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Modeling and analysis of six-phase synchronous generator for stand-alone renewable energy generation
Energy 36 (2011) 5621e5631
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Modeling and analysis of six-phase synchronous generator for stand-alone renewable energy generation G.K. Singh* Department of Electrical Engineering, Indian Institute of Technology, Roorkee 247667, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 February 2011 Received in revised form 6 May 2011 Accepted 2 July 2011 Available online 6 August 2011
This paper presents a mathematical model of six-phase synchronous generator (SPSG) for analysis of its transient and dynamic behavior for stand-alone renewable energy generation in conjunction with a hydro power plant. In the analytical model, effect of common mutual leakage reactance between the two three-phase winding sets, and the mutual leakage coupling between d- and q-axis of the two stator windings have been considered. Paper also discusses the applicability of SPSG for supplying two individual loads by presenting the results of analytical and experimental study of transient and steady-state behavior under various operating conditions. It is shown that it can be used to supply two independent three-phase loads. While the interaction between the two windings is inevitable and variation of load at one winding set changes the operating conditions at the other winding, the situation is still satisfactory for a wide range of rural resistive loads. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Renewable energy generation Six-phase synchronous generator Small hydro power generation scheme
1. Introduction Utilities in many developing countries are finding it difficult to establish and maintain remote rural area electrification. The cost of delivering power in such areas is becoming extensively large due to large investments in transmission lines for locally installed capacities and large transmission line losses. For these reasons, distributed generation has received attention in recent years for remote and rural electrification. Thus suitable stand-alone systems using locally available energy sources have become a preferred option with increased emphasis on eco-friendly technologies, and the use of renewable sources. Most of the renewable energy from wind, micro hydro, tidal, geothermal, solar, and biomass are converted into electrical energy that is delivered either to utility grid or isolated loads [1e3]. Though the initial cost of hydro system and capital cost involved in wind generation is high, but they have negligible fuel cost and relatively low maintenance cost. Process of generating biomass fuel or heat energy depends on waste, woody biomass, agriculture crops and residues and oil bearing plants. One of the biggest drawbacks that this energy source has is that there are some green house gas emissions from the process. Some renewable power sources are completely clean, but biomass is not one of them. Carbon Dioxide and other gases can be released into
* Tel.: þ91 1332 285070; fax: þ91 1332 273560. E-mail address: [email protected]. 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.07.005
the air, to harm the ozone and damage the earth, contributing to an acceleration of global warming and associated effects. Massive amount of land and water are needed to grow enough plants to provide all the energy required by the global population. Long term fuel supply and pricing, public perception as dirty fuel, and transportation of waste to power plant are the major issues involved in the biomass energy production. Many experts believe that there will not be one single alternative renewable source to replace fossil fuels, but rather that a number of different clean energy sources will be used instead. To achieve significant new growth will require new collaboration among energy, agriculture and forest production industries. To replace fossil fuels completely with biomass derived power is not really feasible, at least in near future [4e8]. The investigations spread over the last two decades indicate the technical and economic viability of using number of phases higher than three in multi-phase ac machines. Electric traction, ship propulsion, more-electric aircraft, thermal power plant, nuclear power plants, hybrid electric vehicles and battery powered electric vehicles have rapidly emerged during the last few years as the main potential application area of multi-phase machine drives. In high power applications such as ship propulsion, use of multi-phase drive enables reduction of required power rating per inverter leg (phase). In safety-critical applications such as more-electric aircraft, use of multi-phase drive enables greater fault tolerance that is of paramount importance. Finally, in electric vehicle and hybrid electric vehicle applications, utilization of multi-phase drives for propulsion enables reduction of the required semiconductor switch current
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G.K. Singh / Energy 36 (2011) 5621e5631
List of symbols
Llm
va, vx
Lldq SPSG H Q Pa
ia, ix vq1, vd1 vq2, vd2 vkq, vkd vfd, efd iq1, id1 iq2, id2 ikq, ikd ifd r1, r2 Ll1, Ll2 Lmq, Lmd
voltage across three-phase winding sets abc and xyz respectively phase current of winding sets abc and xyz respectively q- and d-axis voltage across winding set abc q- and d-axis voltage across winding set xyz q- and d-axis voltage across damper winding voltage across the field winding and field excitation voltage respectively q- and d-axis current for winding set abc q- and d-axis current for winding set xyz q- and d-axis current in damper winding field winding current resistance per phase of winding sets abc and xyz respectively stator leakage inductance per phase for winding sets abc and xyz respectively q- and d-axis mutual inductance
rating (although these drives are not characterized by high power, low voltage available in vehicles makes current high). The research in this area is still in its infancy, yet some extremely important findings have been reported in the literature indicating general feasibility of multi-phase systems [9,10]. However, practical applications of multi-phase machines in renewable energy generation scheme such as wind energy and hydro power have not been reported so far. Practical utilization of multi-phase synchronous generators was considered in the 1970’s and 1980’s. The perceived applications were predominantly related to uninterruptible power supply systems. Fuchs and Rosenberg in 1973 have analyzed the behavior of an alternator with two 3-phase stator windings displaced by an arbitrary angle by means of an orthogonal transformation of the phase variables into a new set of (d-q-) variables. They have concluded that the orthogonal transformation eliminates partly the time-dependence of the coefficients of the system of differential equations, and the phasors can be used in the analysis of the steady-state behavior of the generator with two stator windings [11]. Kataoka and Watanabe have published a detailed steady-state analysis of a dc-to-ac conversion system consisting of a currentsource inverter, a double wound synchronous machine, a position sensor and a control circuit. An equivalent circuit for predicting the steady-state behavior of the circuit is also derived and based on this equivalent circuit, the output voltage waveforms are then examined. They have also presented a method for keeping the output voltage and frequency constant [12]. Hanna and Macdonald have tested a model six-phase generator together with a model transformer giving six-to-three phase conversion with a view to assess the harmonic performance of the system [13]. An analytical model of a six-phase synchronous machine, wherein the mutual leakage couplings between the two sets of three-phase stator windings are considered, have been presented by Schiferl and Ong [14]. They have examined the steady-state operations with sinusoidal voltage inputs, using phasor diagrams to illustrate the transformer and motor mode of power transfer. Steady-state operations with ac-dc stator connections are also considered. Schiferl and Ong have also derived the relationships of mutual leakage inductances with winding displacement angle and pitch for a number of practical sixphase winding configurations, and have proposed a single machine uninterruptible power supply scheme using six-phase synchronous machine [15]. But, the output of the systems described above in [12e15] is three-phase. Sudhoff and Wasynczuk in [16] have discussed the analysis and average-value modeling of line-
h L
ht g
hg hshp V
d, a
mutual leakage inductance between the two sets of armature winding cross-saturation coupling between d- and q-axis stator six-phase synchronous generator water head in meter discharge of water water pressure at turbine inlet measured by pressure gauge (in Pascal) height of water level over the tip of rectangular weir (in meter) length of weir aperture (in meter) efficiency of hydro turbine acceleration due to gravity efficiency of the induction generator overall efficiency of the system rated or ‘bus’ voltage, torque angle and angle of displacement between the two three-phase winding sets abc and xyz respectively
commutated converter-synchronous machine systems, whereas in [17], Rockhill and Lipo have given a simplified model of a nine-phase synchronous machine using vector space decomposition. In [18], Abuishmais et al have presented the analysis of VSI-DTC six-phase synchronous machine with emphasis on redundancy, fault conditions, the machine behavior under non-sinusoidal voltage profiles and sensitivity of the design parameters. Tessarolo et al in [19] have investigated the high-power electric drives using split-phase synchronous machine equipped with N stator windings, each supplied by a load commutated inverter. To describe the split-phase machine dynamics during commutation transients (including simultaneous commutations), a simple mathematical model have also been proposed. To assess the model validity, experimental results are also presented. Findings reported in [16e19] are related to the motoring operation of the six-phase synchronous machine. A parametric approach for the development of dynamic average-value model of a machine-rectifier system is presented by Jatekevich and Abdul-Seoud [20]. Aghamohammdi and Porgholi have discussed a procedure using asset of measured data from stand-still Frequency Response Test for synchronous generator parameter identification using Hook-Jeeves optimization method [21]. Recently, a detailed experimental analysis of six-phase synchronous generator for stand-alone renewable energy generation in conjunction with the hydro power plant has been presented [22]. In this paper, Singh has covered the steady-state performance of the machine for constant voltage operation and for constant frequency operation under independent loading (symmetrical and asymmetrical) on its two three-phase set of windings. In recent times, interest in the use of multi-phase generators in conjunction with renewable energy sources has reappeared [2,23e25]. It needs to be emphasized here that there is no evidence at present of any industrial uptake of such solutions, multi-phase synchronous generator may become a viable solution for renewable energy generation in conjunction with hydro power plant. However, as the author of this paper has been able to ascertain on the basis of detailed literature review on six-phase synchronous machine, transient and dynamic analysis of six-phase synchronous generator (SPSG) have not been reported so far. This paper, therefore, presents the mathematical modeling of the six-phase synchronous generator taking into account the effect of common mutual leakage reactance between the two three-phase winding sets, and the mutual leakage coupling between d- and qaxis of the two stator windings. A detailed analytical analysis has
G.K. Singh / Energy 36 (2011) 5621e5631
been carried out in this paper to assess the transient and dynamic behavior of the machine. In particular, it is shown that the SPSG can operate with a single three-phase winding set, so that fault at one winding does not lead to the system shutdown. The generator can also supply two separate three-phase loads which represents an additional advantage. Key analytical results have been verified through experimental results conducted on the test machine powered by a cross-flow hydro turbine. MATLAB/SIMULINK were used for analytical study, whereas Fluke 43-B Power Quality Analyzer was used for measurement and for recording of the various experimental waveforms.
