A Soft Start Method for Doubly Fed Induction Machines Based on Synchronization with the Power System at Standstill Conditions

Abstract

Due to their exceptional operational versatility, doubly fed induction machines (DFIM) are widely employed in power systems comprising variable renewable energy-based electrical generation sources, such as wind farms and pumped-storage hydropower plants. However, their starting and grid synchronization methods require numerous maneuvers or additional components, making the process challenging. In this paper, a soft start method for DFIM, inspired by the traditional synchronization method of synchronous machines, is proposed. This method involves matching the frequencies, voltages, and phase angles on both sides of the main circuit breaker, by adjusting the excitation through the controlled power converter at standstill conditions. Once synchronization is achieved, the frequency is gradually reduced to the rated operational levels. This straightforward starting method effectively suppresses large inrush currents and voltage sags. The proposed method has been validated through computer simulations and experimental tests, yielding satisfactory results.

1. Introduction

Addressing environmental challenges is one of the foremost issues in today’s world. They are inherently tied to the adoption of cleaner energy sources for electrical power generation [1,2]. In this regard, wind power and hydropower generation are among the most extensively adopted renewable energy sources worldwide, due to their abundant availability, scalability, and relatively low environmental impact.

In the realm of wind power generation [3,4], doubly fed induction machines (DFIM) technology remains the most widely implemented, as part of the notably known Type-III wind energy conversion systems. Similarly, DFIMs are also predominantly utilized in pumped storage hydropower plants [5,6,7,8,9,10,11,12], where water is pumped or turbined based on demand requirements.

DFIMs play a crucial role in integrating variable renewable energy into the grid [13,14,15], ensuring voltage and frequency controls under varying primary energy inputs, according to applicable regulations. Designed for adjustable speed operation, DFIM systems offer numerous operational advantages, including high energy yield, reduced mechanical stress, low power output fluctuations, and precise control over both active and reactive power.

Typically, DFIM systems are directly grid-connected, featuring a reduced-power converter [16] connected to the rotor that operates at variable frequency. This configuration facilitates the straightforward adjustment of the DFIM’s operating point, to accommodate varying primary energy inputs.

Despite the aforementioned benefits, DFIMs also present certain drawbacks [17,18,19]: being directly grid-connected, they exhibit high sensitivity to external grid faults or disturbances. Additionally, they require regular maintenance due to the wear and tear of slip rings and brushes, and in the case of wind turbines, gearbox maintenance also becomes necessary.

Another significant limitation of DFIMs is their start-up process, extensively addressed in the literature [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. Most of the proposed approaches involve additional elements such as auxiliary power converters and switches to adjust DFIM conditions to the grid, necessitating multiple maneuvers during the start-up process. Consequently, this complexity not only challenges the start-up procedure but also increases the overall cost of electric generation units.

This paper proposes a soft start-up method for DFIMs, based on the synchronization with the power system at standstill conditions. This approach simplifies DFIM starting and eliminates the need for additional components. Analogous to the paralleling of synchronous generators, this technique primarily involves aligning DFIM conditions with those of the grid, and, once achieved, synchronizing with the grid by closing the main circuit breaker (CB) at standstill conditions. Subsequently, using the rotor’s power converter for voltage and frequency control, the machine accelerates to operating speed. This procedure mitigates inrush currents and voltage sags while reducing the complexity of maneuvers and devices required during the start-up process.

This paper is structured as follows: Section 2 provides a brief overview of DFIM start-up procedures. Section 3 describes the proposed start-up method in detail. Section 4 presents computer simulation results for a DFIM start-up using the proposed method. Section 5 reports experimental test results under the same conditions as the simulations, with a discussion of the obtained results. Finally, Section 6 concludes the paper by summarizing its main ideas and contributions.

2. State of the Art

The approaches to DFIM start-up have been classified into four main groups. The main advantages and drawbacks of each of them are summarized in

Table 1. DFIM start-up methods: state of the art sum-up.

