Fuzzy Control Strategy Applied to an Electromagnetic Frequency Regulator in Wind Generation Systems

Abstract

This paper presents the implementation of a fuzzy control strategy for speed regulation of an electromagnetic frequency regulator (EFR) prototype, aiming to eliminate the dependence on knowledge of physical parameters in the most diverse operating conditions. Speed multiplication is one of the most important steps in wind power generation. Gearboxes are generally used for this purpose. However, they have a reduced lifespan and a high failure rate, and are still noise sources. The search for new ways to match the speed (and torque) between the turbine and the generator is an important research area to increase the energy, financial, and environmental efficiency of wind systems. The EFR device is an example of an alternative technology that this team of researchers has proposed. It considers the main advantages of an induction machine with the rotor in a squirrel cage positively. In the first studies, the EFR control strategy consisted of the conventional PID controllers, which have several limitations that are widely discussed in the literature. This strategy also limits the EFR’s performance, considering its entire operating range. The simulation program was developed using the Matlab/Simulink platform, while the experimental results were obtained in the laboratory emulating the EFR-based system. The EFR prototype has 2 poles, a nominal power of 2.2 kW, and a nominal frequency of 60 Hz. Experimental results were presented to validate the efficiency of the proposed control strategy.

1. Introduction

Due to environmental issues, electricity generation systems using wind energy have increased rapidly all over the world. However, the variation in wind speed is the main problem for this type of system. Considering the wide range of wind variations and taking into account that turbine torque and power are very sensitive to such variations (torque varies as the square and power as the cube of wind speed), wind turbines are oversized concerning the energy they actually produce over time, which is characterized by the capacity factor. In addition, the need to expand generation capacity has led to turbines with increasingly larger diameters, which increases the torque produced on the turbine shaft and reduces the permissible speed at the blade tip. Thus, a speed multiplier is used in many of the technologies to match the wind turbine and the electric generator speeds [1].

Currently, speed multipliers are the main cause of noise in wind turbines. In addition, they are the equipment that most require maintenance and replacement in a wind power system [2,3,4] and have a very short lifespan when compared to other elements of a wind generation system [5,6]. On the other hand, conventional wind systems are connected to the electrical power system (EPS) through power electronic devices, which can contribute to the increase of voltage and current harmonic distortion at the point of common coupling (PCC) of the system AC, whose intensity needs to be limited [7]. In order to overcome these limitations, the line of research that deals with the EFR stand out, which is defined as a device consisting of an induction machine with adaptations [8]. Among the main objectives of the EFR are:

• Contribute to the reduction of mechanical impacts that shorten the useful life of the speed multiplier;
• Reduce disturbances in active and reactive power and harmonics caused by connecting electronic converters in the interconnection of wind turbines, photovoltaic systems, or other forms of generation with the electrical grid;
• Provide an alternative for the hybridization of renewable, intermittent energy sources, whose synergy, under adequate dimensioning, allows the generation of firm energy, regardless of the climatic conditions of each moment;
• Enable distributed generation systems from intermittent renewable sources, which can operate in isolation from the electricity grid, ensuring full service to demand with a high level concerning the quality of the energy supplied.

In recent years, some works related to the application and control of the EFR device have been proposed in the literature [8,9,10,11,12,13,14]. In order to increase the reliability and efficiency of the wind generation system, the replacement of the speed multiplied by the EFR was proposed in [8,9,10]. In these works, it was installed between the wind turbine and a synchronous generator connected to the electrical grid. In this case, the main objective was to ensure that the EFR’s rotor shaft, which was mechanically coupled to the rotor shaft of the synchronous generator, had the necessary rotation speed so that the frequency of the voltage generated was compatible with the electrical grid frequency, regardless of the variation in wind speed. The EFR-based system presented a satisfactory performance for a small range of speeds. However, it did not obtain the same performance in more abrupt variations of the speed reference values. In addition, the system behavior for low values of armature speed, in which wind turbines are usually affected (6–20 rpm), was also not evaluated. In [11], a method was proposed to track the maximum wind power extraction point through the control structure associated with the EFR. In this work, unlike the applications found in the literature, the EFR device was used to drive a squirrel-cage induction generator connected to the electrical network. The system presented a satisfactory performance for large variations in wind speed. Furthermore, as the converter has no connection to the grid, this topology proved to be more effective at withstanding a severe short circuit at the induction generator terminals than a conventional doubly-fed induction generator (DFIG) topology. Subsequently, a power quality analysis applied to the wind generation topology discussed in [11] was proposed by [12]. The authors concluded that the high-frequency components of the voltage generated in an EFR-based system are naturally attenuated by the inertia inherent in the EFR-SCIG mechanical system, which results in an advantage compared to DFIG wind generation and permanent magnet synchronous generator (PMSG) topologies.

One application of EFR would be for low-power wind farms. As for the application in small/large systems, it is possible that in particular situations, the use of small systems may dispense with the speed multiplier. Large systems, due to the very high torque and low speed transmitted by the turbine and, on the other hand, the high speed and low torque required by the generator, make the speed multiplier essential; however, there exist operational and useful life advantages.

