An improved predictive control for parallel grid-connected doubly fed induction generator-based wind systems under unbalanced grid conditions

Abstract

Recently, the massive integration of renewable energy sources, especially wind and solar ones, has attracted researchers to new issues such as power quality. In this context, this article deals with an improved deadbeat predictive control for parallel grid-connected doubly fed induction generator-based wind systems under unbalanced grid conditions. The impact of an asymmetrical voltage sag has been treated for a doubly fed induction generator- wind system with emphasis on the occurrence of the negative current. In the case of a micro-grid based on wind systems, the effect of this current increases with the line impedance and thereby the system location. An improved predictive deadbeat control technique is proposed for the rotor side converter to enhance the behaviour of the wind system. A dynamic modelling of the doubly fed induction generator in both positive and negative reference frames has been proposed to focus on the behaviour of the system for these various operating conditions. Results of different simulation scenarios prove the effectiveness of the proposed improved predictive deadbeat control.

Keywords

Micro-grid doubly fed induction generator unbalanced grid negative sequence improved predictive deadbeat control line impedance

Introduction

Nowadays, to find reliable ways to provide clean electricity and to integrate renewable energy sources, especially solar and wind, micro-grids are becoming very attractive (Parhizi et al., 2015). When several researchers care about micro-grids operating in the islanded mode (Choi et al., 2018; Han et al., 2017; Pouryekta et al., 2018), grid-connected mode attracts others (Arbi et al., 2009; Kerrouche et al., 2018; Kesraoui et al., 2016; Talapur et al., 2018). In this case, micro-grids based on doubly fed induction generator (DFIG)-based wind systems are widely treated because of variable speed operation, fractional converter rating and output filter cost-effectiveness of this type of machine (Flannery and Venkataramanan, 2008). However, such system is vulnerable to grid faults and disturbances especially asymmetrical ones (Ling, 2014; Zeraati et al., 2018). That is why many authors focus on the study of grid code requirements (GCR) and low voltage ride through (LVRT) (Ling, 2016; Liu et al., 2019; Niu et al., 2019). Several other authors investigate parallel working of wind systems under unbalanced grid conditions (Han et al., 2016; Wang et al., 2018). They study the impact of defaults and propose controls to enhance operation of micro-grid based on wind systems. Sreekumar and Khadkikar (2016) proposed a control strategy for harmonic power sharing in a micro-grid, without affecting voltage quality at load bus. Hore and Sarma (2018) used artificial neural network controllers to track the reference active power more precisely at specified power factor under various conditions. Wu et al. (2019) proposed a small-signal sequence impedance model of a micro-grid to study its stability. Han and Ha (2019) suggested a droop control that uses the leakage inductances of DFIG as the output filter inductance. Shuai et al. (2016) studied the possibility of cancelling effect of coupling line voltage drop to enhance droop control performances. However, effect of unbalanced grid fault for a micro-grid based on several wind systems located at different distances is rarely inspected in the literature; Kafi (2017) described the behaviour of an electrical power distribution system with DFIG-based wind farm and gave a review on voltage sag. Chakraborty et al. (2017) analysed different impacts of sudden grid disturbances on a MW-level grid-connected large DFIG-based wind farm. Skander-Mustapha and Slama-Belkhodja (2011) proposed supervisory for parallel-operated grid-connected DFIG-based variable wind systems.

This article investigates parallel working of DFIG-based wind systems under unbalanced grid conditions. The impact of an asymmetrical voltage sag has been investigated for DFIG-based wind systems and for different wind system locations. Furthermore, an improved predictive deadbeat control (IPDBC) technique is proposed to enhance wind system-based micro-grid behaviour. The idea of this enhanced control technique is to introduce power harmonic components to calculate rotor current references. The goal is to improve wind system behaviours even at critical locations.

This article is structured as follows. In section ‘Micro-grid modelling under unbalanced grid conditions’, the model of a micro-grid composed of several variable speed wind systems based on DFIGs at different locations is presented. The impact of DFIG locations on the behaviour of the wind systems and their controls under an asymmetrical voltage sag is studied. In section ‘Wind system modelling and harmonic analysis under unbalanced grid conditions’, the dynamic DFIG model in both positive and negative reference frames is given. Then, the system behaviour under unbalanced grid conditions is investigated. Section ‘Proposed controls’ describes the predictive deadbeat control (PDBC) technique and deals with the IPDBC technique.