Start-Up Type	Method	References	Advantages	Disadvantages
Opposite phase sequence-based		[20]	✓ Fast start-up	× High oscillation torque and high torsional forces in the shaft
Reduced voltage-based	With autotransformer	[21,22]	✓ Partial winding start-up and smoother than other methods	× Slow start-up × Additional autoransformer and rotor resistances to start the machine are required
	Stator short-circuited	[23,24,25,26,27,28,29,30,31,32,33,34,35,36]	✓ Lower power losses in the start-up than other methods ✓ Acceptable soft start-up	× High power commutation switch to support the stator short-circuit currents is needed × Reduced starting torque
	Rotor short-circuited	[23,26,37]	✓ Fast DFIM start-up compared to other methods	× The power converter must be able to carry the DFIM up to its rated speed by feeding the stator (it can increase the converter rated power) × High power commutation switch to support the rotor short-circuit currents is needed
Auxiliary converter-based		[32,38,39]	✓ Soft start-up of the machine ✓ Auxiliary converters can be used for power enhancement in case of low load ✓ Synchronization in DC is simpler than in 3-phase AC	× Additional power electronic devices and switches required
Proposed start-up			✓ Simple to execute ✓ No additional devices needed ✓ Soft start with no torque pulses and low inrush currents	× Slow start-up as a consequence of the soft start-up

. In the following, the categories are described based on Figure 1.

2.1. Opposite Phase Sequence-Based Start-Up Methods

In these methods, the excitation power converter placed in the rotor of the DFIM and an additional switch (S1, initially closed) is utilized, as illustrated in Figure 1a. The start-up procedure involves feeding both the stator and the rotor of the DFIM through the power converter, with two phases swapped at the connection between the stator and the rotor using S1. Under these conditions, the machine is driven to its rated speed. Then, S1 is opened and the CB connecting the DFIM stator to the power system is closed.

The main advantage of this method is its short starting time [20]. However, the dead time during the commutation between S1 and the CB can induce pulsed torques that may severely damage the machine shaft if synchronization is not achieved shortly after the opening of S1. In [20], these pulsed torques are examined and compared with other methods.

2.2. Reduced Voltage-Based Start-Up Methods

There are various methods to perform a DFIM start-up at low voltage. One approach uses an autotransformer (AT) connected to the stator terminals and a variable resistor (R_var) in the rotor terminals [21], as shown in Figure 1b. Consequently, two additional switches (S2 and S3, initially closed) are needed to connect and disconnect these elements. The variable resistor enables a progressive start-up. When the motor reaches approximately 95% of its rated speed [22], S2 is disconnected. At this point, the AT functions as a current limiter. Simultaneously, S3 is opened, and S1 is closed, feeding the rotor through the power converter. Finally, the CB is connected, bypassing the AT.

Other techniques rely on the converter to control the variable speed drive, to achieve reduced voltage-based start-up without the need of the AT and the variable resistor [23]. One of the techniques for starting a DFIM at low voltage involves short-circuiting the stator winding [24,25,26,27,28,29,30,31,32,33,34]. This technique is most commonly used for large generator units due to its low pulsed torques and currents. Figure 1c shows the electrical circuit for a stator short-circuit start-up. Only one additional switch (S1, initially closed) is required to perform the short-circuit. First, the rotor converter increases the rotor frequency (f_r) up to the rated frequency. Once the DFIM reaches its rated speed, S1 is opened, and after meeting the synchronization conditions, the CB is closed. With this start-up method, the power converter must supply the rotor with a voltage proportional to f_r and reduce the voltage as the frequency decreases (constant V/Hz ratio) [24,25]. This ensures that the air gap flux remains constant [24,25,26].

Additionally, the stator short-circuit approach requires fast switching between S1 and the CB, e.g., in [28] this process occurs in 40 ms. Otherwise, the machine and grid conditions may differ significantly, leading to an abrupt grid connection. Several variants of stator short-circuit start-ups exist: using Field Oriented Control (FOC) to accelerate the machine [28,29,30,31,32], applying maximum torque start-up [33], or implementing power loss reduction techniques [34,35]. The dynamic behavior of this approach under converter and sensor faults has also been addressed in previous works [36].

