I. INTRODUCTION
Rotating electrical energy conversion systems, which are driven by wind turbines, have been widely used all over the world. Similarly, wind energy conversion systems are suitable for isolated and remote areas [1] and are known to employ either synchronous or induction machines as their generator systems. Compared with synchronous machines, cage-rotor induction machines (CRIMs) feature low cost, simple construction, and little maintenance. Moreover, CRIMs are considerably reliable and rugged [2], [3].
Self-excited induction generators (SEIGs) are usually used to feed autonomous loads. However, SEIGs suffer from poor voltage and frequency regulation characteristics [4]-[7]. In other words, generator output voltage and frequency change under the influence of load power demand or rotor speed variations. Furthermore, the magnetizing reactive power of SEIGs must be supplied by an appropriate source [8], [9]. Using a full-rate back-to-back (BTB) converter is a direct method to solve these problems. Such BTB converters impose additional cost upon the system, especially in high-power ratings.
The popular wound-rotor doubly fed induction generator (DFIG) system needs to use a fraction-rate multi-quadrant BTB converter in the rotor circuit [10]. Unlike SEIGs, DFIG systems are highly expensive and require a complicated control scheme. However, the output frequency of a DFIG system is constant and independent of load power demand and prime mover speed.
The three-phase permanent magnet synchronous generator (PMSG) with a full-rate BTB converter is an attractive type of wind-based generation system. Although PMSGs have high power density and efficiency, they are susceptible to permanent magnet demagnetization and startup difficulties because of their cogging torque [11].
Today, multi-phase machines are used in wind turbine generation systems because of their desirable properties, such as low per-phase power rating requirement, minor torque ripple, and good fault tolerances [12]. Six-phase SEIGs were respectively modeled, implemented, and analyzed in [1], [2], and [12]-[14]. One of the best configurations in the proposed multi-phase generators is the brushless DFIG. Although brushless DFIGs enjoy the advantage of low-cost converters and do not require brush gears, they are not highly attractive because they require specially designed machines. In brushless DFIGs, the pole numbers of two stator windings are chosen so as to avoid direct coupling, and a special rotor design is needed to couple with the two stator windings. The nested loop type is the most widely used rotor [15]. In [16]-[18], a double winding induction generator (IG) was used to generate a variablefrequency ac power. The proposed generation systems in [16]-[18] are only applicable to special loads, such as the main demand of some giant civil airplanes in which frequency variations are not important (A380 and B787).
Although the abovementioned generation systems are widely used in wind energy conversion systems, there is a need for a CRIM-based system which its output frequency is intrinsically constant and independent of the prime mover speed and load power demand. Such system should be capable of delivering converted energy to the local load or main grid without a BTB converter so as to significantly reduce the overall system cost.
A single-phase IG with a constant frequency independent of prime mover speed and generator load demand was described in [19]. This generator is excited by a single-phase pulse width modulation (PWM) inverter, which feeds the stator auxiliary winding of the machine. The main stator winding is connected to a single-phase load. In the continuation of the research work described in [19], a single-phase IG was proposed with a three-phase CRIM [20]. The first stator reference phase of the machine is fed by a single-phase static synchronous compensator (STATCOM) and is used to excite the machine while the series connection of the other two phases is connected to a single-phase load. The authors of [20] proposed a three-phase double stator winding IG in [21]. The first three-phase stator winding is fed by a three-phase PWM voltage source inverter and is used to excite the machine. The second stator winding is connected to a three-phase balanced load. In this three-phase generator, similar to the single-phase IGs described in [19] and [20], the generator output frequency is constant and independent of the generator active power demand and its prime mover speed. The generator system described in [21] is driven by a hydro-turbine and is supported only by computer simulation results.