In section ‘Study cases: discussions and results’, simulation results are carried out for a 2 MW wind system and several case studies are presented to focus on parallel working of DFIG-based wind systems under unbalanced grid conditions and to prove the proposed IPDBC performances under unbalanced operation even at critical locations. Section ‘Conclusion’ concludes the article.

Micro-grid modelling under unbalanced grid conditions

In this section, the model of a grid-connected micro-grid composed of $N$ variable speed wind systems at different locations is presented. The purpose is to focus on the parallel working of DFIG-based wind systems and the impact of DFIG location on the behaviour of the wind systems and their controls under an asymmetrical voltage sag.

Figure 1 depicts the model of the grid-connected micro-grid with $N$ wind systems, and impedances $Z_{1}$ to $Z_{N}$ represent the line impedances. One wind system is closer to the point of common coupling (PCC) than another one, which is connected to the grid through a smaller line impedance.

Figure 1.

Model of the micro-grid with N DFIG wind systems.

Under unbalanced grid conditions, symmetrical component theory can be used. According to this theory, any direct unbalanced three-phase system, oscillating at a frequency $ω$ , can be decomposed into three balanced systems: the first oscillating at the frequency $ω$ and called positive sequence, the second oscillating at the frequency $- ω$ and called negative sequence and the third is composed of three signals in phase oscillating at the frequency $ω$ and called the zero sequence system.

Thus, voltages, currents and fluxes can be decomposed into positive and negative sequences. Zero sequence components are neglected in this article, since all DFIGs are considered three-phase three-wire. Negative sequences are equal to zero for a balanced three-phase system. However, when an asymmetrical grid sag occurs, negative sequences appear in both the stator voltages and currents. Current and voltage negative sequences cause oscillating terms in stator powers at twice grid frequency. Consequently, double grid frequency fluctuation appears in DFIG electromagnetic torque, causing acoustic noise and reducing lifetime of rotating parts by creating vibrations in the DFIG shaft. In addition, current negative sequence leads to an increase in winding loss DFIG, which reduces the efficiency.

Furthermore, active power oscillations lead to DC-link voltage oscillations. Thus, unbalanced grid voltages decrease DFIG-based wind system performance.

As all wind systems are fed by the same grid voltage, the attention soars towards currents to focus on unbalance effect.

Thus, grid current $i_{g}$ can be expressed by equation (1)

{\bar{i}}_{g} = {\bar{i}}_{g p} + {\bar{i}}_{gn}

(1)

Figure 2 depicts the model of the grid-connected micro-grid with $N$ wind systems in the negative reference frame. Only negative sequences are considered to focus on the effect of negative current that appears during the unbalanced operation.

Figure 2.

Negative sequence of the current in the lines.

It is obvious that negative sequence of current crossing the $j th$ line ${\bar{i}}_{w j n}$ depends on line impedance $Z_{j}$ as expressed in equation (2)

{\bar{i}}_{w j n} = \frac{{\bar{v}}_{w j n} - {\bar{v}}_{P C C n}}{Z_{j}}

(2)

The total negative grid current is equally shared between the parallel wind systems if:

All wind systems have same parameters.

All DFIGs are controlled with the same control.

All wind systems are at the same location from the PCC.

For different wind systems locations, as shown in equation (2), negative sequence of the current crossing the line is inversely proportional to line impedance. This current effect is greater at the closest wind systems to PCC than other wind systems.

Wind system modelling and harmonic analysis under unbalanced grid conditions

System topology and dynamic DFIG modelling

The basic wind system in this work is shown in Figure 3. The adopted configuration is a grid-connected variable speed wind system based on DFIG.

Figure 3.

DFIG wind system configuration.

The stator is connected directly to the grid. The rotor is supplied by controlled back-to-back converters that are connected to grid through an inductive filter. The rotor side converter (RsC) ensures stator power control and the grid side converter (GsC) ensures DC-link and rotor power controls.

