A New Grid-Connected Constant Frequency Three-Phase Induction Generator System under Unbalanced-Voltage Conditions

: This paper presents a new constant frequency, direct grid-connected wind-based induction generator system (IGS). The proposed system includes a six-phase cage rotor with two separate three-phase balanced stator windings and a three-phase SV-PWM inverter which is used as a STATCOM. The ﬁrst stator winding is connected to the STATCOM and is used to excite the machine. The main frequency of the STATCOM is considered to be constant and equal to the main grid frequency. In the second stator winding, the frequency of the induced emf is equal to the constant frequency, so the generator output frequency is independent of the load power demand and its prime mover speed. The second stator winding is directly connected to the main grid without an intermediate back-to-back converter. In order to regulate the IGS output active and reactive power components, a sliding mode control (SMC) is designed. Assuming unbalanced three-phase voltages for the main grid, a second SMC is developed to remove the machine output’s negative sequence currents. Moreover, a conventional PI controller is used to force the average exchanging active power between the machine and STATCOM to zero. This PI controller generates the reference value of the rotor angular speed. An adjustable speed pitch angle-controlled wind turbine is used as the IGS’s prime mover. The effectiveness and capability of the proposed control scheme have been supported by the simulation results.


Introduction
The use of wind energy by the electrical power generation industry has significantly enhanced in the past two decades. Today, use of wind energy conversion systems (WECSs) for distributed generation, especially in remote areas with weak networks, has grown significantly [1]. During the development of wind-based power generation systems, a new type of generator system has been introduced which supports the improvement of the overall system performance and ensures a higher cost-effectiveness of the system. Nowadays, the wound-rotor doubly fed induction generators (DFIGs), the brush-less DFIGs (BDFIGs), the cage-rotor induction generators (CRIGs), equipped with full-rate back-to-back (BTB) converters, and the permanent magnet synchronous generators (PMSGs), equipped with full-rate BTB converters, are the most widely used generators in WECSs [2,3]. The CRIGs • to obtain constant active and reactive powers without a ripple; • to obtain constant electromagnetic torque and reactive power without a ripple; • to obtain a symmetrical and sinusoidal stator current.
In Reference [27], a negative sequence compensation control scheme is studied for the magnetizing current in a DFIG. The reference value for the current is modified to have a negative sequence compensating component for the magnetizing current. To minimize the ripple in power and electromagnetic torque, the rotor-side converter is controlled to remove the pulsations in magnetizing current. Additionally, the grid-side converter is employed to maintain unity power factor and a constant DC-link voltage. It was shown that choosing the magnetizing current as a single control target enabled simultaneous reductions in pulsations in torque, power, and DC-link voltage and also minimized unbalance in currents. A stator/rotor current vector control of a doubly fed induction generator connected to the unbalanced three-phase voltage power grid is presented in [28]. The selected control targets were considered as fixed electromagnetic torque and symmetrical stator or rotor current. These vector control schemes did not use a separate negative sequence calculator and controller. On the other hand, signal filtration is employed to achieve the positive sequence components of variables.
A new CRIG-based WECS with a fixed output frequency, independent of the generator shaft speed and load power demand, is introduced in [29,30]. This induction generator system (IGS) is composed of a six-phase CRIG with a stator consisting of two three-phase balanced winding sets along with an SV-PWM inverter operating as a STATCOM. The first three-phase stator winding set, called exciting winding (EW), is connected to the STATCOM and used to excite the generator. The second stator winding set, used as the generator outlet and called power winding (PW), is directly connected to the local load. The control system based on conventional PI controllers [29] or sliding mode controllers [30] is used to regulate the three-phase generator output and DC-link voltage in symmetrical conditions. This proposed generator is used as a remote WECS under the unbalanced threephase local load condition [31]. The conventional PI controllers were employed for three different control targets. The first one is to regulate the load positive sequence voltage while simultaneously removing the load negative sequence voltage. In the second and third control targets, the positive sequence voltage is regulated while simultaneously removing the load either negative-sequence-current or active power double-frequency-component.
Although the induction generator system presented in [29][30][31] can be used either as an isolated or a grid-connected distributed generation system, only the isolated mode of operation is reported either in balanced or unbalanced three-phase local loads. Therefore, the main aim of this paper is to evaluate the performance assessment of this new induction generation system in the grid-connected mode of operation.
In this paper, the recently discussed SCIG is used in a grid-connected asymmetrical condition. In order to regulate the IGS output's active and reactive power components, a sliding mode control (SMC) was designed. This controller determines the STATCOM positive sequence reference voltages. Upon assumption of network having unbalanced three-phase voltages, a second SMC was developed to remove the generator output's negative sequence currents injected into the network. In addition, a PI controller was employed to force the average active power, exchanged between the STATCOM and the EW machine, to zero by determining the rotor reference speed. An adjustable speed wind turbine with a pitch angle controller was used as the prime mover of the generator. The proposed IGS is simulated by a C++ computer program under either symmetrical or asymmetrical three-phase grid voltage conditions. The simulation results verify the effectiveness and capabilities of the proposed system. Figure 1 shows the overview of the proposed IGS. Based on this figure, the IGS modeling can be described in the following:

