, Singh BP. Dynamic behavior of three-phase self-excited induction generator for single-phase power generation. Electr Power Syst Res 1998;48:37–44. [13] Wang L, Deng RY. Transient performance of an isolated induction generator under unbalanced excitation capacitor. IEEE Trans Energy Convers 1999;14:887–93.
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[14] Jain SK, Sharma JD, Singh SP. Transient performance of three-phase selfexcited induction generator during balanced and unbalanced faults. IEE Proc, Gener, Transm Distrib 2002;149:50–7. [15] Sridhar L, Singh B, Jha CS, Singh BP. Analysis of self-excited induction generator feeding induction motor. In: IEEE power engineering society summer meetings; 1994. p. 1–7. [16] Alghuwainem SM. Steady-state analysis of an isolated self-excited induction generator supplying an induction motor load. IEEE Int Conf Electr Mach Drives 1999:351–3. [17] Singh SP, Jain SK, Sharma J. Voltage regulation optimization of compensated self-excited induction generator with dynamic load. IEEE Trans Energy Convers 2004;19:724–32.
[18] Singh B, Sridhar L, Jha CS. Transient analysis of self-excited induction generator supplying dynamic load. Electr Mach Power Syst 1999;27:941–54. [19] Singh B, Murthy SS, Gupta S. Transient analysis of self-excited induction generator with electronic load controller (ELC) supplying static and dynamic loads. Int Conf Power Electr Drive Syst 2003;1:771–6. [20] Singh B, Murthy SS, Gupta S. An electronic voltage and frequency controller for single-phase self-excited induction generators for pico hydro applications. Proc Int Conf Power Electr Drives Syst 2005;1:240–5.
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Dynamic behavior of a single-phase self-excited induction generator using a three-phase machine feeding single-phase dynamic load S.N. Mahato a,⇑, S.P. Singh b, M.P. Sharma c a
Department of Electrical Engineering, National Institute of Technology, Durgapur 713 209, India Department of Electrical Engineering, Indian Institute of Technology, Roorkee 247 667, India c Alternate Hydro Energy Centre, Indian Institute of Technology, Roorkee 247 667, India b
a r t i c l e
i n f o
Article history: Received 29 June 2012 Received in revised form 25 October 2012 Accepted 27 October 2012
Keywords: Damping resistance Dynamic load Eigenvalue analysis Self-excited induction generator Single-phase power generation Transient analysis
a b s t r a c t This paper is motivated to analyze the transient behavior of a single-phase self-excited induction generator (SEIG) using a three-phase machine due to switching of single-phase dynamic load like induction motors. The generator consists of a three-phase star connected induction machine excited with threecapacitors and a single-phase induction motor (IM) load. The developed dynamic models of the SEIG and the motor are based on stationary reference frame d–q axes theory incorporating the effect of cross-saturation in the magnetic circuit of the machine and the equations of excitation capacitors are described by three-phase abc model. The system suffers from heavy transients during switching of induction motor and becomes unstable. These problems may be due to resonance caused by series capacitors and the inductive motor load. The use of damping resistors across one series capacitor is proposed to damp out the starting transients for the stable operation. The motor can be started up successfully using the damping resistor. The variation of the damping resistance with the increase in load on the motor after successful starting to maintain constant terminal voltage has been presented. The eigenvalue technique is also employed to examine the transient conditions in the studied SEIG-IM system. The simulated and experimental results are presented for both the unsuccessful and successful starting of the motor. These results are in close agreement with each other, which show the effectiveness of the approach. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The induction machines are increasingly being used as small capacity generators for isolated applications because of their distinct advantages like simplicity, low cost, ruggedness, little maintenance, absence of DC excitation. In remote and rural areas, the population is sparsely distributed and the electric loads are usually of single-phase types. In such cases, the single-phase power supply is preferred over three-phase one in order to make the distribution system simple and cost effective. Single-phase induction motor can be operated as SEIG [1], but limited to relatively small power outputs. For power ratings above 3 kW, three-phase machines being cheaper, more readily available with higher efficiency than equivalent sized single-phase machine, may be used for single-phase power generation. The single-phase induction motors used for different home appliances, constitute a major part of the domestic loads. However, a very little information on the operation of the SEIG feeding single-phase dynamic load has been reported. The steady-state analysis of three-phase SEIG feeding static load [2–5] has been reported. With C-2C configuration [2], almost ⇑ Corresponding author. Tel.: +91 9734734024; fax: +91 343 2547375. E-mail address: [email protected] (S.N. Mahato). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.10.067
balanced operation of three-phase delta connected SEIG feeding single-phase load is obtained at partial power output. However, the scheme is suitable only for constant power application. The steady-state performance of a single-phase self-regulated SEIG using a three-phase machine has been analyzed by Chan and Lai [3] using symmetrical component theory. A self-regulated self-excited single-phase induction generator using a three-phase machine was reported by Fukami et al. [4] by including series compensation capacitances for improved voltage regulation, but phase unbalance was a problem and the output power was small compared to the three-phase rating of the machine. An approach employing genetic algorithm for the analysis of single-phase operation of three-phase self-excited induction generator has been presented by Kumaresan [5]. Murthy et al. [6] have presented the dynamic and steady-state performance of a stand-alone SEIG feeding single-phase and three-phase loads with digitally controlled electronic load controller. The methodologies to use a three-phase SEIG for providing single-phase power using appropriate renewable energy sources with suitable prime-movers have been explored in [7]. The dynamic analysis of a self-excited induction generator (SEIG) considering the iron losses in the model that is both simple and accurate, has been carried out by Basic et al. [8]. Rahimi and Parniani [9] have investigated the effects of system and controller