Similarly, the short-circuit can be applied to the rotor winding [23]. In this case, the power converter feeds the stator through an additional switch. The start-up is conducted as if the machine were an ordinary squirrel-cage induction machine-based variable frequency drive. Once synchronization with the grid is achieved, the power converter is disconnected from the stator, which is then fed directly from the grid, and subsequently connected to the rotor [26]. Improvements such as FOC can also be applied in this case [37].

2.3. Auxiliary Converter-Based Start-Up Methods

Auxiliary converter-based start-up methods are softer than the previously presented alternatives, but they require additional electronic devices [32,38,39].

In [38], an auxiliary power converter is installed at the stator terminals to initiate the DFIM operation. The electrical scheme is shown in Figure 1d. Initially, S1, S2, and S3 are closed, allowing the auxiliary converter to feed the stator at the rated frequency. The converter also supplies the rotor to achieve the required rotor speed. Once the operational point is set, the CB is closed under proper synchronization conditions of voltage, frequency, and phase, while the auxiliary power converter remains bypassed. At this point, S2 and S3 are opened, concluding the start-up process. Meanwhile, in [32], the DC bus of the rotor power converter feeds with an additional inverter the machine in the stator and rotor at the same time.

The use of DC/DC converters in the main rotor power converter is another option for synchronizing the machine [39]. When both sides of the DC bus have the same voltage, the DC bus is closed, connecting the grid side converter (GSC) with the rotor side converter (RSC).

2.4. Proposed Start-Up Methods

It is worth noting that all the previously discussed methods require additional elements, such as switches, resistors, or power electronic devices, making their implementation more complex and costlier.

The method proposed in this work solves these issues through a simple synchronization-based approach that reduces complexity and costs. One of the main advantages of this method is that only the main CB is needed for the start-up. Additionally, it retains the benefits of other soft start-up methods, such as avoiding high inrush currents and pulsing torques.

3. Description of the Proposed Soft Start-Up Method

This section describes the theoretical background of the proposed soft start-up method and outlines the steps to implement it (Section 3.1). To this end, the dynamic equations of the DFIM are presented (Section 3.2). Since the present method is based on synchronization to the power system, the conditions on both sides of the switch/CB must be equal in terms of phase sequence, voltage amplitude, frequency, and phase angle. Initially, the DFIM does not rotate unless it is driven by an external torque, because the stator windings are open before synchronization by the time the DFIM is energized through the rotor. This synchronization at standstill conditions is analyzed (Section 3.3). Finally, using the rotor’s power converter voltage/frequency control, the machine is accelerated, which is addressed at the end of this section (Section 3.4).

The electrical scheme required for the implementation of the proposed method in pumped storage hydropower plants is shown in Figure 2.

As shown in Figure 2, the stator of the DFIM is connected to the system through the main power transformer and the main CB, which is equipped with an automatic synchronizing relay. The rotor winding is supplied via two back-to-back converters (grid side and rotor side converters, interfaced by a DC link), powered through an excitation transformer. The shaft is mechanically coupled to the hydro turbine.

3.1. Method Overview

The algorithm that summarizes the start-up process is presented in Figure 3. At the initial conditions, the DFIM is at standstill conditions (zero mechanical speed, ω_mec = 0), with the main CB in an open state, i.e., isolated from the grid. In this scenario, grid synchronization conditions must be met.

To achieve the synchronization conditions (voltage amplitude, frequency, and phase angle), the rotor’s power converter must control the voltage frequency and amplitude at its terminals. The frequency of the rotor’s currents should be defined according to Equation (1):

$${\omega }_{mec}={\displaystyle \frac{2\pi }{p}}\left(f_s-f_r\right)$$

(1)

where p is the number of pole pairs of the DFIM, f_s is the stator frequency and f_r is the rotor frequency.

