Controlling Transformer Magnetizing Offset Current in Isolated Phase-Shift Full-Bridge Converters Using a Luenberger Observer

Neumann, Angelika; Meynen, Sönke; Rahmoun, Ahmad; Ziegler, Daniel; Kirchartz, Thomas

doi:https://doi.org/10.1155/2022/9243429

International Transactions on Electrical Energy Systems

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Abstract Introduction Results Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 9243429 | https://doi.org/10.1155/2022/9243429

Controlling Transformer Magnetizing Offset Current in Isolated Phase-Shift Full-Bridge Converters Using a Luenberger Observer

Angelika Neumann,¹Sönke Meynen,¹Ahmad Rahmoun,²Daniel Ziegler,²and Thomas Kirchartz³

Academic Editor: mahdiyeh eslami

Received21 Jun 2022

Revised28 Jul 2022

Accepted08 Aug 2022

Published26 Sept 2022

Abstract

This paper proposes a flexible digital control scheme for isolated phase-shift full-bridge (PSFB) converters. The required transformer suffers from inevitable imbalance of magnetic flux resulting in an increased magnetizing DC-offset current that threatens system reliability due to saturation effects. The paper addresses two major issues of the occurrence of a magnetizing DC-offset current. First, caused by the change of duty cycle due to output power regulation and second caused by initial manufacturer tolerances of devices. In contrast to common methods the novel control scheme uses a Luenberger observer to estimate the magnetizing current requiring only simple measurement of transformer voltages without additional and lossy auxiliary networks. The observer model, in combination with a PI-controller, directly interventions the duty cycle and removes any DC-offset current resulting from both issues. A detailed deviation of the state-space model of the transformer and a subsequently design of the observer are presented. Simulation and experimental results on a PSFB prototype verify the principal functionality of the proposed control scheme to prevent transformer saturation.

1. Introduction

Regarding the worldwide increasing climate problematic the portion of clean and renewable energy generation has increased over three-fold since the last ten years [1]. Unfortunately, renewable energies like photovoltaic (PV) or wind power reduce the reliability of power generation with its dependency on weather conditions [2, 3]. To utilize the maximum capacity of fluctuating renewable energies different storage technologies have been developed. Although lithium-ion battery systems are not the only solution to store energy, this technology has prevailed in various mobile DC-DC applications and also becomes more and more important for the high and medium power DC-DC charging sector. Typically, high power DC-DC systems use a liquid cooling system due to large heat development while charging batteries, but especially non-industrial DC-DC applications with medium power have to manage cooling without liquid cooling system and therefore a high efficiency is very important [4].

The high efficiency and power density of an isolated phase-shift full-bridge (PSFB) converter in Figure 1 make this topology very attractive for DC-DC medium and high power applications such as DC-storage battery systems for PV or battery chargers for electric vehicles [5–7]. Its phase-shift control scheme allows for zero-voltage-switching (ZVS) operation with negligible switching losses and reaches higher efficiency compared to conventional hard-switched topologies [8].

Two full-bridges on primary H_A and secondary H_B side make the topology suitable for bidirectional operation. The transformer TR, with ratio between primary and secondary winding, compensates a high voltage difference between input voltage and output voltage to avoid low duty cycles with decreased efficiency. Additionally, its naturally galvanic isolation satisfies the normative requirements for e.g. battery chargers in electric vehicles for safety reasons [9]. Nevertheless, a transformer isolated converter suffers from issues such as an imbalance of magnetic flux resulting in an increasing DC-offset current that drives the transformer into saturation [10]. To prevent damage due to high saturation currents and guarantee system reliability must be eliminated.

Common topologies connect a blocking capacitor in series to the transformer in the main power path to suppress any DC-offset . However, placed in series with the transformer the blocking capacitor must be dimensioned for the maximum current of the converter at full power and additionally increases conduction losses due to its series resistance. As consequence the blocking capacitor is not preferred for applications with high power density and efficiency [11]. Considering bidirectional operation, a blocking capacitor must be placed in series to primary and secondary side of transformer. This method needs several additional power devices compared to controller-based methods and therefore results in increased size of power stage and overall system costs [12, 13].

