Control of the powerquality for a DFIG powered by multilevel inverters

Received Aug 23, 2019 Revised Feb 24, 2020 Accepted Mar 25, 2020 This paper treats the modeling, and the control of a wind power system based on a doubly fed induction generator DFIG, the stator is directly connected to the grid, while the rotor is powered by multilevel inverters. In order to get a decoupled system of controlfor an independently transits of active and reactive power, a vector control method based on stator flux orientation SFOC is considered: Direct vector control based on PI controllers. Cascaded H-bridge CHBI multilevel inverters are used in the rotor circuit to study its effect on supply power quality. All simulation models are built in MATLAB/Simulink software. Results and waveforms clearly show the effectiveness of vector control strategy. Finally, performances of the system will tested and compared for each levels of inverter.


INTRODUCTION
The generation of electricity that comes from nuclear power and fossil natural resources, pose continued problems whose importance is growing over the years; as the nuclear untreatable waste and disappearance expected in the 21 st century, for major source of fossil energy. Environmental constraints on atmospheric emissions of greenhouse gases has led researchers a way of generating clean, economic and sustainable electricity [1].
Various studies carried out in this context have shown that far-reaching changes are essential in energy strategies to ensure better management of the production, transformation, distribution and use of energy [2]. From this perspective, controlling energy in a broad sense constitutes an important challenge in the development of sustainable energy. Energy efficiency and renewable energies are therefore interesting avenues for more sustainable energy development and are considered to be among the most environmentally friendly components, particularly in the fight against climate change [3]. Thus, the modes of production based on the transformation of renewable energy (solar, wind ...) are expected to be increasingly used in the context of sustainable development, and thanks to recent developments of power electronics and micro processing.
The production area of variable speed wind energy has in recent years a boom. A great attention is paid today to doubly fed machine DFIM for various applications suchas generator for wind energy. This interest is mainly due to the fact of accessibility for its rotor and therefore the possibility of supplying a converter as well as the stat side gold on the rotor side.
Power-electronic converters have been developed for integrating wind power with the electric grid. The use of power-electronic converters allows for variable-speed operation of the wind turbine, and enhanced power extraction. In variable-speed operation, a control method designed to extract maximum power from the wind turbine and provide constant grid voltage and frequency is required [4]. In this paper, a variable-speed wind turbine is considered with DFIG and a multilevel cascaded H-Bridge Inverter CHBI. Multilevel inverters are AC-DC-AC converters, well suited for medium and high-power applications [5] due to their ability to meet the increasing demand of power ratings and power quality associated with reduced harmonic distortion, lower electromagnetic interference, and higher efficiencies when compared with the conventional two or three level topology [6]. The increasing number of voltage levels lead to the production of high-power quality waveforms [7], causing the total harmonic distortion THD to be lower. Multilevel converters are a good tradeoff solution between performance and cost in wind high-power systems [8].
The most typical connection diagram of this DFIG is to connect stator directly to the grid, while the rotor is supplied through a controlled power converter. This solution is more attractive for all applications where speed variations are limited around the synchronous speed because this area operating presents low slip, and therefore the converter associated with the rotor has to be treated only for a fraction of 20 to 30 % of the nominal conversion system power; this means that the losses in the converter are reduced (power supplied to the rotor is low) and the cost thereof is reduced. That is why we find this machine in high power variable speed and constant frequency for production systems. A second reason is the possibility of controlling the active and reactive power in the stator via the control of the power converter [9].
Further variable speed wind turbine is modeled to find a relationship between the electromagnetic torque and the mechanical wind speed. After describing mechanical and electrical model of the DFIG in section 3, a vector control method based on stator flux orientation SFOC is considered: direct vector control based on PI controllers. The sinus pulse wave modulation (SPWM) control strategyfor multilevel invertersis given in section 4. Finally, simulation and results are presented; performances of the system are then evaluated.