vq1 ¼ r1 iq1 þ ður =ub Þjd1 þ ðp=ub Þjq1
(1)
vd1 ¼ r1 id1 ður =ub Þjq1 þ ðp=ub Þjd1
(2)
vq2 ¼ r2 iq2 þ ður =u2 Þjd2 þ ðp=ubÞjq
(3)
vd2 ¼ r2 id2 ður =ub Þjq2 þ ðp=ub Þjd2
(4)
v01 ¼ r1 i01 þ ðp=ub Þj01
(5)
v02 ¼ r2 i02 þ ðp=ub Þj02
(6)
KQ
Y
b
q-axis
KQ
KD
(7)
vkd ¼ rkd ikd þ ðp=ub Þjkd
(8)
vfd ¼ rf ifd þ ðp=ub Þjfd
(9)
where, ur is the rotor speed (also the speed of the reference frame), p denotes differentiation w.r.t. time, ub is the base speed, and all other symbols have their usual meaning. Here, rotor quantities are referred to stator. The expressions for stator and rotor flux linkages per second are:
jq1 ¼Xl1 iq1 Xlm iq1 þiq2 þXldq id2 þXmq iq1 iq2 þikq
A schematic representation of the stator and rotor windings for a two pole, six-phase synchronous generator is given in Fig. 1. The six-stator phases are divided into two wye-connected three-phase sets, labeled abc and xyz, whose magnetic axes are displaced by an arbitrary angle a. The windings of each three-phase set are uniformly distributed and have axes that are displaced 120 apart. The field winding F and the short-circuited winding KD modelizing the effects of the damper winding are shown along the direct axis. The short-circuited damper winding KQ is shown along quadrature axis. Neutral point of the two three-phase winding sets are kept isolated in order to prevent the physical fault propagation from one three-phase set to other one, and to prevent the flow of triplen harmonics. The voltage equations of a six-phase synchronous generator in rotor reference frame [14] can be given by:
F
vkq ¼ rkq ikq þ ðp=ub Þjkq
2. Mathematical modeling and circuit representation
x
5623
α
a d-axis
c Z Fig. 1. Schematic representation of two-pole, salient pole six-phase synchronous machine.
jd1 ¼ Xl1 id1 Xlm ðid1 þ id2 Þ Xldq iq2 þ Xmd id1 id2 þ ikd þ ifd
(11)
jq2 ¼Xl2 iq2 Xlm iq1 þiq2 Xldq id1 þXmq iq1 iq2 þikq
jd2 ¼ Xl2 id2 Xlm ðid1 þ id2 Þ þ Xldq iq1
jfd
þ Xmd id1 id2 þ ikd þ ifd ¼ Xlf ifd þ Xmd id1 id2 þ ifd
jkq ¼ Xlkq ikq þ Xmq iq1 iq2 þ ikq
(10)
(13) (14)
jkd ¼ Xlkd ikq þ Xmd id1 id2 þ ikd þ ifd
(12)
(15)
(16)
where, Xlm is the common mutual leakage reactance between the two sets of stator winding and Xldq is the cross-saturation coupling between the d- and q-axis of stator. Xlm and Xdq is given by:
Xlm ¼ Xlax cos a þ Xlay cos ða þ 2p=3Þ þ Xlaz cos ða 2p=3Þ
(17)
Xldq ¼ Xlax sin a þ Xlay sin ða þ 2p=3Þ þ Xlaz sin ða 2p=3Þ
(18)
These equations suggest the equivalent circuit as shown in Fig. 2. The common mutual leakage inductance Llm in Fig. 2 represents the fact that the two sets of stator windings occupy the same slots and are, therefore, mutually coupled by a component of leakage flux. The mutual leakage inductance, Llm has an important effect on the harmonic coupling between the two stator winding sets and depends on the winding pitch and displacement angle between the two stator winding sets. Alger has explained this in detail, and has given a technique for finding the slot reactance [26]. Standard test procedures are available to determine the various machine parameters [21,27]. As for as transient behavior is concerned, it has been found that neglecting the stator mutual leakage inductance Llm has no noticeable effect except some changes in voltage harmonic distortion (VHD). The detailed simulation of a multi-phase machine is based on the integral form of the machine’s voltage and torque equations with flux linkage per second and speed as state variables, winding currents as output variables, applied voltage and load torque as input variables. Thus, solving for the currents and back substituting these currents into the voltage equations and rewriting them as differential equations yields:
h pjq1 ¼ ub vq1 ður =ub Þjd1 ðr1 =XÞ ðXl2 þXlm Þjq1 Xlm jq2 i Xl2 jmq þXldq ðjd2 jmd Þ
(19)
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G.K. Singh / Energy 36 (2011) 5621e5631
Ll1
r1 iq1
Ll2
r2
Let (P1, Q1) and (P2, Q2) be the active and reactive power supplied by the winding sets abc and xyz respectively
ωr λd1
-
+
ωr λd2
+
Llm
Lkq
rkq
-
vq1
ikq iq2
vkq
P1 ¼ vd1 id1 þ vq1 iq1
(26)
Q1 ¼ vq1 id1 vd1 iq1
(27)
P2 ¼ vd2 id2 þ vq2 iq2
(28)
Q2 ¼ vq2 id2 vd2 iq2
(29)
Lmq
vq2 Ldq Ldq
Lkd Ll1
r1
id1
-
Ll2
r2
vd1
Solving Equations (26)e(29) for current:
rkd
ωr λq1
-
+
Llm
Lfd
rfd
ikd
ωr λq2
+
vkd
ifd
id2
vfd
vd2
Lmd
Fig. 2. An equivalent circuit of a six-phase synchronous generator.
h pjd1 ¼ ub vd1 þ ður =ub Þjq1 ðr1 =XÞððXl2 þ Xlm Þjd1 i Xlm jd2 Xl2 jmd Þ Xldq jq2 jmq h
h ¼ ub vd2 þ ður =ub Þjq2 ðr2 =XÞððXl1 þ Xlm Þjd2 i Xlm jd1 Xl1 jmd Þ þ Xldq jq1 jmq
(30)
id1 ¼ Q1 *vq1 þ P1 *vd1 vq1 *vq1 þ vd1 *vd1
(31)
iq2 ¼ P2 =vq2 vd2 =vq2 * Q2 *vq2 þ P2 *vd2 vq2 *vq2 þ vd2 *vd2
(32)
vq2 *vq2 þ vd2 *vd2 id2 ¼ Q2 *vq2 þ P2 *vd2
(33)
q- and d-axis stator voltages are given by:
(20)
vq1 ¼ Vcos d vd1 ¼ Vsin d
pjq2 ¼ ub vq2 ður =ub Þjd2 ðr2 =XÞ ðXl1 þ Xlm Þjq2 i Xlm jq1 Xl1 jmq Xldq ðjd1 jmd Þ
iq1 ¼ P1 =vq1 vd1 =vq1 * Q1 *vq1 þ P1 *vd1 vq1 *vq1 þ vd1 *vd1
(21)
vq1 ¼ Vcos ðd aÞ vd1 ¼ Vsin ðd aÞ
(22)
jkq jmq pjkq ¼ ub vkq rkq =Xkq
where, V is the rated or ‘Bus’ voltage, d is torque/rotor angle and a is angle of displacement between the two three-phase winding sets abc and xyz. The torque and rotor dynamics equations can be expressed as:
(23)
i h Tem ¼ ð3=2ÞðP=2Þ iq1 þ iq2 jmd ðid1 þ id2 Þjmq
pjkd ¼ ub vkd rkd =Xkd jkd jmd
(24)
pjd2
pjfd ¼ ub vfd rfd =Xfd
jfd jmd
(25)
x
30°
a
o. hn i X þ jkq =Xkq Xl2 jq1 þXl1 jq2 þXldq ðjd2 jd1 Þ
hn o. ðXl2 jd1 þ Xl1 jd2 Þ þ Xldq jq1 jq2 ðXÞ i þ ðjkd =Xkd Þ þ jfd =Xfd
h . i 1 Xmq þ 1=Xkq þ ððXl1 þ Xl2 Þ=XÞ Aq ¼ 1
Ad ¼ 1
Contactor
Vb Va Vc
vfd ¼ efd * rfd =Xmd
jmd ¼ Ad
L O A D
MCB Six-Phase Synchronous Generator
where,
jmq ¼ Aq
(34)
z
DC FIELD WINDING
b c
+
-
y
Vy
Vx
h . i ð1 Xmd Þ þ ð1=Xkd Þ þ 1=Xfd þ ððXl1 þ Xl2 Þ=XÞ
Vz
Contactor
MCB Prime Mover
X ¼ ½Xl1 Xl2 þ Xlm ðXl1 þ Xl2 Þ
Fig. 3. Schematic diagram of the six-phase synchronous generator system.
L O A D
G.K. Singh / Energy 36 (2011) 5621e5631
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system takes the speed reference that is specified by the Speed Reference Selection Block and compares it to the speed feedback. The Speed Regulator uses proportional (Kp) and integral (Ki) gains to adjust the torque reference that is sent to the machine. This torque reference attempts to operate the machine at the specified torque necessary to maintain the speed. This regulator also produces a high bandwidth response to speed command and load change. The output of the Speed PI regulator is used to produce the desired torque reference. For the purpose of this work, the proportional and integral gain was Kp ¼ 10, and Ki ¼ 500. 3. Description of experimental set-up
Fig. 4. Layout of semi closed loop SHP test rig with cross-flow turbine equipped with pressure gauge for head measurement and coupled with six-phase synchronous generator through belt.