In this study, DFIG is connected to a faulty grid, especially with asymmetrical voltage sag. Therefore, positive and negative reference frames are used to model the DFIG. Park transformations preserve active and reactive powers with powers of the system in the abc reference frame. Figure 4 illustrates positive and negative rotating reference frames $d_{p} - q_{p}$ and $d_{n} - q_{n}$ . Positive reference frame axis rotates at an angular speed $ω_{s}$ , while negative reference frame axis rotates at an angular speed $- ω_{s}$ . Dynamic DFIG model in positive and negative reference frames is given by equations (3) to (6)

{\bar{v}}_{s d q p} = {\bar{v}}_{s d p} + j {\bar{v}}_{s q p} = R_{s} {\bar{i}}_{s d q p} + \frac{d {\bar{φ}}_{s d q p}}{d t} + j ω_{s} {\bar{φ}}_{s d q p}

(3)

{\bar{v}}_{r d q p} = {\bar{v}}_{r d p} + j {\bar{v}}_{r q p} = R_{r} {\bar{i}}_{r d q p} + \frac{d {\bar{φ}}_{r d q p}}{d t} + j ω_{r} {\bar{φ}}_{r d q p}

(4)

{\bar{v}}_{s d q n} = {\bar{v}}_{s d n} + j {\bar{v}}_{s q n} = R_{s} {\bar{i}}_{s d q n} + \frac{d {\bar{φ}}_{s d q n}}{d t} + j ω_{s} {\bar{φ}}_{s d q n}

(5)

{\bar{v}}_{r d q n} = {\bar{v}}_{r d n} + j {\bar{v}}_{r q n} = R_{r} {\bar{i}}_{r d q n} + \frac{d {\bar{φ}}_{r d q n}}{d t} + j ω_{r} {\bar{φ}}_{r d q n}

(6)

Stator and rotor fluxes are also decomposed into positive and negative sequences. Positive and negative sequences of stator and rotor fluxes are expressed in equations (7) to (10)

{\bar{φ}}_{s d q p} = L_{s} {\bar{i}}_{s d q p} + L_{m} {\bar{i}}_{r d q p}

(7)

{\bar{φ}}_{r d q p} = L_{r} {\bar{i}}_{r d q p} + L_{m} {\bar{i}}_{s d q p}

(8)

{\bar{φ}}_{s d q n} = L_{s} {\bar{i}}_{s d q n} + L_{m} {\bar{i}}_{r d q n}

(9)

{\bar{φ}}_{r d q n} = L_{r} {\bar{i}}_{r d q n} + L_{m} {\bar{i}}_{s d q n}

(10)

In order to complete the DFIG model, mechanical equation is given by equation (11)

T_{e m} = p \frac{L_{m}}{L_{s}} (φ_{s q} i_{r d} - φ_{s d} i_{r q})

(11)

Figure 4.

Positive and negative reference frames.

System behaviour under unbalanced grid conditions

Under unbalanced grid conditions, voltage and current decomposition in symmetrical sequences leads to the expressions of active and reactive stator powers given by equation (12)

{\begin{cases} P_{s} = P_{s o} + P_{s \cos} \cos (2 ω_{s} t) + P_{s \sin} \sin (2 ω_{s} t) \\ Q_{s} = Q_{s o} + Q_{s \cos} \cos (2 ω_{s} t) + Q_{s \sin} \sin (2 ω_{s} t) \end{cases}

(12)

where $P_{s o}$ , $P_{s \cos}$ , $P_{s \sin}$ , $Q_{s o}$ , $Q_{s \cos}$ and $Q_{s \sin}$ are stator power components expressed in positive and negative rotating reference frames. These components are given by equation (13)

(\begin{array}{l} P_{s o} \\ Q_{s o} \\ P_{s \cos} \\ P_{s \sin} \\ Q_{s \cos} \\ Q_{s \sin} \end{array}) = (\begin{matrix} v_{s d p} & v_{s q p} & v_{s d n} & v_{s q n} \\ v_{s q p} & - v_{s d p} & v_{s q n} & - v_{s d n} \\ v_{s d n} & v_{s q n} & v_{s d p} & v_{s q p} \\ v_{s q n} & - v_{s d n} & - v_{s q p} & v_{s d p} \\ v_{s q n} & - v_{s d n} & v_{s q p} & - v_{s d p} \\ - v_{s d n} & - v_{s q n} & v_{s d p} & v_{s q p} \end{matrix}) . (\begin{array}{l} i_{s d p} \\ i_{s q p} \\ i_{s d n} \\ i_{s q n} \end{array})