Without additional passive devices in the main power path a controller needs to eliminate [14]. Designing of a stable feedback control loop requires the measurement of as process variable. However, considering the transformer as a four terminal device the acquisition of is not directly possible as it overlays the transformer primary current [15]. The current-mode control (CMC) is a very popular analog controller-based method to prevent the transformer from saturation. Its fast response due to analog comparators allows for stable operating conditions even at high switching frequencies . Unfortunately, in certain operating conditions instabilities, known as sub-harmonic oscillations, occur [16, 17]. The slope compensation technique normally is used to compensate the oscillation but overcompensation may result in a response delay [18, 19]. Additionally, the CMC method is not suitable for flexible digital control schemes as it needs analog comparators [20].

Numerous research works concern the adjustment of PWM signals of power switches to balance the transformer magnetizing current in isolated DC-DC converters. However, the method of gathering the magnetizing current as process variable for a controller differs. [12] extends current-mode control with a hybrid peak and valley current control and does not need for slope compensation. The valley current detection requires AC-current sensing on the primary side of transformer with a suitable bandwidth for high switching frequencies. Considering bidirectional operation, the study in [21] uses primary and secondary transformer current to estimate magnetizing current from the previous switching period. A similar method in [22] only uses the averaged primary current to estimate the DC-offset from the previous period assuming the inductor current to be in steady state and average secondary current to be zero. [23] addresses the problem of magnetizing DC-offset causing DC-offsets in primary and secondary current. Here, two control loops need to scene also both, primary and secondary current and calculate the magnetizing current accordingly. In [24] a sensor directly measures the magnetic flux in the transformer core. The sensor requires modification of transformer core to mount the sensing coil through hole. An extended Kalman-Filter-approach to estimate the primary transformer current is presented in [25]. However, the study only concerns the discrimination of the transformer inrush current from internal faults to trigger a protective relay.

This article presents a novel digital feedback control loop scheme for eliminating DC-offset without additional devices in the main power path. In contrast to related work a Luenberger observer is used that only requires the measurements of the transformer voltages to estimate the magnetizing current as process variable for a PI-controller. Main purpose of the study is to develop a digital controller that allows for simple application or flexible modification of existing controller structures only by adding the voltage measurement feature and to improve system reliability. At the beginning Section 2 explains the inevitable occurrence of DC-offset in isolated PSFB converters in detail. In Section 3 conventional methods, like a blocking capacitor or CMC, used to overcome this problem are introduced. Section 4 explains the structure of the proposed digital control scheme. Section 5 describes an approach of acquiring the not measurable DC-offset using a Luenberger observer with a detailed derivation of the state space model of the transformer and the subsequently design of the observer. In Section 6 the principal functionality of the proposed control scheme is evaluated by simulation and experimental results with an isolated PSFB converter prototype operating with a power at a switching frequency . Finally, Section 7 gives a conclusion of the presented results.

2. Transformer DC-Offset Current

The magnetizing current creates the magnetic field of the transformer required for power transfer from primary to secondary side and flows through the magnetizing inductor of the transformer. adds either to primary or secondary current of transformer depending on power transfer direction. The transformer is not capable to transfer any DC component of [26]. Therefore, the magnetizing current needs to be detected on primary and secondary side when operating in bidirectional direction. The following considerations refer exemplary to a power transfer direction from primary side A with to secondary side B with .

Figure 2 shows the typical schematic characteristics of applied voltage in Figure 2(a), primary current in Figure 2(b) and magnetization current in Figure 2(c) for transformer of the PSFB converter shown in Figure 1.

