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Modelling and analysis of distributed power generation schemes supplying unbalanced and non-linear load
Electrical Power and Energy Systems 119 (2020) 105878
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Modelling and analysis of distributed power generation schemes supplying unbalanced and non-linear load
T
Rupa Mishra , Tapas Kumar Saha ⁎
Department of Electrical Engineering, National Institute of Technology, Durgapur 713209, West-Bengal, India
ARTICLE INFO
ABSTRACT
Keywords: Squirrel cage induction generator Permanent magnet synchronous generator Voltage control Current control Stand-alone load
This study presents a combined control strategy for stand-alone distributed power generation scheme, utilizing the squirrel cage induction generator (SCIG), and the permanent magnet synchronous generator (PMSG) in its structure. The combined control consists of both the machine side and load side converter control. The proposed load voltage controller, cascaded with the inner filter current controller, is designed for a load-side converter (LSC) to remove the harmonic component during non-linear loading and negative sequence component in case of unbalanced loading respectively. The control algorithm ensures to produce constant load voltage amplitude and frequency, with the change in both input power and non-linear and unbalanced loading scenarios. It also guarantees the sinusoidal load voltage under the mentioned loading conditions. Simultaneously, the dc-link voltage controller cascaded with the inner q-axis stator current controller is used for machine side converter (MSC) to keep the dc-link voltage at the prescribed level for both SCIG and PMSG during all the operating conditions. In this paper, an analysis of both the distributed generators based wind energy conversion systems under vector control for MSC provides the enhanced machine variable performance. The proposed control scheme is successfully implemented in MATLAB/Simulink environment. One scaled experimental prototype is developed, and real-time results are shown in the paper to validate the theoretical claims of the controllers.
1. Introduction Recently renewable energy sources (RES) are growing at a phenomenal pace due to the depletion of fossil fuel and degradation of the environment [1]. The wind energy system (WES) is gaining renewed attention for the utility of consumers [2] in comparison with other RES. Various types of distributed generators are chosen for wind turbine driven applications [3,4]. The doubly-fed induction generator (DFIG) is found to be essential for variable WES [5]. The growth in power electronic converters such as back to back converter, matrix converter (MC), has been considered a factor of special attention regarding the interfacing of the machine with the load [6]. The extraction of maximum power, using DFIG for standalone application, has been proposed in [7]. The stator voltage and frequency control in the case of standalone operation of DFIG based wind turbines have been discussed in [8]. However, this reference investigates the control issue associated with the machine side converter (MSC) and load side converter (LSC) for a balanced linear load only. The control algorithm plays a crucial role in the enhancement of system performances. Various control methods have been suggested to deal with the control of MSC, which includes field-oriented control [9], ⁎
sensor-less control [4], direct torque control [10], direct power control, direct voltage control [11], model predictive control [12]. Moreover, the LSC control objective is to regulate the dc-link voltage. The control systems for all the regulations have been developed in the dq reference frame. The distributed generation system during unbalance and nonlinear loading operation causes voltage quality degradation and current distortion. Several control strategies have been employed to eliminate these negative impacts [13–16]. The analysis, control, and operation of the DFIG driving stand-alone non-linear load have been outlined in [15]. The controller tends to eliminate harmonics by the design of a proper load controller by considering the LC filter. Further, the brushless doubly-fed induction generator (BDFIG) has been tested for nonlinear and unbalance stand-alone load in [14]. A compensation technique has been employed for LSC to compensate for the unbalance load current at the point of common coupling (PCC). However, the controller needs to extract positive and negative sequence component which may lead to system instability. The hierarchical control strategy is implemented for non-linear and unbalance load is discussed in [17]. In this case, a four-leg converter is used for the compensation of harmonics. The PR controller used in [13,14,16,17] suffers from a slow
Corresponding author. E-mail address: [email protected] (R. Mishra).
https://doi.org/10.1016/j.ijepes.2020.105878 Received 3 October 2019; Received in revised form 20 January 2020; Accepted 22 January 2020 0142-0615/ © 2020 Elsevier Ltd. All rights reserved.
Electrical Power and Energy Systems 119 (2020) 105878
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Fig. 1. Schematic diagram of distributed generation fed to variety of stand-alone load. Table 1 Parameter of the Simulated and Experimental setup. SCIG Specification: Power Frequency pole Rated speed Stator (Y connected) Rotor (Y connected) Stator Resistance (Rs ) Stator inductance (Ls ) Rotor inductance (Lr ) Magnetising inductance (Lm)
PMSG Specification: 746 W 50 Hz 4 1500 rpm 415 V, 2 A(RMS) 415 V, 2 A(RMS) 9.919 Ω per phase 0.9291 H per phase 0.9291 H per phase 0.8895 H per phase
Power Frequency pole Rated speed Stator (Y connected) Stator Resistance (Rs ) d-axis Inductanceq-axis InductanceFlux linkage
response. Meanwhile, very few publications are reported for the operation of the squirrel cage induction generator (SCIG), and a Permanent magnet synchronous generator (PMSG) [23] fed to the stand-alone load. The STATCOM assisted self-excited induction generator (SEIG) based wind energy conversion feeding to non-linear load is discussed in [18]. The topology uses indirect harmonic compensation technique (state feedback control technique using pole placement) to eliminate the harmonic component. To achieve stability of the system, the desired pole location is chosen individually for all the operating conditions. Also, smallsignal analysis for the system is necessary to design the control topology. The power quality mitigation problem for distributed static compensator (DSTACOM) with PMSG fed to the nonlinear load is discussed in [19]. The control technique uses a quasi Newton-based algorithm for harmonic mitigation. The algorithm is dependent upon the proper selection of step size. The control analysis of a SCIG fed to standalone balanced load through a back to back converter has been developed in [20]. However, the development and implementation of only the MSC control strategy are discussed in this literature. The stand-alone operation of SCIG and PMSG based systems, feeding different types of loads, from uncontrolled sources, are needed to be addressed. The present work has proposed a model of a combined control to handle distributed generation feeding isolated load, and analysed in detail. The implementation has followed the design and analysis of the proposed scheme. The control scheme is designed with the use of vector control in dq-reference frame for the MSC. The LSC model has been developed in the arbitrary synchronous reference frame. The prime objective of the proposed control is to deal with the transition from balance load to unbalance and non-linear load. The
1000 W 50 Hz 6 1000 rpm 415 V, 2 A(r.m.s.) 12 Ω per phase 0.0133 H 0.0147 H 0.3 wb/m2
problem of poor load voltage quality, due to the presence of harmonics in case of nonlinear load, is handled in this work. The main focus of LSC is to maintain the load amplitude and frequency of load voltage in spite of the variety of loads. The variation in wind speed is also to be handled by the controller. The proposed work has considered, developed, and implemented a combined control to handle both the load and source variation. The proposed controller is presented for uncontrolled prime mover driven SCIG and PMSG, supplying unbalanced and non-linear load successfully. The specific contributions of the paper are the following:
• A vector control scheme for LSC has been developed in a synchro• • • •
nous reference frame to supply fixed load voltage and frequency with the transition from a linear balanced load to non-linear load and unbalance load, respectively. This development is not reported in the existing literature for SCIG and PMSG. The designed load voltage controller cascaded with an inner filter current controller can eliminate the negative sequence component during the unbalance conditions. The designed filter current controller bandwidth can remove the harmonic component of load current during non-linear loading. During both the loading conditions, the load voltage harmonics are successfully compensated to maintain at the reference level of it, with the use of the proposed filter current controller. The combined controller of both the DG is successfully handling the random variation of wind speed. The two-stage controller for the MSC has been proven an effective
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Fig. 2. Proposed control structure for MSC (a) SCIG (b) PMSG.
choice for maintaining the dc-link voltage and other machine variables at the prescribed level during the variable loading scenarios for both the DGs. To confirm the feasibility of the proposed control algorithm, a laboratory prototype is developed and real-time results are shown in the paper to validate the theoretical claims of the controllers.
