Analysis and control of wind-driven self-excited induction generators connected to the grid through power converters

Abstract

The analysis of the wind-driven self-excited induction generators (SEIGs) connected to the grid through power converters has been developed in this paper. For this analysis, a method of representing the grid power as equivalent load resistance in the steady-state equivalent circuit of SEIG has been formulated. The technique of genetic algorithm (GA) has been adopted for making the analysis of the proposed system simple and straightforward. The control of SEIG is attempted by connecting an uncontrolled diode bridge rectifier (DBR) and a line commutated inverter (LCI) between the generator terminals and three-phase utility grid. A simple control technique for maximum power point tracking (MPPT) in wind energy conversion systems (WECS), in which the firing angle of the LCI alone needs to be controlled by sensing the rotor speed of the generator has been proposed. The effectiveness of the proposed method of MPPT and method of analysis of this wind-driven SEIG-converter system connected to the grid through power converters has been demonstrated by experiments and simulation. These experimental and simulated results confirm the usefulness and successful working of the proposed system and its analysis.

Keywords

self-excited induction generator (SEIG) / renewable power generation / power converters / maximum power point tracking (MPPT) / steady state analysis / power generation systems

Introduction

It is well known that the electric power generation using wind energy source is receiving considerable attention, since it is inexhaustible, safe, environmental friendly and capable of supplying significant amount of power [1-5]. However, wind is not constant and fluctuates at different times of the day. So, due to the aerodynamic characteristics of the wind turbine, the rotational speed has to be varied with wind velocity to achieve the maximum power (MP) output [6]. Thus, the variable speed wind turbine systems are required for extracting MP available at all wind velocities [6-9]. In such variable speed wind turbine systems, permanent magnet alternators (PMA) or induction generators can be employed for electrical power generation. Due to low cost, simple and robust construction, squirrel-cage induction machines acting as generator are more attractive than PMA. Further, for achieving the MP available in the wind, the rotor speed of the induction generators has to be allowed to vary greatly. So, the induction generator output terminals have to be decoupled from the grid for operating these generators with wide rotor speeds. To achieve this, several authors have proposed the generator system configuration as shown in Fig. 1, in which pulse width modulation (PWM) rectifier is placed between the generator and the dc link and PWM inverter is connected to the grid [10-16]. The attractive features of this induction generator back-to-back PWM converter systems are ① low harmonic distortion at the generator and grid terminals, ② controllable power factors and ③ PWM rectifier supplies reactive requirement of the generator. However, the drawbacks of the system are ① the PWM converters must be oversized in order to supply the reactive power requirement of the generator, ② complex control strategy which is dependent on machine parameters which vary with temperature and frequency and ③ issues in synchronising with the grid.

So, in this paper, induction generator is proposed to operate in self-excited mode so that the reactive power requirement of the machine is supplied locally through capacitor banks and decoupled from the grid. Thus, the generator can be operated over wide speed range and also the over rating of the power converter can be eliminated. An uncontrolled diode bridge rectifier (DBR) is employed at the generator terminals, which helps in reducing the reactive power burden on the excitation capacitor banks since displacement factor at the uncontrolled rectifier is unity [17,18]. Further, to have the simple control strategy and self-synchronisation with the grid, a line commutated thyristor inverter is proposed to be used at the grid side. The overall schematic of the proposed wind energy conversion system is illustrated in Fig. 2, in which self-excited induction generator (SEIG) is connected to the grid through power converters. In fact, this asynchronous AC-DC-AC power converter has been adopted by Hilloowalla and sharaf [17] for a utility interactive wind energy conversion scheme using a supplementary control loop for MP tracking employing induction generators. Lavanya et al. [18] have used this power converter for connecting the PMA to the grid. Therefore, it is felt that the detailed study of the proposed system gains importance in extracting MP available in the wind by operating it in variable speed mode with simple control strategy and power converter configuration.

It is known that the output voltage and frequency of SEIGs vary with the driving speed, excitation capacitance and load. Extensive literature is available on the analysis of these generators primarily for isolated loads [19-24]. In the present paper, the analysis of such SEIGs connected to the grid through power converters has been attempted and presented. The relevant analytical expressions have been derived for representing the value of grid power at the generator terminals. A simple control strategy has also been proposed for extracting MP available in the wind. The method of analysis and efficacy of the control strategy proposed have been validated with experimental results conducted on a three-phase, 4-pole, 50 Hz, 2.2 kW induction machine with power converters fabricated for this purpose in the laboratory. Starting from the analysis of SEIG, the performance predetermination of the proposed system, the relevant simulated waveforms, and the experimental results are described.