The power transfer cycles and are determined according to the effective duty cycle applied to the transformer TR. For desired duty cycle the phase-shift between lagging S₁ + S₃ and leading leg S₂ + S₄ of H_A varies and applies either the positive or the negative input voltage to the magnetizing inductor of the transformer TR according to Figure 2(a). For positive voltages the magnetizing current increases and for negative voltages , decreases respectively. During the interval no voltage is applied to resulting in a constant . The alternating positive and negative voltage-second products applied to the transformer within one period determines the peak value and , assuming to be constant during , in Figure 2(c) according to:

Therefore, the DC-offset can approximately be defined as the average value of magnetizing current during one period with:

Figure 2(b) explains the sloped magnetizing current as an additional comparable small portion to the high main primary current with [15]. As consequence cannot be measured directly considering the transformer as a four terminal device. Assuming negligible variations of and during one switching period the DC-offset can be calculated from the difference between the peak values of during one complete period according to:

For a present asymmetrical voltage-second product , the absolute value of increases each period with

and the resulting DC-offset drives the transformer into saturation. Ideally, the symmetrical structure of the PSFB topology ensures no DC-offset as positive and negative current slope of balance each other. Unfortunately, various inevitable effects can cause a small asymmetrical voltage-second product on primary side of transformer [14]. One transient reason is the unbalanced duty cycle between power cycle for the lagging leg and for the leading leg due to ZVS-operation or the change of for regulating the output current of the PSFB [12]. Even in steady state operation manufacturing tolerances of devices as well as circuit board layout (PCB) cause different voltage drops and apply different voltages to the magnetizing inductor and increase [10]. Beside of the transformer the resulting high saturation current threatens the switching devices H_A and H_B and general system reliability. Additionally, the conduction loss unnecessarily increases with an unbalanced magnetizing current as it does not contribute to power transfer from primary to secondary side. Therefore, system efficiency is directly related to minimize .

3. Conventional Methods

Several methods have been proposed either to suppress or to control DC-offset in [11, 12, 16, 17, 27, 28].

3.1. Blocking Capacitor

Connecting a blocking capacitor in series to the transformer suppresses any DC component in the transformer current and allows for symmetrical operation [11]. Therefore, this method is suitable for acquiring only secondary side output current and apply proportional integral current control [27]. Additionally, in phase-shift control scheme the blocking capacitor method reduces the circulating currents during the free-wheel interval of the lagging leg and minimizes conduction loss. However, the timing of the leading leg becomes more complicated [12]. On the other hand, the blocking capacitor method simultaneously increases the conduction loss as the capacitor is located in the main power path with maximum current of the PSFB [28]. For bidirectional operation the magnetizing current occurs on either side, primary and secondary, according to power direction. Therefore, this method needs two blocking capacitors and significantly increases volume and overall costs.

3.2. Current-Mode Control

The current-mode control (CMC) method is well known for non-isolated converters such as buck or boost converter topologies [16–18]. For non-isolated converters the inductor current serves as process variable for the control loop. Fast response analog comparators generate PWM signals and directly trigger the power switches when inductor current reaches a given threshold value and provide output control. Reference [18] distinguishes CMC between peak detect, valley detect and emulated control mode. However, either method suffers from sub-harmonic oscillation when inductor current does not return to its initial value by the start of next switching cycle in continuous current-mode (CCM). In peak detect CMC the sub-harmonic oscillations occur at duty cycles and for valley detect at duty cycles respectively. A slope compensation circuit needs to correct the ripple current and results in a response delay for the controller [19]. In isolated converters the CMC method can additionally provide the elimination of DC-offset with small modifications. Any DC component of cannot pass the transformer. Therefore, the input current must serve as process variable for control with power direction from A to B side.

Figure 3 explains the compensation principle of CMC with the schematic characteristic curves of primary voltage in Figure 3(a), input current in Figure 3(b) and magnetizing current in Figure 3(c) of transformer with a present flux imbalance. Neglecting parasitic inductors, the magnetizing current slopes up with during power cycle and with during power cycle respectively. Parasitic effects reduce the applied voltage for power cycle in Figure 3(a). Assuming a symmetrical duty cycle for both power cycles the peak of input current does not reach the threshold value of the analog comparator and the negative DC-offset rises [12]. The current-mode controller directly influences the duty cycle and extends until reaches the threshold current . Therefore, the CMC ensures flux balance of the transformer with and provides a symmetrical voltage-second product [12, 18].

Common control schemes prefer an analog controller with comparators compared to digital controller as the erratic increasing of needs high bandwidth to detect the peak current exactly. In consequence, the CMC is hard to combine with a flexible digital control scheme [20]. An additional challenge for the measured process variable is the accuracy to properly detect the small portion of as Figure 2(b) explains as a comparable small additional sloped offset to the high input current or rather .