converter (MSC) and load side converter (LSC). The stand-alone load considered here may be unbalanced and non-linear load in nature. To emulate nonlinear load, a three-phase diode bridge rectifier feeding RL load on the dc end is used. The parameter used in simulation and experiment is tabulated in Table 1. An approach based on vector control (VC) is proposed for MSC to regulate the independent control of active and reactive power. Also, the control strategy can adjust the dc-link voltage during both the scenarios successfully. Since the stand-alone load can supply non-linear and unbalance load, there may be changes in load voltage quality degradation. Therefore, the LSC can be controlled to address the problem for removing harmonic components during non-linear loading and negative sequence component in case of unbalanced loading. In conclusion, the control target for the LSC is to maintain fixed voltage and frequency in
2. System configuration The overall set up for the stand-alone operation of the DGs is shown in Fig. 1. The DGs considered here are SCIG and PMSG individually. The power circuit schematic consists of a DG driven by an uncontrolled prime mover, a back to back converter (two three-phase insulated gate bipolar transistors (IGBT) with a common dc link), LC filter and a standalone load. A back to back converter comprised of the machine side
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Fig. 3. Analysis of MSC controller in (a) Frequency domain (b) pole zero mapping.
Fig. 4. Control strategy for LSC.
spite of the variation of load. 3. Control strategy
power. The controller gain is calculated with the help of dc-link capacitance. Meanwhile, the flux is controlled by the d-axis component of the machine in the case of SCIG.
3.1. Controller scheme of MSC
idc = kp +
The block diagram of the MSC control strategy of both the DG is shown in Fig. 2(a). The stator current is sensed and converted to d,q reference frame using park transformation. A two-loop cascaded control structure associated with the outer dc-link voltage loop and inner q-axis stator current loop can regulate the dc-link voltage for all the load and input power variation. The dc-link voltage error passing through the PI controller generates the dc-link current, as shown in (1). The dc-link current, in turn, produce the q-axis stator current, as shown in (2) to maintain the
vdc idc =
ki (vdc s
3 vqs iqs 2
vdc )
(1) (2)
In conclusion, the stator current controller can generate the d,q-axis component of stator voltage in the case of SCIG, as shown in (3), and (4). The current controller is calculated with the help of stator resistance and inductance. These voltages are transformed into threephase voltage using inverse park transform, as shown in Fig. 2(a). The controller performance and stability analysis are shown in Fig. 3(a).
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Ts
dids v + ids = ds dt Rs
(1 M
) Ts d r + Ts iqsr ( dt
mr
+
ele )
(4)
= 1 = Lr Ls where Ts = Ls Rs ; The realization of the three-stage control configuration is detailed in [30]. However, here two-stage control technique is employed. The MSC control strategy of PMSG is shown in Fig. 2(b). The dynamic equation in the dq reference frame, using park transformation as: M2
vds = Ids rs +
vqs = Iqs rs +
d ds dt d
qs
dt
+
ele qs
(5)
ele ds
(6)
where ds = LS Ids + f , qs = LS Iqs The control structure of the dc-link voltage controller and q-axis stator current controller of PMSG is the same as SCIG discussed above. But the d,q-axis current controller gain is calculated with the help of stator resistance and d,q-axis reactance respectively in case of PMSG. The controller gain is designed with the help of optimal modulus. The controller performance is shown in Fig. 3(b). The frequency response shows the stability of the system during all the operating conditions. 3.2. Controller scheme of LSC In this study, the load voltage (vl), filter current, (if) and load current (il) is detected and transformed to d, q component with the use of park transformation in the synchronous reference frame. The control block diagram of LSC for both SCIG and PMSG fed to a variety of stand-alone load as shown in Fig. 4. The scheme has been adopted for removing the harmonic component of load current during non-linear loading. In previous literature, an extra low pass filter adjoined to the system had been employed. This makes the controller bulky. But, here, the author has designed a load voltage controller cascaded with the inner filter current controller in such a way; it can compensate the harmonics during nonlinear loading and negative sequence components during unbalance loading. The references for the filter current are obtained by adding the voltage control loops output, with the respective load components and cross-coupling terms of filter current. The proposed configuration can keep the load voltage unchanged and undistorted during both the scenarios. A closed-loop controller for the load voltages follows a cascade structure with an inner filter current controller. The main focus of the LSC control strategy is to regulate the load voltage and frequency. Here a voltage orientation scheme, i.e., the load voltage vector, ( vl ) is aligned with d-axis. As a consequence, the controller is able for independent control active and reactive power. It could be realized as follows:
Fig. 5. Analysis of LSC controller in (a) Frequency domain (b) pole zero mapping (c) Filter current controller analysis at various bandwidth.
This generated signal works as an input to the PWM generator block, which produces switching pulses for the MSC. Here for the SCIG VC oriented in rotor flux reference frame is implemented to achieve the decoupling between active and reactive power. The model in the dq reference frame is illustrated by the following [20]:
Ts
diqs dt
+ iqs =
vqs Rs
(1
) Ts Lm
r
(
mr
+
ele )
r Ts ids (
mr
+
vdl = | vl |; vql = 0 The expression between load and inverter voltage expressed as:
ele )
vf = vi (3)
i f rf + lf
dif dt
Based on Fig. 3, the filter current can be written as:
5
(7)
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Fig. 6. Performance indices of load variable during SCIG fed to nonlinear load at 6 s (a) Load current (b) d-axis component of load voltage (c) q-axis component of load voltage.
Fig. 7. Load voltage performance of SCIG during transition from linear load to nonlinear load (a) Load Voltage (b) FFT analysis of load voltage.
Fig. 8. Performance indices of load variable during PMSG fed to nonlinear load at 6 s (a) Load current (b) d-axis component of load voltage (c) q-axis component of load voltage.
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where
Table 2 Compensation strategy of load voltage. Harmonic order
THD of Load voltage (For SCIG driven stand-alone load)
THD of Load voltage (For PMSG driven stand-alone load)
5th 7th 11th 13th 17th
0.71% 0.13% 0.15% 0.11% 0.05%
0.21% 0.77% 0.19% 0.08% 0.06%
idf = cf
dvdl dt dvql
+ idl
e cf vql
+ iql +
e cf vdl
fcc: filter current controller bandwidth fsw: Switching frequency of the converter, i.e. at 5 kHz f: output frequency, i.e. 50 Hz Accordingly, the filter current bandwidth is kept at close to 1250 Hz in this work. The target of the controller is to keep the load voltage undistorted by removing the higher-order harmonic component (idlh) and unbalance component, (idl ) as shown in (9) and (10), respectively. Finally, the inverter d,q-axis component of load voltage expressed in term of filter current as: (8)
vdi = kpi +
kii (idf s
idf ) + vdf
e l f i qf
Under non-linear loading, the load current divided into two-part, i.e., fundamental and harmonic components. So, the (8) can be rewritten as:
vqi = kpi +
kii (iqf s
iqf ) + vqf +
e l f i df
iqf = cf
idf = cf iqf = cf
dt
dvdl dt dvql dt
+ (idl1 + idlh)
e cf vql
+ (iql1 + iqlh) +
e cf vdl
iqf = cf
dvdl dt dvql dt
+ (idl+ + idl ) +
(iql+
+ iql ) +
(9)
e cf vql e cf vdl
(10)
Here kpi and kii is designed with the help of filter resistance and inductance. The PI controller can eliminate the presence of the dc component of the load current, and the harmonic and negative sequence component can be eliminated with the proper choice of bandwidth [18,21]. The gain of the controller is calculated with the help of the chosen bandwidth of it. For compensating the effect of the non-linear load, the tuning frequency should be an even multiple of the 50 Hz [18], since the balanced, nonlinear, and unbalanced fundamental/harmonic components in the load voltage appear at these frequencies in the synchronously rotating reference frame. The selection criterion of the bandwidth of the filter current controller to remove harmonic components is [21]:
(10 × f )
fcc
(12)
Here kpi and kii is designed with the help of filter resistance and inductance. The frequency alysis of LSC is giving a clear idea about system stability. Fig. 5(b) illustrated the time response of the filter current controller. From the plot, it is clear that all the poles are situated in the negative half of the s-plane. Therefore, the system is stable. The stand-alone load voltage controller can be connected with the grid, with two necessary modifications. The angle θ can be calculated using the load voltage sensor. The load voltage and grid voltage will be the same in the grid-connected scenario. The magnitude of vdl and vql will be generated through grid voltage information. The stand-alone system is developed without the help of the grid in this work and is implemented in simulation and real-time environments.