From Equation (1), it follows that for a start-up from ω_mec = 0, the electrical frequency of the rotor (f_r) imposed at the terminals of the power converter must be equal to the stator frequency (f_s), which is also the grid frequency (f_grid). Furthermore, for a start-up from zero ω_mec, which is a common scenario for motor start-ups, the imposed voltage at the power converter terminals must be the rotor rated voltage (U_r) for f_r = f_s. This ensures that the induced stator voltage (U_s) matches the grid voltage (U_grid) prior to synchronization (U_r = U_grid/r_t, with r_t being the rotor/stator voltage ratio). The imposed voltage at the power converter terminals should be controlled under a constant flux strategy. It must be noticed that in the case of turbine start-up mode, i.e., the shaft can be already rotating, f_r should be the difference between shaft frequency and f_grid to impose f_s = f_grid and then perform the CB closure. The following explanations describe the motor start-up mode, as it is more critical than the turbine one due to the counter torque present in this mode of operation.

Provided that the phase sequence is identical on both sides of the CB, once the converter control has matched the voltage and frequency values with those of the grid (ΔU = |U_grid|−|U_s| = 0 and Δf = f_grid−f_s = 0), the breaker (CB) is closed when the phase shift is null (Δφ = 0). The machine is thus synchronized to the grid at standstill conditions. Since the rotor’s frequency is the same as the stator’s, their fluxes are synchronized, preventing the generation of a torque. Consequently, the shaft remains at ω_mec = 0 after synchronization.

After synchronization, the power converter gradually reduces its output frequency, causing the shaft to start rotating according to (1). The rotor voltage (U_r) should also be proportionally reduced to maintain the DFIM flux (constant U_r/f_r). The starting process concludes once the power converter reaches the rated f_r. During this process, the DFIM accelerates from a unitary slip (s) value to the rated s value in a downward ramp progression.

The main advantage of this method over the methods analyzed in Section 2 is that it does not require additional elements such as switches, breakers, autotransformers, variable resistances, or auxiliary converters. Only the main CB is needed. Moreover, the method is characterized by its simplicity and safety, as it avoids any short-circuit conditions. Additionally, inrush currents and voltage sags during start-up are eliminated.

However, despite the benefit of using only the main CB, synchronization conditions must be carefully observed in the stator. Consequently, the high-frequency pulses generated by the power converter, due to pulse width modulation (PWM), will flow through the DFIM during the start-up process. This results in increased electrical insulation stress. Finally, it is important to note that the lower the frequency variation in the power converter, the smoother the start-up will be.

3.2. Dynamic Equations of the DFIM

In order to set up the dynamic equations of a DFIM [40], it is assumed that there is a sinusoidal field distribution along the periphery of the airgap, no zero-sequence currents, and constant saturation throughout the process. In the per unit (p.u.) system, the phasor equations for the stator and rotor are given in the excitation or stator-flux reference frame by Equations (2) and (3), respectively:

$${\underset{\_}{U}}_s={\displaystyle \frac{d{\underset{\_}{\Psi }}_s}{dt}}+j{\omega }_0{\underset{\_}{\Psi }}_s+R_s{\underset{\_}{I}}_s$$

(2)

$${\underset{\_}{U}}_r={\displaystyle \frac{d{\underset{\_}{\Psi }}_r}{dt}}+j{(\omega }_0-{{\omega }_{mec})\underset{\_}{\Psi }}_r+R_r{\underset{\_}{I}}_r$$

(3)

where Ψ_s is the stator flux, Ψ_r is the rotor flux, ω₀ is the angular speed, R_s is the stator resistance, R_r is the rotor resistance, and I_s and I_r are the stator and rotor currents, respectively.