Fig. 5. Voltage and current waveforms for six-phase synchronous generator at no-load.
pður =ub Þ ¼ ½ðP=2Þð1=JÞðTem Tsh Þ
(35)
where, Tsh is shaft torque (prime mover torque), P is the number of poles, and J is moment of inertia. To simulate the constant frequency operation of six-phase synchronous generator, a Speed PI regulator was used. The
To investigate the performance characteristics SPSG and for experimental validation of the key analytical results, a three-phase, 50 Hz, 6-pole, 36-slots, 3.7 kW synchronous machine was selected. All the 72 stator coil terminals were taken out to the terminal box mounted on the top of the machine casing, so that various winding schemes for different number of poles and phases can be realized. The six-pole, six-phase winding was obtained by employing phase belt splitting of six-pole three-phase winding. The six-stator phases are divided into two star-connected three-phase sets (winding set abc and xyz), with magnetic axis of the two three-phase sets dis placed by an angle of 30 electrical. Neutral point of the two threephase sets are kept isolated in order to prevent the physical fault propagation from one three-phase set to other one, and also to prevent the flow of triplen harmonics. The test machine was coupled to a semi closed-loop small hydro power (SHP) test rig, installed at Alternate Hydro Energy Centre of the Institute. The complete scheme is shown in Fig. 3. The SHP test rig shown in Fig. 4, consists of two identical service pumps, each having 150 L per second discharge capacity at the head of 10 m, connected to a cross-flow turbine of efficiency 56% through pipe line networks. The turbine is fitted with 24 blades around its shaft and has runner diameter of 300 mm. Control valves installed at the pipe line and the turbine are used to vary the head and discharge of water for controlling the speed of turbine shaft. The head and discharge are measured with the help of a calibrated rectangular weir and a precise digital pressure gauge. This regulated hydraulic cross-flow turbine serves as prime mover through belt coupling in order to achieve desired speed with smooth control throughout the operation [20]. The empirical formulas used for head and discharge calculation are as below:
H ¼ 10*Pa
(36)
Q ¼ 1:8ðL 0:2*hÞ*h3=2
(37)
Fig. 6. Steady-state waveforms at no-load (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc, (b) voltage and current waveforms across winding set xyz under constant voltage operation.
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G.K. Singh / Energy 36 (2011) 5621e5631
Fig. 7. Steady-state waveforms at no-load (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc, (b) voltage and current waveforms across winding set xyz under constant frequency operation.
If hg is the efficiency of the Induction generator, the overall efficiency of the system can be expressed as
hSHP ¼ ht *hg ¼
Fig. 8. Voltage and current waveforms for six-phase synchronous generator when three-phase winding set abc is subjected to 1.0 p.u. of resistive load while winding set xyz is kept open i.e. at no-load.
where, H ¼ water head in meter, Q ¼ discharge of water, Pa ¼ water pressure at turbine inlet measured by pressure gauge (in Pascal), h ¼ height of water level over the tip of rectangular weir (in meter), L ¼ length of weir aperture (in meter). The hydraulic turbine exploits and converts the available hydro power into mechanical power by taking its efficiency in to account as follows:
Pmech ¼ ht gHQ N m=sec where, ht ¼ efficiency of hydro turbine, g ¼ acceleration due to gravity.
(38)
Pelect Pmech
(39)
In this work, the entire tests were conducted on prototype SPSG reconfigured for six-pole, six-phase as well as six-pole, three-phase operation. A micron make speed transducer (model: 2176) and digital encoder (range: 60e9999 rpm) unit, installed suitably to the SPSG system, senses and displays the speed in revolution per minute (rpm). The set-up was instrumented to monitor voltage, current, power and frequency at desired locations of the network. In addition to the three-phase lamp load, a Y-connected three-phase purely resistive load banks were also used to load the prototype adequately. For experimental verification of the analytical results, tests were conducted on six-phase synchronous generator with the load on (i) single three-phase winding set, (ii) both the three-phase winding sets. All the tests were carried out for (i) constant voltage operation, and (ii) constant frequency operation. Tests were also conducted on the same test machine for six-pole three-phase configuration for comparative study of the performance. It is worthwhile to mention here that the combination with two three-phase windings dis placed 30 in phase is the configuration of greatest practical interest for very large generators since it permits the re-combination of two three-phase power displaced at 30 in the step-up transformer bank without the need for increased transformer kVA for phase shifting. In the study, it was found that the transformer cost increments (relative to a three-phase application of same kVA and voltage rating) could be limited to 5% or less [11,22]. Fluke 43-B Power Quality Analyzer was used for measurements and for recording of the various waveforms. It seems necessary to mention here that the small discrepancy in the data shown on various experimental waveforms for the same configuration and operating condition depicted in this work is due to the time lag in
Fig. 9. Steady-state waveforms (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc at 1.0 p.u. resistive load (b) voltage and current waveforms across winding set xyz at no-load under constant voltage operation.
G.K. Singh / Energy 36 (2011) 5621e5631
5627
Fig. 10. Steady-state waveforms at full load on winding set abc (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc, (b) voltage and current waveforms across winding set xyz under constant frequency operation.
Fig. 11. Voltage and current waveforms for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to equal resistive loading of 0.5 p.u.
recording the waveforms in absence of a system to record the waveforms simultaneously. 4. Analytical response and experimental validation The theoretical studies using MATLAB/SIMULINK have been carried out on a six-phase synchronous generator. As the circuit contains no voltage source imposing the reference angle, the load flow have been performed controlling the voltage and the angle at its terminals (i.e. as Swing Bus). The desired terminal voltage was initialized as one per unit (machine nominal voltage). Parameters of the test machine are:
Stator winding: resistance r1 ¼ r2 ¼ 2.1 U, leakage reactance xl1 ¼ xl2 ¼ 0.1758 U. Damper winding: resistance rkq ¼ 5.07 U, rkd ¼ 140.0 U, reactance xkq ¼ 0.66097 U, xkd ¼ 1.54959 U. Field winding: resistance rfd ¼ 0.00160 U, reactance xfd ¼ 0.24021 U. Mutual leakage reactance between the two three-phase winding sets xlm ¼ 0.001652 U. Xdq ¼ 0 (for 30 displacement). For the purpose of experimental validation of analytical results, each three-phase winding set (abc and xyz) was independently loaded with a variable three-phase resistive load. Contactors were provided to enable the connection of load to either only one of the three-phase winding set or to both the three-phase winding sets. For constant voltage operation, terminal voltage was maintained constant (188 V approximately) by regulating the field current of the machine. Although, in absence of a standard excitation system (a very little variation in excitation current of the machine was possible by regulating the voltage across field using rheostat), it was difficult to get a constant voltage during loading. For constant frequency operation, speed of the six-phase generator was kept constant from no-load to full load by varying the head and discharge of water for controlling the speed of the turbine shaft. Performance of the machine was evaluated with resistive loading subjected to (i) one of the three-phase winding set, and (ii) both the three-phase winding sets. Analytical waveforms for voltages and currents for the machine operating at no-load are given in Fig. 5, where va, ia, and vx, ix are the phase voltage and phase current of three-phase winding sets abc and xyz respectively. The corresponding experimental voltage and current waveforms for constant voltage and constant frequency operation are shown in Fig. 6 and Fig. 7 respectively. Percentage error in terminal voltage measurement in case of Fig. 6 was found to be 1.6%, whereas in case of Fig. 7, percentage error in frequency measurement was 0.4%. Computer traces shown in Fig. 8
Fig. 12. Experimental voltage and current waveforms for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to approximately equal resistive loading.
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G.K. Singh / Energy 36 (2011) 5621e5631
Fig. 13. Steady-state waveforms at full load (under safe operating condition) (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across the winding set abc, (b) voltage and current waveforms across the winding set xyz under constant frequency operation for equal loading condition.
Fig. 14. Voltage and current waveforms for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to a step change of resistive load from 0.5 p.u. to 1.0 p.u. under constant frequency operation.
illustrates the behavior of the six-phase synchronous generator when only one three-phase winding set abc is subjected to 1.0 p.u. of resistive loading while the winding set xyz is kept open i.e. at no load. Experimental voltage and current waveforms when 1.0 p.u.
resistive load was applied to three-phase winding set abc with winding set xyz kept open (no-load) for constant voltage and for constant frequency operation are respectively given in Fig. 9 and Fig. 10. Maximum percentage errors in voltage measurement in case of Fig. 9, and in frequency measurement in case of Fig. 10 was calculated as 0.64% and 1.2%. Analytical voltage and current waveforms when both the three-phase winding sets abc and xyz are subjected to equal resistive loading are given in Fig. 11. Fig. 12 depicts the experimental voltage and current waveforms when both the winding sets were subjected to equal resistive loading. In this case the initial terminal voltage was set at 188 V. Experimental voltage and current waveforms for equal resistive loading on both the winding sets under constant frequency operation is given in Fig. 13. Maximum percentage error in current measurement in case of characteristic curves shown in Fig. 12, and maximum percentage error in frequency measurement in case of performance curves depicted in Fig. 13 was obtained as 2.1% and 1.2% respectively. To assess the dynamic behavior of SPSG, both the three-phase winding sets were subjected to a step change of resistive load from 0.5 p.u. to 1.0 p.u. Corresponding analytical voltage and current waveforms are depicted in Fig. 14. Computer traces for torque, speed and rotor angle for step change of load under constant frequency operation are illustrated in Fig. 15. From the characteristic curves shown in Fig. 15, it can be observed that in order to maintain the speed at its reference value (1.0 p.u.), speed regulator has reduced the mechanical torque to 0.85 p.u. approximately. Voltage and current profile of all the analytical results clearly show the effect of angle of displacement between the two three-phase winding sets. It is worth mentioning here that error in various measurements was due to the time lag in recording of the waveforms in absence of a system to record the waveforms simultaneously as stated in Section 3, and also because of supply voltage fluctuation fed to service pumps of the SHP test rig.
Speed (rpm)
3
800 600
2
400
speed KVA
200
1
0
volt-ampere (KVA)
4 1000
0 0
4
8
12
Load current for set abc (A) Fig. 15. Traces of torque, speed and rotor angle for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to a step change of resistive load from 0.5 p.u. to 1.0 p.u. under constant frequency operation.
Fig. 16. Variation of power (volteampere) and speed with load current when only one winding set abc is subjected to resistive loading.
G.K. Singh / Energy 36 (2011) 5621e5631
8
6
800 600
4
400 2
speed
200
volt-ampere (KVA)
speed (rpm)
1000
KVA
0
0 0
4
8
12
Load current (A)
200
5
160
4
120
3
80
2 Vt KVA
40
1
0
volt-ampere (KVA)
Terminal voltage for both set (V)
Fig. 17. Variation of power (volteampere) and speed with load current when both the winding sets abc and xyz are subjected to resistive loading for constant voltage operation.