Moreover, during unbalance loading, the load current divided into positive and negative sequence components. So, the (8) can be rewritten as:
idf = cf
(11)
4. Simulation results The distributed power generation scheme feeding non-linear and unbalanced load is simulated, and the performance of the machine and load side variables are as presented below. The DG driven variety of load, as shown in Fig. 1, is modelled in SIMULINK environment of MATLAB, and parameters are given in Table 1. 4.1. Performance analysis with non-linear load The load variable performances of both SCIG and PMSG for the connection of a non-linear load to the load terminal at 6 s are shown in Figs. 6 and 8, respectively. A three-phase diode rectifier feeding RL load is used as a non-linear load. The non-linear nature of the load current is
fsw 4
Fig. 9. Load voltage performance of PMSG during transition from linear load to nonlinear load (a) Load Voltage (b) FFT analysis of load voltage.
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Fig. 10. Machine variables Performance of SCIG during transition from linear load to non-linear load (a) dc link voltage (b) q-axis component of machine current (c) Stator Flux (d) d-axis component of machine current.
Fig. 11. Machine variables performance of PMSG during transition from linear load to nonlinear load (a) dc link voltage (b) q-axis component of machine current.
Fig. 12. Performance indices of load variable of SCIG during transition from linear load to nonlinear load (a) Load current (b) d-axis component of load voltage (c) qaxis component of load voltage.
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Fig. 13. Load variable performance of SCIG during transition from linear balance load to unbalance load (a) Load Voltage (b) FFT analysis of load voltage.
Fig. 14. Performance indices of load variable of PMSG during transition from linear balance load to unbalance load (a) Load current (b) d-axis component of load voltage (c) q-axis component of load voltage.
Fig. 15. Load variable performance of PMSG during transition from linear balance load to unbalance load (a) Load Voltage (b) FFT analysis of load voltage.
shown in Fig. 6(a). The proposed control strategy to mitigate the harmonics discussed in Section 3 can remove the harmonic component from the load voltage. The controller is implemented successfully to maintain the d,q-axis component of load voltage at its prescribed value, as shown in Fig. 6(b), (c), respectively. The controller can keep the d- axis load voltage at 60 V and q-axis voltage at 0 V during this operation successfully. There is no such
variation observed during transients. With the compensation of the fifth and seventh order harmonic component of load current, the load voltage at the PCC becomes sinusoidal as seen in Fig. 7(a). The load side controller is successfully maintaining the load voltage THD at 1.73% is shown in Fig. 7 (b). Similarly, the load variable performances of PMSG during the transition from linear load to non-linear load at 6 s are shown in Fig. 8. The same load controller strategy discussed in Section 3 is
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Fig. 16. Machine variables Performance of SCIG during transition from linear balance load to unbalance load (a) dc link voltage (b) q-axis component of machine current (c) Stator Flux (d) d-axis component of machine current.
Fig. 17. Machine variables performance of PMSG during transition from linear load to unbalance load (a) dc link voltage (b) q-axis component of machine current.
implemented. The performances of load variables are satisfactory. The load voltage compensation strategy is working successfully to remove the higher-order harmonic component, as shown in Table 2. As a result, THD of the load voltage is maintained at 1.83% as shown in Fig. 9(b). The performances of generator variables on the transition from linear load to nonlinear load for both the DG are shown in Figs. 10 and 11, respectively. The proposed control scheme described in Fig. 2 is employed for MSC. Both the dc-link voltage and flux controller have to be considered in case of SCIG driven stand-alone load. The dc-link voltage and flux maintaining the reference values during the operations are shown in Fig. 10(a), (c), respectively. A very small transient is observed in the case of dc-link voltage. The magnetizing flux is constant throughout the operation. The dc-link voltage controller is used to generate the reference active power component (q-axis component) of the generator, which can be used to maintain the power balance of the system. The q-axis current increases substantially to sustain the active power flow and controller working successfully to match the actual current as shown in Fig. 10(b). The flux controller is used to generate
Fig. 18. Comparison of Load voltage THD with the existing system during nonlinear loading.
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Table 3 Performances comparison of the proposed system with the existing literature. Paper/ Schemes
[22] [14] [24] [25] Proposed
Control Scheme
PI PI-dual frequency resonance controller (PI-DFR) PR Hyperbolic tangent based LMS algorithm PI
Unbalanced loading
Non-linear loading
% of loading
DC link voltage
Load voltage
DC link voltage
Load voltage
Variation
Settling time
Variation
Settling time
Variation
Settling time
Variation
Settling time
25 61.7
6% –
0.5 s –
Negligible –
Negligible 200 ms
–
–
0.2 V
160 ms
NA 100
–
0.02 s
–
0.02 s
5.5% –
0.6 s 0.02 s
9.09% –
0.2 s 0.02 s
100
Negligible
Negligible
Negligible
Negligible
Negligible
Negligible
Negligible
Negligible
Fig. 19. Machine and load variable performance of SCIGdriven load, during random variation in wind speed (a) generated torque (b) iqs (c) vdc (d) vdl.
Fig. 20. Machine and load variable performance of PMSG driven load, during random variation in wind speed (a) generated torque (b) iqs (c) vdc (d) vdl.
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undistorted as shown in Fig. 15(a). The changes in the stator side variables for both the DG in case of the unbalanced nature of load are as shown in Figs. 16 and 17, respectively. In the case of SCIG, dc-link voltage settles within 0.6 s. But a significant dip in dc-link voltage is observed because of the high moment of inertia of the machine. The 2% variation in the transient condition is shown in Fig. 16(a). The 47.2% decrement in load resistance increases the power demand, which is accommodated with increment in machine speed. This power balance, in turn, is adjusted by the reference q-axis component of the machine as shown in Fig. 16(b). The controller is working successfully to match with the actual current. The d-axis current controller remains invariant throughout the operation as shown in Fig. 16(d). But in the case of PMSG, a negligible transient is observed in case dc-link voltage and as shown in Fig. 17(a). The dc-link voltage controller is working successfully during the transition without any disturbance. The bar chart illustrated in Fig. 18 demonstrates the comparison of THD performance of load voltage of the proposed scheme with the existing literature. It is noticed that the THD of the proposed scheme is lower, reaching as low as 1.73% than the results provided in the works of literature. Table 3 compares the transient performance of the proposed system with existing literature. As can be seen, in this table, the dc-link voltage and load voltage variation are negligible during both non-linear and unbalanced loading scenarios.
Fig. 21. Test rig for the proposed topology.
4.3. Variation of wind speed with random noise
the reference d-axis component of the machine. But it remains a free control variable during the load transition. In the case of the PMSG, a dc-link voltage controller is working successfully without significant transient as shown in Fig. 11(a). The qaxis component of machine current remains invariant during its transition and following its reference successfully throughout the operation, as shown in Fig. 11(b).
The input variation is shown with the change in prime mover speed of the distributed generator. The combined controller is working successfully to handle the random variation of wind speed at 4 s and 2 s for SCIG and PMSG, respectively. The q-axis component of the machine current is successfully controlled to withstand the variation of generator speed as shown in Figs. 19(b) and 20(b) for both the generators. The dclink voltage is maintained at the reference voltage 300 V with negligible transient, as shown in Figs. 19(c) and 20(c). Accordingly, the load voltages are found to be unaffected during this operation and are presented in Fig. 20(d).