The control strategy adopted in the works mentioned above was based on a vector control technique that consists of two cascaded control loops, as discussed in [13]. In addition, the control framework employs standard PI-type controllers. However, the controller design was not presented in these works, making it difficult to adjust the control gains to achieve a desired dynamic response. Thus, a design methodology for a vector control strategy applied to EFR was proposed in [14]. The system controllers were designed using the root locus method (RLM) and presented dynamic performance compatible with the desired transient response specifications. However, the controller’s performance was not evaluated for parametric variation of the system. Thus, a system dynamic analysis considering variations in the EFR’s parameters was proposed in [15]. The analysis based on transient and steady-state response specifications showed the varying influence of the EFR device parameters on its dynamic behavior. The authors concluded that large parametric variations could result in degradation in the transient response of the system controllers. Consequently, it is necessary to evaluate the dynamic behavior of the EFR operating with more robust control strategies with parametric variations and system disturbances.

2. System Description

Figure 1 presents the EFR-based system block diagram employed for conducting performance studies. In this configuration, a DC motor is responsible for emulating the kinect energy stored in turbine blades of a wind power system which is then transmitted through the low-speed shaft. DC motor is mechanically coupled to EFR’s armature, and along this connection it is possible to access its armature phases by slip rings that is fed by means of a three-phase voltage source inverter (VSI) with L-filter. The EFR is the speed conversion stage main device and allows torque transmission to the synchronous generator that supplies energy to a three-phase resistive load.

The measurement, supervision and control stage deals with the main system variables such as DC-link voltage (v_bar), EFR’s armature currents (i${}_{S_{abc}}$), DC motor ($\omega$${}_{RA}$) and EFR’s rotor speed ($\omega$${}_R$), and a single-phase voltage (v_g) and current (i_g) absorbed by the resistive load. These data are sent to a LabView supervisory through a digital acquisition device DAQ 6008 and to the control system that is performed by a Texas Instruments TMS320f28335 which runs the control strategy. In the

Table 1. DC Motor Nominal Parameters.

Parameters	Value
Power	1.5 cv
Velocity	1800 rpm
Voltage	180 V
Current	6.0 A

,

Table 2. EFR Nominal Parameters.

Parameters	Value
Nominal Power	3.0 cv
Nominal Speed	3600 rpm
Number of poles	2
Voltage	180 V
Resistance of rotor and armature	2.3 and 2.8 Ohm
rotor and armature reactance	3.7 and 3.9 Ohm
Mutual Inductance	220 mH

and

Table 3. Synchronous Generator Nominal Parameters.

Paramaters	Value
Power	1.0 kW
Velocity	1800 rpm
Number of poles	4
Voltage	180 V
Resistance of rotor and armature	1.7 and 4.1 Ohm
Field Resistance and Reactance	1.1 and 2.8 Ohm
Mutual Inductance	300 mH

, we present the main specifications of the EFR Based system in Figure 1.

A summary of the most important system parameters is given in Table 1, Table 2 and Table 3.

The EFR constructive aspect is depicted in Figure 2. The armature consists of a conventional induction machine stator with adaptations that enables its rotation by a prime mover, represented, in this work, by the DC motor rotor shaft. The electrical contact at coils of this rotor is carried out by means of slip rings, which allow injection and monitoring of the flowing currents through the EFR armature windings. The rotor consists of a squirrel-cage rotor and its rotation is the EFR’s output speed, which in turn drives the synchronous-machine-rotor shaft. The junction and the support of the EFR’s rotor with the synchronous generator rotor are carried out using a coupler and mechanical bearing, respectively. Thus, the rotor is responsible for maintaining the voltage and frequency stability of the power supplied to the resistive load. More information about EFR features are found in [9,10,15].

The armature is powered by a frequency inverter that produces currents that determine the speed of the rotating field, in relation to the fixed reference “F”, presented in Figure 3 as $\stackrel{⟶}{{\omega }_{f_{\_A}}^F}$, which, added to the turbine speed (${\omega }_v$) results in a rotor speed (${\omega }_r$), subtracting the value of the slip (S), following the vector of the rotating field of the synchronous rotor $\stackrel{⟶}{{\omega }_{f_{\_R}}^F}$, in the value of the desired synchronous speed in the generator shaft. If the wind speed is equal to zero, the diagram resembles the operation of a conventional induction machine in [10].