Steady-state analysis of SEIG using GA technique

The analysis of SEIGs can be made under steady state operation using the equivalent circuit demonstrated in Fig. 3, where all the parameters are referred to the rated frequency. In this circuit, all the parameters are assumed to be known, except the magnetizing reactance which varies with the wind speed and the core loss in the machine is neglected. Traditionally, the steady state performance of SEIG is carried out first by writing the loop or nodal equation of the circuit in Fig. 3.

Then, equating the real and reactive parts of the loop impedance or nodal admittance of the circuit to zero, a higher order polynomial is derived with X_m and a as unknown variables. This polynomial is solved by some numerical method for obtaining these unknown values for the given values of b, excitation capacitance and machine and load parameters. Such traditional methods involve derivation of lengthy equations and are time consuming [19-23]. So, in this paper, SEIG has been analysed employing an approach recently suggested in Refs. [24-27] which has been shown to be simple compared to all other earlier methods. In this analysis, the loop impedance expression is taken as such without any further simplification and its absolute value is taken as the objective function. Thus, the objective function to be minimized for obtaining the unknown values a and X_m for the given values of b, excitation capacitance, machine and load parameters is

(1)f(a,X_{\mathrm{m}})=\mathrm{a}\mathrm{b}\mathrm{s}(Z),

where Z=\left\{{\left[{\displaystyle \frac{R}{a}}+jX\right]\Vert }^{el}\left[{\displaystyle \frac{-j{X}_C}{a^{\mathrm{2}}}}\right]\right\}+\left\{{\displaystyle \frac{R_{\mathrm{1}}}{a}}+j{X}_{\mathrm{1}}\right\}+\left\{{j{X}_m\Vert }^{el}\left[{\displaystyle \frac{R_{\mathrm{2}}}{a-b}}+j{X}_{\mathrm{2}}\right]\right\}.

The steps involved in obtaining the values of a and X_m for a given value of b, machine parameters and load parameters had been given in Refs. [24,25]. For the sake of continuity, these steps are presented in the form of flow chart displayed in Fig. 4.

Thus, after arriving at the values of a and X_m for a given b, the induced emf can be determined from the magnetization characteristic of the machine. Then, the load phase voltage (V_p), load current (I_p) and power output (P_e) can be computed from the expressions derived from the equivalent circuit in Fig. 3, which are summarized in Appendix A.

To illustrate the method of analysis of SEIG employing genetic algorithm (GA), a 3-phase, 4-pole, 400 V, 50 Hz (1 p.u. frequency), 2.2 kW, star-connected squirrel-cage induction machine with a 3-phase star-connected capacitor bank of 60 μF per phase was considered. The measured parameters of the generator are R₁ = 3.7 Ω, R₂ = 2.7 Ω, X₁ = X₂ = 3.4 Ω. The (E/a) against X_m characteristics was obtained experimentally at the rated frequency of 50 Hz, following the procedure described in Refs. [23-25] and this relationship was expressed in third order polynomial as

(2)E/a=-\mathrm{0.0003}{X}_{\mathrm{m}}^{\mathrm{3}}+\mathrm{0.0330}{X}_{\mathrm{m}}^{\mathrm{2}}-\mathrm{1.4545}{X}_{\mathrm{m}}+\mathrm{295.53.}

Figure 5 shows the predetermined load performance characteristics of the generator employing the above procedure for resistive load at the generator terminals. Load tests were conducted on the generator. Figure 5 also shows the experimental performance characteristics along with the corresponding predicted results. A separately excited dc motor was used as a prime mover for the experimental purpose. A close agreement between the experimental and predicted values validates the method of analysis of SEIGs using GA technique.

Steady-state analysis of the proposed system

The performance analysis of the proposed system consisting of SEIG, power converters and grid can also be carried out using the simple method described in Section 2. However, for using this method, the grid power should be appropriately reflected at the output terminals of the generator, i.e., the R and X in the equivalent circuit of Fig. 3 should be replaced with equivalent values, R_e and X_e of the proposed system. It is to be noted that, the fundamental displacement angle at the input side of the DBR is zero and so, the value of X_e is zero. Therefore, the loading effect of the grid power at the SEIG terminals will come out to be resistance only.