4.2. Performance analysis with an unbalanced load The distributed generation scheme is operated with an unbalanced load with resistances of 240 Ω, 120 Ω, and 240 Ω for the three phases, respectively. The application of the unbalanced load has been initiated at 6 s and the nature of load current for both the DG is shown in Figs. 12(a) and 14 (a), respectively (see . The said control strategy for LSC, as discussed in Section 3, can maintain the amplitude of the load voltage and frequency by eliminating the negative sequence component of load current. The d,q-axis component of the load voltage is working successfully by maintaining with the reference value for both the DG are shown in Figs. 12 and 14 respectively. As a consequence, the load voltage remains undistorted during this scenario. Considered filter current controller can compensate for the unbalance component within the standard limit. The THD of the load voltage is 2.37% in the case of SCIG driven stand-alone load as shown in Fig. 13(b). The flexibility of the controller is tested by implementing the same controller for different DGs. It is verified that the LSC is working successfully in the case of PMSG to keep the harmonic level at 1.83%, as shown in Fig. 15(b). Also, the controller is able to keep the load voltage
5. Experimental results 5.1. Test setup The experimental tests are conducted to provide the effectiveness of the designed controller for non-linear and unbalance loading. The experimental arrangement is as shown in Fig. 21 and Table 1 represents the detailed parameters used in the test rig. The information about the interfacing circuits for machine applications in the experimental setup has been provided in Table 4. The SCIG, coupled with dc machines that work as a prime mover. The stator of the SCIG is connected to the standalone load through a back-to-back converter. For real-time execution, MATLAB software is interfaced with the digital signal processor (dSPACE 1104) controller. 5.2. System performances The steady-state experimental results with the transition from a
Table 4 Interfacing circuits for machine applications in experimental setup. Name of the circuit
Number of circuit
Sensor used
Stator current sensor Filter current sensor Load voltage sensor DC link voltage sensor Speed sensor
2 2 2 1 1
Current sensor Current sensor Voltage sensor Voltage sensor Six signal QEP
12
Interfaced through with noise with noise with noise with noise encoder
filter filter filter filter
ADC of ds1104 ADC of ds1104 ADC of ds1104 ADC of ds1104 Incremental encoder terminal of ds1104
Electrical Power and Energy Systems 119 (2020) 105878
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Fig. 22. The transient behaviour of variables during transition from balance to unbalance load, (a) dc link voltage (b) d-axis component of load voltage, (c) Load current, load voltage in DSO (d) FFT analysis of load voltage.
balanced linear load to an unbalanced linear load are shown in Fig. 22. The experimental results obtained to validate the excellent performance of the load voltage regulation during an unbalanced load. The system is initially operated with a balanced load of 60 Ω per phase. The R-phase load is changed to represent the unbalanced loading condition. The unbalanced loading is demonstrated with 31 Ω per in R-phase and 60 Ω each in the other two phases. The small transient in dc-link voltage observed at 3.85 s. It settles back to 50 V within 0.15 s, as shown in Fig. 22(a). The d-axis component of the load voltage is maintained at its reference level, as shown in Fig. 22 (b). The unbalanced load current and the variation in load voltage are portrayed in Fig. 22(c). The THD of the load voltage is kept at 2.61% after compensation of the unbalance nature of load current and as shown in Fig. 22(d). It is matching nearly with the simulation counterparts as shown in Table 2.
loading is negligible. The control is successfully implemented in the simulation environment. The THD of the load voltage has been maintained at less than 3% during both the scenarios. Additionally, the combined controller is able to keep machine and load variables within the prescribed limit successfully during random variation of wind speed. The proposed control algorithm is operated in real-time with a developed lower scale experimental set up through dSPACE 1104. The experimental results demonstrate the excellent matching with their simulation counterparts for unbalance loading conditions.
6. Conclusion
References
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The work has addressed the variable speed and constant frequency (VSCF) generation from the uncontrolled prime mover-based scheme for a stand-alone system. This system has addressed issues like balanced loading, unbalanced loading, non-linear loading and wind speed with random noise. The LSC controller is successfully removing the harmonics component and the negative sequence component during unbalanced and non-linear loading respectively. Accordingly, the controller is found to be able to fix the load voltage amplitude and frequency in spite of the variations in loads. The load voltage remains undistorted during both the scenarios successfully. The two-stage control strategy is used for MSC for steady-state analysis of dc-link voltage, generator speed, d,q-axis component of machine current. The same bandwidth is selected for the MSC of both the DG to maintain the machine variables. The transient performance i.e. settling time and overshoot of the dc-link voltage, stator current during a variety of
[1] Cheng M, Zhu Y. The state of the art of wind energy conversion systems and technologies: a review. Energy Convers Manage 2014;88:332–47. https://doi.org/ 10.1016/j.enconman.2014.08.037. [2] Gualtieri G. A comprehensive review on wind resource extrapolation models applied in wind energy. Renew Sustain Energy Rev 2019. https://doi.org/10.1016/j. rser.2018.12.015. [3] Apata O, Oyedokun DTO. Wind turbine generators: Conventional and emerging technologies. Proc. - 2017 IEEE PES-IAS PowerAfrica Conf. Harnessing Energy, Inf. Commun. Technol. Afford. Electrif. Africa, PowerAfrica 2017 Accra, Ghana: IEEE; 2017. p. 606–11. https://doi.org/10.1109/PowerAfrica.2017.7991295. [4] Shotorbani AM, Mohammadi-Ivatloo B, Wang L, Marzband M, Sabahi M. Application of finite-time control Lyapunov function in low-power PMSG wind energy conversion systems for sensorless MPPT. Int J Electr Power Energy Syst 2019;106:169–82. https://doi.org/10.1016/j.ijepes.2018.09.039. [5] Abad G. Doubly fed induction machine: modeling and control for wind energy generation applications. Wiley-Blackwell Pub; 2011. [6] Zhong QC, Hornik T. Control of power inverters in renewable energy and smart grid integration. John Wiley and Sons; 2012. https://doi.org/10.1002/9781118481806. [7] Liu Y, Wang Z, Xiong L, Wang J, Jiang X, Bai G, et al. DFIG wind turbine sliding
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mode control with exponential reaching law under variable wind speed. Int J Electr Power Energy Syst 2018. https://doi.org/10.1016/j.ijepes.2017.10.018. Marques GD, Iacchetti MF. Stator frequency regulation in a field-oriented controlled DFIG connected to a DC link. IEEE Trans Ind Electron 2014;61:5930–9. https://doi. org/10.1109/TIE.2014.2311403. Qi X, Holtz J. Modelling and control of low switching frequency high performance induction motor drives. IEEE Trans Ind Electron 2019;0046:1. https://doi.org/10. 1109/tie.2019.2924602. Gundavarapu A, Misra H, Jain AK. Direct torque control scheme for dc voltage regulation of the standalone DFIG-DC system. IEEE Trans Ind Electron 2017;64:3502–12. https://doi.org/10.1109/TIE.2016.2644623. Malekpour M, Azizipanah-Abarghooee R, Terzija V. Maximum torque per ampere control with direct voltage control for IPMSM drive systems. Int J Electr Power Energy Syst 2020;116. https://doi.org/10.1016/j.ijepes.2019.105509. Zhang X, Li Y, Wang K, Zhang W, Gao D. Model predictive control of the openwinding PMSG system based on three-dimensional reference voltage-vector. IEEE Trans Ind Electron 2019;0046:1. https://doi.org/10.1109/tie.2019.2938478. Phan VT, Nguyen DT, Trinh QN, Nguyen CL, Logenthiran T. Harmonics rejection in stand-alone doubly-fed induction generators with nonlinear loads. IEEE Trans Energy Convers 2016;31:815–7. https://doi.org/10.1109/TEC.2016.2521331. Cheng M, Jiang Y, Han P, Wang Q. Unbalanced and low-order harmonic voltage mitigation of stand-alone dual-stator brushless doubly fed induction wind generator. IEEE Trans Ind Electron 2018;65:9135–46. https://doi.org/10.1109/TIE. 2017.2779422. Pattnaik M, Kastha D. Harmonic compensation with zero-sequence load voltage control in a speed-sensorless DFIG-based stand-alone VSCF generating system. IEEE Trans Ind Electron 2013;60:5506–14. https://doi.org/10.1109/TIE.2012.2235396. Wei F, Vilathgamuwa DM, Choi SS, Zhang X. Improved control of rotor- and loadside converters of stand-alone DFIGs under nonlinear loads conditions. 2013 IEEE ECCE Asia Downunder - 5th IEEE Annu Int Energy Convers Congr Exhib IEEE ECCE Asia 2013 2013. p. 687–91. https://doi.org/10.1109/ECCE-Asia.2013.6579175.