4. Proposed Control Scheme ctrIh

The proposed control scheme ctr_Ih uses flexible digital design. It requires neither lossy and expensive additional passive devices in the main power path of the PSFB nor analog comparator for triggering power switches. Similar to CMC, the proposed digital control scheme ctr_Ih directly interventions the duty cycle of the leading leg to equalize the peak values of primary current and eliminates any magnetizing DC-offset within a few switching cycles.

Figure 4 depicts the control loop of the PSFB converter with ctr_IL for output current regulation and ctr_Ih for DC-offset control. The output controller ctr_IL is built up with a PI-controller PI_IL and feedback control for the output voltage for better adjustment of output operating point. The transfer function of the PSFB determines the effective duty cycle for desired output current . The proposed magnetization controller ctr_Ih adds or subtracts a small offset between duty cycle for the lagging and duty cycle for the leading leg until . As and vary only a little during one switching period and also the impact of parasitic effects contribute only to a small amount, the ctr_Ih limits the magnitude of to a few percentage of . Therefore, the influence of ctr_Ih on the output controller ctr_IL is negligible [14]. According to and the phase-shift calculator provides eight separate PWM signals for power switches S₁–S₈ of PSFB power electronics. In the feedback path the main control unit (MCU) performs the acquisition of process variables , , and with analog digital converters (ADC). For output control the rippled inductor current averages to the desired output current . Therefore, the moving average finite impulse response (FIR) filter with averages over number of periods with:

Accordingly, the DC-offset is defined as the average of rippled magnetization current over several periods. Again, a moving average FIR filter with provides the process variable of ctr_Ih. As and are already DC values there is no need for averaging with a FIR filter.

For proper design of ctr_Ih the relation must be obtained. As mentioned before several effects, such as an unbalanced duty cycle either due to ZVS operation or output regulation as well as parasitic effects influence the occurrence of unbalanced flux leading to . Therefore, these effects have to be considered in the transfer function . Figure 5 illustrates the influence of on the DC-offset for analyzing the impact of unbalanced duty cycle due to output regulation ctr_IL over two consecutive switching periods and . According to phase shifted PWM signals for power switches S₁–S₄ in Figure 5(a) the voltage in Figure 5(b) applies to the transformer. Figure 5(c) shows the time course of magnetizing current resulting from unbalanced duty cycles .

The PWM signals of power switches S₁–S₄ obtain the duty cycle difference to:

Assuming equal voltages for power cycles and the magnetizing current slopes with the same gradient . In period , the output regulator ctr_IL increases . Due to the increased duty cycle the magnetizing current surpasses the peak value before the end of power cycle , thus, leading to an increased DC-offset in the following period according to:

This behavior expresses also for small differences between duty cycle and in the same period .

Furthermore, defines as the average of magnetizing current with a linear slope . Therefore, between two consecutive switching periods due to unbalanced duty cycle approximately calculates as follows:

As long as there is a duty cycle imbalance present, the magnetizing current needs to diverge until the PSFB gets damaged if not compensated.

Another reason causing are different parasitic resistances such as switch resistances or general PCB-design resulting in unequal voltages . [14] derives the influence of parasitic elements and can approximately be calculated as follows:

As the impact of resistance is comparable low during transition times, (9) only considers the dominant time intervals of free-wheeling and power cycle. Regarding (9) parasitic resistances contribute proportionally with to magnitude of . Therefore, the impact of represents a steady-state fault of ctr_Ih [14].

During the transition between power and free-wheeling cycles mainly the switching characteristics of the power switches and dead time control influence the DC-offset . The dead time control determines different duty cycle for the lagging and for the leading leg according to ZVS-conditions. In [14], the detailed derivation results in:

again, with propoportional gain .

For a unified transfer function the three main effects influencing must be considered according to [14] with:

The effects of resistance and switch transition both prevent the development of in either direction and therefore have to be subtracted while the transient supports the development of [14].

Equation (12) calculates the transfer function of and in domain as follows:

According to (12) the magnetization controller ctr_Ih requires an integrator for steady state stability. For the experimental results the ctr_Ih is implemented as PI-controller PI_Ih.