(13)

Thereby, negative sequences of both stator voltages and currents lead to oscillating terms in stator powers at twice grid frequency. Such oscillations cause torque ripples at the same frequency, and the DFIG electromagnetic torque can be written as in equation (14)

T e m = P_{s} \frac{p}{ω_{s}} = T e m_{o} + T e m_{\cos} \cos (2 ω_{g} t) + T e m_{\sin} \sin (2 ω_{g} t)

(14)

These oscillations can lead to acoustic noise and reduce rotating part lifetime by creating vibrations in the shaft. In addition, because of the coupling between controlled DC-link voltage and grid currents, any oscillation in grid currents can lead to DC-link voltage oscillations. Thus, asymmetrical grid voltages can decrease DFIG-based wind system performance, so protective measures have to be taken to avoid these adverse effects.

Proposed controls

Predictive deadbeat control

Field-oriented control (FOC) structure with predictive deadbeat controllers (PDBC), as depicted in Figure 5, has been developed for the RsC. The predictive deadbeat controller structure is presented in Figure 6. The d–q rotating reference frame is chosen such as the stator flux vector is linked to the direct axis d, since the active and reactive powers are decoupled and can be controlled through rotor currents under this stator flux orientation. This reference frame orientation results in a zero flux component for $φ_{s q}$ . Stator and rotor resistances are neglected. Stator angle $θ_{s}$ and electrical angular frequency $ω_{s}$ are generated using a second-order generalized integrator phase locked loop (SOGIPLL).

Figure 5.

PDBC topology.

Figure 6.

Predictive deadbeat controller structure.

Under these conditions, rotor current references for the controllers can be expressed by equations (15) and (16)

i_{r d r e f} = \frac{L_{s}}{L_{m} v_{s q}} (\frac{v_{s q} φ_{s d}}{L_{s}} - Q_{s r e f})

(15)

i_{r q r e f} = - \frac{L_{s}}{L_{m} v_{s q}} P_{s r e f}

(16)

Obtained references are applied to predictive deadbeat controllers that ensure fast dynamic responses. Figure 6 shows predictive deadbeat controller structure. The main objective of these controllers is to meet a prediction criterion of zero error between predicted rotor current components $i_{r d} [k + 1]$ and $i_{r q} [k + 1]$ and their references $i_{r d r e f} [k]$ and $i_{r q r e f} [k]$ at $k th$ sampling period. The prediction criterion is given by equation (17)

{\begin{cases} i_{r d} [k + 1] = i_{r d r e f} [k] \\ i_{r q} [k + 1] = i_{r q r e f} [k] \end{cases}

(17)

From the DFIG model described in section ‘Micro-grid modelling under unbalanced grid conditions’, and using Euler discretization method, prediction equations expressed by equations (18) and (19) are derived

v_{r d} [k] = a_{1} i_{r d} [k] + a_{2} i_{r d} [k + 1] - ω_{r} φ_{r q} [k]

(18)

v_{r q} [k] = a_{1} i_{r q} [k] + a_{2} i_{r q} [k + 1] - ω_{r} φ_{r d} [k]

(19)

where $a_{1} = R_{r} - (σ / T_{s})$ , $a_{2} = σ / T_{s}$

Improved predictive deadbeat control for the RsC

As shown in section ‘Micro-grid modelling under unbalanced grid conditions’, the effect of negative sequence of line current is greater at the closest wind system to PCC than other wind systems. Thus, asymmetrical grid fault impact on the closer wind system to the PCC is greater than farther one under the same operation conditions. Objective of the proposed IPDBC technique is to enhance the behaviour of the closer wind system to the PCC under asymmetrical grid fault by extracting current harmonic components from conventional rotor current references.

The IPDBC structure is presented in Figure 7. Under unbalanced grid conditions, power expressions given by equation (12) are substituted into expressions of rotor currents references given in equations (15) and (16).

Figure 7.

IPDBC topology.