0 0
2
4
6
8
Load current for both sets (A) Fig. 18. Variation of power (volteampere) and voltage with load current when both the winding sets abc and xyz are subjected to equal resistive loading under constant frequency operation.
5. Comparative study of steady-state performance The SPSG was driven at synchronous speed and the steady-state performance indices were studied with resistive loading. A threephase star connected resistive load was switched on to the three-
5629
phase winding set abc while the other winding set xyz was kept open. Variation of power (volt-ampere) and speed with load current for constant voltage operation is depicted in Fig.16. Generator is able to deliver power of 2.6 kW within the safe current limit. At full load, the speed drops to 918 rpm. The full load power delivered by the machine with single winding loading is 70.3% of the rated power of the test machine, whereas speed regulation is found to be 8.2%. Independent three-phase star connected resistive load was switched on to both the three-phase winding sets abc and xyz for equal loading condition. Fig. 17 shows the variation of power (voltampere) and speed with the load current. Total power delivered by the machine is found to be 6.4 kW under safe operating condition. Under full load operation, the speed drops to 940 rpm. This power is approximately 173% of the rated power of the three-phase synchronous machine. The speed regulation is found to be 6%. Under constant frequency operation, the power delivered by the machine is found to be 2.3 kW (maximum safe loading) when only one three-phase winding set is subjected to resistive loading. Variation of power (volt-ampere) and voltage with load current under constant frequency operation when both the three-phase winding sets are subjected to equal resistive loading is given in Fig. 18. The total power delivered under this mode of operation is obtained as 4.4 kW. The behavior of SPSG system as shown in Fig. 19, where a sixphase to three-phase transformer is used to provide the supply to a three-phase load from SPSG was also examined. As noted, such a configuration improves reliability of the supply since, should one three-phase winding of the generator fail, the load can still be supplied from the remaining healthy three-phase winding. Output of the two winding sets abc and xyz of the SPSG is combined through a D-Y/Y six-phase to three-phase transformer to provide power to a variable three-phase resistive load connected to the transformer output terminals. All the tests were performed for the constant voltage operation. Fig. 20 depicts the variation of power (volt-ampere) and speed with armature current of one three-phase winding set (armature current of both the winding sets will be approximately equal for equal loading condition). The power delivered by the system was found to be 6.2 kW (approximately 168% of the rated power of the test machine) whereas drop in speed is 6.5%. It is observed that the maximum achievable power is lower when the transformer is used to combine the two three-phase power of SPSG. This is a consequence of additional losses that
a
MCB Six-Phase Synchronous Generator
b Contactor
Vb Va Vc x
30° 30°
1:1:1 T/F
a
z
DC FIELD EXCITATION
c
b c
+
x
-
y
Vy
IL L O A D
y
Vx
Vz
Contactor
MCB Prime Mover
z
Fig. 19. Schematic diagram of six-phase synchronous generator supplying a three-phase load through interposed D-Y/Y six-phase to three-phase transformer.
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G.K. Singh / Energy 36 (2011) 5621e5631
8
6
800 600
4
400 2
speed
200
volt-ampere (KVA)
speed (rpm)
1000
through an interposed D-Y/Y six-phase to three-phase transformer and the test results of three-phase synchronous generator. Results embodied in Tables 1 and 2; clearly shows that the performance of SPSG under equal loading condition for both the operating conditions (constant voltage and constant frequency operation) is better in terms of voltage regulation, frequency regulation, and power delivered [22]. 6. Conclusion
KVA 0
0 0
4
8
12
Load current (A) Fig. 20. Variation of power (volteampere) and speed with load current when both the three-phase winding sets abc and xyz are subjected to resistive loading through interposed D-Y/Y six-phase to three-phase transformer for constant voltage operation.
Table 1 Comparative performance evaluation of six-phase synchronous generator in different mode of operation with resistive loading for constant voltage operation. Operating mode of synchronous generator
Performance indices variation from no-load to full load
Poutput (kW) (Maximum)
% change in speed Six-phase configuration and resistive loading on both the winding sets abc and xyz Six-phase configuration and resistive loading on single winding set abc Six-phase configuration and resistive loading on both the winding sets through interposed D/Y-Y six-phase to three-phase transformer Three-phase configuration and resistive Loading
6.0 (1000e940)
6.4
8.2 (1000e918)
2.6
6.5 (1000e935)
6.2
9.8 (1000e902)
3.2
now take place in the system, in the transformer winding. In another test, output of the one winding set xyz was disconnected from the input of the transformer. In this case, power delivered was found to be 2.5 kW. Based on the experimental findings, the comparative performance evaluation of six-phase synchronous generator coupled to a cross-flow hydro turbine was carried out with the resistive loading on single three-phase winding set abc and on both the winding sets abc and xyz, for constant voltage and for constant frequency operation as shown in Table 1 and Table 2 respectively. Table 1 also includes the performance indices of six-phase synchronous generator where resistive loading is subjected Table 2 Comparative performance evaluation of six-phase synchronous generator in different mode of operation with resistive loading for constant speed/frequency operation. Operating mode of synchronous generator
Performance indices variation from no-load to full load
Poutput (kW) (Maximum)
% change in terminal voltage Six-phase configuration and resistive 9.5 (188e170) loading on both the winding sets abc and xyz Six-phase configuration and resistive 7.8 (192e177) loading on single winding set abc Three-phase configuration and 15 (220e187) resistive Loading
In this paper, a simple deq model of a six-phase synchronous generator for stand-alone operation is presented. In the analytical model, effects of common mutual leakage reactance between the two three-phase winding sets have been included. Mathematical model developed in the paper can be easily applied to analyze the machine behavior for any angle of displacement. Inclusion of active power and reactive power components supplied by the two winding sets in calculation of q- and d-axis current (Eqs. 30e33) provides an additional tool to take into account the power factor of the load. The paper also discusses the applicability of a six-phase synchronous generator for supplying two individual three-phase loads by presenting the results of an analytical and experimental study of the steady-state behavior for various operating conditions. No-load and loading performances under typical resistive loading are elaborated. The emphasis is placed on additional possibilities offered by using a six-phase synchronous generator, which are not available with a three-phase synchronous generator. It means that, in normal operation, fault in one of the two three-phase windings can be sustained and operation continued. Hence, SPSG offers an improved reliability, when compared to its three-phase counterpart. Further, it is also shown that the SPSG can be used to supply two different and independent three-phase loads. While the interaction between the two windings is inevitable and variation of load at one winding changes the operating conditions at the other winding, the situation is still satisfactory for a wide range of rural resistive loads. A further advantage of SPSG with respect to a threephase synchronous generator is the possibility of combining the outputs of two three-phase windings to supply a single three-phase load, by means of a three-winding transformer with dual star-delta connected primary. Failure of one three-phase generator winding in this case does not mean the shutdown of the system, since the load can still be supplied through the remaining healthy generator winding (with an appropriate reduction of the delivered power). On the basis of a comparative performance study conducted on six-phase synchronous generator as depicted in Section 5, it can be concluded that: variation in SPSG terminal voltage with the change in loading for constant frequency operation is lower; change in frequency for constant voltage operation is lower; power delivered by the hydro power scheme employing six-phase synchronous generator is better than the three-phase generator. Further, a single generator is able to deliver power to two independent loads/ customers. Generation and customer supply can also continue when one of the two three-phase winding fails if a single threephase load is supplied through an interconnecting six-phase to three-phase transformer. References
4.4
2.3 2.6
[1] Canale M, Fagiano I, Milanese M. KiteGen. A revolution in wind energy generation. Energy 2009;34:355e61. [2] Singh GK, Senthilkumar A, Saini RP. Performance evaluation of series compensated self-excited six-phase induction generator for stand-alone renewable energy generation. Energy 2010;35:288e97. [3] Abdula M, Yung VC, Anyi M, Kothman A, Abdul Hamid KB, Tarawe J. Review and comparison study of hybrid diesel /solar /hydro /fuel cell energy schemes for rural ICT telecentre. Energy 2010;35:639e46.
G.K. Singh / Energy 36 (2011) 5621e5631 [4] Tien W, Kuo K- C. An analysis of power generation from municipal solid waste (MSW) incineration plants in Taiwan. Energy 2010;35:4824e30. [5] Kalogirou S. Energy, environment and development. Energy; 35: 4620e4621. [6] Lior N. Sustainable energy development: present situation and possible paths to the future. Energy 2009;35:3976e94. [7] Dimitris I, Spyros V, Panos S, Fotis S, simira P, Costal E. The effect of hysteresis band on power management strategies in a stand alone power system. Energy 2008;33:1537e50. [8] Pillai IR, Banrjee R. Renewable energy in India: status and potential. Energy 2009;34:970e80. [9] Singh GK. Multi-phase induction machine drive research e a survey. Electric Power Systems Research 2002;61:139e47. [10] Levi E. Multiphase electric machines for variable speed applications. IEEE Transactions on Industrial Electronics 2008;55:1893e909. [11] Fuchs EF, Rosenberg LT. Analysis of an alternator with two displaced stator windings. IEEE Transactions on Power Apparatus System 1973;93:1776e86. [12] Kataoka T, Watanabe EH. Steady-state characteristics of a current source inverter /double-wound synchronous machine system for ac power supply. IEEE Transactions on Industry Applications 1980;16:262e70. [13] Hanna RA, Macdonald DC. The six-phase generator and transformer into a three-phase power system. IEEE Transactions on Power Apparatus System 1983;102:2600e7. [14] Schiferl RF, Ong CM. Six-phase synchronous machine with ac and dc stator connections, Part I: equivalent circuit representation and steady-state analysis. IEEE Transactions on Power Apparatus System 1983;102:2685e93. [15] Schiferl RF, Ong CM. Six-phase synchronous machine with ac and dc stator connections, Part II: harmonic studies and a proposed uninterruptible power supply schemes. IEEE Transactions on Power Apparatus System 1983;102: 2694e701. [16] Sudhoff SD, Wasynczuk O. Analysis and average value modeling of line commutated converter-synchronous machine systems. IEEE Transactions on Energy Conversion 1993;8:92e9.