When adding the turbine speed (${\omega }_v$) to the fixed reference axis (F), the armature is displaced, resulting in a new reference axis (RA), rotating at the same speed as the turbine. The vector of the rotating field velocity of the currents injected by the inverter concerning the axis of the asynchronous rotor is called $\stackrel{⟶}{{\omega }_{rf\_RA}^{RA}}$, also illustrated in Figure 3. Although the reference system between the armature and the rotor remains equivalent to that of a conventional induction machine, the relative positioning between the rotor and the fixed reference axis becomes different as the armature undergoes a vector displacement called $\stackrel{⟶}{{\omega }_v^f}$. In this way, it can be observed that the stationary fields between the armature and the rotor are maintained, which is an essential condition for maintaining the electromagnetic torque that moves the synchronous rotor. Analyzing Equation (1), it can be seen that, for zero wind speed, there is the traditional reference system, with the field vector of the asynchronous rotor rotating with speed equal to the vector of the rotating field of the currents injected into it. Thus, the field speed of the asynchronous rotor is equal to the speed of the synchronous rotor.

$$\stackrel{⟶}{{\omega }_{f_{\_R}}^F} = \stackrel{⟶}{{\omega }_{r{f}_{\_R}}^{RA}} + \stackrel{⟶}{{\omega }_v^f}$$

(1)

3. Efr Modeling and Simulation

In this Section 3 the EFR’s model is described, as is a simulation by numerical computation software for later validation.

3.1. Efr’S Dynamic Model

The dynamic model of the EFR device is based on the model of a squirrel-cage rotor induction machine given by:

$$v_{sd}=R_s{i}_{sd}+\frac{d{\lambda }_{sd}}{dt}-{\omega }_s{\lambda }_q$$

(2)

$$v_{sq}=R_s{i}_{sq}+\frac{d{\lambda }_{sq}}{dt}-{\omega }_s{\lambda }_d$$

(3)

$${\lambda }_{sd}=L_s{i}_{sd}+L_m{i}_{rd}$$

(4)

$${\lambda }_{sq}=L_s{i}_{sq}+L_m{i}_{rq}$$

(5)

$$v_{rd}=R_r{i}_{rd}+\frac{d{\lambda }_{rd}}{dt}-({\omega }_s-{\omega }_r){\lambda }_{rq}$$

(6)

$$v_{rq}=R_r{i}_{rq}+\frac{d{\lambda }_{rq}}{dt}-({\omega }_s-{\omega }_r){\lambda }_{rd}$$

(7)

$${\lambda }_{rd}=L_r{i}_{rd}+L_m{i}_{sd}$$

(8)

$${\lambda }_{rq}=L_r{i}_{rq}+L_m{i}_{sq}$$

(9)

The electromagnetic torque is the variable that works as the connecting link between the electrical and mechanical system of the EFR and can be described by the Equation (10). In this Equation (10) can be seen that if $i_{sd}$ is kept at zero, the entire electromagnetic torque can only be obtained by regulating $i_{sq}$.

$$T_{EFR}=p_{efr}({\lambda }_{sd}·i_{sq}-{\lambda }_{sq}·i_{sd})$$

(10)

The Equation (11) describes the EFR’s mechanical behavior, with $J_m$, $F_m$, $T_m$, ${\omega }_r$ being the moment of inertia of the entire mass connected to the rotor, the friction coefficient of the rotor, the resistant torque of the load coupled to the motor shaft and the angular speed of the rotor.

$$J_m\frac{d{\omega }_r}{dt}=T_{EFR}-T_m-F_m{\omega }_r$$

(11)

From the prototype constructive aspect with the EFR, it is known that the armature is free to rotate favorably to the movement of the mechanical driving force emulated by the DC motor. Thus, this movement also has a mechanical behavior, as shown in Equation (12).

$$J_a\frac{d{\omega }_{ra}}{dt}=T_v-T_{EFR}-F_a{\omega }_{ra}$$

(12)

where $J_a$, $F_a$, $T_v$, ${\omega }_{ra}$ represent the inertia moment in the entire connected mass to the armature, the friction coefficient of armature, conjugate imposed by the wind emulation, and the angular velocity of armature. The Equations (11) and (12) demonstrate that $T_{EFR}$ performs as the intermediate between the speeds of rotor and armature.

3.2. Model Simulation Validation

For validation through simulation, the Simulink/Matlab software is used. Initially, the induction machine model is implemented traditionally by the Equations (2) to (11). However, incorporating the mechanical behavior of the armature into the model generates an alteration that deserves to be mentioned. The synchronous speed depends only on the frequency of the voltages applied to the machine armature. Thus, the armature angular speed perturbs this variable, increasing or decreasing the rotor’s liquid field. So, for this effect to be perceived by the rotor, the block diagram, illustrated in Figure 4, is inserted in the induction machine model code. Another change concerns the Equations (2), (3), (6) and (7), which instead of receiving ${\omega }_s$ directly, now get ${\omega }_{sa}$ on input of its blocks, which represents the angular speed resulting from the sum of ${\omega }_{ra}$ and ${\omega }_s$.

Thus, in order to approximate the simulation to the real scenario with the EFR, an induction machine with the same rated power as the EFR and with similar dimensions is used. The main simulation specifications are summarized in

Table 4. Specifications for the simulation of the EFR elementary model.