Thereby, rotor current references expressions for the proposed IPDBC technique are obtained by equations (20) and (21)

i_{r d r e f} = \frac{L_{s}}{L_{m} v_{s q}} (\frac{v_{s q} φ_{s d}}{L_{s}} - Q_{s r e f}) + i h_{r d r e f}

(20)

i_{r q r e f} = - \frac{L_{s}}{L_{m} v_{s q}} P_{s r e f} + i h_{r q r e f}

(21)

where $i h_{r d r e f}$ and $i h_{r q r e f}$ are double grid frequency rotor current harmonic components given by equations (22) and (23)

i h_{r d r e f} = - \frac{L_{s}}{L_{m} v_{s q}} (Q_{s \cos} \cos (2 ω_{g} t) + Q_{s \sin} \sin (2 ω_{g} t))

(22)

i h_{r q r e f} = - \frac{L_{s}}{L_{m} v_{s q}} (P_{s \cos} \cos (2 ω_{g} t) + P_{s \sin} \sin (2 ω_{g} t))

(23)

Study cases: discussions and results

In this section, several case studies are performed to focus on the parallel working of DFIG-based wind systems under unbalanced grid conditions. The aim is to investigate negative current effect and to prove the effectiveness of the proposed IPDBC technique in enhancing micro-grid based on wind system behaviour under unbalanced operation. All tested wind systems in this section are 2 MW system with four-pole doubly fed induction machines. All DFIGs have same parameters that are reported in Table 1.

Table 1.

DFIG parameters.

Description	Symbol	Value
Rated power (MW)	P	2
Rated stator voltage (V)	V_s	690
Rated rotor voltage (V)	V_r	2070
Rated stator current (A)	I_s	1760
Number of pairs of poles	p	2
Frequency (Hz)	f_s	50
Stator resistance (mΩ)	R_s	0.34
Rotor resistance (mΩ)	R_r	2.9
Stator cyclic inductance (mH)	L_s	2.587
Rotor cyclic inductance (mH)	L_r	2.587
Mutual cyclic inductance (mH)	L_m	2.5

DFIG: doubly fed induction generator.

Case 1: symmetrical and asymmetrical sag

PDBC algorithm is applied to a grid-connected DFIG system under balanced fault then unbalanced one to show effect of these faults in wind system behaviour. Two simulation tests are performed. Initially, a balanced 400 V three-phase voltage represents 50 Hz grid. Then, at $t = 0.7 s$ , a 30% voltage sag is applied. For the first test, the sag is symmetrical (three-phase sag) and for the second test, the voltage sag is asymmetrical (single-phase sag in the first-phase V_a).

Grid voltages and grid current negative sequence are shown in Figure 8. Under normal operation, there is no negative sequence in grid current. Negative sequence appears only under an unbalanced operation, namely, under asymmetrical voltage sag. Therefore, this negative sequence leads to additional oscillations in stator powers and, thereby, in electromagnetic torque, as depicted in Figure 9. Frequency analysis, depicted in Figure 10, shows that these additional oscillations are at twice grid frequency that is equal to 100 Hz, as demonstrated in section ‘Wind system modelling and harmonic analysis under unbalanced grid conditions’.

Figure 8.

Grid voltages and negative grid currents for (a) asymmetrical sag and (b) symmetrical sag.

Figure 9.

Stator power and electromagnetic torque for (a) asymmetrical sag and (b) symmetrical sag.

Figure 10.

Electromagnetic torque in the frequency domain for (a) asymmetrical sag and (b) symmetrical sag.

Case 2: two wind systems at the same location with the same RsC control

A micro-grid composed of two DFIGs at same location is considered. Both DFIGs are directly connected to grid. Two line impedances are considered equal to zero. Both DFIGs have same parameters and are operating at same speed.

Initially, a balanced 400 V three-phase voltage represents the 50 Hz grid. Then, at $t = 0.5 s$ , a 30% asymmetrical voltage sag (single-phase sag in the first-phase V_a) is applied.

Figure 11 shows three-phase voltages, grid current negative sequence and negative sequences of the currents crossing two lines under normal and unbalanced operations. Under unbalanced operation, a negative sequence appears in grid current. Total negative grid current is equally shared between the two parallel wind systems. Figure 12 depicts electromagnetic torques and speeds of the two systems that have same operation. Same oscillations appear in both electromagnetic torques and speeds.