The stator and rotor currents and fluxes are related by Equations (4) and (5) as follows:

$${\omega }_0{\underset{\_}{\Psi }}_s=X_s{\underset{\_}{I}}_s+X_m\left({\underset{\_}{I}}_s+{\underset{\_}{I}}_r\right)$$

(4)

$${{\omega }_0\underset{\_}{\Psi }}_r=X_r{\underset{\_}{I}}_r+X_m\left({\underset{\_}{I}}_s+{\underset{\_}{I}}_r\right)$$

(5)

where X_s is the stator leakage reactance, X_m is the magnetizing reactance and X_r is the rotor leakage reactance of the DFIM.

Substituting Equations (4) and (5) into Equations (2) and (3), the following Equations (6) and (7) are obtained:

$${\underset{\_}{U}}_s=\left[R_s+j\left(X_s+X_m\right)\right]{\underset{\_}{I}}_s+{\displaystyle \frac{\left(X_s+X_m\right)}{{\omega }_0}}{\displaystyle \frac{d{\underset{\_}{I}}_s}{dt}} +\left({\displaystyle \frac{d}{dt}}+j{\omega }_0\right){\displaystyle \frac{X_m}{{\omega }_0}}{\underset{\_}{I}}_r$$

(6)

$${\underset{\_}{U}}_r=\left[R_r+js\left(X_r+X_m\right)\right]{\underset{\_}{I}}_r+{\displaystyle \frac{\left(X_r+X_m\right)}{{\omega }_0}}{\displaystyle \frac{d{\underset{\_}{I}}_r}{dt}}+\left({\displaystyle \frac{d}{dt}}+js{\omega }_0\right){\displaystyle \frac{X_m}{{\omega }_0}}{\underset{\_}{I}}_s$$

(7)

Additionally, the mechanical characteristics are expressed by Equations (8) and (9):

$${\displaystyle \frac{{d\omega }_{mec}}{dt}}={\displaystyle \frac{T_m-T_r}{2H}}$$

(8)

$$T_m=X_m·Im\left\{{\underset{\_}{I}}_s·{\underset{\_}{I}}_r^{*}\right\}$$

(9)

where T_m is the mechanical torque, T_r is the mechanical counter-torque in the shaft of the DFIM and H is the rotor inertia constant.

These equations completely define the transient evolution of the machine state variables.

3.3. Stator Synchronization Analysis

The power converter should provide the magnetizing current during the process and should impose the synchronization voltage. Consequently, I_s should be zero when closing the CB. According to Equations (6) and (7), Equations (10) and (11) are derived, respectively, as the time derivatives should be null and f_r = f_s:

$${\left.{\underset{\_}{I}}_r\right|}_{sync}={\displaystyle \frac{{\underset{\_}{U}}_s}{j{X}_m}}$$

(10)

$${\left.{\underset{\_}{U}}_r\right|}_{sync}={\displaystyle \frac{\left[R_r+j\left(X_r+X_m\right)\right]}{j{X}_m}}{\underset{\_}{U}}_s$$

(11)

This implies that the converter should impose a voltage slightly larger than the rated one. As this is usually not possible, the strategy should be adjusted: U_r will be set at its rated value and its phase angle (φ) should be such that the stator voltage phase angle coincides with U_grid phase angle (zero phase shift condition). Taking U_grid as a reference, then, from Equation (6) just before closing the CB:

$${\left.{\underset{\_}{I}}_r\right|}_{sync}=-j{\left.I_r\right|}_{sync}$$

(12)

Introducing Equation (12) into Equation (7), and assuming that U_r = 1 p.u. (with unknown phase angle, φ_r):

$$e^{j{\phi }_r}=-j\left[R_r+j\left(X_r+X_m\right)\right]I_r$$

(13)

Therefore, the I_r amplitude and the phasor difference between U_grid and the stator voltage at the synchronization instant are given by Equations (14) and (15), respectively:

$${\left.I_r\right|}_{sync}={\displaystyle \frac{1}{\sqrt{R_r^2+{\left(X_r+X_m\right)}^2}}}$$

(14)

$${\left.{\underset{\_}{∆U}}_s\right|}_{sync}=1-{\displaystyle \frac{X_m}{\sqrt{R_r^2+{\left(X_r+X_m\right)}^2}}}$$