The research work described in this paper is in fact a continuation of the previous work described in [21]. Specifically, the research is conducted for the following purposes:
In this work, we introduce a stand-alone three-phase induction generator system (IGS), which consists of a six-phase CRIM with two sets of balanced stator windings and a three-phase space vector- (SV-) PWM inverter that operates as a STATCOM. In this generator scheme, one of the stator windings, hereafter called excitation winding (EW), is fed by a three-phase STATCOM. At the same time, the second stator winding, hereafter called power winding (PW), is connected to a three-phase local load. The main frequency of the STATCOM is chosen to be exactly equal to the load desired frequency. Since the machine air-gap magnetic flux vector rotates at this frequency, therefore the frequency of the induced emf in the PW is the same as this constant frequency. Under generator loading conditions, the generator output frequency remains constant and independent of the load power demand and generator prime mover speed. An adjustable speed wind or a hydro-turbine can be used as a generator prime mover. An SMC is designed to regulate the generator output voltage, and a second SMC is developed to force the EW to only feed the reactive power to the machine. To regulate the generator output voltages, the first SMC generates STATCOM reference voltages. The frequency of these STATCOM reference voltages is chosen to be equal to the desired generator output frequency. For a given three-phase load, the second SMC produces the rotor reference speed such that no active power exchange occurs between the machine and the STATCOM. The proposed IGS is practically implemented using a dc motor as the main prime mover of the system. The simulation results are obtained with an adjustable-speed wind turbine based on a pitch angle controller. Some simulation and experimental results confirm the validity and effectiveness of the performance of the proposed IGS.
The advantages of the IGS proposed in this work, in comparison with isolated systems based on DFIGs or PMSGs/SEIGs with a full-rate BTB converter, are summarized as follows.
II. IGS MATHEMATICAL MODEL
The overall configuration of the proposed IGS is shown in Fig. 1. The IGS modeling based on the figure is described below.
Fig. 1.Overall system configuration.
A. Machine Model
In a three-phase ac machine, the space vector of a general variable fi in the stationary reference frame is defined by [22]
where fi denotes the voltage, current, and linkage flux; superscript s denotes the stationary reference frame; and subscript i stands for either stator (i = s) or rotor (i = r) variables. According to [22], the space vector in the synchronous reference frame is defined by
where superscript e denotes the synchronous reference frame and ωe indicates the synchronous electrical angular speed of the machine.
The phasor diagram of the generator windings is illustrated in Fig. 2. Two three-phase stator windings are located in α electrical degree spatial phase difference related to each other.
Fig. 2.Phasor diagram of the generator.
The equivalent generator windings in the (de, qe) synchronous reference frame are shown in Fig. 3.
Fig. 3.Representation of generator windings in the (de, qe) reference frame.
Referring to [22], the induction machine voltage space vectors in the (de, qe) synchronous reference frame are described by
where subscripts s1, s2, and r refer to EW, PW, and rotor variables, respectively; ωr is the rotor electrical angular speed; are the machine voltage space vectors; are the space vectors of the machine linkage fluxes; are the machine current space vectors; and Rs1, Rs2, Rr are the stator and rotor winding resistances.
The space vectors of the machine linkage fluxes in the (de, qe) synchronous reference frame are described as
with
where Lm is the spatial magnetizing inductance; Lls1, Lls2, Llr are the leakage inductances of machine windings; and Lls1, Lls2, Llr are the spatial machine self-inductances.
A static (R, L) three-phase balanced load is assumed to be supplied by the generator. In this case, the load equation in the (de, qe) reference frame is described by
The machine mechanical equation is
with
where Te is the generator electromagnetic torque, Tturb is the generator prime mover torque, ωm is the rotor mechanical angular speed, J is the rotor moment of inertia, and B is the friction coefficient.
B. Generator State Space Model
The machine state space equation in matrix form is
with
The fi functions and aij coefficients are given in Appendix A.
C. Wind Turbine Model
The mechanical power developed by a wind turbine is given by [23]
where Pw is the turbine mechanical output power, ρ is the air density, r is the radius of the turbine blades, Vwind is the wind speed, CP (λ, β) is the power coefficient of the wind turbine, β is the pitch angle of the turbine blades, and λ is the tip speed ratio, which is defined as:
where ωrt is the angular speed of the turbine shaft. Referring to [24], the power coefficient of a wind turbine is given as
III. SLIDING MODE CONTROLLERS
A first SMC is designed for the proposed IGS output voltage regulation and a second SMC is developed to regulate the exchanging active power between the EW and the STATCOM equal to zero.
The first SMC is designed to regulate the generator output voltage in the following way:
The output voltage error signals are defined as
where are the voltage references of the generator load. By substituting Equ. (4) with Equ. (7) and rewriting it in terms of the state variables, the following equations can be obtained:
The zi coefficients and Ei functions are defined in Appendix B. The following sliding mode switching surfaces are chosen:
where K1v and K2v are constant positive coefficients.