Figure 11.

Grid voltages, grid currents and line currents for wind systems at the same location.

Figure 12.

Electromagnetic torques and the speeds of the wind systems at the same location.

Case 3: two wind systems at different locations with the same RsC control

To focus on the effect of line impedance on wind system behaviour, a micro-grid composed of two DFIGs at different locations is considered. Both DFIGs have same parameters and are operating with same references of powers and DC voltage. Wind system 1 and wind system 2 are distant wind system and closer wind system, respectively. Wind system 1 is connecting to the PCC through a line impedance. Impedance value is $(R / L) = (0.5 Ω / 0.3 m H)$ . Wind system 2 is very close to the PCC; line impedance is neglected.

Initially, a balanced 400 V three-phase voltage represents the 50 Hz grid. Then, at $t = 0.5 s$ , a 30% asymmetrical voltage sag (single-phase sag in the first-phase V_a) is applied.

Figure 13 presents three-phase voltages, negative sequence of grid current and negative sequences of currents crossing the two lines under normal and unbalanced operations. Result shows that DFIG with short electrical distance from PCC has greater negative sequence current level than that with long distance. These results are in line with theory presented in section ‘Micro-grid modelling under unbalanced grid conditions’.

Figure 13.

Grid voltages and line currents for wind systems at different locations.

Figure 14 depicts electromagnetic torques and speeds of the two systems that have same operation. Speed and electromagnetic torque are greater for the closer wind system because of grid voltage drop but the fault effect is lower. In fact, electromagnetic torque and speed oscillations are more important for the farthest wind system.

Figure 14.

Electromagnetic torques and speeds of the two wind systems at different locations.

Thus, the impact of the grid fault on the closer wind system is greater than the impact on the farther one under the same operation conditions.

Case 4: two wind systems with different RsC controls

To verify the performances of the proposed IPDBC technique, a micro-grid composed of two DFIGs at the same location is considered. For the wind system 1, the PDBC technique is adapted and for the wind system 2, the IPDBC technique is adapted.

Initially, a balanced 400 V three-phase voltage represents the 50 Hz grid. Then, at $t = 0.5 s$ , a 30% asymmetrical voltage sag (single-phase sag in the first-phase V_a) is applied.

Figure 15 depicts electromagnetic torques of the two wind systems in both time and frequency domains. For the second wind system, controlled with the IPDBC technique, it can be noted that the torque ripples are reduced by more than 50% in comparison with the system controlled with the PDBC technique. The frequency analysis reveals that the double grid frequency harmonics are notably reduced for the electromagnetic torque.

Figure 15.

Electromagnetic torques of the two wind systems with the two proposed control techniques: (a) DFIG electromagnetic torques in time domain, (b) DFIG 1 electromagnetic torque in frequency domain and (c) DFIG 2 electromagnetic torque in frequency domain.

These simulation results show the effectiveness of the proposed IPDBC technique in mitigating the effect of the unbalance, in the case of asymmetrical grid sags.

Conclusion

This article investigates and analyzes the parallel operation of DFIG-based wind systems under unbalanced grid conditions. Asymmetrical voltage sag impact has been studied for DFIG-based wind systems. This effect has been treated in the case of a micro-grid based on wind systems to investigate system location effect. Harmonic analysis shows that grid voltage sags cause negative sequence of line currents. This current effect depends on line impedance, and its impact is greater at the closest wind system to the PCC than the other wind systems. An enhanced control technique, named here IPDBC, has been proposed to reduce asymmetrical sag impact. The proposed enhanced control technique introduces a new method for calculating rotor current references for predictive deadbeat controllers. Different tested simulation scenarios have proven the effectiveness of the proposed IPDBC in mitigating voltage sag effects even if the wind system is in a critical location.

Footnotes

Appendix 1 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by the Tunisian Ministry of High Education and Research under Grant LSE-ENIT-LR 11ES15 and the Tuniso-South African Collaboration project ‘Generator Test Platform for Assessing the Impact of Wind Integration and Power Quality Issues’.

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