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Nomenclature Cp, Cs Cm Rs, Rr
capacitances start/run capacitor of the motor per phase stator and rotor (referred to stator) resistances of the SEIG Rdsm, Rqsm resistance of stator main and auxiliary winding of the motor Rdrm, Rqrm rotor main and auxiliary winding resistance referred to stator winding Xls, Xlr per phase stator and rotor (referred to stator) leakage reactances of the SEIG Lls, Llr per phase stator and rotor (referred to stator) leakage inductances of the SEIG Lldsm, Llqsm stator main and auxiliary winding leakage inductances of the motor Lldrm, Llqrm rotor main and auxiliary winding leakage inductances referred to stator of the motor Lm magnetizing inductance of the SEIG Lmd, Lmq d-axis and q-axis magnetizing inductance of the SEIG considering cross-magnetization Lmdm, Lmqm d, q components of the magnetizing inductance of the motor Ldqm, Lqdm cross-saturation inductances of the motor
parameters and operating conditions on the dynamic and transient behavior of wind turbines with doubly-fed induction generators. The application of the model predictive control approach to control the voltage and frequency of a stand-alone wind generation system consisting of a wind turbine which drives an induction generator feeding an isolated load, has been investigated by Kassem [10]. A sliding mode control associated to the field oriented control of a dual-stator induction generator based wind energy conversion systems has been reported in [11]. The study on the transient performance of SEIG under unbalanced conditions is very much scarce. Shilpakar et al. [12] have studied the transient performance of three-phase SEIG supplying single-phase load with C-2C configuration of excitation. However, the voltage regulation is large and the de-excitation of the generator occurs for short-circuit fault at load terminals. Wang and Deng [13] have specified the transient performance of the induction generator under unbalanced excitation capacitor using an approach based on three-phase induction machine model to derive the dynamic equations of an isolated SEIG under unbalanced conditions. Jain et al. [14] have presented the generalized dynamic model of a delta connected three-phase self-excited induction generator under unbalanced operating conditions. The analysis was done considering the effect of main and cross flux saturation for load perturbation, three-phase and line-to-line short-circuit, opening of one capacitor, two capacitors and a single line at the capacitor bank, opening of single-phase load, two-phase load and a single line at load. But all the above analyses deal with static load. The study of the performance of SEIG feeding IM load is of importance, because these loads cause voltage dip and inrush current when put into operation. Sridhar et al. [15] reported a method to predict the steady-state behavior of a SEIG supplying an IM. The steady-state analysis and control of a wind-driven stand-alone SEIG feeding a three-phase induction motor was presented by Alghuwainem [16]. Singh et al. [17] identified the unstable behavior of shortshunt SEIG-IM configuration during the starting of the induction motor load and proposed damping resistors across series capacitors to obtain the stable operation. Transient analysis of SEIG feeding dynamic load is reported in [18,19]. But three-phase SEIG-IM system has been considered in all the above reported works [15–19]. The
Im, ILm
magnetizing current of the SEIG and the motor respectively ids, iqs d-axis and q-axis components of stator currents of the SEIG idr, iqr d-axis and q-axis components of rotor currents (referred to stator) of the SEIG idsm, iqsm main and auxiliary winding currents of the motor idrm, iqrm d, q components of rotor currents (referred to stator) of the motor isa, isb, isc stator phase currents in a, b, c phases of the SEIG current through capacitance Cp icp vsa, vsb, vsc stator voltages of a, b, c phases of the SEIG vds, vqs d-axis and q-axis components of stator voltages of the SEIG vdsm, vqsm voltage across main and auxiliary winding of the motor vmc, VL voltages across the start/run capacitor of the motor and output of the generator respectively xr, xrm rotor speed of the SEIG and the motor respectively Tshaftm shaft load torque Rb damping resistance
transient behavior of a single-phase SEIG with electronic load controller during the starting of a single-phase induction motor has been investigated by Singh et al. [20]. Hence, it is observed that the analysis of SEIG feeding single-phase dynamic load is inadequate. The single-phase induction motors are widely used in household applications. Considering the importance of single-phase induction motor in domestic use, further investigation is very much required for the single-phase SEIG feeding dynamic load. Further, the single-phase supply requirement is in the order of 230–240 V. The voltage ratings of normally available three-phase induction machines are 415 V. The output in the range of 230– 240 V is available by using a three-phase, 415 V, star connected induction machine with suitable connection. Moreover, considering the advantages of single-phase distribution system in remote and rural areas, this paper deals with the dynamic behavior of a single-phase SEIG using a three-phase star connected induction machine during the switching of induction motor load. The dynamic model of the SEIG and the motor have been developed in d–q axes stationary reference frame incorporating the effect of cross-saturation and the equations of the excitation capacitors are described by three-phase abc model. The machine performances are computed by solving the non-linear first order differential equations of the developed dynamic model using famous fourth-order Runge–Kutta numerical technique of integration. The transient behavior of the system has also been analyzed with eigenvalue analysis. Experimental results have been compared with the simulated results to validate the developed model.