Parameter	Value
Poles number ($P_{efr}$)	2
Rotor resistance ($R_r$)	6 Ω
Armature resistance ($R_s$)	6 Ω
Armature inductance ($L_s$)	30 mH
Rotor inductance ($L_r$)	30 mH
Mutual coupling inductance ($L_m$)	500 mH
Nominal Power (P)	2.0 kW
Nominal Voltage ($V_L$)	380 V
Nominal Current ( $I_f$ )	2.8 A
Nominal frequency	60 Hz
Nominal Velocity	1740 rpm
Inertia Moment (Rotor+Generator) ($J_m$)	0.02 kg·m
Inertia Moment (Armature+Turbine) ($J_a$)	0.978 kg·m
Friction coefficient (Rotor+Generator) ($F_m$)	0.003 N·m/rad·s
Friction coefficient (Rotor+Turbine) ($F_a$)	9.0 N·m/rad·s

.

The test for the elementary model validation consists of a direct start of the machine for an analysis period of 5 s, and the results is shown in Figure 5. There is no velocity regulation in this simulated scenario. The rotor speed reaches the nominal value after 0.7 s has elapsed, as illustrated in Figure 5a, while no torque value $T_v$ is imposed on the model, as shown in to Figure 5b. Under these conditions, the EFR’s model behaves like a traditional induction motor, with armature inrush currents that reach almost five times the rated current value and with reduced rotor currents for the nominal slip at no load, as shown in Figure 5c,d.

After 2.0 s, the wind emulator starts with a torque $T_v$ equivalent to 300 N. Under these conditions, the resulting armature speed reaches 164.5 rpm. This velocity is transferred to the rotor motion, even with the main frequency maintained at 60 Hz. Another interesting outcome is the effective reduction in current consumed by the armature from 2.819 A to 2.653 A, as illustrated in Figure 5d. Meanwhile, the rotor suffers from the synchronous speed increase and the speed of the armature, as the amplitude of the current signals of rotor. Here, it is possible to manage the system’s power flow with EFR. As of 3.0 s, a constant torque load equivalent to 5 N·m is entered in the rotor. With this disturbance in the system, it is possible to see that the model remains functional, as it manages to overcome the resistant conjugate with the increase of currents from rotor and armature. There is also a reduction in rotor speed at 45 rpm, which causes an increase in the EFR’s slip.

4. Control Strategy

In section is presented aspects related to the EFR-based system control, together with the detailing of the main contribution to speed regulation.

4.1. Rotor Flux Oriented Control (Foc)

The control strategy initially proposed by [9] consists of an adaptation of the FOC and is illustrated in Figure 6. The estimation of the rotor flux is important to obtain the rotor angle ($\rho$) that is necessary for the decoupling of the variables that influence the rotor flux ($i_{sd}$) and also the conjugate ($i_{sq}$). From these variables, current controllers $R_{id}$(s) and $R_{iq}$(s) were used, which initially employ PI-type controllers. These controllers determine the reference voltages (${v_f^{*}}_{abc}$) that should be applied to the VSI via PWM modulation.

With the measurement of mechanical velocity ($\omega$), it is possible to elaborate a control loop responsible for determining the reference torque from the quadrature-axis current (${i_{sq}^{*}}_{efr}$), which is necessary for the system energy balance, which is guaranteed using a speed regulator ($R_{\omega }$) of the PI controller. Due to its direct relationship with the quadrature-axis current, as already determined by [13], the reference current (${i_{sq}^{*}}_{efr}$) plays an important role in the transmission of energy by the EFR through the conjugate ($T_{EFR}$) see in Equation (10).

It is necessary to adopt a suitable rotor flux for system operation without considerable vibrations and minimal heating losses. This flux regulation is performed by a PI controller $R_{\varphi }$(s) that acts on the direct-axis current (${i_{sd}^{*}}_{efr}$). The dimensioning of controller gains used for the conventional regulation follows the procedures proposed in [13].

4.2. Fuzzy Control Implementation

An essential contribution of this article is the regulation of speed and torque through a Sugeno model Fuzzy-PI controller replacing the PI controller, adopted by [9]. The schematic diagram of the proposed fuzzy speed control is illustrated in Figure 7. A fuzzy controller requires knowledge of the error signal and also the error variation to determine the control signal, which must be integrated to represent the reference stream (${i_{sq}^{*}}_{efr}$ ).

The gains tuning associated with the fuzzy controller was performed according to the procedures available in the works of [16,17]. This controller considered three triangular membership functions for the error signal with the following linguistic variables: Negative Error—EN; Zero Error—EZ; Positive Error—EP. In Figure 8, the literal intervals of relevance function to the speed error as a function of its respective universe of discourse. In the figure on screen, the axis that represents the discourse universe is not on a linear scale. For the error derivative, were used three triangular membership functions with the following nomenclatures: Negative Derivative—DN; Derivative Zero—DZ; and Positive Derivative—DP, because in the analysis of the derivative, it is only necessary to evaluate if it increases, remains constant or decreases and, with that, know if the signal is moving away from or approaching the reference. Figure 9 illustrates the ranges of membership functions for the derivative of the velocity error. Once again, the axis that represents the discourse universe is not on a linear scale.