WIND TURBINE MODEL
Mechanical power available on the shaft of a wind turbine is expressed by [10]: where: ρ :air density (1.25 Kg/m 3 ); R : Blade length in meters; Vv : wind velocity in m/s. The aerodynamic power extracted from wind turbine canbe calculated as: = Ω . ( where: Cp : Power coefficient; β : Pitch angle (deg); λ :Tip speed ratio; ΩTurb : Turbine speed (rd/s).
No wind turbine could convert more than 59 % of the kinetic energy of the wind into mechanical energy turning a rotor [11]. This is known as the Betz limit, and it is the theoretical maximum coefficient of power for any wind turbine: Cpmax= 16/27 ≈ 0.593. The multiplier is mathematically modeled by the following equations: Ωturb, Ωm: Turbine speed respectively before and afterthe multiplier;Tturb: aerodynamic torque; Tm: torque after the multiplier; G: Gear ratio; Jg: Generator inertia; JT: Total inertia; JTurb: Turbine inertia.
The fundamental equation of dynamics to determine the evolution of the mechanical speed from the total mechanical torque applied to the rotor: where: Tem : Electromagnetic torque; Cf: Viscous friction coefficient.

Modeling of the DFIG, Park's model
The d-q axis representation of DFIG is used for modeling, considering flux as variable based on Park's model. All rotor quantities are referred to stator side. The DFIG model represented by voltage (6). The stator and rotor side flux linkage equations are given as [12][13][14]: The stator and rotor flux can be expressed as: Electromagnetic torque is also expressed in terms of currents and flux: where: Rs, Rr, are respectively the stator and rotor resistances; L s , L r : inductances of the stator and rotor windings; L m is the mutual inductance; Vds, Vqs, Vdret Vqr: Direct and quadrate components of the space phasors of the stator and rotor voltages; Ids, Iqs, Idr, Iqr: Direct and quadrate components of the space phasors of the stator and rotor currents; φds, φqs, φdret φqr: Direct and quadrate components of the space phasors of the stator and rotor flux respectively; ɷs: Rotational speed of the synchronous reference frame; ɷr: Rotor speed, p: Number of pair poles. Active and reactive powers at the stator (Ps, Qs), and the rotor (Pr, Qr) are defined as [15][16]:

Control strategy of the DFIG
Once the DFIG is connected to an existing grid, the transit of active and reactive powers must be controlled separately. To obtain a decoupled powers control of DFIG, the method based on field orientation can be regarded as the efficient one. The principle of this method consists to orientate the stator flux in such a way that the stator flux vector points into d-axis direction; this approach is realized by setting the quadratic component of the stator flux to the null value, detailed representation is show in Figure 1 [17,18].

Figure 1. Stator flux orientation
The stator fluxes of (6) will be simplified as follows: The stator resistance will be neglected, for medium power machines used in WECS; the stator voltage vector is consequently in quadrate advance in comparison with the stator flux vector.
Using (10), we can establish the connection between the rotor and stator currents: Using (11) and (12), the stator active and reactive power and rotor voltage are given by: For controlling the DFIG, established expressions showing the relationship between current and rotor voltages will be applied to it.
By considering σ as the cross coupling term, (14) can be rewrite as: The block diagram representing the internal model of the system is shown in Figure 2. Field oriented control of the DFIG can then be applied with the active and reactive power considered as variables to be controlled. The input blocks relating to represent the simplified rotor converter model. Knowing (13) and (15), it is then possible to synthesize the regulators [19].

Figure 2. Block diagram of the system to regulate
In order to improve the last command, we will introduce an additional control loop at the currents to eliminate the static error while preserving the dynamics of the system, then, two additional PI controllers are added to regulate the active and reactive powers. So, we need sixcurrents sensors, three to control the rotor currents (iar, ibr and icr) and three associated with three voltage sensors to measure the stator powers Ps and Qs. The active power PI controller regulates the rotor current reference iqr from the error between the active power measured Ps and the desired active power Pref. Furthermore, the reactive power PI controller regulates the rotor current reference idr from the error between the reactive power measured Qs and the desired reactive power Qref. The closed loop control of active and reactive powers is presented in Figure 3:

CASCADED H-BRIDGE INVERTER CHBI THEORY
Several multilevel topologies used for grid connection have been proposed in [20,21]. Multilevel converter structures have three major classifications; neutral point clamped (NPCor diode clamped), flying capacitor (FC or capacitor clamped), and cascaded H-bridge inverter CHBI, with isolated DC source Figure 4. Compared with the latter two, the multilevel CHBI has many distinct advantages:  Switch devices required are less under the same switching frequency and level number.  The harmonic content is lower in the output voltage for a given switching frequency.  Modularized circuit layout and packaging is possible because each cell has the same structure, and there are no extra clamping diodes as in the case of diode clamped topology, or voltage balancing capacitors as in the case of the capacitor clamped topology [22].