2. Dynamic modeling The schematic diagrams of the SEIG without damping resistance and also the SEIG including damping resistance and the motor load are shown in Figs. 1a and 1b respectively. The generator consists of a three-phase star connected induction machine with three capacitors, Cp and two Cs’s, and a single-phase induction motor. Two capacitors (Cs’s) are connected in series with the two phases of the stator winding and one (Cp) is connected in parallel with the motor load.
S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
p½i ¼ ½L1 1 f½m ½R1 ½i xr ½G1 ½ig
3
ð2Þ
Also, from Figs. 1a and 1b, the following equations can be written:
Fig. 1a. Connection diagram of the single-phase self-excited induction generator.
pmcp ¼
1 icp Cp
ð3Þ
pmbcs ¼
1 isb Cs
ð4Þ
pmccs ¼
1 isc Cs
ð5Þ
icp ¼ isa iL
ð6Þ
msb þ mbcs mccs msc ¼ 0
ð7Þ
and,
msa þ mcp mbcs msb ¼ 0
ð8Þ
where vsa, vsb and vsc are voltages across stator phases A, B and C respectively, and vcp, vbcs and vccs are voltages across capacitances Cp, Cs of phase B and Cs of phase C respectively and p = (d/dt) is a time derivative operator. When the damping resistance Rb is connected across the series capacitor of phase B, as shown in Fig. 1b, the Eq. (4) is modified as:
pmbcs ¼
1 mbcs isb Cs Rb
ð9Þ
Expressing the stator phase variables of Eqs. (7) and (8) in terms of d–q variables, we get, Fig. 1b. Connection diagram of the single-phase self-excited induction generator including damping resistance.
mds ¼
mbcs þ mccs 2mcp 3
ð10Þ
and, 2.1. Modeling of the SEIG
mqs ¼ The dynamic model of the three-phase squirrel cage induction generator is developed by using stationary d–q axes reference frame and the relevant volt-ampere equations are as:
½m ¼ ½R1 ½i þ ½L1 p½i þ xr ½G1 ½i
ð1Þ
The matrices of Eq. (1) are defined as:
½m ¼ ½mds
mqs mdr mqr T ; ½i ¼ ½ids iqs idr iqr T
2
Lls þ Lmd
Ldq
Lmd
Ldq
Ldq
Lls þ Lmq
Ldq
Lmq
Lmd
Ldq
Llr þ Lmd
Ldq
Ldq
Lmq
Ldq
Llr þ Lmq
6 6 ½L1 ¼ 6 4 2
0 6 0 6 ½G1 ¼ 6 4 0 Lm
0 0
0 0
Lm
0
0
Llr þ Lm
7 7 7 5
dLm imd imq ; djIm j jIm j
7 7 7 Llr Lm 5
Te ¼
imd imq
and Lmq ¼ Lm þ Ldq
2 pxr P
ð12Þ
where the developed electromagnetic torque of the SEIG is expressed as:
0
Lmd ¼ Lm þ Ldq
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffi 2 2 imd þ imq 2;
T shaft ¼ T e þ J
Here, suffixes d, q refer to d and q axis (in stationary reference frame), and s and r refer to stator and rotor. The equations of Ldq, Lmd and Lmq are given as:
Ldq ¼
ð11Þ
where imd = ids + idr and imq = iqs + iqr are direct and quadrature axes components of the magnetizing current. The magnetizing inductance is calculated from the magnetizing characteristics between Lm and im. The torque balance equation of SEIG is defined as:
3
3
0 0
pffiffiffi 3
where vds and vqs are d-axis and q-axis components of stator voltages respectively. Since, the magnetization characteristics of the SEIG are non-linear due to saturation, the magnetizing inductance depends on the instantaneous value of the magnetizing current. The magnetizing current must be calculated at each step of the integration as:
im ¼ ½R1 ¼ diag½Rs Rs Rr Rr
mbcs mccs
imq : imd
From the Eq. (1), the current derivative can be expressed as:
3P Lm ðidr iqs iqr ids Þ 4
ð13Þ
The shaft torque, Tshaft of prime-mover and speed is represented by a linear curve given as:
T shaft ¼ k1 k2 xr where Tshaft is the shaft torque which shows the drooping characteristic of prime-mover and k1 and k2 are constants. J is the moment of
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S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
inertia of the induction machine including the machine (primemover) coupled on its shaft. From Eq. (12), we get,
2 pxrm Pm
ð18Þ
From Eq. (18), the speed derivative may be defined as:
P ðT shaft T e Þ 2J
pxr ¼
T e m ¼ T shaftm þ J m
ð14Þ pxrm ¼
The differential Eqs. (2)–(5) and (14) describe the dynamic model for the prediction of transient performance of the three-phase SEIG for single-phase power generation.
Pm ðT e m T shaftm Þ 2J m
ð19Þ
Hence, Eqs. (16), (17), and (19) represent the dynamic model of the single-phase induction motor.