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[17] Rockhill AA, Lipo TA. A simplified model of a nine-phase synchronous machine using vector space decomposition. Electric Power Components and Systems 2010;38:477e89. [18] Abuishmais I, Arshad WM, Kanerva S. Analysis of VSI-DTC fed six-phase synchronous machines. Proc. 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008), p. 883e888. [19] Tessarolo A, Castellan S, Menis R, Ferrari G. On the modeling of commutation transients in split-phase synchronous motors supplied by multiple loadcommutated inverters. IEEE Transactions on Industrial Electronics 2010;57: 35e43. [20] Jateskevich J, Abdul-Seoud T. Impedance characterization of a six-phase synchronous generator-rectifier system using average-value model. Proc. IEEE International Conference CCECE-2004 e CCGE I 2004, Niagara falls, p. 2231e2234. [21] Aghamohammadi MR, Pourgholi M. Experience with SSFR test for synchronous generator model identification using Hook-Jeeves optimization method. International Journal of Systems Applications, Engineering and Development Issues 2008;2:122e7. [22] Singh GK. A six-phase synchronous generator for stand-alone renewable energy generation: experimental analysis. Energy 2011;36:1768e75. [23] Singh GK. Modeling and experimental analysis of a self-excited six-phase induction generator for stand-alone renewable energy generation. Renewable Energy 2008;33:1605e21. [24] Singh GK, Senthilkumar A, Saini RP. Steady-state modeling and analysis of sixphase self-excited induction generator for satnd-alone renewable energy generation. Electric Power Components and Systems 2010;38:137e51. [25] Singh GK, Senthilkumar A, Saini RP. Selection of capacitance for self-excited six-phase induction generator for stand-alone renewable energy generation. Energy 2010;35:3273e83. [26] Alger PL. Induction machine. New York: Gordon & Breach; 1970. [27] Jones CV. The unified theory of electric machines. London: Butterworths; 1967.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Modeling and analysis of six-phase synchronous generator for stand-alone renewable energy generation G.K. Singh* Department of Electrical Engineering, Indian Institute of Technology, Roorkee 247667, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 February 2011 Received in revised form 6 May 2011 Accepted 2 July 2011 Available online 6 August 2011
This paper presents a mathematical model of six-phase synchronous generator (SPSG) for analysis of its transient and dynamic behavior for stand-alone renewable energy generation in conjunction with a hydro power plant. In the analytical model, effect of common mutual leakage reactance between the two three-phase winding sets, and the mutual leakage coupling between d- and q-axis of the two stator windings have been considered. Paper also discusses the applicability of SPSG for supplying two individual loads by presenting the results of analytical and experimental study of transient and steady-state behavior under various operating conditions. It is shown that it can be used to supply two independent three-phase loads. While the interaction between the two windings is inevitable and variation of load at one winding set changes the operating conditions at the other winding, the situation is still satisfactory for a wide range of rural resistive loads. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Renewable energy generation Six-phase synchronous generator Small hydro power generation scheme
1. Introduction Utilities in many developing countries are finding it difficult to establish and maintain remote rural area electrification. The cost of delivering power in such areas is becoming extensively large due to large investments in transmission lines for locally installed capacities and large transmission line losses. For these reasons, distributed generation has received attention in recent years for remote and rural electrification. Thus suitable stand-alone systems using locally available energy sources have become a preferred option with increased emphasis on eco-friendly technologies, and the use of renewable sources. Most of the renewable energy from wind, micro hydro, tidal, geothermal, solar, and biomass are converted into electrical energy that is delivered either to utility grid or isolated loads [1e3]. Though the initial cost of hydro system and capital cost involved in wind generation is high, but they have negligible fuel cost and relatively low maintenance cost. Process of generating biomass fuel or heat energy depends on waste, woody biomass, agriculture crops and residues and oil bearing plants. One of the biggest drawbacks that this energy source has is that there are some green house gas emissions from the process. Some renewable power sources are completely clean, but biomass is not one of them. Carbon Dioxide and other gases can be released into
* Tel.: þ91 1332 285070; fax: þ91 1332 273560. E-mail address: [email protected]. 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.07.005
the air, to harm the ozone and damage the earth, contributing to an acceleration of global warming and associated effects. Massive amount of land and water are needed to grow enough plants to provide all the energy required by the global population. Long term fuel supply and pricing, public perception as dirty fuel, and transportation of waste to power plant are the major issues involved in the biomass energy production. Many experts believe that there will not be one single alternative renewable source to replace fossil fuels, but rather that a number of different clean energy sources will be used instead. To achieve significant new growth will require new collaboration among energy, agriculture and forest production industries. To replace fossil fuels completely with biomass derived power is not really feasible, at least in near future [4e8]. The investigations spread over the last two decades indicate the technical and economic viability of using number of phases higher than three in multi-phase ac machines. Electric traction, ship propulsion, more-electric aircraft, thermal power plant, nuclear power plants, hybrid electric vehicles and battery powered electric vehicles have rapidly emerged during the last few years as the main potential application area of multi-phase machine drives. In high power applications such as ship propulsion, use of multi-phase drive enables reduction of required power rating per inverter leg (phase). In safety-critical applications such as more-electric aircraft, use of multi-phase drive enables greater fault tolerance that is of paramount importance. Finally, in electric vehicle and hybrid electric vehicle applications, utilization of multi-phase drives for propulsion enables reduction of the required semiconductor switch current
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G.K. Singh / Energy 36 (2011) 5621e5631
List of symbols
Llm
va, vx
Lldq SPSG H Q Pa
ia, ix vq1, vd1 vq2, vd2 vkq, vkd vfd, efd iq1, id1 iq2, id2 ikq, ikd ifd r1, r2 Ll1, Ll2 Lmq, Lmd
voltage across three-phase winding sets abc and xyz respectively phase current of winding sets abc and xyz respectively q- and d-axis voltage across winding set abc q- and d-axis voltage across winding set xyz q- and d-axis voltage across damper winding voltage across the field winding and field excitation voltage respectively q- and d-axis current for winding set abc q- and d-axis current for winding set xyz q- and d-axis current in damper winding field winding current resistance per phase of winding sets abc and xyz respectively stator leakage inductance per phase for winding sets abc and xyz respectively q- and d-axis mutual inductance
rating (although these drives are not characterized by high power, low voltage available in vehicles makes current high). The research in this area is still in its infancy, yet some extremely important findings have been reported in the literature indicating general feasibility of multi-phase systems [9,10]. However, practical applications of multi-phase machines in renewable energy generation scheme such as wind energy and hydro power have not been reported so far. Practical utilization of multi-phase synchronous generators was considered in the 1970’s and 1980’s. The perceived applications were predominantly related to uninterruptible power supply systems. Fuchs and Rosenberg in 1973 have analyzed the behavior of an alternator with two 3-phase stator windings displaced by an arbitrary angle by means of an orthogonal transformation of the phase variables into a new set of (d-q-) variables. They have concluded that the orthogonal transformation eliminates partly the time-dependence of the coefficients of the system of differential equations, and the phasors can be used in the analysis of the steady-state behavior of the generator with two stator windings [11]. Kataoka and Watanabe have published a detailed steady-state analysis of a dc-to-ac conversion system consisting of a currentsource inverter, a double wound synchronous machine, a position sensor and a control circuit. An equivalent circuit for predicting the steady-state behavior of the circuit is also derived and based on this equivalent circuit, the output voltage waveforms are then examined. They have also presented a method for keeping the output voltage and frequency constant [12]. Hanna and Macdonald have tested a model six-phase generator together with a model transformer giving six-to-three phase conversion with a view to assess the harmonic performance of the system [13]. An analytical model of a six-phase synchronous machine, wherein the mutual leakage couplings between the two sets of three-phase stator windings are considered, have been presented by Schiferl and Ong [14]. They have examined the steady-state operations with sinusoidal voltage inputs, using phasor diagrams to illustrate the transformer and motor mode of power transfer. Steady-state operations with ac-dc stator connections are also considered. Schiferl and Ong have also derived the relationships of mutual leakage inductances with winding displacement angle and pitch for a number of practical sixphase winding configurations, and have proposed a single machine uninterruptible power supply scheme using six-phase synchronous machine [15]. But, the output of the systems described above in [12e15] is three-phase. Sudhoff and Wasynczuk in [16] have discussed the analysis and average-value modeling of line-
h L
ht g
hg hshp V
d, a
mutual leakage inductance between the two sets of armature winding cross-saturation coupling between d- and q-axis stator six-phase synchronous generator water head in meter discharge of water water pressure at turbine inlet measured by pressure gauge (in Pascal) height of water level over the tip of rectangular weir (in meter) length of weir aperture (in meter) efficiency of hydro turbine acceleration due to gravity efficiency of the induction generator overall efficiency of the system rated or ‘bus’ voltage, torque angle and angle of displacement between the two three-phase winding sets abc and xyz respectively
commutated converter-synchronous machine systems, whereas in [17], Rockhill and Lipo have given a simplified model of a nine-phase synchronous machine using vector space decomposition. In [18], Abuishmais et al have presented the analysis of VSI-DTC six-phase synchronous machine with emphasis on redundancy, fault conditions, the machine behavior under non-sinusoidal voltage profiles and sensitivity of the design parameters. Tessarolo et al in [19] have investigated the high-power electric drives using split-phase synchronous machine equipped with N stator windings, each supplied by a load commutated inverter. To describe the split-phase machine dynamics during commutation transients (including simultaneous commutations), a simple mathematical model have also been proposed. To assess the model validity, experimental results are also presented. Findings reported in [16e19] are related to the motoring operation of the six-phase synchronous machine. A parametric approach for the development of dynamic average-value model of a machine-rectifier system is presented by Jatekevich and Abdul-Seoud [20]. Aghamohammdi and Porgholi have discussed a procedure using asset of measured data from stand-still Frequency Response Test for synchronous generator parameter identification using Hook-Jeeves optimization method [21]. Recently, a detailed experimental analysis of six-phase synchronous generator for stand-alone renewable energy generation in conjunction with the hydro power plant has been presented [22]. In this paper, Singh has covered the steady-state performance of the machine for constant voltage operation and for constant frequency operation under independent loading (symmetrical and asymmetrical) on its two three-phase set of windings. In recent times, interest in the use of multi-phase generators in conjunction with renewable energy sources has reappeared [2,23e25]. It needs to be emphasized here that there is no evidence at present of any industrial uptake of such solutions, multi-phase synchronous generator may become a viable solution for renewable energy generation in conjunction with hydro power plant. However, as the author of this paper has been able to ascertain on the basis of detailed literature review on six-phase synchronous machine, transient and dynamic analysis of six-phase synchronous generator (SPSG) have not been reported so far. This paper, therefore, presents the mathematical modeling of the six-phase synchronous generator taking into account the effect of common mutual leakage reactance between the two three-phase winding sets, and the mutual leakage coupling between d- and qaxis of the two stator windings. A detailed analytical analysis has
G.K. Singh / Energy 36 (2011) 5621e5631
been carried out in this paper to assess the transient and dynamic behavior of the machine. In particular, it is shown that the SPSG can operate with a single three-phase winding set, so that fault at one winding does not lead to the system shutdown. The generator can also supply two separate three-phase loads which represents an additional advantage. Key analytical results have been verified through experimental results conducted on the test machine powered by a cross-flow hydro turbine. MATLAB/SIMULINK were used for analytical study, whereas Fluke 43-B Power Quality Analyzer was used for measurement and for recording of the various experimental waveforms.