Equivalence for grid power at generator terminals

For making this derivation, the dc link inductor, L_d is assumed to be lossless and large so that the dc current is constant and continuous. Let it be assumed that the generator terminal voltage, i.e., per phase voltage at the input terminals of the DBR is

(3)v_{\mathrm{p}}=\sqrt{\mathrm{2}}{V}_{\mathrm{p}}\sin \omega t.

The fundamental component of ac input current per phase at DBR is

(4)i_{\mathrm{P}\mathrm{1}}=\sqrt{\mathrm{2}}{I}_{R\mathrm{1}}\sin \omega t.

Then, the power supplied by the generator at the DBR input terminals is

(5)P_{\mathrm{e}}=\mathrm{3}{V}_{\mathrm{p}}{I}_{R\mathrm{1}}.

Thus, the equivalent resistance per phase at the generator terminal is

(6)R_{\mathrm{e}}={\displaystyle \frac{V_{\mathrm{p}}}{I_{\mathrm{R}\mathrm{1}}}}.

The averag voltage at the output of DBR is

(7)V_{\mathrm{d}\mathrm{r}}={\displaystyle \frac{\mathrm{3}\sqrt{\mathrm{6}}}{\mathrm{\pi }}}{V}_{\mathrm{p}}.

The average dc input voltage, the fundamental component of ac current and power factor at the output of line commutated inverter (LCI) are

(8)V_{\mathrm{d}\mathrm{i}}={\displaystyle \frac{\mathrm{3}\sqrt{\mathrm{6}}}{\mathrm{\pi }}}{V}_{\mathrm{g}\mathrm{p}}\cos \alpha ,

(9)I_{\mathrm{g}\mathrm{1}}={\displaystyle \frac{\sqrt{\mathrm{6}}}{\mathrm{\pi }}}{I}_{\mathrm{d}},

(10)\mathrm{P}.\mathrm{F}.={\displaystyle \frac{\mathrm{3}}{\mathrm{\pi }}}\cos \alpha .

The three-phase grid power can be evaluated as

(11)P_{\mathrm{g}}=\mathrm{3}{V}_{\mathrm{g}\mathrm{p}}{I}_{\mathrm{g}\mathrm{1}}\cdot {\displaystyle \frac{\mathrm{3}}{\mathrm{\pi }}}\cos \alpha .

Further, for the lossless dc link inductor V_dr ≈ V_di and using Eqs. (7) and (8), the per phase voltage at the generator terminals can be written as

(12)V_{\mathrm{p}}=V_{\mathrm{g}\mathrm{p}}\cos \alpha .

When the loss in the converter is neglected, the power at the generator terminals is equal to the power at the grid,

P_{\mathrm{g}}=P_{\mathrm{e}},

i.e.,

(13)P_{\mathrm{g}}=\mathrm{3}{V}_{\mathrm{p}}{I}_{\mathrm{R}\mathrm{1}}.

Then using Eqs. (6), (12) and (13), the equivalent resistance at the generator terminals is given by

(14){\mathit{R}}_{\mathrm{e}}={\displaystyle \frac{V_{\mathrm{p}}}{{\mathit{I}}_{\mathrm{R}}}}={\displaystyle \frac{V_{\mathrm{g}\mathrm{p}}\cos \alpha }{{\mathit{P}}_{\mathrm{g}}{\mathit{V}}_{\mathrm{p}}/\mathrm{3}}}={\displaystyle \frac{\mathrm{3}{(V_{\mathrm{g}\mathrm{p}}\cos \alpha )}^{\mathrm{2}}}{P_g}}.

Predetermination of performance

The sequence of steps involved in the predetermination of the performance of the proposed SEIG-converter system for any required value of power at the grid is given in the flowchart of Fig. 6. To illustrate the efficacy of the proposed method of analysis of SEIG connected to the grid through power converters, predetermination has been carried out on the same 3-phase, 4-pole, 400 V, 2.2 kW, star-connected squirrel-cage induction machine considered in Section 2. Figure 7 shows the predetermined performance characteristics of the generator-converter system for supplying required power at the grid. It can be inferred from Fig. 7 that, for the same rotor speed and excitation capacitance, the power supplied to the grid can be varied by only controlling the firing angle, α of the LCI. Further it is seen that the value of R_e and generator terminal voltage increase with grid power.