5. Derivation of Observer Model

In the proposed digital control scheme of ctr_Ih, represents the process variable. Considering TR as a four terminal device with and as inputs and and as outputs, cannot be measured at clamps directly. Therefore, needs to be calculated from a related value depending on physically measurable in- and outputs.

In technical systems, a state observer is able to estimate an internal state value, such as from measurable in- and outputs of the real system [29, 30]. Figure 6 simplifies a part of the PSFB converter with four terminal devices of full-bridge H_A and transformer TR. The measurable primary voltage and secondary voltage of transformer serve as in- and output for the observer model and allow for estimating the internal value of .

The state observer method is typically computer-implemented and therefore suitable for the proposed digital controller ctr_Ih.

The measuring method for the observer model requires only the average value of transformer voltages and and can be measured with operational amplifiers at naturally high bandwidth . Additionally, the voltage measurement only needs small signal currents and therefore it is comparable lossless. The measuring method serves as reference to compare with conventional methods with an inductor connected in parallel to transformer. According to: the reference magnetization current reflects the real magnetization current and can be measured with a current clamp.

The proposed digital control scheme ctr_Ih uses the well-known Luenberger observer for estimation of [30]. For the design of a Luenberger observer, in Section 5.1 first a stable linear state space model of the real transformer must be developed. Although the observer allows for controlling a time continuous system, a discretization is necessary for realistic applications with a digital control as described in Section 5.2. Section 5.3 examines the observability criteria according to Kalman of derived transformer model and Section 5.4 explains the design of the Luenberger gain parameters for observer model.

5.1. Transformer State Space Model

The Luenberger observer requires a linear state space model of transformer in form of:

In (14a) and (14b) represents the state variables with input current , output current and magnetization current . The primary voltage represents the system input and the secondary voltage serves as measurable system output according to:

Figure 7 shows the equivalent circuit diagram (ECD) of a real transformer. Parasitic resistances and and leakage inductors and depict the loss component of primary and secondary windings while simulates the magnetic resistance of the transformer core. The core magnetization is regarded with magnetizing inductor . Nonlinear behavior of magnetizing inductor is neglected as the controller ctr_Ih prevents saturation of transformer. The ratio of primary winding to secondary winding represents the ideal transformer TR with:

In this model the parasitic capacitors are neglected as their time constants are very small compared to switching frequency and time constant of inductors. represents the impedance of the load for gathering secondary current .

The reference-arrow system in Figure 7 defines the sign of variables for further derivations. Secondary side values with indexes are referred to primary side with respect to transformer ratio according to:

The Kirchhoff current (KCL) and voltage (KVL) laws obtain the main equations of the transformer model according to:

Reshaping (18a)–(18d) delivers the time continuous state space vector to:

Referred to (14a) the system and input matrices can be obtained to:

The terms of voltage drop and in (18c) depend on the dynamic change of input and output current due to leakage inductors. However, the small time constant of transient process of leakage inductors in H-range is not detected due to FIR filtering of signal with . Neglecting the dynamic terms in (18c) provides the equation for system output to:

with output matrix and direct feed-through matrix from (14b) according to:

5.2. Analysis and Discretization of the Transformer Model

The transformer model includes three state variables and building a third order system with .

From the derived transformer model in the previous Section 5.1 the eigenvalues or poles of the system matrix describe the dynamic behavior of the system.

The values in Table 1 refer to the measured values from PSFB prototype or from the corresponding data from manufacturer. Analyzing the system with transformer parameter according to Table 1 delivers the poles for all three state variables , and shown in Table 2. As all poles are in the left-hand plane (LHP), the system provides stability [31].

The pole of according to Table 2 is too fast for realistic sampling time required for discretization of observer model. As the desired value of the observer only includes the state variable , the state variable with the fastest pole can be ignored. The reduction of system order eliminates the first state variable and reconfigures the matrices , and with and poles according to Table 3.

Again, all poles of the system with reduced order are located in LHP with negative values. Therefore, also the reduced system is stable.