[17] Naderipour A, Abdul-Malek Z, Ramachandaramurthy VK, Kalam A, Miveh MR. Hierarchical control strategy for a three-phase 4-wire microgrid under unbalanced and nonlinear load conditions. ISA Trans 2019;94:352–69. https://doi.org/10. 1016/j.isatra.2019.04.025. [18] Satpathy AS, Kastha D, Kishore K. Control of a STATCOM-assisted self-excited induction generator-based WECS feeding non-linear three-phase and single-phase loads. IET Power Electron 2019;12:829–39. https://doi.org/10.1049/iet-pel.2018. 5482. [19] Giri AK, Arya SR, Maurya R, Babu BC. Mitigation of power quality problems in PMSG-based power generation system using quasi-Newton–based algorithm. Int Trans Electr Energy Syst 2019:1–17. https://doi.org/10.1002/2050-7038.12102. [20] Mishra R, Saha TK. Three stage control of SCIG for distributed power generation. IEEE Int. Conf. Power Electron. Drives Energy Syst. PEDES 2016, vol. 2016- Janua 2017. https://doi.org/10.1109/PEDES.2016.7914312. [21] Dannehl J, Wessels C, Fuchs FW. Limitations of voltage-oriented PI current control of grid-connected PWM rectifiers with LCL filters. IEEE Trans Ind Electron 2009;56:380–8. https://doi.org/10.1109/TIE.2008.2008774. [22] Abdoune F, Abdoune K, Aouzellag D. Improved control strategy for a stand-Alone DFIG under unbalanced load conditions. Proc 2018 3rd Int Conf Electr Sci Technol Maghreb, Cist 2018 2019. p. 1–6. https://doi.org/10.1109/CISTEM.2018.8613571. [23] Singh B, Sharma S. Voltage and frequency controllers for standalone wind energy conversion systems. IET Renew Power Gener 2014;8:707–21. https://doi.org/10. 1049/iet-rpg.2013.0186. [24] Tischer CB, Tibola JR, Scherer LG, De Camargo RF. Proportional-resonant control applied on voltage regulation of standalone SEIG for micro-hydro power generation. IET Renew Power Gener 2017;11:593–602. https://doi.org/10.1049/iet-rpg. 2016.0857. [25] Singh B, Niwas R, Dube SK. Load leveling and voltage control of permanent magnet synchronous generator-based DG Set for standalone supply system. IEEE Trans Ind Inform 2014;10:2034–43. https://doi.org/10.1109/TII.2014.2341952.
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Modelling and analysis of distributed power generation schemes supplying unbalanced and non-linear load
T
Rupa Mishra , Tapas Kumar Saha ⁎
Department of Electrical Engineering, National Institute of Technology, Durgapur 713209, West-Bengal, India
ARTICLE INFO
ABSTRACT
Keywords: Squirrel cage induction generator Permanent magnet synchronous generator Voltage control Current control Stand-alone load
This study presents a combined control strategy for stand-alone distributed power generation scheme, utilizing the squirrel cage induction generator (SCIG), and the permanent magnet synchronous generator (PMSG) in its structure. The combined control consists of both the machine side and load side converter control. The proposed load voltage controller, cascaded with the inner filter current controller, is designed for a load-side converter (LSC) to remove the harmonic component during non-linear loading and negative sequence component in case of unbalanced loading respectively. The control algorithm ensures to produce constant load voltage amplitude and frequency, with the change in both input power and non-linear and unbalanced loading scenarios. It also guarantees the sinusoidal load voltage under the mentioned loading conditions. Simultaneously, the dc-link voltage controller cascaded with the inner q-axis stator current controller is used for machine side converter (MSC) to keep the dc-link voltage at the prescribed level for both SCIG and PMSG during all the operating conditions. In this paper, an analysis of both the distributed generators based wind energy conversion systems under vector control for MSC provides the enhanced machine variable performance. The proposed control scheme is successfully implemented in MATLAB/Simulink environment. One scaled experimental prototype is developed, and real-time results are shown in the paper to validate the theoretical claims of the controllers.
1. Introduction Recently renewable energy sources (RES) are growing at a phenomenal pace due to the depletion of fossil fuel and degradation of the environment [1]. The wind energy system (WES) is gaining renewed attention for the utility of consumers [2] in comparison with other RES. Various types of distributed generators are chosen for wind turbine driven applications [3,4]. The doubly-fed induction generator (DFIG) is found to be essential for variable WES [5]. The growth in power electronic converters such as back to back converter, matrix converter (MC), has been considered a factor of special attention regarding the interfacing of the machine with the load [6]. The extraction of maximum power, using DFIG for standalone application, has been proposed in [7]. The stator voltage and frequency control in the case of standalone operation of DFIG based wind turbines have been discussed in [8]. However, this reference investigates the control issue associated with the machine side converter (MSC) and load side converter (LSC) for a balanced linear load only. The control algorithm plays a crucial role in the enhancement of system performances. Various control methods have been suggested to deal with the control of MSC, which includes field-oriented control [9], ⁎
sensor-less control [4], direct torque control [10], direct power control, direct voltage control [11], model predictive control [12]. Moreover, the LSC control objective is to regulate the dc-link voltage. The control systems for all the regulations have been developed in the dq reference frame. The distributed generation system during unbalance and nonlinear loading operation causes voltage quality degradation and current distortion. Several control strategies have been employed to eliminate these negative impacts [13–16]. The analysis, control, and operation of the DFIG driving stand-alone non-linear load have been outlined in [15]. The controller tends to eliminate harmonics by the design of a proper load controller by considering the LC filter. Further, the brushless doubly-fed induction generator (BDFIG) has been tested for nonlinear and unbalance stand-alone load in [14]. A compensation technique has been employed for LSC to compensate for the unbalance load current at the point of common coupling (PCC). However, the controller needs to extract positive and negative sequence component which may lead to system instability. The hierarchical control strategy is implemented for non-linear and unbalance load is discussed in [17]. In this case, a four-leg converter is used for the compensation of harmonics. The PR controller used in [13,14,16,17] suffers from a slow
Corresponding author. E-mail address: [email protected] (R. Mishra).