vq1 ¼ r1 iq1 þ ður =ub Þjd1 þ ðp=ub Þjq1
(1)
vd1 ¼ r1 id1 ður =ub Þjq1 þ ðp=ub Þjd1
(2)
vq2 ¼ r2 iq2 þ ður =u2 Þjd2 þ ðp=ubÞjq
(3)
vd2 ¼ r2 id2 ður =ub Þjq2 þ ðp=ub Þjd2
(4)
v01 ¼ r1 i01 þ ðp=ub Þj01
(5)
v02 ¼ r2 i02 þ ðp=ub Þj02
(6)
KQ
Y
b
q-axis
KQ
KD
(7)
vkd ¼ rkd ikd þ ðp=ub Þjkd
(8)
vfd ¼ rf ifd þ ðp=ub Þjfd
(9)
where, ur is the rotor speed (also the speed of the reference frame), p denotes differentiation w.r.t. time, ub is the base speed, and all other symbols have their usual meaning. Here, rotor quantities are referred to stator. The expressions for stator and rotor flux linkages per second are:
jq1 ¼Xl1 iq1 Xlm iq1 þiq2 þXldq id2 þXmq iq1 iq2 þikq
A schematic representation of the stator and rotor windings for a two pole, six-phase synchronous generator is given in Fig. 1. The six-stator phases are divided into two wye-connected three-phase sets, labeled abc and xyz, whose magnetic axes are displaced by an arbitrary angle a. The windings of each three-phase set are uniformly distributed and have axes that are displaced 120 apart. The field winding F and the short-circuited winding KD modelizing the effects of the damper winding are shown along the direct axis. The short-circuited damper winding KQ is shown along quadrature axis. Neutral point of the two three-phase winding sets are kept isolated in order to prevent the physical fault propagation from one three-phase set to other one, and to prevent the flow of triplen harmonics. The voltage equations of a six-phase synchronous generator in rotor reference frame [14] can be given by:
F
vkq ¼ rkq ikq þ ðp=ub Þjkq
2. Mathematical modeling and circuit representation
x
5623
α
a d-axis
c Z Fig. 1. Schematic representation of two-pole, salient pole six-phase synchronous machine.
jd1 ¼ Xl1 id1 Xlm ðid1 þ id2 Þ Xldq iq2 þ Xmd id1 id2 þ ikd þ ifd
(11)
jq2 ¼Xl2 iq2 Xlm iq1 þiq2 Xldq id1 þXmq iq1 iq2 þikq
jd2 ¼ Xl2 id2 Xlm ðid1 þ id2 Þ þ Xldq iq1
jfd
þ Xmd id1 id2 þ ikd þ ifd ¼ Xlf ifd þ Xmd id1 id2 þ ifd
jkq ¼ Xlkq ikq þ Xmq iq1 iq2 þ ikq
(10)
(13) (14)
jkd ¼ Xlkd ikq þ Xmd id1 id2 þ ikd þ ifd
(12)
(15)
(16)
where, Xlm is the common mutual leakage reactance between the two sets of stator winding and Xldq is the cross-saturation coupling between the d- and q-axis of stator. Xlm and Xdq is given by:
Xlm ¼ Xlax cos a þ Xlay cos ða þ 2p=3Þ þ Xlaz cos ða 2p=3Þ
(17)
Xldq ¼ Xlax sin a þ Xlay sin ða þ 2p=3Þ þ Xlaz sin ða 2p=3Þ
(18)
These equations suggest the equivalent circuit as shown in Fig. 2. The common mutual leakage inductance Llm in Fig. 2 represents the fact that the two sets of stator windings occupy the same slots and are, therefore, mutually coupled by a component of leakage flux. The mutual leakage inductance, Llm has an important effect on the harmonic coupling between the two stator winding sets and depends on the winding pitch and displacement angle between the two stator winding sets. Alger has explained this in detail, and has given a technique for finding the slot reactance [26]. Standard test procedures are available to determine the various machine parameters [21,27]. As for as transient behavior is concerned, it has been found that neglecting the stator mutual leakage inductance Llm has no noticeable effect except some changes in voltage harmonic distortion (VHD). The detailed simulation of a multi-phase machine is based on the integral form of the machine’s voltage and torque equations with flux linkage per second and speed as state variables, winding currents as output variables, applied voltage and load torque as input variables. Thus, solving for the currents and back substituting these currents into the voltage equations and rewriting them as differential equations yields:
h pjq1 ¼ ub vq1 ður =ub Þjd1 ðr1 =XÞ ðXl2 þXlm Þjq1 Xlm jq2 i Xl2 jmq þXldq ðjd2 jmd Þ
(19)
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G.K. Singh / Energy 36 (2011) 5621e5631
Ll1
r1 iq1
Ll2
r2
Let (P1, Q1) and (P2, Q2) be the active and reactive power supplied by the winding sets abc and xyz respectively
ωr λd1
-
+
ωr λd2
+
Llm
Lkq
rkq
-
vq1
ikq iq2
vkq
P1 ¼ vd1 id1 þ vq1 iq1
(26)
Q1 ¼ vq1 id1 vd1 iq1
(27)
P2 ¼ vd2 id2 þ vq2 iq2
(28)
Q2 ¼ vq2 id2 vd2 iq2
(29)
Lmq
vq2 Ldq Ldq
Lkd Ll1
r1
id1
-
Ll2
r2
vd1
Solving Equations (26)e(29) for current:
rkd
ωr λq1
-
+
Llm
Lfd
rfd
ikd
ωr λq2
+
vkd
ifd
id2
vfd
vd2
Lmd
Fig. 2. An equivalent circuit of a six-phase synchronous generator.
h pjd1 ¼ ub vd1 þ ður =ub Þjq1 ðr1 =XÞððXl2 þ Xlm Þjd1 i Xlm jd2 Xl2 jmd Þ Xldq jq2 jmq h
h ¼ ub vd2 þ ður =ub Þjq2 ðr2 =XÞððXl1 þ Xlm Þjd2 i Xlm jd1 Xl1 jmd Þ þ Xldq jq1 jmq
(30)
id1 ¼ Q1 *vq1 þ P1 *vd1 vq1 *vq1 þ vd1 *vd1
(31)
iq2 ¼ P2 =vq2 vd2 =vq2 * Q2 *vq2 þ P2 *vd2 vq2 *vq2 þ vd2 *vd2
(32)
vq2 *vq2 þ vd2 *vd2 id2 ¼ Q2 *vq2 þ P2 *vd2
(33)
q- and d-axis stator voltages are given by:
(20)
vq1 ¼ Vcos d vd1 ¼ Vsin d
pjq2 ¼ ub vq2 ður =ub Þjd2 ðr2 =XÞ ðXl1 þ Xlm Þjq2 i Xlm jq1 Xl1 jmq Xldq ðjd1 jmd Þ
iq1 ¼ P1 =vq1 vd1 =vq1 * Q1 *vq1 þ P1 *vd1 vq1 *vq1 þ vd1 *vd1
(21)
vq1 ¼ Vcos ðd aÞ vd1 ¼ Vsin ðd aÞ
(22)
jkq jmq pjkq ¼ ub vkq rkq =Xkq
where, V is the rated or ‘Bus’ voltage, d is torque/rotor angle and a is angle of displacement between the two three-phase winding sets abc and xyz. The torque and rotor dynamics equations can be expressed as:
(23)
i h Tem ¼ ð3=2ÞðP=2Þ iq1 þ iq2 jmd ðid1 þ id2 Þjmq
pjkd ¼ ub vkd rkd =Xkd jkd jmd
(24)
pjd2
pjfd ¼ ub vfd rfd =Xfd
jfd jmd
(25)
x
30°
a
o. hn i X þ jkq =Xkq Xl2 jq1 þXl1 jq2 þXldq ðjd2 jd1 Þ
hn o. ðXl2 jd1 þ Xl1 jd2 Þ þ Xldq jq1 jq2 ðXÞ i þ ðjkd =Xkd Þ þ jfd =Xfd
h . i 1 Xmq þ 1=Xkq þ ððXl1 þ Xl2 Þ=XÞ Aq ¼ 1
Ad ¼ 1
Contactor
Vb Va Vc
vfd ¼ efd * rfd =Xmd
jmd ¼ Ad
L O A D
MCB Six-Phase Synchronous Generator
where,
jmq ¼ Aq
(34)
z
DC FIELD WINDING
b c
+
-
y
Vy
Vx
h . i ð1 Xmd Þ þ ð1=Xkd Þ þ 1=Xfd þ ððXl1 þ Xl2 Þ=XÞ
Vz
Contactor
MCB Prime Mover
X ¼ ½Xl1 Xl2 þ Xlm ðXl1 þ Xl2 Þ
Fig. 3. Schematic diagram of the six-phase synchronous generator system.