For realistic application of the observer, the reduced system matrices must be available in a discrete time form with sampling time . The transfer of the reduced transformer model into discrete form affects only the system matrix and the input matrix [32]. One approach of discretization presented in [20] according to:

delivers the discrete system matrix without approximation.

The MATLAB order of matrix exponential function can directly perform the discretization and is suitable for the experimental approach.

With reduced discrete system matrix the reduced discrete input matrix calculates as follows:

The reduced discrete output matrix and reduced discrete direct feed-through matrix are not affected and remain the same.

The analysis of the reduced discrete transformer model in -domain delivers the poles of according to Table 4 with one stable pole at and one critically stable pole at . Therefore, a suitable design of the observer gain factors must guarantee the stability of the system.

5.3. Observability of the Transformer Model

To use the reduced discrete transformer model and realizing a Luenberger observer the reduced system must be observable. For a completely observable system the initial state must be reconstructible form known input and output value within a finite time interval [31]. According to Kalman criteria of observability, the observability is proved if the observability matrix in (25) has the same as the reduced system matrix with

According to (25) the rank of observability matrix equals the rank of reduced discrete system matrix and so the system is completely observable. Additionally, its determinant is not zero [30, 33].

5.4. Design of Luenberger Observer

In the structure of a Luenberger observer the derived transformer model works in parallel to real transformer. The observer compares the measured output with the calculated value of the transformer model and feeds back the estimation error with feedback matrix to the model [30].

From observer model the estimated state vector calculates as follows:

Suitable values of feedback matrix adjust the dynamical behavior of the model to match the real transformer and react to disturbances or transient variations of duty cycle . The design of feedback matrix with pole placement according to Ackermann [31, 33] is used and the known poles of from Table 4 deliver the first approach according to:

6. Results

The proposed digital control scheme regulates the magnetizing current of a PSFB to prevent transformer saturation. First approaches concern the simulation of electronics to prove principal functionality of ctr_Ih, supported through experimental tests on a PSFB prototype with . Table 5 lists the specifications of analyzed operating point of PSFB prototype electronics, also used for simulation.

To validate the simulated results in Section 6.1 the following Sections 6.2 and 6.3 explain the experimental measuring setup up and show the achieved results in operating point according to Table 5.

6.1. Simulation of Observer

For the evaluation of proposed ctr_Ih in Section 4 and derived observer model in Section 5, the PSFB topology from Figure 1 is built up in a MATLAB/SIMSCAPE simulation model according to parameters in Table 1 and operating point listed in Table 5. The control scheme for ctr_Ih and observer model are implemented in MATLAB/SIMULINK.

The simulation results in Figure 8 demonstrate the behavior of the PSFB magnetizing current at operating point in Table 5 for the different disturbances mentioned in Section 2, dynamic change of output current through duty cycle and initial static differences due to manufacturing process of devices. Fluctuations of due to ctr_Ih thereby influence the magnetization current in a similar way as . The simulation starts at with a desired output current and a corresponding duty cycle . The series resistance of switch S₂ is doubled compared to other switches with , simulating an initial voltage-second product imbalance. Figure 8(a) shows the simulated average values for magnetizing current and estimated observer current . Without ctr_Ih, the magnetizing current steadily raises due to the unbalanced voltage-second product till saturation of transformer. In Figure 8(a) the observer current reflects the dynamic behavior of simulated current with the model error in Figure 8(b) fluctuating around zero with a DC-offset . The influence of ctr_Ih on controlled variable is shown in Figure 8(c).

The increased resistance forces ctr_Ih to increase and compensates the voltage-second product imbalance. After initial transition process the ctr_Ih is able to correct the error resulting from static difference due to within . Either change due to step at or control at and causes fluctuations in . The estimated observer current follows the dynamics of with a small delay mainly resulting from computation and FIR filter. According to the ctr_Ih adjusts for regulating . Figure 9 explains the dynamic changes exemplary on in detail. At simulation time the desired output current raises to resulting in a dynamic change of duty cycle . For the magnetizing current approximately slopes up with . For time the magnetizing current steps up according to equation (8) and (9), raising . The step expresses as slope with due to FIR filter in MCU. With increased magnetizing current the rising slope of magnetizing current due to enlarges after encouraging saturation of transformer. The controlled estimated observer current matches the dynamics of magnetizing current and the change can be controlled out by ctr_Ih with . According to applied to voltage to and moving average filter, the magnitude value results to .