2.2. Modeling of the single-phase induction motor 3. Experimental set-up The circuit diagram of a single-phase induction motor is shown in Fig. 2. The dynamic model has been developed in d–q axis stationary reference frame. The voltage-current equations can be written as:
½mm ¼ ½R2 ½iL þ ½L2 p½iL þ xrm ½G2 ½iL
ð15Þ
The matrices of Eq. (15) are defined as:
½mm ¼ ½mdsm
mqsm mdrm mqrm T ; ½iL ¼ ½idsm iqsm idrm iqrm T
½R2 ¼ diag½Rdsm Rqsm Rdrm Rqrm 2
Lldsm þ Lmdm
6 6 ½L2 ¼ 6 4
Ldqm
Lmdm
Ldqm
Lqdm
Llqsm þ Lmqm
Lqdm
Lmqm
Lmdm
Ldqm
Lldrm þ Lmdm
Ldqm
Lqdm
Lmqm
Lqdm
Llqrm þ Lmqm
2
0
0
0
6 6 ½G2 ¼ 6 4
0 0
0 L mqm a
0 0
aLmdm
0
aðLldrm þ Lmdm Þ
0
3
0
7 7
3
4. Experimental procedure
7 7 7 5
ðL þL Þ7 lqrm a mqm 5
0
From the Eq. (15), the current derivative can be expressed as:
p½iL ¼ ½L2 1 f½mm ½R2 ½iL xrm ½G2 ½iL g
ð16Þ
In order to use the correct value of magnetizing inductance, the amplitude of the magnetizing current space vector is evaluated at each step of computation as:
iLm
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 2 2 ¼ iLmd þ iLmq = 2
where iLmd = idsm + idrm and iLmq = iqsm + iqrm are direct and quadrature axes components of the magnetizing current space vector. The derivative of the voltage across the capacitor connected in series with the auxiliary winding is defined as:
pmmc ¼
1 iqsm Cm
ð17Þ
The equation of the mechanical motion is given by,
In the laboratory test rig, a three-phase star-connected squirrel cage induction machine, coupled to a separately excited DC motor, which operates as the prime-mover, has been used for experimentation. One single-phase induction motor is used as a dynamic load. The parameters of both the induction machines are obtained by conducting DC resistance test and block rotor test. The magnetization characteristics of the induction machines under test are achieved using synchronous speed test. All these are given in Appendix A.
Initially, the SEIG is excited at no-load condition and the voltages are built-up in the stator windings. After successful voltage build-up, the single-phase induction motor i.e., the dynamic load is suddenly switched onto the terminals of the generator. The voltage and the current waveforms of Phase-A of the SEIG and the main winding of the single-phase induction motor are recorded with Fluke-43B Power Quality Analyzer. The observations are discussed in the next section. In some cases, the values of the capacitors Cp and/or Cs are changed at the time of switching of the motor load. While performing the experimentation with damping resistance, it is connected across the series capacitor Cs of phase-B at the time of switching of the dynamic load. The waveforms are recorded using the same instrument. 5. Results and discussion The simulated performance and experimental results are presented for starting of the induction motor load with different values of capacitors and also with and without damping resistances. The experimental results are compared with the simulated results to validate the developed mathematical model. From the steadystate model of the generator, it has been found that to obtain a voltage of 235 V at no-load, the required capacitances are Cp = Cs = 44 lF. The performance of the SEIG has been studied during switching of the induction motor load for different cases as follows:
Fig. 2. Circuit diagram of the single-phase induction motor.
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S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
5.1. Without damping resistance
300 250
Vsa (volt)
Wrm (rad/sec.)
The generator is initially excited at no-load with Cp = Cs = 44 lF and there is voltage build-up of the SEIG. Keeping the values of the capacitors unchanged when the single-phase motor load is switched onto the SEIG terminals, the inrush transients are obtained in both the generator and motor currents. The motor cannot be started-up successfully and highly oscillatory behavior of sustained nature due to resonance problem of series capacitors and the motor load being inductive in nature is observed. Figs. 3–5 show such oscillatory waveforms of the voltage and current of the phase A of the generator, main winding of the motor and the motor speed respectively. The starting of the single-phase motor without any load has been attempted by changing the capacitances Cp and/or Cs. Initially, the SEIG is excited with Cp = Cs = 44 lF at no-load and after voltage build-up, the dynamic load is switched onto the terminals of the generator. The values of Cp and/or Cs are changed at the instant of switching of the motor load. With different variations of Cp and Cs at the instant of switching of the motor, attempts have been made to start the motor successfully but without result. It is found that the sustained oscillations are present in all these cases and the system becomes unstable. The reason for such type of oscillations is the resonance because of the series capacitors and the inductive dynamic load. These results have been listed in Table 1, which shows the different cases when the generator is excited at no-load with Cp = Cs = 44 lF and the values of Cp and/or Cs are changed at the instant of switching of the motor. It is found that sustained oscillations are present in all the cases. Hence, simply by changing
200 150 100 50 0 -50 1.6
1.8
2
2.2
2.4
2.6
2.8
3
Table 1 Summary of results of starting of the motor without damping resistance. Sl. no.
1 2 3 4 5 6 7
Values of Cp and Cs before switching on the motor
Values of Cp and Cs after switching on the motor
Cp (lF)
Cs (lF)
Cp (lF)
Cs (lF)
44 44 44 44 44 44 44
44 44 44 44 44 44 44
44 44 44 SO 30 SO 30
44 80 30 44 44 80 30
Remarks
Sustained Sustained Sustained Sustained Sustained Sustained Sustained
200 0 -200 1 .8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
Isa (amp.)
time (sec.) 20 10 0 -10 -20 1 .6
1 .8
2
2.2
2.4
2.6
2.8
time (sec.) simulated
experimental
Vmw (volt)
Fig. 3. Voltage and current waveforms of phase A of the SEIG during switching of the motor load with constant Cp and Cs.