The range used for error signals depends on the imposed reference value to speed control and may consider the possibility of the EFRs operating in both rotation directions with nominal values. As for the error variation of velocity, the polarity of the variation measured by the acquisition system was considered data. Based on this organization, the ranges of membership functions are summarized in the

Table 5. Parameters of Membership Functions $e_w$ and $d{e}_w$.

FP	Parameter	Value	Parameter	Value	Parameter	Value
EN	$a_1$	$-2{\omega }_{efr}^{*}$	$b_1$	$-{\omega }_{efr}^{*}$	$c_1$	$-0.01{\omega }_{efr}^{*}$
EP	$a_2$	$-0.01{\omega }_{efr}^{*}$	$b_2$	${\omega }_{efr}^{*}$	$c_2$	$2{\omega }_{efr}^{*}$
EZ	$a_3$	$-0.5{\omega }_{efr}^{*}$	$b_3$	0.0	$c_3$	$0.5{\omega }_{efr}^{*}$
DN	$a_4$	−1000	$b_4$	−0.00001	$c_4$	0.0
DP	$a_5$	0.0	$b_5$	0.00001	$c_5$	1000
DZ	$a_6$	−0.0003	$b_6$	0.0	$c_6$	0.0003

.

After implementing the controller inputs, it was necessary to design the functions output suggestion for each of the angles, as illustrated in the

Table 6. Fuzzy rules framework for EFR speed regulation.

	${\mathit{e}}_{\mathit{\omega }}$	EN	EZ	EP
${\mathit{de}}_{\mathit{\omega }}$
DN		$S_1$	$S_2$	$S_3$
DZ		$S_4$	$S_5$	$S_6$
DP		$S_7$	$S_8$	$S_9$

. The rules of inference implemented follow the Equation (13), with n = 1, 2, …, 9:

$$S_n=K_{pn}·d{e}_w+K_{in}·e_w+H_0$$

(13)

where $H_0$ is a homopolar component that can be inserted into the control to compensate for offset values, with $H_0=0$. Thus, the rules of inference implemented follow the Equation (14), with n = 1, 2, …, 9:

$$S_n=K_{pn}·d{e}_{\omega }+K_{in}·e_{\omega }$$

(14)

Based on Table 5 and the Equation (13) were obtained $S_1,S_2,S_3,S_4,S_5,S_6,S_7,S_8$ and $S_9$ described in the Table 6. Thus, the fuzzification process is represented by the two inputs ($e_w$ and $d{e}_w$) and respective rules and the defuzzification process is represented by the output with the values obtained in $S_1,S_2,S_3,S_4,S_5,S_6,S_7,S_8$ and $S_9$.

In this Section 4, the control characteristics of the generation prototype of wind energy developed in laboratory elucidate the application of the fuzzy controller in the system speed regulation. In addition, the tuning procedure was described in the above-mentioned controller.

5. Experimental Results

The EFR-based system prototype evaluation using the control strategies described in the section is based on the transient and steady-state performance analysis for different operating scenarios. In this section, the details of the tests carried out are described. In addition, the experimental results for each oprational scenario are discussed and a comparative analysis between employed control strategies is presented.

5.1. Description of Operation Scenarios

In this work, the operating scenarios are characterized by synchronous generator mode traction, which can be both no-load and loaded. Both discuss the main differences in performance based on the control strategy adopted. In the first scenario, the generator electrical terminals are disconnected from any element that consumes electrical energy and, therefore, there is no relevant value of current or power electrical system that requires evaluation. In this scenario, power is expressive only during start-up, as the drive system must overcome the inertia of an equivalent mass to the sum of the EFR’s rotor and the synchronous generator rotor individual masses. In the EFR’s rotor and the synchronous generator rotor individual masses scenario, two resistors are connected in parallel to each phase of the synchronous generator so that the power to be consumed can exceed 200 W per phase, depending on the field winding excitation circuit. In addition, the equivalent mass of the rotating parts together with the resistive load connected to the synchronous generator terminals gives rise to a counter-conjugate, proportional to the excitation current $I_f$ in the synchronous generator rotor shaft, which must be compensated for by the EFR’s drive system. For this study, the load is kept constant throughout all scenarios operating under load.

The set of technical specifications for the operating conditions of the EFR-based system prototype analyzed in this EFR-based system is summarized in

Table 7. Technical specifications for the operating scenarios.

Parameter	Value
DC motor power range	$v_{cc}$ = 0–50 V, $i_{cc}$ = 0–6 A
VSI DC bus voltage	$v_{bar}$ = 100 V
DC-link capacitors	C = 4700 μF
Filter inductors L	lc = 500 μF
EFR magnetizing inductance	$l_m$ = 0.22 H
Voltage in the generator field winding	$v_f$ = 0–7.0 V
Current in the generator field winding	$i_f$ = 0–4.5 A
DAQ—electrical signal sampling	1 kHz
DAQ—mechanical velocity signal sampling	5 Hz
Resistive load per phase	$P_r$ = 200 ohms per phase

.