L O A D
G.K. Singh / Energy 36 (2011) 5621e5631
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system takes the speed reference that is specified by the Speed Reference Selection Block and compares it to the speed feedback. The Speed Regulator uses proportional (Kp) and integral (Ki) gains to adjust the torque reference that is sent to the machine. This torque reference attempts to operate the machine at the specified torque necessary to maintain the speed. This regulator also produces a high bandwidth response to speed command and load change. The output of the Speed PI regulator is used to produce the desired torque reference. For the purpose of this work, the proportional and integral gain was Kp ¼ 10, and Ki ¼ 500. 3. Description of experimental set-up
Fig. 4. Layout of semi closed loop SHP test rig with cross-flow turbine equipped with pressure gauge for head measurement and coupled with six-phase synchronous generator through belt.
Fig. 5. Voltage and current waveforms for six-phase synchronous generator at no-load.
pður =ub Þ ¼ ½ðP=2Þð1=JÞðTem Tsh Þ
(35)
where, Tsh is shaft torque (prime mover torque), P is the number of poles, and J is moment of inertia. To simulate the constant frequency operation of six-phase synchronous generator, a Speed PI regulator was used. The
To investigate the performance characteristics SPSG and for experimental validation of the key analytical results, a three-phase, 50 Hz, 6-pole, 36-slots, 3.7 kW synchronous machine was selected. All the 72 stator coil terminals were taken out to the terminal box mounted on the top of the machine casing, so that various winding schemes for different number of poles and phases can be realized. The six-pole, six-phase winding was obtained by employing phase belt splitting of six-pole three-phase winding. The six-stator phases are divided into two star-connected three-phase sets (winding set abc and xyz), with magnetic axis of the two three-phase sets dis placed by an angle of 30 electrical. Neutral point of the two threephase sets are kept isolated in order to prevent the physical fault propagation from one three-phase set to other one, and also to prevent the flow of triplen harmonics. The test machine was coupled to a semi closed-loop small hydro power (SHP) test rig, installed at Alternate Hydro Energy Centre of the Institute. The complete scheme is shown in Fig. 3. The SHP test rig shown in Fig. 4, consists of two identical service pumps, each having 150 L per second discharge capacity at the head of 10 m, connected to a cross-flow turbine of efficiency 56% through pipe line networks. The turbine is fitted with 24 blades around its shaft and has runner diameter of 300 mm. Control valves installed at the pipe line and the turbine are used to vary the head and discharge of water for controlling the speed of turbine shaft. The head and discharge are measured with the help of a calibrated rectangular weir and a precise digital pressure gauge. This regulated hydraulic cross-flow turbine serves as prime mover through belt coupling in order to achieve desired speed with smooth control throughout the operation [20]. The empirical formulas used for head and discharge calculation are as below:
H ¼ 10*Pa
(36)
Q ¼ 1:8ðL 0:2*hÞ*h3=2
(37)
Fig. 6. Steady-state waveforms at no-load (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc, (b) voltage and current waveforms across winding set xyz under constant voltage operation.
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G.K. Singh / Energy 36 (2011) 5621e5631
Fig. 7. Steady-state waveforms at no-load (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc, (b) voltage and current waveforms across winding set xyz under constant frequency operation.
If hg is the efficiency of the Induction generator, the overall efficiency of the system can be expressed as
hSHP ¼ ht *hg ¼
Fig. 8. Voltage and current waveforms for six-phase synchronous generator when three-phase winding set abc is subjected to 1.0 p.u. of resistive load while winding set xyz is kept open i.e. at no-load.
where, H ¼ water head in meter, Q ¼ discharge of water, Pa ¼ water pressure at turbine inlet measured by pressure gauge (in Pascal), h ¼ height of water level over the tip of rectangular weir (in meter), L ¼ length of weir aperture (in meter). The hydraulic turbine exploits and converts the available hydro power into mechanical power by taking its efficiency in to account as follows:
Pmech ¼ ht gHQ N m=sec where, ht ¼ efficiency of hydro turbine, g ¼ acceleration due to gravity.
(38)
Pelect Pmech
(39)
In this work, the entire tests were conducted on prototype SPSG reconfigured for six-pole, six-phase as well as six-pole, three-phase operation. A micron make speed transducer (model: 2176) and digital encoder (range: 60e9999 rpm) unit, installed suitably to the SPSG system, senses and displays the speed in revolution per minute (rpm). The set-up was instrumented to monitor voltage, current, power and frequency at desired locations of the network. In addition to the three-phase lamp load, a Y-connected three-phase purely resistive load banks were also used to load the prototype adequately. For experimental verification of the analytical results, tests were conducted on six-phase synchronous generator with the load on (i) single three-phase winding set, (ii) both the three-phase winding sets. All the tests were carried out for (i) constant voltage operation, and (ii) constant frequency operation. Tests were also conducted on the same test machine for six-pole three-phase configuration for comparative study of the performance. It is worthwhile to mention here that the combination with two three-phase windings dis placed 30 in phase is the configuration of greatest practical interest for very large generators since it permits the re-combination of two three-phase power displaced at 30 in the step-up transformer bank without the need for increased transformer kVA for phase shifting. In the study, it was found that the transformer cost increments (relative to a three-phase application of same kVA and voltage rating) could be limited to 5% or less [11,22]. Fluke 43-B Power Quality Analyzer was used for measurements and for recording of the various waveforms. It seems necessary to mention here that the small discrepancy in the data shown on various experimental waveforms for the same configuration and operating condition depicted in this work is due to the time lag in
Fig. 9. Steady-state waveforms (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc at 1.0 p.u. resistive load (b) voltage and current waveforms across winding set xyz at no-load under constant voltage operation.
G.K. Singh / Energy 36 (2011) 5621e5631
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Fig. 10. Steady-state waveforms at full load on winding set abc (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across winding set abc, (b) voltage and current waveforms across winding set xyz under constant frequency operation.
Fig. 11. Voltage and current waveforms for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to equal resistive loading of 0.5 p.u.
recording the waveforms in absence of a system to record the waveforms simultaneously. 4. Analytical response and experimental validation The theoretical studies using MATLAB/SIMULINK have been carried out on a six-phase synchronous generator. As the circuit contains no voltage source imposing the reference angle, the load flow have been performed controlling the voltage and the angle at its terminals (i.e. as Swing Bus). The desired terminal voltage was initialized as one per unit (machine nominal voltage). Parameters of the test machine are:
Stator winding: resistance r1 ¼ r2 ¼ 2.1 U, leakage reactance xl1 ¼ xl2 ¼ 0.1758 U. Damper winding: resistance rkq ¼ 5.07 U, rkd ¼ 140.0 U, reactance xkq ¼ 0.66097 U, xkd ¼ 1.54959 U. Field winding: resistance rfd ¼ 0.00160 U, reactance xfd ¼ 0.24021 U. Mutual leakage reactance between the two three-phase winding sets xlm ¼ 0.001652 U. Xdq ¼ 0 (for 30 displacement). For the purpose of experimental validation of analytical results, each three-phase winding set (abc and xyz) was independently loaded with a variable three-phase resistive load. Contactors were provided to enable the connection of load to either only one of the three-phase winding set or to both the three-phase winding sets. For constant voltage operation, terminal voltage was maintained constant (188 V approximately) by regulating the field current of the machine. Although, in absence of a standard excitation system (a very little variation in excitation current of the machine was possible by regulating the voltage across field using rheostat), it was difficult to get a constant voltage during loading. For constant frequency operation, speed of the six-phase generator was kept constant from no-load to full load by varying the head and discharge of water for controlling the speed of the turbine shaft. Performance of the machine was evaluated with resistive loading subjected to (i) one of the three-phase winding set, and (ii) both the three-phase winding sets. Analytical waveforms for voltages and currents for the machine operating at no-load are given in Fig. 5, where va, ia, and vx, ix are the phase voltage and phase current of three-phase winding sets abc and xyz respectively. The corresponding experimental voltage and current waveforms for constant voltage and constant frequency operation are shown in Fig. 6 and Fig. 7 respectively. Percentage error in terminal voltage measurement in case of Fig. 6 was found to be 1.6%, whereas in case of Fig. 7, percentage error in frequency measurement was 0.4%. Computer traces shown in Fig. 8
Fig. 12. Experimental voltage and current waveforms for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to approximately equal resistive loading.
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G.K. Singh / Energy 36 (2011) 5621e5631
Fig. 13. Steady-state waveforms at full load (under safe operating condition) (trace 1 ¼ voltage, trace 2 ¼ current): (a) voltage and current waveforms across the winding set abc, (b) voltage and current waveforms across the winding set xyz under constant frequency operation for equal loading condition.
Fig. 14. Voltage and current waveforms for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to a step change of resistive load from 0.5 p.u. to 1.0 p.u. under constant frequency operation.
illustrates the behavior of the six-phase synchronous generator when only one three-phase winding set abc is subjected to 1.0 p.u. of resistive loading while the winding set xyz is kept open i.e. at no load. Experimental voltage and current waveforms when 1.0 p.u.
resistive load was applied to three-phase winding set abc with winding set xyz kept open (no-load) for constant voltage and for constant frequency operation are respectively given in Fig. 9 and Fig. 10. Maximum percentage errors in voltage measurement in case of Fig. 9, and in frequency measurement in case of Fig. 10 was calculated as 0.64% and 1.2%. Analytical voltage and current waveforms when both the three-phase winding sets abc and xyz are subjected to equal resistive loading are given in Fig. 11. Fig. 12 depicts the experimental voltage and current waveforms when both the winding sets were subjected to equal resistive loading. In this case the initial terminal voltage was set at 188 V. Experimental voltage and current waveforms for equal resistive loading on both the winding sets under constant frequency operation is given in Fig. 13. Maximum percentage error in current measurement in case of characteristic curves shown in Fig. 12, and maximum percentage error in frequency measurement in case of performance curves depicted in Fig. 13 was obtained as 2.1% and 1.2% respectively. To assess the dynamic behavior of SPSG, both the three-phase winding sets were subjected to a step change of resistive load from 0.5 p.u. to 1.0 p.u. Corresponding analytical voltage and current waveforms are depicted in Fig. 14. Computer traces for torque, speed and rotor angle for step change of load under constant frequency operation are illustrated in Fig. 15. From the characteristic curves shown in Fig. 15, it can be observed that in order to maintain the speed at its reference value (1.0 p.u.), speed regulator has reduced the mechanical torque to 0.85 p.u. approximately. Voltage and current profile of all the analytical results clearly show the effect of angle of displacement between the two three-phase winding sets. It is worth mentioning here that error in various measurements was due to the time lag in recording of the waveforms in absence of a system to record the waveforms simultaneously as stated in Section 3, and also because of supply voltage fluctuation fed to service pumps of the SHP test rig.