https://doi.org/10.1016/j.ijepes.2020.105878 Received 3 October 2019; Received in revised form 20 January 2020; Accepted 22 January 2020 0142-0615/ © 2020 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic diagram of distributed generation fed to variety of stand-alone load. Table 1 Parameter of the Simulated and Experimental setup. SCIG Specification: Power Frequency pole Rated speed Stator (Y connected) Rotor (Y connected) Stator Resistance (Rs ) Stator inductance (Ls ) Rotor inductance (Lr ) Magnetising inductance (Lm)
PMSG Specification: 746 W 50 Hz 4 1500 rpm 415 V, 2 A(RMS) 415 V, 2 A(RMS) 9.919 Ω per phase 0.9291 H per phase 0.9291 H per phase 0.8895 H per phase
Power Frequency pole Rated speed Stator (Y connected) Stator Resistance (Rs ) d-axis Inductanceq-axis InductanceFlux linkage
response. Meanwhile, very few publications are reported for the operation of the squirrel cage induction generator (SCIG), and a Permanent magnet synchronous generator (PMSG) [23] fed to the stand-alone load. The STATCOM assisted self-excited induction generator (SEIG) based wind energy conversion feeding to non-linear load is discussed in [18]. The topology uses indirect harmonic compensation technique (state feedback control technique using pole placement) to eliminate the harmonic component. To achieve stability of the system, the desired pole location is chosen individually for all the operating conditions. Also, smallsignal analysis for the system is necessary to design the control topology. The power quality mitigation problem for distributed static compensator (DSTACOM) with PMSG fed to the nonlinear load is discussed in [19]. The control technique uses a quasi Newton-based algorithm for harmonic mitigation. The algorithm is dependent upon the proper selection of step size. The control analysis of a SCIG fed to standalone balanced load through a back to back converter has been developed in [20]. However, the development and implementation of only the MSC control strategy are discussed in this literature. The stand-alone operation of SCIG and PMSG based systems, feeding different types of loads, from uncontrolled sources, are needed to be addressed. The present work has proposed a model of a combined control to handle distributed generation feeding isolated load, and analysed in detail. The implementation has followed the design and analysis of the proposed scheme. The control scheme is designed with the use of vector control in dq-reference frame for the MSC. The LSC model has been developed in the arbitrary synchronous reference frame. The prime objective of the proposed control is to deal with the transition from balance load to unbalance and non-linear load. The
1000 W 50 Hz 6 1000 rpm 415 V, 2 A(r.m.s.) 12 Ω per phase 0.0133 H 0.0147 H 0.3 wb/m2
problem of poor load voltage quality, due to the presence of harmonics in case of nonlinear load, is handled in this work. The main focus of LSC is to maintain the load amplitude and frequency of load voltage in spite of the variety of loads. The variation in wind speed is also to be handled by the controller. The proposed work has considered, developed, and implemented a combined control to handle both the load and source variation. The proposed controller is presented for uncontrolled prime mover driven SCIG and PMSG, supplying unbalanced and non-linear load successfully. The specific contributions of the paper are the following:
• A vector control scheme for LSC has been developed in a synchro• • • •
nous reference frame to supply fixed load voltage and frequency with the transition from a linear balanced load to non-linear load and unbalance load, respectively. This development is not reported in the existing literature for SCIG and PMSG. The designed load voltage controller cascaded with an inner filter current controller can eliminate the negative sequence component during the unbalance conditions. The designed filter current controller bandwidth can remove the harmonic component of load current during non-linear loading. During both the loading conditions, the load voltage harmonics are successfully compensated to maintain at the reference level of it, with the use of the proposed filter current controller. The combined controller of both the DG is successfully handling the random variation of wind speed. The two-stage controller for the MSC has been proven an effective
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R. Mishra and T.K. Saha
Fig. 2. Proposed control structure for MSC (a) SCIG (b) PMSG.
choice for maintaining the dc-link voltage and other machine variables at the prescribed level during the variable loading scenarios for both the DGs. To confirm the feasibility of the proposed control algorithm, a laboratory prototype is developed and real-time results are shown in the paper to validate the theoretical claims of the controllers.
converter (MSC) and load side converter (LSC). The stand-alone load considered here may be unbalanced and non-linear load in nature. To emulate nonlinear load, a three-phase diode bridge rectifier feeding RL load on the dc end is used. The parameter used in simulation and experiment is tabulated in Table 1. An approach based on vector control (VC) is proposed for MSC to regulate the independent control of active and reactive power. Also, the control strategy can adjust the dc-link voltage during both the scenarios successfully. Since the stand-alone load can supply non-linear and unbalance load, there may be changes in load voltage quality degradation. Therefore, the LSC can be controlled to address the problem for removing harmonic components during non-linear loading and negative sequence component in case of unbalanced loading. In conclusion, the control target for the LSC is to maintain fixed voltage and frequency in
2. System configuration The overall set up for the stand-alone operation of the DGs is shown in Fig. 1. The DGs considered here are SCIG and PMSG individually. The power circuit schematic consists of a DG driven by an uncontrolled prime mover, a back to back converter (two three-phase insulated gate bipolar transistors (IGBT) with a common dc link), LC filter and a standalone load. A back to back converter comprised of the machine side
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Fig. 3. Analysis of MSC controller in (a) Frequency domain (b) pole zero mapping.
Fig. 4. Control strategy for LSC.
spite of the variation of load. 3. Control strategy
power. The controller gain is calculated with the help of dc-link capacitance. Meanwhile, the flux is controlled by the d-axis component of the machine in the case of SCIG.
3.1. Controller scheme of MSC
idc = kp +
The block diagram of the MSC control strategy of both the DG is shown in Fig. 2(a). The stator current is sensed and converted to d,q reference frame using park transformation. A two-loop cascaded control structure associated with the outer dc-link voltage loop and inner q-axis stator current loop can regulate the dc-link voltage for all the load and input power variation. The dc-link voltage error passing through the PI controller generates the dc-link current, as shown in (1). The dc-link current, in turn, produce the q-axis stator current, as shown in (2) to maintain the
vdc idc =
ki (vdc s
3 vqs iqs 2
vdc )
(1) (2)
In conclusion, the stator current controller can generate the d,q-axis component of stator voltage in the case of SCIG, as shown in (3), and (4). The current controller is calculated with the help of stator resistance and inductance. These voltages are transformed into threephase voltage using inverse park transform, as shown in Fig. 2(a). The controller performance and stability analysis are shown in Fig. 3(a).
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R. Mishra and T.K. Saha
Ts
dids v + ids = ds dt Rs
(1 M
) Ts d r + Ts iqsr ( dt
mr
+
ele )
(4)
= 1 = Lr Ls where Ts = Ls Rs ; The realization of the three-stage control configuration is detailed in [30]. However, here two-stage control technique is employed. The MSC control strategy of PMSG is shown in Fig. 2(b). The dynamic equation in the dq reference frame, using park transformation as: M2
vds = Ids rs +
vqs = Iqs rs +
d ds dt d
qs
dt
+
ele qs
(5)
ele ds
(6)
where ds = LS Ids + f , qs = LS Iqs The control structure of the dc-link voltage controller and q-axis stator current controller of PMSG is the same as SCIG discussed above. But the d,q-axis current controller gain is calculated with the help of stator resistance and d,q-axis reactance respectively in case of PMSG. The controller gain is designed with the help of optimal modulus. The controller performance is shown in Fig. 3(b). The frequency response shows the stability of the system during all the operating conditions. 3.2. Controller scheme of LSC In this study, the load voltage (vl), filter current, (if) and load current (il) is detected and transformed to d, q component with the use of park transformation in the synchronous reference frame. The control block diagram of LSC for both SCIG and PMSG fed to a variety of stand-alone load as shown in Fig. 4. The scheme has been adopted for removing the harmonic component of load current during non-linear loading. In previous literature, an extra low pass filter adjoined to the system had been employed. This makes the controller bulky. But, here, the author has designed a load voltage controller cascaded with the inner filter current controller in such a way; it can compensate the harmonics during nonlinear loading and negative sequence components during unbalance loading. The references for the filter current are obtained by adding the voltage control loops output, with the respective load components and cross-coupling terms of filter current. The proposed configuration can keep the load voltage unchanged and undistorted during both the scenarios. A closed-loop controller for the load voltages follows a cascade structure with an inner filter current controller. The main focus of the LSC control strategy is to regulate the load voltage and frequency. Here a voltage orientation scheme, i.e., the load voltage vector, ( vl ) is aligned with d-axis. As a consequence, the controller is able for independent control active and reactive power. It could be realized as follows:
Fig. 5. Analysis of LSC controller in (a) Frequency domain (b) pole zero mapping (c) Filter current controller analysis at various bandwidth.