In the wind energy conversion system, for any given wind velocity, the MP available in the wind can be extracted by appropriately adjusting the rotor speed of the wind turbine so that the power coefficient (C_p) is maintained at the maximum possible value [6-9]. Thus, for MP tracking, the wind turbine has to be operated in variable speed to follow the ideal cube law power curve. To ascertain the working of the proposed system for such maximum power point tracking (MPPT), a predetermination of performance characteristics was made by assuming that the generator delivers 2.2 kW at 1500 r/min. Then, as the speed decreases, the power output from the generator follows ideal cube law power curve as depicted in Fig. 8, which shows the variation of firing angle needed to be set at the LCI to capture the MP available in the wind. In addition, the corresponding generator-converter system characteristics are also given Fig. 8. From Fig. 8, it is revealed that as per cube law power variation, the generator-converter system could work only up to a speed of approximately 1400 r/min for a excitation capacitance of 80 µF/phase. So, to extend the speed for further low values, the excitation capacitance value has to be increased. This has been attempted in this paper. Furthermore, the corresponding predetermined characteristics are given in Fig. 8, too, for three different values of capacitors. Thus, it is seen from Fig. 8 that the proposed system can be satisfactorily continued till the least discernable power output of approximately 600 W with the lowest operating wind speed.

Experimental investigation

To demonstrate the working and usefulness of the proposed system, a three-phase DBR and LCI along with the firing circuits were fabricated in the laboratory. For producing the firing pulses to operate the thyristors in LCI as per the requirement of the grid power and rotor speed, suitable PIC16F876 microcontroller programs were developed. Thus, the SEIG, DBR, LCI and control circuits were set as indicated in Fig. 9, for demonstrating the successful working of the proposed system in the laboratory. Experiments have been conducted on the same 3-phase, 4-pole, 400 V, 50 Hz, 2.2 kW induction machine considered for predetermination and a separately excited DC motor was used as a prime mover for the generator. An inductor of 60 mH has been used in the dc link for reducing the ripple in the dc current. It can be noticed from Fig. 8 that the MP can be extracted by varying only the firing angle of LCI for a given rotor speed and excitation capacitance. So, for each speed, the appropriate firing angle was set to the LCI with the excitation capacitor of 80 µF and 60 µF at the generator terminals. It was observed experimentally that the proposed system delivered the power to the grid as that of the ideal cube law power curve for each speed setting. The experimental results such as stator line voltage and current, dc voltage and firing angle, for various speeds along with predicted values are given in Fig. 8.

A close agreement between the experimental and predicted ones validates the proposed method of analysis for the SEIG connected to the grid through power converters and also confirms its successful working. The experimental waveforms of the generator-converter system were also observed using digital storage oscilloscope. The proposed system was also simulated in Matlab/Simulink using the abc-dq model given in Ref. [28] and a close agreement between the simulated and experimental results has also been noted. For the sake of brevity, the waveforms for one operating point of the generator-converter system obtained experimentally along with the simulated waveforms are given in Fig. 10.

Figure 10 further illustrates the utility of SEIG-converter system for MPPT from wind energy and confirms the expected working of the system. For developing the closed-loop control scheme employing PIC16F876 microcontroller, the value of rotor speed and the corresponding firing angle for extracting MP available in the wind have been stored in the form of look-up table. Of course, in practical application, the rotor speed depends on the wind velocity for the given wind turbine. To check the successful working of this simple closed-loop control scheme for MPPT, the speed of the generator has been varied using the dc motor and it has been noticed that the controller automatically adjusts the firing angle of LCI as per the values stored in the look-up table.

Conclusions

The SEIGs supplying power to the grid through DBR-dc link-LCI has been studied and predetermination of performance of the system has been developed using GA techniques. It is shown that the grid power can be represented in the equivalent circuit of SEIG as an equivalent resistance (R_e) only, since the fundamental component of input current to the DBR is in-phase with the generator terminal voltage. Further, the expression for this equivalent resistance, R_e has been derived in terms of firing angle, α, grid voltage and power. The sequence of the steps involved for the predetermination of performance of the proposed system has been illustrated in the form of flowchart and predicted results are presented.

The MPPT of the proposed system has been shown to be possible by controlling only the firing angle of the LCI for the given rotor speed and excitation capacitor. For this purpose, a microcontroller assembly language program has been developed in the form of look-up table relating rotor speed of the generator and firing angle, α. The experimental results obtained on a 3-phase, 4-pole, 400 V, 50 Hz, squirrel-cage induction machine along with the power converters demonstrate the successful working of the proposed system. The closeness between the experimental and predicted results validates the proposed method of analysis and also the simple control technique for MPPT from such wind-driven SEIG-converter systems.

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