5.2. Empty Synchronous Generator Traction

5.2.1. Open-Loop Speed Regulation

The open-loop system dynamic performance is presented in Figure 10. Initially, a reference voltage with a frequency equal to 15 Hz is imposed on the EFR’s armature terminals causing its rotor to reach a speed of approximately 932 rpm at t = 4 s as shown in Figure 10a. At instant ${\tau }_1$, the synchronous generator field circuit is supplied with $v_f$ = $7.0$ V and $i_f$ = $4.5$ A, which results in rms empty voltages equal to 105 V per phase, as illustrated in Figure 10b. In this case, since the synchronous generator has 4 poles, the empty voltages frequency is equal to approximately 31 Hz, which represents half of its nominal value. Due to the counter-conjugate generated after powering the generator field winding, EFR’s rotor speed is subjected to a small deceleration, as illustrated in Figure 10a. At the instant ${\tau }_2$, the DC motor is gradually activated to reach a speed equal to 310.4 rpm. This speed is imposed on the EFR’s armature mass as illustrated in Figure 10c, which results in the EFR’s rotor speed increasing to 1224 rpm.

After stabilizing the armature speed at a value close to 30% of rotor speed, the voltages available at the synchronous generator terminals have a value effective and electrical frequency equivalent to 138 V and 40.8 Hz, respectively, which represent an increase of 21% and 31.6%, respectively, with the initial performance. Thus, the increase in rotor speed is proportional to the speed imposed on the armature mass. This essay describes the operation principle of the EFR device, since the amplitude and frequency of the generated voltage depend both on the voltage at the armature terminals and on the rotation speed of the armature mass. However, due to the amplitude and frequency variation of the voltage at the synchronous generator output terminals, the operation of the EFR-based system in open-loop is not feasible in practice, since the electrical loads connected to the generator as well as the power grid, requires a voltage with constant amplitude and frequency.

5.2.2. Speed Regulation by Foc Control

The amplitude and frequency stability of the synchronous generator output voltage is only possible by regulating the EFR’s rotor speed. For this purpose, rotor-flux-oriented control is performed as discussed in the Section 4. The controller gains employed in the current, flux and speed control loops are summarized in

Table 8. Current regulator parameters in the synchronous reference $R_{\mathit{i}\mathit{d}\mathit{q}}\left(s\right)$.

Parameters ${\mathit{R}}_{\mathit{idq}}\left(s\right)$
$k_{p_{id}}$	25.0	$k_{p_{iq}}$	60.0
$k_{i_{id}}$	20.0	$k_{i_{iq}}$	25.0

,

Table 9. Rotor flux regulator parameters $R_{\varphi }\left(s\right)$.

Parameters ${\mathit{R}}_{\mathit{\varphi }}\left(\mathit{s}\right)$
${\varphi }_{efr}^{*}$	0.8 $W_b$
$k_{p_{\varphi }}$	3.0
$k_{i_{\varphi }}$	3.5

and

Table 10. Speed regulation parameters $R_{\omega }\left(s\right)$.

Parameters ${\mathit{R}}_{\mathit{\omega }}\left(\mathit{s}\right)$
${\omega }_{efr}^{*}$	1800 rpm
$k_{p_{\omega }}$	1.3
$k_{i_{\omega }}$	2.0

respectively. The criteria adopted for generator traction at no load were a settling time ($T_s$ 2%) less than or equal to 15 s and a percent overshoot (${\mu }_p$) less than or equal to 5%. The dimensioning of the controller gains goes through a process of fine-tuning to compensate the nonlinearities and non-modeled dynamic of the system.

Figure 11 shows the rotor-flux-oriented control based speed regulation dynamic performance. According to Figure 11a, a 1800 rpm step-type reference signal results to a speed controller transient response with settling time and percent overshoot approximately equal to 23 s and 7.53%, respectively, which corresponds to a peak value approximately equal to 1935.5 rpm. On the other hand, steady-state error is equal to 0.078%, which can be considered null. Therefore, despite the rotor speed accurately tracking its reference value, the transient response does not match the desired performance criteria. This can be explained by the PI controller negative phase contribution characteristic, which tends to degrade the system transient response. The speed controller transient performance is reflected in the dynamic behavior of voltages at the synchronous generator output terminals, as shown in Figure 11b, which can damage the electrical loads connected to the generator. Figure 11c shows a DC motor speed variation that drives the EFR’s armature. For the evaluated period, two speed profiles with 400 and 800 rpm are imposed on the armature. The rotor-flux-oriented control based speed regulation keeps the EFR’s rotor speed constant during armature speed variations, which contributes to steady-state stability of the synchronous generator output voltage.

5.2.3. Speed Regulation by Fuzzy Control

The experimental validation of the Fuzzy controller dynamic performance is performed using a test similar to the applied to rotor-flux-oriented control.The desired performance criteria are also the same, that is, ${\mu }_p \le 5$% and $T_{s}2$%$\le 15$ s. In this experiment, the field circuit of the synchronous generator is fed with $v_f$ = 5.9 V and $i_f$ = 3.6 A. The gains associated with the inference rules defined in (14) are summarized in the

Table 11. Fuzzy controller gains after empirical adequacy.