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
Isa (amp.)
time (sec.) 20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
time (sec) simulated
2.8
3.4
Fig. 5. Simulated waveform of the motor speed during switching on with constant Cp and Cs.
400
-400 1 .6
3.2
time (sec.)
experimental
Fig. 4. Voltage and current waveforms of main winding of the single-phase motor during switching on with constant Cp and Cs.
oscillation oscillation oscillation oscillation oscillation oscillation oscillation
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S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
To examine the different transient conditions due to switching of IM load, eigenvalue technique has also been employed. Table 2 gives the eigenvalues for the conditions when the SEIG is at noload, at the moment of connection of the IM load and after starting of the IM with Cp = Cs = 44 lF without using damping resistance. From the second column, it is found that the third complex-conjugated eigenvalue pair (i.e., 0.03 ± j 313.27) is very close to the imaginary axis and one eigenvalue is at the origin when the IM load is not connected. Hence, at no-load, the SEIG can maintain sustained self-excitation to generate voltage. The third column lists the eigenvalue results at the moment of connecting the IM load to SEIG. The fifth complex conjugated eigenvalue pair (i.e., 9.2 ± j 299.7) have positive real parts. This signifies the condition of self-excitation of the SEIG feeding IM load and means that when the IM load is connected to the SEIG terminals, the SEIG has the ability to start the IM load. The eigenvalues listed in the fourth column of Table 2 are obtained after starting of the IM load. It is found
Table 2 Eigenvalues for Cp = Cs = 44 lF without damping resistance. Eigenvalues
Without IM load Cp = 44 lF, Cs = 44 lF
1 2 3 4 5 6 7
With IM load and without damping resistance (Cp = 44 lF and Cs = 44 lF)
132.30 ± j 878.98 96.58 ± j 878.25 0.03 ± j 313.27 0.0 – – –
At the moment of connection
After starting of the IM load
150.0 ± j 114.4 ± j 162.9 ± j 161.8 ± j 9.2 ± j 16.0 13.1
150.5 ± j 114.4 ± j 167.4 ± j 175.8 ± j 9.1 ± j 4.5 ± j
1449.4 877.8 470.1 291.3 299.7
1448.5 877.8 467.2 313.9 300.0 141.7
the values of the capacitors at the instant of switching of the motor, it is not possible to start it successfully.
Table 3 Eigenvalues for different values of capacitances without damping resistance. Eigenvalues
Vsa (volt)
1 2 3 4 5 6
Without IM load
With IM load and without damping resistance (after starting of the IM load)
Cp = 44, Cs = 44 (lF)
Cp = 80, Cs = 44 (lF)
Cp = 30, Cs = 44 (lF)
Cp = 44, Cs = 80 (lF)
Cp = 44, Cs = 30 (lF)
Cp = 80, Cs = 80 (lF)
Cp = 30, Cs = 30 (lF)
132.30 ± j 878.98 96.58 ± j 878.25 0.03 ± j 313.27 0.0 – –
151.8 ± j 114.3 ± j 171.3 ± j 171.6 ± j 8.7 ± j 5.7 ± j
150.0 ± j 114.4 ± j 166.0 ± j 177.5 ± j 9.3 ± j 4.1 ± j
152.0 ± j 120.8 ± j 188.5 ± j 148.3 ± j 8.4 ± j 6.8 ± j
148.8 ± j 112.2 ± j 156.5 ± j 184.9 ± j 4.5 ± j 3.5 ± j
154.9 ± j 120.6 ± j 187.7 ± j 147.7 ± j 8.7 ± j 7.7 ± j
148.9 ± j 112.3 ± j 154.2 ± j 186.8 ± j 4.6 8 ± j 3.0 ± j
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
1096.8 878.1 467.0 306.6 300.5 140.9
2.6
2.8
1740.5 877.7 467.4 316.7 299.8 142.0
3
3.2
3.4
3.6
3
3.2
3.4
3.6
1436.8 647.3 400.9 287.2 283.8 139.1
1461.7 1065.8 539.8 320.6 307.8 142.4
1080.2 647.5 402.8 280.4 285.1 138.2
time (sec.) 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
2.8
time (sec.)
experimental
simulated Fig. 6. Voltage and current waveforms of phase A of the SEIG during switching on of the motor load with damping resistance.
Vmw (volt)
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
time (sec.) Imw (amp.)
Isa (amp.)
20
20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
2.8
time (sec.) simulated
experimental
Fig. 7. Voltage and current waveforms of the main winding of the motor during switching on with damping resistance.
1750.9 1065.7 542.0 323.1 307.8 142.7
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S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
400
Wrm (rad/sec.)
300 200 100 0 -100 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
time (sec.) Fig. 8. Simulated waveform of the motor speed during switching on with damping resistance.
Vsb (V)
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
Isb (A)
20 10 0 -10 -20 1.6
Time (Sec.) simulated
experimental
Vsc (V)
Fig. 9. Voltage and current waveforms of phase B of the SEIG during switching on of the motor load with damping resistance.
400 200 0 -200
Isc (A)
-400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
20 10 0 -10 -20 1.6
Time (Sec.) simulated
experimental
Fig. 10. Voltage and current waveforms of phase C of the SEIG during switching on of the motor load with damping resistance.
Fig. 11a. Measured THD of the voltage and current of the main winding of the motor after successful starting.