Speed (rpm)
3
800 600
2
400
speed KVA
200
1
0
volt-ampere (KVA)
4 1000
0 0
4
8
12
Load current for set abc (A) Fig. 15. Traces of torque, speed and rotor angle for six-phase synchronous generator when both the three-phase winding sets abc and xyz are subjected to a step change of resistive load from 0.5 p.u. to 1.0 p.u. under constant frequency operation.
Fig. 16. Variation of power (volteampere) and speed with load current when only one winding set abc is subjected to resistive loading.
G.K. Singh / Energy 36 (2011) 5621e5631
8
6
800 600
4
400 2
speed
200
volt-ampere (KVA)
speed (rpm)
1000
KVA
0
0 0
4
8
12
Load current (A)
200
5
160
4
120
3
80
2 Vt KVA
40
1
0
volt-ampere (KVA)
Terminal voltage for both set (V)
Fig. 17. Variation of power (volteampere) and speed with load current when both the winding sets abc and xyz are subjected to resistive loading for constant voltage operation.
0 0
2
4
6
8
Load current for both sets (A) Fig. 18. Variation of power (volteampere) and voltage with load current when both the winding sets abc and xyz are subjected to equal resistive loading under constant frequency operation.
5. Comparative study of steady-state performance The SPSG was driven at synchronous speed and the steady-state performance indices were studied with resistive loading. A threephase star connected resistive load was switched on to the three-
5629
phase winding set abc while the other winding set xyz was kept open. Variation of power (volt-ampere) and speed with load current for constant voltage operation is depicted in Fig.16. Generator is able to deliver power of 2.6 kW within the safe current limit. At full load, the speed drops to 918 rpm. The full load power delivered by the machine with single winding loading is 70.3% of the rated power of the test machine, whereas speed regulation is found to be 8.2%. Independent three-phase star connected resistive load was switched on to both the three-phase winding sets abc and xyz for equal loading condition. Fig. 17 shows the variation of power (voltampere) and speed with the load current. Total power delivered by the machine is found to be 6.4 kW under safe operating condition. Under full load operation, the speed drops to 940 rpm. This power is approximately 173% of the rated power of the three-phase synchronous machine. The speed regulation is found to be 6%. Under constant frequency operation, the power delivered by the machine is found to be 2.3 kW (maximum safe loading) when only one three-phase winding set is subjected to resistive loading. Variation of power (volt-ampere) and voltage with load current under constant frequency operation when both the three-phase winding sets are subjected to equal resistive loading is given in Fig. 18. The total power delivered under this mode of operation is obtained as 4.4 kW. The behavior of SPSG system as shown in Fig. 19, where a sixphase to three-phase transformer is used to provide the supply to a three-phase load from SPSG was also examined. As noted, such a configuration improves reliability of the supply since, should one three-phase winding of the generator fail, the load can still be supplied from the remaining healthy three-phase winding. Output of the two winding sets abc and xyz of the SPSG is combined through a D-Y/Y six-phase to three-phase transformer to provide power to a variable three-phase resistive load connected to the transformer output terminals. All the tests were performed for the constant voltage operation. Fig. 20 depicts the variation of power (volt-ampere) and speed with armature current of one three-phase winding set (armature current of both the winding sets will be approximately equal for equal loading condition). The power delivered by the system was found to be 6.2 kW (approximately 168% of the rated power of the test machine) whereas drop in speed is 6.5%. It is observed that the maximum achievable power is lower when the transformer is used to combine the two three-phase power of SPSG. This is a consequence of additional losses that
a
MCB Six-Phase Synchronous Generator
b Contactor
Vb Va Vc x
30° 30°
1:1:1 T/F
a
z
DC FIELD EXCITATION
c
b c
+
x
-
y
Vy
IL L O A D
y
Vx
Vz
Contactor
MCB Prime Mover
z
Fig. 19. Schematic diagram of six-phase synchronous generator supplying a three-phase load through interposed D-Y/Y six-phase to three-phase transformer.
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G.K. Singh / Energy 36 (2011) 5621e5631
8
6
800 600
4
400 2
speed
200
volt-ampere (KVA)
speed (rpm)
1000
through an interposed D-Y/Y six-phase to three-phase transformer and the test results of three-phase synchronous generator. Results embodied in Tables 1 and 2; clearly shows that the performance of SPSG under equal loading condition for both the operating conditions (constant voltage and constant frequency operation) is better in terms of voltage regulation, frequency regulation, and power delivered [22]. 6. Conclusion
KVA 0
0 0
4
8
12
Load current (A) Fig. 20. Variation of power (volteampere) and speed with load current when both the three-phase winding sets abc and xyz are subjected to resistive loading through interposed D-Y/Y six-phase to three-phase transformer for constant voltage operation.
Table 1 Comparative performance evaluation of six-phase synchronous generator in different mode of operation with resistive loading for constant voltage operation. Operating mode of synchronous generator
Performance indices variation from no-load to full load
Poutput (kW) (Maximum)
% change in speed Six-phase configuration and resistive loading on both the winding sets abc and xyz Six-phase configuration and resistive loading on single winding set abc Six-phase configuration and resistive loading on both the winding sets through interposed D/Y-Y six-phase to three-phase transformer Three-phase configuration and resistive Loading
6.0 (1000e940)
6.4
8.2 (1000e918)
2.6
6.5 (1000e935)
6.2
9.8 (1000e902)
3.2
now take place in the system, in the transformer winding. In another test, output of the one winding set xyz was disconnected from the input of the transformer. In this case, power delivered was found to be 2.5 kW. Based on the experimental findings, the comparative performance evaluation of six-phase synchronous generator coupled to a cross-flow hydro turbine was carried out with the resistive loading on single three-phase winding set abc and on both the winding sets abc and xyz, for constant voltage and for constant frequency operation as shown in Table 1 and Table 2 respectively. Table 1 also includes the performance indices of six-phase synchronous generator where resistive loading is subjected Table 2 Comparative performance evaluation of six-phase synchronous generator in different mode of operation with resistive loading for constant speed/frequency operation. Operating mode of synchronous generator
Performance indices variation from no-load to full load
Poutput (kW) (Maximum)
% change in terminal voltage Six-phase configuration and resistive 9.5 (188e170) loading on both the winding sets abc and xyz Six-phase configuration and resistive 7.8 (192e177) loading on single winding set abc Three-phase configuration and 15 (220e187) resistive Loading
In this paper, a simple deq model of a six-phase synchronous generator for stand-alone operation is presented. In the analytical model, effects of common mutual leakage reactance between the two three-phase winding sets have been included. Mathematical model developed in the paper can be easily applied to analyze the machine behavior for any angle of displacement. Inclusion of active power and reactive power components supplied by the two winding sets in calculation of q- and d-axis current (Eqs. 30e33) provides an additional tool to take into account the power factor of the load. The paper also discusses the applicability of a six-phase synchronous generator for supplying two individual three-phase loads by presenting the results of an analytical and experimental study of the steady-state behavior for various operating conditions. No-load and loading performances under typical resistive loading are elaborated. The emphasis is placed on additional possibilities offered by using a six-phase synchronous generator, which are not available with a three-phase synchronous generator. It means that, in normal operation, fault in one of the two three-phase windings can be sustained and operation continued. Hence, SPSG offers an improved reliability, when compared to its three-phase counterpart. Further, it is also shown that the SPSG can be used to supply two different and independent three-phase loads. While the interaction between the two windings is inevitable and variation of load at one winding changes the operating conditions at the other winding, the situation is still satisfactory for a wide range of rural resistive loads. A further advantage of SPSG with respect to a threephase synchronous generator is the possibility of combining the outputs of two three-phase windings to supply a single three-phase load, by means of a three-winding transformer with dual star-delta connected primary. Failure of one three-phase generator winding in this case does not mean the shutdown of the system, since the load can still be supplied through the remaining healthy generator winding (with an appropriate reduction of the delivered power). On the basis of a comparative performance study conducted on six-phase synchronous generator as depicted in Section 5, it can be concluded that: variation in SPSG terminal voltage with the change in loading for constant frequency operation is lower; change in frequency for constant voltage operation is lower; power delivered by the hydro power scheme employing six-phase synchronous generator is better than the three-phase generator. Further, a single generator is able to deliver power to two independent loads/ customers. Generation and customer supply can also continue when one of the two three-phase winding fails if a single threephase load is supplied through an interconnecting six-phase to three-phase transformer. References
4.4
2.3 2.6
[1] Canale M, Fagiano I, Milanese M. KiteGen. A revolution in wind energy generation. Energy 2009;34:355e61. [2] Singh GK, Senthilkumar A, Saini RP. Performance evaluation of series compensated self-excited six-phase induction generator for stand-alone renewable energy generation. Energy 2010;35:288e97. [3] Abdula M, Yung VC, Anyi M, Kothman A, Abdul Hamid KB, Tarawe J. Review and comparison study of hybrid diesel /solar /hydro /fuel cell energy schemes for rural ICT telecentre. Energy 2010;35:639e46.
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