(15)

Due to the typical values of DFIM parameters, this voltage difference is very small. Thus, the closing transient I_s will be also small and lower than its rated value. The initial (just after closing CB) time derivative of I_s is expressed by Equation (16):

$${\left.{\displaystyle \frac{d{\underset{\_}{I}}_s}{dt}}\right|}_{sync}={\omega }_0·{\displaystyle \frac{1-\frac{X_m}{\sqrt{R_r^2+{\left(X_r+X_m\right)}^2}}}{X_s+X_m}}$$

(16)

3.4. DFIM Acceleration

Once the DFIM is synchronized with the grid, it should be accelerated by reducing the magnetizing current provided by the power converter. As a consequence, the power consumption from the grid increases to compensate for this reduction.

To better analyze this process, starting electromagnetic transients shall be neglected. This can be safely completed because the starting is designed to be smooth, i.e., electrical variables will change slowly, and their time (t) decay is fast. So, time derivatives in Equations (6) and (7) will be assumed null. Additionally, to keep the magnetic flux constant, the ratio between U_r and f_r will also be constant (U_r/f_r = 1 p.u.). Under these assumptions, I_r can be calculated as in Equation (17):

$${\underset{\_}{I}}_r={\displaystyle \frac{{\underset{\_}{U}}_r\left[R_s+j\left(X_s+X_m\right)\right]-j{sX}_m{\underset{\_}{U}}_s}{s{X}_m^2+\left[R_r+js\left(X_r+X_m\right)\right]\left[R_s+j\left(X_s+X_m\right)\right]}}$$

(17)

Therefore, I_s follows Equation (18):

$${\underset{\_}{I}}_s={\displaystyle \frac{{\underset{\_}{U}}_s-j{X}_m{\underset{\_}{I}}_r}{R_s+j\left(X_s+X_m\right)}}$$

(18)

These equations, along with Equations (8) and (9), allow calculating the machine’s starting dynamics. The acceleration process finalizes when the power converter reaches the rated rotor’s frequency, i.e., the machine slip is reduced from the unitary value to the rated value.

4. Computer Simulations

To validate the proposed method, numerous computer simulations have been performed using Matlab-Simulink^® (R2023a). For these simulations, a conventional 0.52-kW DFIM model was considered. In this section, the simulation model and the results of the proposed start-up technique are described.

4.1. Simulation Model

In Figure 4 the simulation model method is shown.

Table 2. Simulated DFIM’s main rated parameters.

Parameter	Magnitude	Units
Real power (Pn)	0.52	kW
Stator voltage (Un)	400	V
Frequency (fn)	50	Hz
Stator/rotor voltage ratio (rt)	10/1	V/V
Stator resistance (Rs)	30.0	Ω
Stator inductance (Ls)	0.120	H
Equivalent rotor resistance (Rr’)	30.0	Ω
Equivalent rotor inductance (Lr’)	0.120	H
Mutual inductance (Lm)	2.432	H
Moment of inertia (J)	0.0015	kg·m2
Number of pole pairs (p)	2
Speed (nn)	1400	rpm

lists the rated values of the DFIM’s most significant parameters.

In this simulation model, the 0.52-kW DFIM is connected to a 400-V, 50-Hz three-phase grid through a CB equipped with a synchronizer. Additionally, high-value resistances have been connected in parallel to the DFIM grid terminals in order to avoid convergence errors during the simulation.

In the rotor circuit, the power converter (fed by a 120-V three-phase grid) is connected in series with a 1-mH choke inductance (equivalent to the secondary of the excitation transformer seen in Figure 2). The grid-side converter is controlled to maintain the voltage at the DC bus (U_DC), which employs a 1600-μF capacitor. The setpoint of U_DC depends on f_r.