Machine Model
The space vector of a general variable for a three-phase machine in a stationary reference frame is defined by [32]: where f i refers to voltage, current, and linkage flux; superscript s denotes the stationary reference frame, and subscript i is referred stator (i = s) or rotor (i = r) variables.
The space vector f s i in a synchronous reference frame can be defined as [32]: where superscript e denotes the synchronous reference frame and machine synchronous electrical angular speed is defined as ω e .
As Figure 2 shows, the two three-phase stator windings are located in the α electrical degree spatial phase related to each other. Based on Figure 3, the IGS voltage space vector equations in (d e ,q e ) synchronous reference frame are described by [29]: where subscripts s1, s2, and r refer to the EW, PW, and rotor variables; electrical angular speed is defined as ω r ; v e s1 , v e s2 , v e r are voltages of the machine in space vectors; λ , i e r are currents of the machine in space vectors; and R s1 , R s2 , R r are the stator and rotor winding resistances. In addition, L m is spatial magnetizing inductance, L ls1 , L ls2 , L lr are leakage inductances of machine windings, and L s1 , L s2 , L r are spatial machine self-inductances. It is necessary to mention that EW and rotor parameters are on the PW side. where superscript e denotes the synchronous reference frame and machine synchronous electrical angular speed is defined as ωe.
As Figure 2 shows, the two three-phase stator windings are located in the α electrical degree spatial phase related to each other. Based on Figure 3, the IGS voltage space vector equations in (d e ,q e ) synchronous reference frame are described by [29]: where subscripts s1,s2, and r refer to the EW, PW, and rotor variables; electrical angular speed is defined as ωr; 1 2 , ,      The PW generator is assumed to be connected to the main grid via an (Rc,Lc) interface impedance. For this case, the grid connection space vector equation in (d e ,q e ) reference frame is described by: where e G v is the space vector of three-phase grid voltages. Additionally, the mechanical equation of the machine is: ds qs qs ds where Te is electromagnetic torque of the generator; Tturb is prime mover torque of the generator; ωm is the mechanical angular speed of the machine; J is the rotor moment of inertia; B is the friction coefficient.

Generator State Space Model
The state-space equation of the machine can be defined in matrix form as follows:  The PW generator is assumed to be connected to the main grid via an (R c ,L c ) interface impedance. For this case, the grid connection space vector equation in (d e ,q e ) reference frame is described by: where v e G is the space vector of three-phase grid voltages. Additionally, the mechanical equation of the machine is: with where T e is electromagnetic torque of the generator; T turb is prime mover torque of the generator; ω m is the mechanical angular speed of the machine; J is the rotor moment of inertia; B is the friction coefficient.

Generator State Space Model
The state-space equation of the machine can be defined in matrix form as follows: .

X=F(X)+G(X)U
with where f i functions and a ij coefficients are given in the paper's Appendix A.

Wind Turbine Model
The mechanical power developed by a wind turbine is given by [33]: where the turbine output power is shown as P w ; air density is defined as ρ; the radius of the turbine blades is shown as r; V wind is the wind speed; C P (λ,β) is the power coefficient of the wind turbine; β is the pitch angle of turbine blades; λ is the tip speed ratio defined as: where ω rt is the angular speed of the turbine shaft. The power coefficient of the wind turbine is given as [33]: Additionally, the wind speed turbulences are considered as: where V av is the average amount of wind speed.

Positive Sequence SMC
An SMC was designed to regulate the generator output active and reactive power components in the following way: where subscript G refers to the grid and + refers to positive sequence components; v e+ qs1−re f and v e+ ds1−re f are the STATCOM positive sequence reference voltages.
The following error signals were used: where P + G−re f and Q + G−re f are the reference values for the grid absorbed powers. Aligning the d e -axis of the reference frame along the main grid positive sequence voltage position, the q e -axis of the grid voltage positive sequence, v + qG will be zero and SMC outputs could be formulated as: Choosing the following sliding mode switching surfaces: where the k 1p and k 1q are positive and constant coefficients. In the sliding manifold and slide along the surface, the system can be defined as [34]: Combining Equations (24)- (28) and (13) results in: From Equations (28) and (29), the equivalent SMC control effort is obtained as: where U + ec is the vector of the STATCOM positive sequence equivalent reference voltages. Equation (31) can be changed to the following equation to guarantee the sliding mode reaching phase [34]: with where k 2p and k 2q are the sliding mode positive control gains and λ i is the sliding mode saturation bandwidth. We used the following Lyapunov function: V is reduced to: V is a negative definite function and as a result, the designed SMC is asymptotically stable.