$K_{p_{1,2,3}}$	$0.2$	$K_{p_{4,5,6}}$	$0.7$	$K_{p_7}$	$2.5$	$K_{p_8}$	$2.9$	$K_{p_9}$	$2.5$
$K_{i_{1,2,3}}$	$0.5$	$K_{i_{4,5,6}}$	$1.1$	$K_{i_7}$	$8.0$	$K_{i_8}$	$12.5$	$K_{i_9}$	$4.0$

, with $H_0=0$. Although tuning the fuzzy controller need not take taking into account specific parameters of the system model, the speed controller gains employed in the rotor-flux-oriented control based speed regulation were used as a starting point for the adjustment of the fuzzy controller gains. After some initial tests, it was empirically found that much smaller gains than those employed in the rotor flow-oriented control strategy were sufficient to achieve the desired dynamic performance. Therefore, the tuning of the fuzzy controller was performed with these smaller gains listed in Table 11.

Figure 12 shows the fuzzy control based speed regulation dynamic performance. According to Figure 12a, for the same speed step of 1800 rpm, the speed control transient response presents settling time approximately equal to 4 s, which meets the desired performance criterion. Contrary to what is expected for a reduction of ts with speed regulation based on a PI controller, the transient response of the speed regulation using the fuzzy controller does not present a percent overshoot and stabilizes at an average value of 1794.2 rpm, which results in a negligible steady-state error of 0.32%. The absence of percent overshoot in the fuzzy based rotor speed control makes the EFR start-up smooth, which contributes to synchronous generator terminal voltages without any level of transient over voltage, as shown in Figure 12b. Furthermore, according to Figure 12a, the Fuzzy controller was able to keep the rotor speed constant during EFR’s armature speed variations illustrated in Figure 12c.

5.2.4. Performance Indices

According to [18], the performance index is a measure quantitative performance of the system and chosen in such a way that it emphasizes specifications system important. In [18] propose the use of the performance index is the integral absolute error IAE, Integral of the Absolute magnitude of the Error), which is defined by:

$$IAE={\int }_0^T\left|e\left(t\right)\right|dt$$

(15)

To avoid the influence of a large input error signal during systems with a step reference. In [18] propose the use of the index of the integral time multiplied by absolute error (ITAE) defined by:

$$ITAE={\int }_0^{T}t\left|e\left(t\right)\right|dt$$

(16)

The ITAE provides better selectivity of performance indices, as the value minimum of the integral is easily distinguished while the system parameters are changed.

5.2.5. Comparison of Control Strategies through Performance Indicators

For the graphical analysis and the analysis of transient regime parameters, the indices controller performance are evaluated in accordance with Equations (15) and (16) in Section 5.2.4. The indices values calculated in the synchronous generator traction empty scenario, with both closed-loop control strategies, are summarized in

Table 12. Comparison of performance indicators for control strategies.

Indicator	Conventional	Fuzzy	Reduction (%)
IAE	9.5084 × 104	5.8363 × 104	38.60
ITAE	7.4050 × 105	4.2112 × 105	43.13

.

According to Table 12, the conventional speed regulation obtained higher values for the accumulated error and for the error in relation to the time when compared to fuzzy regulation indices. The absence of overshoot, together with the reduced $T_s$ due to fuzzy control, causes a reduction average of 43.13% of the performance indicators in relation to the conventional control.

5.3. Synchronous Generator Traction under Load

For evaluating the power flow of the power generation prototype based on the EFR, the two closed-loop control strategies are used for the traction of the synchronous generator when it supplies constant power to the resistive load of 200 W per phase. Under these conditions, the field circuit of the synchronous generator is driven with $v_f$ = $3.15$ V and $i_f$ = $1.79$ A. The operating point chosen for the analysis had to change. Based on a test build, the operating speed of the synchronous generator has been reduced to 1200 rpm. Furthermore, for the purposes of this analysis, only the steady-state will be considered for the following calculations. In these operating scenarios, the influences of the armature speed variation through driving force were emulated by the DC motor.