This generated signal works as an input to the PWM generator block, which produces switching pulses for the MSC. Here for the SCIG VC oriented in rotor flux reference frame is implemented to achieve the decoupling between active and reactive power. The model in the dq reference frame is illustrated by the following [20]:
Ts
diqs dt
+ iqs =
vqs Rs
(1
) Ts Lm
r
(
mr
+
ele )
r Ts ids (
mr
+
vdl = | vl |; vql = 0 The expression between load and inverter voltage expressed as:
ele )
vf = vi (3)
i f rf + lf
dif dt
Based on Fig. 3, the filter current can be written as:
5
(7)
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R. Mishra and T.K. Saha
Fig. 6. Performance indices of load variable during SCIG fed to nonlinear load at 6 s (a) Load current (b) d-axis component of load voltage (c) q-axis component of load voltage.
Fig. 7. Load voltage performance of SCIG during transition from linear load to nonlinear load (a) Load Voltage (b) FFT analysis of load voltage.
Fig. 8. Performance indices of load variable during PMSG fed to nonlinear load at 6 s (a) Load current (b) d-axis component of load voltage (c) q-axis component of load voltage.
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where
Table 2 Compensation strategy of load voltage. Harmonic order
THD of Load voltage (For SCIG driven stand-alone load)
THD of Load voltage (For PMSG driven stand-alone load)
5th 7th 11th 13th 17th
0.71% 0.13% 0.15% 0.11% 0.05%
0.21% 0.77% 0.19% 0.08% 0.06%
idf = cf
dvdl dt dvql
+ idl
e cf vql
+ iql +
e cf vdl
fcc: filter current controller bandwidth fsw: Switching frequency of the converter, i.e. at 5 kHz f: output frequency, i.e. 50 Hz Accordingly, the filter current bandwidth is kept at close to 1250 Hz in this work. The target of the controller is to keep the load voltage undistorted by removing the higher-order harmonic component (idlh) and unbalance component, (idl ) as shown in (9) and (10), respectively. Finally, the inverter d,q-axis component of load voltage expressed in term of filter current as: (8)
vdi = kpi +
kii (idf s
idf ) + vdf
e l f i qf
Under non-linear loading, the load current divided into two-part, i.e., fundamental and harmonic components. So, the (8) can be rewritten as:
vqi = kpi +
kii (iqf s
iqf ) + vqf +
e l f i df
iqf = cf
idf = cf iqf = cf
dt
dvdl dt dvql dt
+ (idl1 + idlh)
e cf vql
+ (iql1 + iqlh) +
e cf vdl
iqf = cf
dvdl dt dvql dt
+ (idl+ + idl ) +
(iql+
+ iql ) +
(9)
e cf vql e cf vdl
(10)
Here kpi and kii is designed with the help of filter resistance and inductance. The PI controller can eliminate the presence of the dc component of the load current, and the harmonic and negative sequence component can be eliminated with the proper choice of bandwidth [18,21]. The gain of the controller is calculated with the help of the chosen bandwidth of it. For compensating the effect of the non-linear load, the tuning frequency should be an even multiple of the 50 Hz [18], since the balanced, nonlinear, and unbalanced fundamental/harmonic components in the load voltage appear at these frequencies in the synchronously rotating reference frame. The selection criterion of the bandwidth of the filter current controller to remove harmonic components is [21]:
(10 × f )
fcc
(12)
Here kpi and kii is designed with the help of filter resistance and inductance. The frequency alysis of LSC is giving a clear idea about system stability. Fig. 5(b) illustrated the time response of the filter current controller. From the plot, it is clear that all the poles are situated in the negative half of the s-plane. Therefore, the system is stable. The stand-alone load voltage controller can be connected with the grid, with two necessary modifications. The angle θ can be calculated using the load voltage sensor. The load voltage and grid voltage will be the same in the grid-connected scenario. The magnitude of vdl and vql will be generated through grid voltage information. The stand-alone system is developed without the help of the grid in this work and is implemented in simulation and real-time environments.
Moreover, during unbalance loading, the load current divided into positive and negative sequence components. So, the (8) can be rewritten as:
idf = cf
(11)
4. Simulation results The distributed power generation scheme feeding non-linear and unbalanced load is simulated, and the performance of the machine and load side variables are as presented below. The DG driven variety of load, as shown in Fig. 1, is modelled in SIMULINK environment of MATLAB, and parameters are given in Table 1. 4.1. Performance analysis with non-linear load The load variable performances of both SCIG and PMSG for the connection of a non-linear load to the load terminal at 6 s are shown in Figs. 6 and 8, respectively. A three-phase diode rectifier feeding RL load is used as a non-linear load. The non-linear nature of the load current is
fsw 4
Fig. 9. Load voltage performance of PMSG during transition from linear load to nonlinear load (a) Load Voltage (b) FFT analysis of load voltage.
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Fig. 10. Machine variables Performance of SCIG during transition from linear load to non-linear load (a) dc link voltage (b) q-axis component of machine current (c) Stator Flux (d) d-axis component of machine current.
Fig. 11. Machine variables performance of PMSG during transition from linear load to nonlinear load (a) dc link voltage (b) q-axis component of machine current.
Fig. 12. Performance indices of load variable of SCIG during transition from linear load to nonlinear load (a) Load current (b) d-axis component of load voltage (c) qaxis component of load voltage.
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Fig. 13. Load variable performance of SCIG during transition from linear balance load to unbalance load (a) Load Voltage (b) FFT analysis of load voltage.
Fig. 14. Performance indices of load variable of PMSG during transition from linear balance load to unbalance load (a) Load current (b) d-axis component of load voltage (c) q-axis component of load voltage.
Fig. 15. Load variable performance of PMSG during transition from linear balance load to unbalance load (a) Load Voltage (b) FFT analysis of load voltage.
shown in Fig. 6(a). The proposed control strategy to mitigate the harmonics discussed in Section 3 can remove the harmonic component from the load voltage. The controller is implemented successfully to maintain the d,q-axis component of load voltage at its prescribed value, as shown in Fig. 6(b), (c), respectively. The controller can keep the d- axis load voltage at 60 V and q-axis voltage at 0 V during this operation successfully. There is no such
variation observed during transients. With the compensation of the fifth and seventh order harmonic component of load current, the load voltage at the PCC becomes sinusoidal as seen in Fig. 7(a). The load side controller is successfully maintaining the load voltage THD at 1.73% is shown in Fig. 7 (b). Similarly, the load variable performances of PMSG during the transition from linear load to non-linear load at 6 s are shown in Fig. 8. The same load controller strategy discussed in Section 3 is
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R. Mishra and T.K. Saha
Fig. 16. Machine variables Performance of SCIG during transition from linear balance load to unbalance load (a) dc link voltage (b) q-axis component of machine current (c) Stator Flux (d) d-axis component of machine current.
Fig. 17. Machine variables performance of PMSG during transition from linear load to unbalance load (a) dc link voltage (b) q-axis component of machine current.
implemented. The performances of load variables are satisfactory. The load voltage compensation strategy is working successfully to remove the higher-order harmonic component, as shown in Table 2. As a result, THD of the load voltage is maintained at 1.83% as shown in Fig. 9(b). The performances of generator variables on the transition from linear load to nonlinear load for both the DG are shown in Figs. 10 and 11, respectively. The proposed control scheme described in Fig. 2 is employed for MSC. Both the dc-link voltage and flux controller have to be considered in case of SCIG driven stand-alone load. The dc-link voltage and flux maintaining the reference values during the operations are shown in Fig. 10(a), (c), respectively. A very small transient is observed in the case of dc-link voltage. The magnetizing flux is constant throughout the operation. The dc-link voltage controller is used to generate the reference active power component (q-axis component) of the generator, which can be used to maintain the power balance of the system. The q-axis current increases substantially to sustain the active power flow and controller working successfully to match the actual current as shown in Fig. 10(b). The flux controller is used to generate
Fig. 18. Comparison of Load voltage THD with the existing system during nonlinear loading.