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S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
5.2. With damping resistance The starting of the motor load has been attempted by inserting the damping resistances across the capacitor of either phase B or phase C of the SEIG. It has been found that successful starting of the motor load is not possible by connecting damping resistance across the capacitor of phase C, but is possible if the damping resistance is connected across the capacitor of phase B. The generator is initially excited at no-load with Cp = Cs = 44 lF. After successful build-up of voltage, the motor is switched onto the terminals of the SEIG. Simultaneously the suitable value of damping resistance is connected across the capacitor of phase B of the generator. It is observed that the starting oscillations are damped out and the motor load is started-up successfully. In this case, the resonance problem is solved by using the damping resistance. The selection procedure of the damping resistance for successful starting of the motor at no-load and to maintain the rated terminal voltage while increasing the load on the motor after successful starting, is given in Appendix B. The voltage and current waveforms of stator phase A of the generator, main winding of the motor and the speed of the motor during starting of the motor with capacitances Cp = Cs = 44 lF and damping resistance Rb = 28 X which is connected across the capacitor of phase B of the generator at the time of switching of the motor are given in Figs. 6–8 respectively. It is found that the motor is started up successfully using the damping resistance. Also, the voltage and current waveforms of stator phases B and C of the generator during starting of the motor including damping resistance are shown in Figs. 9 and 10 respectively. Both the voltages and the currents are reduced slightly. The measured THD of the voltage and current of the main winding and few cycles of the main winding voltage and current of the motor at steady-state after successful starting with Cp = Cs = 44 lF are given in Figs. 11a and 11b respectively. It is observed that the harmonics content in the voltage and current of main winding of the motor are very low, which indicates the good quality of power supplied to the motor. Table 4 gives the eigenvalue results for successful starting of the motor with damping resistance. In the third column, the complex conjugated eigenvalues (0.2 ± j 296.9) are located in the right half of complex plane at the moment of connection of the IM load to the SEIG terminals. It means that the SEIG has the capability to start the motor. In the fourth column, it is found that one complex conjugated eigenvalue pair (0.0 ± j 305.1) lie on imaginary axis and all the other eigenvalues have negative real parts. Hence, according to the view point of system dynamic stability, the SEIG-IM system is stable at steady-state condition with damping resistance and
Fig. 11b. Main winding voltage and current waveforms of the motor at steady-state after successful starting.
Table 4 Eigenvalues for Cp = 44 lF and Cs = 44 lF with damping resistance. Eigenvalues
Without IM load Cp = 44 lF Cs = 44 lF
1 2 3 4 5 6 7
132.30 ± j 878.98 96.58 ± j 878.25 0.03 ± j 313.27 0.0 – – –
With IM load including damping resistance (Cp = 44 lF and Cs = 44 lF) At the moment of connection
Under steadystate condition
152.6 ± j 186.5 ± j 205.4 ± j 178.0 ± j 0.2 ± j 15.3 13.1
215.2 ± j 141.0 ± j 291.7 ± j 402.4 ± j 16.3 ± j 0.0 ± j
1449.3 870.7 489.3 289.7 296.9
2135.6 1120.7 709.8 467.6 268.1 305.1
that there are two eigenvalue pairs (i.e., 9.1 ± j 300.0 and 4.5 ± j 141.7) having positive real parts which indicates that the system is unstable after starting of the IM. Similarly, Table 3 lists the eigenvalues of the SEIG-IM system after starting of the IM when the values of Cp and/or Cs are either reduced or increased at the time switching of the motor load. The second column is same as the second column of Table 2, because of the same conditions. It is found that the fifth and sixth eigenvalue pairs of all the other columns of Table 3 have positive real parts indicating the unstable system after connecting the motor load for those values of capacitances. Hence, the eigenvalue analysis confirms the unsuccessful starting and the unstable behavior of the SEIG-IM system without any damping resistance.
Vmw (volt)
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
2.8
3
3.2
3.4
3.6
time (sec.) Imw (amp.)
20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
time (sec.)
experimental
simulated Fig. 12. Voltage and current waveforms of the main winding of the motor during switching on with high value of damping resistance.
9
Vmw (volt)
S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
400 200 0 -200 -400 1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3
3.2
3.4
3.6
Imw (amp.)
time (sec.) 20 10 0 -10 -20 1.6
1.8
2
2.2
2.4
2.6
2.8
experimental
time (sec.) simulated
Fig. 13. Voltage and current waveforms of the main winding of the motor during switching on with low value of damping resistance.
Stator phase currents (amp)
5 4
Isa Isb Isc
3 2 1 0 200
300
400
500
600
700
Motor load (watt) Fig. 14. Experimentally obtained variation of stator phase currents with increase of load on the motor after successful starting.