Theory of cascaded H-Bridge multilevel inverter
The cascaded H bridge multilevel inverter circuit consists of individual H-bridge cells which are fed by individual dc supply. Each H-bridge cell contains four switches. In this topology, IGBT is used as switch because of its low switching losses. Each H-bridge generates three different output voltages, +Vdc, 0 and -Vdc using various combinations of switching with the four switches [22,23]. The switching tableof the three level CHB is given in Table 1. Cascaded multilevel inverter is the cascade connection of N H-bridge inverters. Each H-bridge inverter has the same configuration as a typical single-phase full-bridge inverter. In this topology the number of phase voltage levels at the converter terminals is 2N+1, where N is the number ofcells or dc link voltages. The IGBT switches have low block voltage and high switching frequency. Consider the seven level inverter; it requires 12 IGBT switches and three dc sources. The power circuit ofinverter is shown in Figure 5. By closing the appropriate switches, each H-bridge inverter can produce three different voltages: +Vdc, 0 and -Vdc. It is also possible to modularize circuit layout and packaging because each level has the same structure, and there are no extra clamping diodes or voltage balancing capacitors. The number of switches is reduced using the newtopology [24,25].  Figure 5. Cascaded H-bridge 7-level inverter

SIMULATION RESULTS
The system based on a variable speed wind turbine with a doubly fed induction generator DFIG. The simulation is carried out using the MatLab/Simulink software. The DFIG is connected directly to the network through the stator, and controlled by its rotor through a three level CHBI. Simulation results are presented in Figure 6 to Figure 14. They show performances of our system. To control the power exchanged between the stator and the network, one uses the vector control with direct stator flux shown in Figure 15. Simulation results are obtained under various stator active and reactive power steps. The both control strategies with 5 levels CHBI, and 13 levels CHBI separately, are simulated, tested and compared in terms of power reference tracking. We initial simulation at first, with an active power step Psref= -5KW. At time t = 0.5s to 2s an application of the echelon of active power Psref = -10KW, and after time t = 2s to 3s we return at step Psref = -5KW. The reactive power step is changed from Qsref = -1 to -4 KVAR at the instant t = 1 s and again from -4 to -1 KVAR at the instant t = 1.5 s; a last variation of the reactive power step at the instant t = 2.5 is applied from Qsref =.-1 KVAR. Simulation results are shown in Figure 16 to Figure 19.
It can be seen that multilevel CHBI can control the active and reactive powers of DFIG with a very fast time response. However, the ripples in powers are more significant from control with 5 levels CHBI. To observe the effectiveness of the proposed control strategy, we increased levels of CHBI gradually up to 13 levels. In order to produce quality energy, it is apparent that the control with 13 levels CHBI, harmonics are almost eliminated. Thus, we estimate that these powers injected into the network will have no significant impact.

CONCLUSION
The aim of this work is to model and control the doubly fed induction generator DFIG based wind energy conversion system powered by multitier inverters with cascaded H-Bridge structure, to increase the power transferred to the network. In this context, a control of the powers of the wind system was carried out. For adjusting the energy quality supplied by the DFIG, vector control by orientation of the stator flow that makes the system similar to that of the DC machine was applied. To be able to directly control the active and reactive DFIG power through multi-level inverters; our strategy was to apply vector control, with a configuration of H. BRIDGE inverters; and then increase their levels, in order to improve the quality of the energy delivered by the DFIG; we thus determined the most efficient system for the different configurations proposed.The global model of our system is at first established. Furthermore, a vector control strategy of the DFIG to perform power reference tracking to machine parameters variation. The structure using the DFIG has a best advantage in terms of high power output, in variable speed operation, while reducing the size of the static converters. Despite this, the use of multilevel converters seems necessary especially for high power wind turbines. These converters increase the power transmitted to the power grid by reducing the current ripple and the harmonic content of the output voltages. This increase is done by means of the voltage, which makes it possible to reduce the losses of power in the lines.The results show that, using multilevels CHBI, the quality of produced energy is improved, in fact the harmonics that decrease the efficiency of the system are extremely diminished.