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Table 3 Performances comparison of the proposed system with the existing literature. Paper/ Schemes
[22] [14] [24] [25] Proposed
Control Scheme
PI PI-dual frequency resonance controller (PI-DFR) PR Hyperbolic tangent based LMS algorithm PI
Unbalanced loading
Non-linear loading
% of loading
DC link voltage
Load voltage
DC link voltage
Load voltage
Variation
Settling time
Variation
Settling time
Variation
Settling time
Variation
Settling time
25 61.7
6% –
0.5 s –
Negligible –
Negligible 200 ms
–
–
0.2 V
160 ms
NA 100
–
0.02 s
–
0.02 s
5.5% –
0.6 s 0.02 s
9.09% –
0.2 s 0.02 s
100
Negligible
Negligible
Negligible
Negligible
Negligible
Negligible
Negligible
Negligible
Fig. 19. Machine and load variable performance of SCIGdriven load, during random variation in wind speed (a) generated torque (b) iqs (c) vdc (d) vdl.
Fig. 20. Machine and load variable performance of PMSG driven load, during random variation in wind speed (a) generated torque (b) iqs (c) vdc (d) vdl.
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undistorted as shown in Fig. 15(a). The changes in the stator side variables for both the DG in case of the unbalanced nature of load are as shown in Figs. 16 and 17, respectively. In the case of SCIG, dc-link voltage settles within 0.6 s. But a significant dip in dc-link voltage is observed because of the high moment of inertia of the machine. The 2% variation in the transient condition is shown in Fig. 16(a). The 47.2% decrement in load resistance increases the power demand, which is accommodated with increment in machine speed. This power balance, in turn, is adjusted by the reference q-axis component of the machine as shown in Fig. 16(b). The controller is working successfully to match with the actual current. The d-axis current controller remains invariant throughout the operation as shown in Fig. 16(d). But in the case of PMSG, a negligible transient is observed in case dc-link voltage and as shown in Fig. 17(a). The dc-link voltage controller is working successfully during the transition without any disturbance. The bar chart illustrated in Fig. 18 demonstrates the comparison of THD performance of load voltage of the proposed scheme with the existing literature. It is noticed that the THD of the proposed scheme is lower, reaching as low as 1.73% than the results provided in the works of literature. Table 3 compares the transient performance of the proposed system with existing literature. As can be seen, in this table, the dc-link voltage and load voltage variation are negligible during both non-linear and unbalanced loading scenarios.
Fig. 21. Test rig for the proposed topology.
4.3. Variation of wind speed with random noise
the reference d-axis component of the machine. But it remains a free control variable during the load transition. In the case of the PMSG, a dc-link voltage controller is working successfully without significant transient as shown in Fig. 11(a). The qaxis component of machine current remains invariant during its transition and following its reference successfully throughout the operation, as shown in Fig. 11(b).
The input variation is shown with the change in prime mover speed of the distributed generator. The combined controller is working successfully to handle the random variation of wind speed at 4 s and 2 s for SCIG and PMSG, respectively. The q-axis component of the machine current is successfully controlled to withstand the variation of generator speed as shown in Figs. 19(b) and 20(b) for both the generators. The dclink voltage is maintained at the reference voltage 300 V with negligible transient, as shown in Figs. 19(c) and 20(c). Accordingly, the load voltages are found to be unaffected during this operation and are presented in Fig. 20(d).
4.2. Performance analysis with an unbalanced load The distributed generation scheme is operated with an unbalanced load with resistances of 240 Ω, 120 Ω, and 240 Ω for the three phases, respectively. The application of the unbalanced load has been initiated at 6 s and the nature of load current for both the DG is shown in Figs. 12(a) and 14 (a), respectively (see . The said control strategy for LSC, as discussed in Section 3, can maintain the amplitude of the load voltage and frequency by eliminating the negative sequence component of load current. The d,q-axis component of the load voltage is working successfully by maintaining with the reference value for both the DG are shown in Figs. 12 and 14 respectively. As a consequence, the load voltage remains undistorted during this scenario. Considered filter current controller can compensate for the unbalance component within the standard limit. The THD of the load voltage is 2.37% in the case of SCIG driven stand-alone load as shown in Fig. 13(b). The flexibility of the controller is tested by implementing the same controller for different DGs. It is verified that the LSC is working successfully in the case of PMSG to keep the harmonic level at 1.83%, as shown in Fig. 15(b). Also, the controller is able to keep the load voltage
5. Experimental results 5.1. Test setup The experimental tests are conducted to provide the effectiveness of the designed controller for non-linear and unbalance loading. The experimental arrangement is as shown in Fig. 21 and Table 1 represents the detailed parameters used in the test rig. The information about the interfacing circuits for machine applications in the experimental setup has been provided in Table 4. The SCIG, coupled with dc machines that work as a prime mover. The stator of the SCIG is connected to the standalone load through a back-to-back converter. For real-time execution, MATLAB software is interfaced with the digital signal processor (dSPACE 1104) controller. 5.2. System performances The steady-state experimental results with the transition from a
Table 4 Interfacing circuits for machine applications in experimental setup. Name of the circuit
Number of circuit
Sensor used
Stator current sensor Filter current sensor Load voltage sensor DC link voltage sensor Speed sensor
2 2 2 1 1
Current sensor Current sensor Voltage sensor Voltage sensor Six signal QEP
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Interfaced through with noise with noise with noise with noise encoder
filter filter filter filter
ADC of ds1104 ADC of ds1104 ADC of ds1104 ADC of ds1104 Incremental encoder terminal of ds1104
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Fig. 22. The transient behaviour of variables during transition from balance to unbalance load, (a) dc link voltage (b) d-axis component of load voltage, (c) Load current, load voltage in DSO (d) FFT analysis of load voltage.
balanced linear load to an unbalanced linear load are shown in Fig. 22. The experimental results obtained to validate the excellent performance of the load voltage regulation during an unbalanced load. The system is initially operated with a balanced load of 60 Ω per phase. The R-phase load is changed to represent the unbalanced loading condition. The unbalanced loading is demonstrated with 31 Ω per in R-phase and 60 Ω each in the other two phases. The small transient in dc-link voltage observed at 3.85 s. It settles back to 50 V within 0.15 s, as shown in Fig. 22(a). The d-axis component of the load voltage is maintained at its reference level, as shown in Fig. 22 (b). The unbalanced load current and the variation in load voltage are portrayed in Fig. 22(c). The THD of the load voltage is kept at 2.61% after compensation of the unbalance nature of load current and as shown in Fig. 22(d). It is matching nearly with the simulation counterparts as shown in Table 2.
loading is negligible. The control is successfully implemented in the simulation environment. The THD of the load voltage has been maintained at less than 3% during both the scenarios. Additionally, the combined controller is able to keep machine and load variables within the prescribed limit successfully during random variation of wind speed. The proposed control algorithm is operated in real-time with a developed lower scale experimental set up through dSPACE 1104. The experimental results demonstrate the excellent matching with their simulation counterparts for unbalance loading conditions.
6. Conclusion
References
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The work has addressed the variable speed and constant frequency (VSCF) generation from the uncontrolled prime mover-based scheme for a stand-alone system. This system has addressed issues like balanced loading, unbalanced loading, non-linear loading and wind speed with random noise. The LSC controller is successfully removing the harmonics component and the negative sequence component during unbalanced and non-linear loading respectively. Accordingly, the controller is found to be able to fix the load voltage amplitude and frequency in spite of the variations in loads. The load voltage remains undistorted during both the scenarios successfully. The two-stage control strategy is used for MSC for steady-state analysis of dc-link voltage, generator speed, d,q-axis component of machine current. The same bandwidth is selected for the MSC of both the DG to maintain the machine variables. The transient performance i.e. settling time and overshoot of the dc-link voltage, stator current during a variety of
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