thus, the eigenvalue results confirm the simulated and the experimental results. Figs. 12 and 13 indicate the effect of damping resistances on starting of the motor load. It is found that if higher value of damping resistance (say, Rb = 50 X) is used keeping the values of the capacitors unchanged, there is sustained oscillation (shown in Fig. 12) and with the lower value of the damping resistance (say, Rb = 10 X), the voltage of the generator collapses (shown in Fig. 13). Actually, for very low value of the damping resistance,
the damping effect becomes very high and the voltage of the SEIG collapses. Hence, for successful starting of the motor, proper value of damping resistance should be chosen. It is seen that after successful starting of the motor without any load, if the damping resistance is increased, the oscillation occurs. Hence, the damping resistances should be kept in the circuit while the motor is at noload. Fig. 14 shows the experimentally obtained variations of stator phase currents with increase of load on the motor after successful starting with proper value of damping resistance. It is found that the motor draws 200 W from the generator at no-load. The currents in both A and C phases increase while in phase B, it decreases with increase of load on the motor. After successful starting of the motor with Cp = Cs = 44 lF and damping resistance Rb = 28 X, the output voltage of the generator becomes 230 V. Now, if the load on the motor is gradually increased, the output voltage reduces. To keep the output voltage constant at this value, either the capacitances have to be increased if damping resistance is kept unchanged, or the damping resistance has to be changed keeping the capacitors’ values fixed. Fig. 15 shows the variation of the damping resistance with increase in load on the motor to maintain terminal voltage constant after successful starting with Cp = Cs = 44 lF which are kept unchanged. It is found that the value of the damping resistance is reduced with increase in load on the motor to keep the terminal voltage of the SEIG at constant value. The theoretical and the experimental values are very close to each other indicating the effectiveness of this approach. There will be small amount of power loss in the damping resistance. The variation of power loss in the damping resistance with increase in load on the motor keeping constant terminal voltage is shown in Fig. 16.
30 simulated 25
experimental values
Rb (ohm)
20 15 10 5 0
0
100
200
300
400
500
600
700
Motor load (watt) Fig. 15. Variation of damping resistance with the increase in load on the motor keeping capacitances unchanged.
S.N. Mahato et al. / Electrical Power and Energy Systems 47 (2013) 1–12
Power loss in Rb (watt)
10
80 60 40 20 0 200
250
300
350
400
450
500
550
600
650
700
Motor load (watt) Fig. 16. Power loss in the damping resistance with increase in load on the motor.
Fig. B1. Flow chart for determination of damping resistance.
It is seen that the power loss in the damping resistance when the motor is at no-load is 80 W i.e., 3.6% of the three-phase rating of the SEIG and decreases with increase in load on the motor. Since, the current in phase B of the SEIG decreases with increase of load, the voltage across the capacitance of phase B i.e., the voltage across the damping resistance reduces, and hence, the power loss in the
damping resistance also reduces with increase in load on the motor. From the figure, it is observed that the power loss is 10 W when the motor load is 700 W i.e., the power loss becomes 0.45% of the three-phase rating of the machine, which is negligible. Hence, though the damping resistance always remains in the circuit, the power loss in it is very small.
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Lmqm
6. Conclusions The transient behavior of a single-phase SEIG using three-phase machine feeding single-phase dynamic load is presented. It is found that the motor cannot be started up successfully while switched onto the SEIG terminals directly, and sustained oscillation is observed. Attempts have been made for successful starting of the motor by changing the values of the capacitors, but without result. Successful starting of the motor load is only possible with the damping resistance connected across the capacitor of phase B of the SEIG. The motor at no-load can be started-up successfully if the damping resistance is chosen properly. During starting, the lower value of damping resistance results into voltage collapse, while the higher value results in sustained oscillations. With the increase in motor load after successful starting, either the capacitances may be increased or the damping resistance may be changed (i.e., Rb is reduced) to maintain the constant terminal voltage. An algorithm has been developed for selection of damping resistance for successful starting of the motor and to maintain the terminal voltage constant while loading the motor. Moreover, the harmonics contents in the voltage and current of the main winding of the motor after successful starting with damping resistance are very small indicating the good quality of power supplied to the motor. The eigenvalue analysis confirms the simulated and experimental results. The experimental results show close agreement with the simulated results and thus the proposed model is validated. Hence, it is concluded that the single-phase induction motors, which are very common in domestic use, can be started-up successfully by using this scheme and with the proposed manner. Appendix A The specifications of the induction machines and the primemover characteristics are given below: A.1. Induction generator 2.2 kW, 3-phase, 4-pole, 50 Hz, 415 V, 4.5 A, star connected, 1440 rpm, Rs = 3.735 X, Rr = 2.91 X, Xls = 4.727 X, Xlr = 4.727 X. Base impedance = 53.24 X. Base speed = 1500 rpm, J = 0.0842 kg m2. The magnetizing inductance Lm is related to the magnetizing current in the following manner:
Lm
¼ 0:3177
for Im 6 0:75
¼ 0:3502 0:0349Im 0:0017I2m ¼ 0:17667
for 0:75 < Im 6 4:25 for Im > 4:25
A.2. Induction motor 1 hp, 230 V, 6 A, 4-poles, capacitor-start capacitor-run singlephase induction motor. Rdsm = 3.41 X, Rdrm = 4.37 X, Xldsm = Xldrm = 3.99 X, Rqsm = 11.22 X, Rqrm = 8.01 X, Xlqsm = Xlqrm = 6.433 X, Turns ratio, a = Nq/Nd = 1.4, and Cm = 100 lF for starting and 6.3 lF for running. The magnetization curves are modeled as given under based on test data: Main winding: Lmdm ¼ 0:3204 for ILm 6 1:22 ¼ 0:6692 þ 1:695ILm 0:9292I2Lm þ 0:168I3Lm for 1:22 < ILm 6 2:24 ¼ 0:4523 0:0476ILm þ 0:00164I2Lm ¼ 0:244
Auxiliary winding:
for 2:24 < ILm 6 5:32 for ILm > 5:32
¼ 0:662
for ILm 6 0:93
¼ 2:074 þ 7:066ILm 6:03I2Lm þ 1:713I3Lm
for 0:93 < ILm 6 1:32
¼ 0:6856 þ 0:0427ILm 0:0317I2Lm ¼ 0:6158
for 1:32 < ILm 6 2:29 for ILm > 2:29
A.3. Prime-mover characteristics
T shaft ¼ k1 k2 xr where k1 = 249.39 and k2 = 0.7875. Appendix B The selection procedure of the damping resistance for successful starting of the motor without load and to maintain the rated terminal voltage while increasing the load on the motor is shown in Fig. B1. In this flowchart, initially a small value of damping resistance has been chosen. For this small value of damping resistance, the generator voltage collapses at the time of switching on the motor load. This resistance is increased gradually such that for a particular value of this resistance, there is no voltage collapse and the motor is started up successfully. This value of the resistance is the damping resistance required to start the motor successfully at noload. It has been found that after successful starting of the motor, the output voltage increases with decrease in the value of the damping resistance. If the load on the motor is increased, the output voltage of the SEIG reduces. Hence, to maintain the terminal voltage constant at 230 V with increase in load on the motor, the damping resistance is reduced gradually. The value of the resistance corresponding to the terminal voltage of 230 V is the required damping resistance for that particular load. References [1] Murthy SS. A novel self-excited self-regulated single-phase induction generator Part 1: basic system and theory. IEEE Trans Energy Convers 1993;8:377–82. [2] Bhattacharya JL, Woodward JL. Excitation balancing of self-excited induction generator for maximum power output. IEE Proc, Gener, Transm Distrib 1988;135:88–97. [3] Chan TF, Lai LL. Steady-state analysis and performance of a single-phase selfregulated self-excited induction generator. IEE Proc, Gener, Transm Distrib 2002;149:233–41. [4] Fukami T, Kaburaki Y, Kawahara S, Miyamoto T. Performance analysis of a selfregulated self-excited single-phase induction generator using a three-phase machine. IEEE Trans Energy Convers 1999;14:622–7. [5] Kumaresan N. Analysis and control of three-phase self-excited induction generators supplying single-phase AC and DC loads. IEE Proc, Electr Power Appl 2005;152:739–47. [6] Murthy SS, Ramrathnam, Gayathri MSL, Naidu K, Siva U. A novel digital control technique of electronic load controller for SEIG based micro-hydel power generation. In: Proc of IEEE int conf on power electronics, drives and energy systems 2006 (PEDES ’06); 2006. [7] Murthy SS, Bhuvaneswari G, Gao S, Ahuja RK. Self-excited induction generator for renewable energy applications to supply single-phase loads in remote locations. In: Proc of IEEE int conf on sustainable energy technologies (ICSET); 2010. [8] Basic M, Vukadinovic D, Petrovic G. Dynamic and pole-zero analysis of selfexcited induction generator using a novel model with iron losses. Int J Electr Power Energy Syst 2012;42:105–18. [9] Rahimi M, Parniani M. Dynamic behavior analysis of doubly-fed induction generator wind turbines – the influence of rotor and speed controller parameters. Int J Electr Power Energy Syst 2010;32:464–77. [10] Kassem AM. Robust voltage control of a stand alone wind energy conversion system based on functional model predictive approach. Int J Electr Power Energy Syst 2012;41:124–32. [11] Amimeur H, Aouzellag D, Abdessemed R, Ghedamsi K. Sliding mode control of a dual-stator induction generator for wind energy conversion systems. Int J Electr Power Energy Syst 2012;42:60–70. [12] Shilpakar LB, Singh B, Singh BP. Dynamic behavior of three-phase self-excited induction generator for single-phase power generation. Electr Power Syst Res 1998;48:37–44. [13] Wang L, Deng RY. Transient performance of an isolated induction generator under unbalanced excitation capacitor. IEEE Trans Energy Convers 1999;14:887–93.
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[14] Jain SK, Sharma JD, Singh SP. Transient performance of three-phase selfexcited induction generator during balanced and unbalanced faults. IEE Proc, Gener, Transm Distrib 2002;149:50–7. [15] Sridhar L, Singh B, Jha CS, Singh BP. Analysis of self-excited induction generator feeding induction motor. In: IEEE power engineering society summer meetings; 1994. p. 1–7. [16] Alghuwainem SM. Steady-state analysis of an isolated self-excited induction generator supplying an induction motor load. IEEE Int Conf Electr Mach Drives 1999:351–3. [17] Singh SP, Jain SK, Sharma J. Voltage regulation optimization of compensated self-excited induction generator with dynamic load. IEEE Trans Energy Convers 2004;19:724–32.
[18] Singh B, Sridhar L, Jha CS. Transient analysis of self-excited induction generator supplying dynamic load. Electr Mach Power Syst 1999;27:941–54. [19] Singh B, Murthy SS, Gupta S. Transient analysis of self-excited induction generator with electronic load controller (ELC) supplying static and dynamic loads. Int Conf Power Electr Drive Syst 2003;1:771–6. [20] Singh B, Murthy SS, Gupta S. An electronic voltage and frequency controller for single-phase self-excited induction generators for pico hydro applications. Proc Int Conf Power Electr Drives Syst 2005;1:240–5.