On the machine side of the power converter, the inverter generates a PWM signal to obtain the required voltage and frequency at each instant. When starting the machine at standstill conditions, the frequency through the windings is about 49.95 Hz, a value close to the grid’s frequency, allowing for soft synchronization. Once the machine is synchronized, assuming the conditions for voltage, frequency, and phase angle are met, this frequency decreases to about 2 Hz as a downward ramp function. The total acceleration t has been set at 5 s to achieve a soft start-up. If the ramp is too steep, there is a risk of overcurrent due to the DFIM’s moment of inertia (J).

4.2. Results

Figure 5 shows the simulation results for the main parameters (ω_mec, T_m, I_r, I_s, and U_r). All variables are in per unit (p.u.) using DFIM rated values as bases.

In Figure 5, synchronization was achieved at t = 0.242 s. Initially, while the rotor’s current maintained a constant value of 0.45 p.u. to magnetize the DFIM, the stator’s current was zero because the machine was not yet coupled to the grid. On the other hand, Ur was set to obtain U_s = U_grid = 1 p.u on both sides of the CB before synchronization. Once the voltage, frequency, and phase angle conditions were optimal, synchronization was performed.

As shown in Figure 5, after closing the CB, a transient occurred in I_s and I_r, while the machine’s shaft remained nearly stationary with negligible torque. The frequency downward ramp was applied at t = 0.3 s. When the frequency slope started at 0.3 s, a larger transient appeared in currents, and consequently in torque, during the first 0.7 s of evolution (up to t = 1 s), as the result of overcoming DFIM inertia. After these transients, the currents and the torque returned to their soft starting state. In this case, both rotor’s and stator’s currents did not exceed 0.5 p.u., except in the initial transient where I_r reached 1 p.u. Once the DFIM was accelerated for approximately 5 s under the constant flux condition, the magnetizing current was proportionally divided into the stator’s and rotor’s currents according to the machine’s impedances. Furthermore, at the beginning U_r and U_DC experienced a transient decrease of around 15% and the torque initially pulsed following the current behavior. The acceleration process ends when U_r is brought down to its rated value. Therefore, the DFIM attains its rated speed.

Finally, in Figure 6 the grid and stator voltages are shown. The voltage on both sides of the CB during the synchronization process is plotted. Before the CB was closed, the stator voltage pulsed due to the PWM converter feeding the rotor of the machine. After closing the CB, U_grid was imposed.

5. Experimental Tests

Obtaining a deeper understanding of the behavior of the previous parameters involved in the start-up process requires thoroughly performed experimental tests. In this section, the experimental setup and the results are described.

5.1. Experimental Setup

The experimental setup implemented in the laboratory is shown in Figure 7 and Figure 8. It consists of a variable frequency drive (VFD) (1) with a squirrel cage induction machine (SCIM) (2) that drives a synchronous generator (SG) (3). The SG feeds the rotor of a 0.52-kW DFIM (4) with the frequency governed by the SCIM speed and the voltage level controlled by the DC excitation system (6) of the SG. The SG is used to provide constant U/f control for the DFIM rotor’s excitation. However, a controlled power converter could be used instead for rotor feeding in this setup. The DFIM’s nameplate parameters are listed in

Table 3. Tested DFIM’s nameplate parameters.

Rated Parameters	Magnitude	Units
Real power (Pn)	0.52	kW
Frequency (fn)	50	Hz
Stator voltage (Un)	380/660	V
Stator current (In)	1.6/0.92	A
Rotor voltage (Un,r)	65 (Y)	V
Rotor current (In,r)	6 (Y)	A
Speed (nn)	1400	rpm
Power factor (cosφn)	0.72

and its equivalent circuit parameters correspond to the ones shown in Table 2.

Therefore, the conditions of f_s = f_grid and U_s = U_grid can be easily imposed on the DFIM stator before the closure of the main CB (7). In addition, the voltages can be adjusted using the autotransformer (5) included on the grid side of the CB. With the help of a synchronoscope (8) and two voltmeters (9, 10), the CB is closed when adequate conditions are met.