Negative Sequence SMC
Assuming a main grid with unbalanced three-phase voltages, an SMC was designed to eliminate the generator output's negative sequence currents. We introduced the following input-output vectors: Using the following error signals: where i e− qG and i e− dG are the negative sequence currents, injected into the grid with zero references. Sliding mode switching surfaces were introduced as: where k 1iq and k 1id are the SMC positive constants. The system in the sliding manifold and slide along the surface can be defined as [34]: Combining (13), (26) and (39)-(41) gives: with From (41) and (42), the equivalent SMC control effort can be obtained as: where Uec is the vector of STATCOM negative sequence equivalent reference voltages. Using Equation (44), the following control action was used to ensure the sliding mode reaches the phase [34]: with where k 2iq and k 2id are the sliding mode positive control gains. Nominating the following Lyapunov function: Taking the derivative of V results in: Combining ( V is reduced to: It can be said that in Equation (49) .
V is a definite function and positive, and therefore the designed SMC is asymptotically stable.

Simulation and Results
Considering the 1.8 kW six-phase CRIG shown in Table 1 with a regulated speed wind turbine based on a pitch angle controller [34] and also the mentioned theory in the previous sections, a C++ computer program, using the static fourth-order Runge-Kutta method, was developed to solve nonlinear differential equations of the machine. The simulation was implemented for both balanced and unbalanced three-phase voltages of the main grid.

Balanced Grid Results
The voltage build-up process occurred in a standalone no-load condition during the first 1 s and the generator connected to the main grid at t = 1 s. The main grid's balanced three-phase voltages are shown in Figure 4. Considering the active and reactive power reference values as (P + G-ref = 700 watt and Q + G-ref = 300 var) at t = 1 s, the steadystate generator output voltage and current waveforms obtained for this test are shown in Figure 5. Additionally, STATCOM waveforms such as voltage and current are shown in Figure 6. It should be noted that a low-pass L-C filter with a cut-off frequency of 1 kHz was utilized to connect the three-phase STATCOM to the EW. This filter is capable of filtering out the STATCOM high-order harmonics and as a result, nearly a pure sinusoidal rotating flux density wave was obtained.               Figure 7 shows the STATCOM output active and reactive power waveforms. It can be seen that the exchanged active power between EW and STATCOM is zero. Figure 8 represents the active and reactive powers absorbed by the grid. Additionally, Figure 9 shows the wind linear speed and wind turbine pitch angle variations. Moreover, the rotor electrical angular speed is shown in Figure 10. . Figure 10. Rotor angular speed in electrical rad/s. Figure 7 shows the STATCOM output active and reactive power waveform be seen that the exchanged active power between EW and STATCOM is zero. represents the active and reactive powers absorbed by the grid. Additionally, shows the wind linear speed and wind turbine pitch angle variations. Moreover, electrical angular speed is shown in Figure 10.  . Figure 10. Rotor angular speed in electrical rad/s. Figure 7 shows the STATCOM output active and reactive power waveform be seen that the exchanged active power between EW and STATCOM is zero. represents the active and reactive powers absorbed by the grid. Additionally, shows the wind linear speed and wind turbine pitch angle variations. Moreover, t electrical angular speed is shown in Figure 10.

Unbalanced Grid Results
Considering unbalanced three-phase voltages for the grid as shown in Figure 11 and assuming the same conditions as mentioned in balanced grid mode, the simulation results are shown in Figures 12-17.           As is shown in Figures 14-15, the active and reactive powers obtained for g windings are composed of a DC part and a double frequency sinusoidal wavef double frequency oscillations resulted from the interaction between voltage neg quence and current positive sequence components. Additionally, the two-axis components of EW and PW voltage and current wa in the synchronous reference frame are demonstrated in Figures 16 and 17 Figure 13. The PW unbalanced three-phase output voltages and currents. Figure 12. The EW unbalanced three-phase voltages and currents. Figure 13. The PW unbalanced three-phase output voltages and currents.
As is shown in Figures 14-15, the active and reactive powers obtained for generator windings are composed of a DC part and a double frequency sinusoidal waveform. The double frequency oscillations resulted from the interaction between voltage negative sequence and current positive sequence components.          As can be seen in the results, the sliding mode chattering is significantly low. Th due to the use of a narrow bandwidth sliding mode saturation layer and a low-pass in software.

Conclusion
In this paper, a new three-phase IGS with a constant frequency, independent of r speed, has been proposed as a distributed generation in local networks or the main This IGS employs a six-phase CRIG with two separate three-phase stator windings. first stator winding set is connected to an SV-PWM inverter, operating as a STATCOM As is shown in Figures 14 and 15, the active and reactive powers obtained for generator windings are composed of a DC part and a double frequency sinusoidal waveform. The double frequency oscillations resulted from the interaction between voltage negative sequence and current positive sequence components.
Additionally, the two-axis components of EW and PW voltage and current waveforms in the synchronous reference frame are demonstrated in Figures 16 and 17. As can be seen, only the generator output current components in (d e ,q e ) are purely DC. The other variable waveforms consisted of a DC value superimposed with a double frequency (100 Hz) sinusoidal term. It is worth mentioning that the DC term refers to the positive sequence and the double frequency part refers to the negative sequence of corresponding variables.
As can be seen in the results, the sliding mode chattering is significantly low. This is due to the use of a narrow bandwidth sliding mode saturation layer and a low-pass filter in software.