5.3.1. Velocity Regulation by Foc Control

For the evaluation of the electrical power transfer performance of the prototype with conventional rotor speed regulation, a test of 280 s is illustrated in Figure 13. The controller gains are the same as used in Section 5.2.2. The armature speed variation is performed in four distinct sectors identified by A, B, C and D, with values of 300, 580, 860 and 1080 rpm, respectively, and can be observed in Figure 13a. A detailed exploration of sector A is carried out based on the Figure 13b–g. The voltages and electrical currents supplied by the VSI to the EFR can be observed in Figure 13b,c, respectively. The profile of voltages and currents supplied by the synchronous generator to the resistive load can be analyzed in Figure 13d,e, respectively. Again, with operation at a speed value far from the rated value, the maximum voltages generated are also lower than expected for the rated performance of the synchronous generator, with maximum values, on average, of 100 V per phase. With the objective of mitigating the influences of oscillations arising from the speed variation imposed on the armature, the evaluation of the power flow is carried out in a period of 10 s, as illustrated in Figure 13f. In this figure, there are the active power curves involved in the system elements. Throughout the analysis, it is possible to observe an average power of approximately 1.0 kW consumed by the EFR, from 600 W by the resistive load, while the DC motor provides something over 300 W to armature. It is worth noting that the active power consumed by the EFR is measured at the output of the three-phase VSI and therefore does not represent the mechanical power available at the tip of the rotor axis. For power flow assessment, the two driving forces emulated by the DC motor and the VSI that powers the EFR are considered positive power flow. On the other hand, resistive load consumption is defined as a negative power flow in the energy balance equation.

System efficiency is estimated based on the percentage of available power at the system’s output in relation to the amount of input power and is illustrated in Figure 13f with the EFR power factor in the same period considered for Figure 13g. The system efficiency reaches an average value of 43.1% in the evaluated period, while the power factor reaches a value of 0.894 inductive. Therefore, the existence of a factor more powerless than unity occurs due to the EFR synchronous field maintenance.

5.3.2. Power Flow Analysis with Fuzzy Speed Regulation

For the evaluation of the electrical power transfer performance of the prototype with rotor speed Fuzzy regulation, a slightly shorter test is analyzed, totalling 120 s, and is illustrated in Figure 14. The associated gains of the Fuzzy controller are the same as those used in the Section 5.2.3, and the generator excitation circuit synchronous remains unchanged. For this test, the armature speed variation follows the same sectoral profile defined previously and can be seen in Figure 14a, with a specific detail of sector A that is illustrated in the Figure 14b–g. The voltages and electrical currents supplied by the VSI to the EFR can be observed in the Figure 14b,c, respectively. Due to the constructive aspects of the EFR, an average RMS value per voltage phase and current of 58.0 V and 13.0 A were reported, respectively, which are very similar values to those obtained for conventional speed regulation. The profile of voltages and currents supplied by the synchronous generator to the resistive load can be analyzed in Figure 14d,e, respectively. For the operation of EFR’s rotor with a speed value lower than the rated value, the maximum voltages generated are also lower than expected for the nominal performance of the synchronous generator, with maximum values, on average, of 99 V per phase. With the objective of mitigating the influences of oscillations arising from the speed variation imposed on the armature, the evaluation of the power flow is carried out in a period of consecutive 5 s, as illustrated in Figure 14f. Over the evaluation time, it is possible to observe an average power slightly less than 1.0 kW consumed by the EFR, of 600 W by the resistive load, while the DC motor provides, on average, 330 W to the armature. The efficiency of the system is illustrated in Figure 14g together with the power factor of the EFR in the same period considered for the analysis of the individual powers of Figure 14f.

The system efficiency reaches an average value of 44.0% in the evaluated period, while the power factor reaches the value of 0.877 inductive. Thus, there is an increase in 0.9% concerning the average efficiency obtained by conventional speed regulation and a reduction in the magnitude of the power factor, still inductive, by 0.017.

6. Conclusions

This article proposed new contributions to the control strategy applied to the power generation prototype based on EFR. Computer simulations were proposed using the models of induction machines, which are widely known in the scientific community. To better identify the operating ranges of the prototype, several tests were undertaken with load variation on the synchronous generator and wind emulation. In the experimental scenarios, the fuzzy controller was compared with the conventional controller, proposed together with the creation of the EFR. In scenarios where the generator is idle, the speed regulation by the fuzzy controller presents the best performance in the transient regime compared to the conventional regulation. The gains associated with the fuzzy controller to obtain better performance are lower than those imposed by conventional regulation based on the PI controller. The fuzzy controller presented a regime error four times higher than the PI controllers for steady state. However, this is not a dissadvantage the fuzzy due to the magnitudes of the errors obtained. An error of 0.32% can be considered zero for this application. Furthermore, for evaluating the controllers, there was a significant reduction in the IAE and ITAE indicators for fuzzy speed regulation. Thus, fuzzy regulation presents better applicability to the prototype concerning the current speed regulation. From the power flow point of view, the prototype’s efficiency presents a tendency for efficiencies to decrease as the armature and rotor speed match. However, for the tests evaluated, the fuzzy regulation presented the advantage of providing a less accentuated reduction, characterizing robustness with the velocity multiplication compared to the conventional controller.

Based on the results obtained in this study and on the limitations found in the prototype generation with the EFR, the following proposals for future works are suggested: (1) Undertaking studies in the sizing of machines to obtain an optimization via the good choice of the numbers of poles of the EFR and the generator; (2) Making a new generation prototype based on the new version of the EFR, with the necessary mechanical corrections; (3) Improvement of the fuzzy controller used, with greater quantity and profiles of membership functions being applied; (4) Implementing a flux-slip-based control strategies rotor; (5) Implementing control strategies that guarantee operation with a factor of the EFR’s nominal power.