Referring to [25], when the system states reach the sliding manifold and slide along the surface,
Combining Equs. (23)–(25) results in
with
From Equs. (26) and (27), the equivalent SMC control action is obtained as
where Uec is the vector of the two-axis reference voltages of the STATCOM. The control law described in Equ. (29) is changed to the following equation to guarantee the sliding mode reaching phase [25].
with
where K1 and K2 are the positive control gains and λi is the saturation bandwidth of the sliding mode. The fllowing Lyapunov function is nominated:
Taking the derivative of Eq. (32) yields
By combining Equs. (27), (30), and (33), is reduced to
Equ. (34) shows that is a negative definite function; hence, the designed SMC is asymptotically stable.
A separate SMC for rotor speed control is designed such that no active power exchange takes place between the EW and the STATCOM. The following error signal is introduced:
with
where Ps1 is the active power exchanged between the EW and the STATCOM and Ps1-ref is its zero reference value. A switching surface is chosen as
where K1p is the positive constant of the SMC. Referring to [25], when the system states reach the sliding manifold and slide along the surface,
Taking the derivative of Equ. (37) and replacing for Ps1 and from Equ. (36) yields
The H3 and D3 functions are defined in Appendix B. As a result, the equivalent of the SMC control action is obtained by using Equs. (38) and (39).
By utilizing Equ. (40), the following equivalent control law guarantees the sliding mode reaching phase [25]:
where k2p is the positive control gain of the SMC.
The following Lyapunov function is nominated:
Taking the derivative of Equ. (42) yields
Combining Equs. (39), (41), and (43) results in
Equ. (44) shows that is a negative definite function; hence, the designed SMC is asymptotically stable.
IV. SIMULATION RESULTS
By using a 1.8 kW six-phase CRIG, whose parameters are given in Table I, along with a regulated speed wind turbine based on a pitch angle controller and following the theory mentioned in the previous sections, a C++ computer program is developed to solve the nonlinear differential equations of the generator. The static fourth-order Runge–Kutta method is used to solve these equations.
TABLE IGENERATOR PARAMETERS
Consider a three-phase static (R = 90 Ω, L = 0.175 H) balanced load connected to the generator output terminals at t = 0 s. This three-phase static balanced load is stepped change to (R = 103 Ω, L = 0.286 H) at t = 5.35 s and to (R = 210 Ω, L = 0 H) at t = 10.83 s. The simulation results obtained from these tests are shown in Figs. 4-9. The three-phase voltage and current waveforms of the load are shown in Fig. 4. The three-phase voltage and current waveforms of the EW input are presented in Fig. 5. The three-phase STATCOM is connected to the EW via an L-C low-pass filter with a cut-off frequency of 1 kHz. This filter is capable of filtering out the high-order harmonics of the STATCOM. As a result, an approximate sinusoidal rotating flux density wave is generated.
Fig. 4.Three-phase voltages and currents of the generator output.
Fig. 5.Excitation voltage and current of the generator.
Fig. 6.Active and reactive powers of the load.
Fig. 7.EW input powers.
Fig. 8.Rotor angular speed in electrical rad/s.
Fig. 9.Wind turbine parameters.
Fig. 6 shows the active and reactive power waveforms of the load. Fig. 7 shows the waveforms of the active and reactive powers of the EW input; as expected, no active power is exchanged between the EW and the STATCOM. Fig. 8 illustrates the rotor electrical angular speed variation. Fig. 9 demonstrates the wind linear speed and wind turbine pitch angular variations.
V. EXPERIMENTAL RESULTS
A PC-based setup is designed and implemented for the closed-loop control of the IGS shown in Fig. 1. In this control system, a 1.8 kW six-phase CRIM, whose parameters are given in Table I, and a 2.2 kW dc motor are employed. The experimental setup shown in Figs. 10–11 consists of the following sections.
Fig. 10.Block diagram of the experimental setup.
Fig. 11.Experimental setup.