Furthermore, the rotor and stator currents (11, 12) and voltages are recorded using a 4-channel oscilloscope (14). An additional voltmeter (13) is used to monitor the SG excitation voltage as a safety measure. Once synchronized, the variable speed drive is controlled to decrease the frequency from 50 Hz to 8 Hz and the SG operates under U_r/f_r = constant control.

5.2. Results

Figure 9 shows the values recorded during a start-up process, which lasts 15 s. The synchronization was performed using two sinusoidal voltage signals because the rotor was fed from an SG.

As shown in Figure 8, the magnetizing current is provided by the rotor’s feeding at an initial constant value of 0.44 p.u. Once synchronization is performed at t = 2 s, the stator inrush current does not contribute to the DFIM’s magnetization. At t = 3.5, the f_r is made to change and the shaft begins its rotational motion. At this point, while the machine is accelerated under the constant flux condition for 14.5 s, the proportion of magnetizing current supported by the stator and rotor varies, as the f_r shifts linearly downward from 50 Hz (standstill initial condition) to 8 Hz (final operating point). This causes I_r to decrease and I_s to increase.

As the simulation results have also shown, the inrush currents are negligible, and the final currents do not exceed 0.4 p.u. However, the start-up is smoother than in the computer simulations, as the initial transient observed from t = 0.3 to t = 1 s in Figure 5 does not appear in Figure 9. The results shown in Figure 9 suggest that the transient is caused by a simulation discontinuity rather than by a physical phenomenon. Additionally, the torque depicted in Figure 9 does not exhibit the oscillations shown in Figure 5. Thus, the experimental results are consistent with the simulations: before and after synchronization, and throughout the controlled acceleration.

If the start-up current is compared with other techniques found in the literature, it can be observed that it presents one of the lowest values. As the RSC only has to provide the magnetizing current (around 0.4 p.u.), this is the higher reachable value at the start. Meanwhile, opposite phase sequence-based techniques reach around 5–6 times the rated I_s [20]. Reduced voltage-based techniques, using autotransformers, reduce up to around 0.8 p.u. the inrush current [21].

Using stator short circuits and, then, performing the synchronization allows obtaining I_s = 0.6–1.5 p.u. [25,26,28,29,30,31,32,33,34,35,36], while rotor short circuits reach I_s = 1 p.u. during the DFIM start-ups [37]. Finally, the use of auxiliary power converter techniques obtain I_s = 0.5 p.u. [39], a value that is in the actual range of the proposed method, and it is an indicator of its viability.

6. Conclusions

This paper proposes a soft start method for DFIM applications. The method feeds the rotor with a frequency equal to the grid frequency, at a standstill and isolated machine conditions, producing the required stator voltage for grid synchronization. Synchronization occurs at standstill conditions through the main CB closure, keeping the rotor still as stator and rotor fluxes are identical, hence no electromotive forces are produced. After synchronization, the rotor frequency and voltage decrease maintaining a constant DFIM flux, gradually increasing the rotor mechanical speed. This enables soft frequency reduction until the desired speed, avoiding high torque transients.

The proposed method stands out from the state-of-the-art because no additional elements are required (switches or breakers, autotransformers, variable resistances, or auxiliary converters, among others). The start-up is achieved using only the main CB and simple converter control. This approach ensures safety by avoiding short-circuit conditions, and it eliminates inrush currents and voltage sags during start-ups.

Computer simulations and experimental tests were conducted for this work. The experimental results are not only consistent with the computer simulations but also demonstrate significant improvements, as some transients observed in the simulations were not present in the experimental measurements. Furthermore, the required currents are substantially lower compared to other start-up methods.

The DFIM start-up method has been validated under free shaft conditions, typical for variable speed hydro reversible generators. However, the main limitation of the method is related to the excitation power converter capacity, because it must be able to introduce the magnetizing current into the rotor up to the synchronization is completed and the rotor frequency starts to decrease. Future works shall aim to adapt the method for loaded start-ups, and also, to overcome this previous limitation by studying alternative DFIM synchronization methodologies that will not utilize the rotor converter to provide the magnetizing current.