A three-phase voltage source inverter is equipped with an isolation board, voltage and current sampling boards, a 48-bit Advantech digital input–output card, a 32-channel Advantech A/D converter card, a CPLD board, and a PC for data processing. An Altera EPM240T100 CPLD is employed to obtain SV-PWM inverter switching patterns with a 5 kHz switching frequency. The CPLD board is set to communicate with the PC via a digital Advantech PCI-1751 I/O board. The CPLD used in the experimental setup is realized as follows: a switching pattern is generated with the SV-PWM technique for IGBT switches; a useful dead time is provided in the so-called switching patterns of the power switches; a synchronizing signal is generated for the data transmission between the PC and the hardware; the inverter is shut down in case of emergency conditions, such as overcurrents or PC hanging states. The designed SV-PWM inverter is implemented by using six single switches of STGW30NC120HD. HCPL316J IC is used to design a fast and intelligent IGBT driver that guarantees a reliable isolation between the high voltage and control boards. The dc-link voltage, along with the voltages and currents of the two stator windings, is measured with Hall-type LEM sensors of LA55P and LV20P. All the measured electrical signals are filtered and then converted into digital signals using an Advantech PCI 1713-U A/D card. The actual rotor position is detected with an absolute encoder with 1024 pulses/rev. In addition, an L-C low-pass filter with a cut-off frequency of 1 kHz is employed to filter out the high-order harmonics of the STATCOM. As a result, a nearly sinusoidal rotating flux density wave is obtained.
An existing separately excited dc motor equipped with a closed-loop speed control system is used as the generator prime mover. The three-phase symmetrical load of the generator is obtained by combining a small three-phase induction motor in parallel with several 40 W incandescent lamps at t = 0 s. At t = 5.35 s, approximately 35% of the lamps are turned off. The three-phase induction motor is finally switched off at t = 10.83 s. The experimental results obtained from these tests are shown in Figs. 12-16. As revealed by the comparison of the simulation and experimental results, extra high-frequency oscillations exist in the wave shapes of the experimental results because of the existence of noises in the laboratory. These noises are mainly generated by the PWM inverter switching process or environmental electro-magnetic sources.
Fig. 12.Output voltage and current of the generator.
Fig. 13.Excitation voltage and current of the generator.
Fig. 14.Active and reactive powers of the load.
Fig. 15.EW input powers.
Fig. 16.Rotor angular speed in electrical rad/s.
For a desired load power demand, the employed prime mover must regulate the rotor speed corresponding to the reference value obtained by the second SMC. Therefore, it does not matter which type of mechanical prime mover with adjustable speed is used. Although different prime movers are utilized for the simulation and experimental results, the two sets of results show excellent agreement. The slight difference between these results during generator load changing, especially with regard to the active power of the EW input (Figs. 7 and 15), is due to the faster dynamic response of the wind turbine pitch control in comparison with that of the dc motor speed control (Fig. 17). The fast dynamic response of a generator prime mover equates to low active power exchanged between the generator and the STATCOM. As the dynamic response of the dc motor control system is slower than that of the wind turbine, higher jump points can be observed in Fig. 15 in comparison with those in Fig. 7 during load step changing.
Fig. 17.Dynamic responses of the wind turbine and dc motor.
As a result of the use of a narrow bandwidth sliding mode saturation layer and software low-pass filters, a low sliding mode chattering is achieved, as shown in Fig. 18.
Fig. 18.Reducing SMC chattering with a software low-pass filter.
V. CONCLUSION
A new stand-alone three-phase IGS with constant frequency and regulated output voltage is proposed. This IGS employs a six-phase cage induction machine with two separate and balanced three-phase stator windings. The first stator winding set connected to an SV-PWM STATCOM is used to excite the machine, and the second stator winding set is directly connected to a desired three-phase load. The load voltage is regulated by an SMC to enable the controller to determine the reference voltages of the STATCOM. The fundamental reference frequency of the STATCOM is chosen to be equal to the desired output frequency of the generator. A second SMC is developed and used to regulate the zero active power exchanged between the STATCOM and the stator excitation winding. Upon the selection of a constant frequency and for a desired generator load, the second SMC identifies the rotor reference rotating speed. This IGS is implemented theoretically via a computer simulation and practically via an experimental setup designed and built for this purpose. The experimental results are obtained with a dc motor as the generator prime mover, whereas the simulation results are obtained with a pitch angle-controlled wind turbine. Although different prime movers are used, the two sets of results show excellent agreement. Simulation and experimental results confirm the feasibility and effectiveness of the proposed IGS.
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