For analyzing the resistance of ctr_Ih, exemplary represents the observer current with a model failure in magnetizing inductance . The model failure produces a time delay for as the bigger magnetizing inductance reduces the slope of magnetizing current and enlarges the initial time for regulating the initial differences. Nevertheless, the ctr_Ih can handle the change in as well as in . A similar result is achieved with an examined model failure in primary resistance and load impedance .

6.2. Measurement Application

In the proposed control scheme the ctr_Ih only needs the average values of voltage and as measuring inputs to control the magnetization DC-offset . Typically, voltage measurements only need a network of low-cost resistors and operational amplifiers with naturally high bandwidth and low self-consumption. Therefore, voltage measurements reach higher efficiency than current measurements with high loss due to shunt resistors or hall sensors with limited bandwidth.

Figure 10 shows the measuring application for acquiring the input and output for the observer model. A simple voltage divider sets the transformer voltages to required level of the main control unit MCU with and . Depending on the switching state of full-bridge H_A the potential of the transformer voltage is floating. As in single ended mode the MCU refers its input signals to , an operational amplifier OP_p’ performs the differential measurement and provides stable and resilient signals for further processing in MCU. Additionally, the differential measurement does not require a floating supply voltage for amplifiers. To maintain isolation of the PSFB the voltage measurement on secondary side needs to be decoupled with an isolated amplifier OP_s’ after differential measurement.

The observer model only needs the average of voltage signals and . Therefore, the low pass filters LP_p’ and LP_s’ smooth the signals and and minimize the measuring noise due to rising edges with high . In the MCU, the digital FIR filters and calculate the moving average over 1000 samples for averaging the signals. According to the observer model the MCU estimates for ctr_Ih.

6.3. Experimental Results

Figure 11 shows the PSFB prototype used for the validation of the proposed control scheme. The modular structure splits the PSFB into 5 separate parts, full-bridges H_A and H_B in the front, transformer TR and filter inductor in the back and a third circuit board equipped with the measuring devices and controller on the second floor to the right. Therefore, separate components can be substituted easily and allows for testing different power devices and combinations of the PSFB for optimization.

In the experimental test set up a National Instrument (NI) Data Acquisition (DAQ) system acquires the values from the measuring circuit board with and performs the calculations of the MCU. Therefore, the NI system includes the observer model, ctr_Ih control scheme with PI-controller and phase-shift calculator. The resulting eight PWM signals are generated on the counter outputs of NI system and directly connected to the drivers for full-bridge switches S₁–S₈.

For validating the observer model and simulation the effects of initial resistance differences and variable operating points are observed. Due to layout and manufacturing tolerances of devices, initial differences are not avoidable and present in prototype electronics. As the effect of resistance in real prototype is much smaller than in simulation, the rising slope of magnetizing current is smaller in experiment and allows for reacting before the prototype gets damaged.

First, Figure 12 compares the measured primary currents of the PSFB prototype in a steady state operating point according to Table 5. Figure 12(a) shows the primary current without any control of magnetization current while Figure 12(b) illustrates controlled by ctr_Ih with observer model. Figure 12(c) explains the according courses of and at higher temporal resolution.

The initial differences cause an unbalanced voltage-second product and lead to an asymmetrical course of with a negative average offset value of . Without compensation this imbalance drives the transformer into saturation for continuous operating time. The ctr_Ih detects the initial imbalance and is able to regulate the average offset to a constant value of . Thus, the ctr_Ih removes the offset difference and improves the system reliability and efficiency.

Figure 13 illustrates the results of the PSFB prototype controlled with ctr_Ih switching between different operating points. Therefore, during the experiment duty cycle varies each time resulting in changed output current shown in Figure 13(d).

In Figure 13(a) the magnetizing current is calculated from measurable reference current with parallel inductor according to (13). Although the magnitude of observer current is scaled due to feedback matrix , the dynamical behavior reflects the magnetizing current and keeps the model error in Figure 13(b) around zero. Equal to theory and simulation in Figure 13(c) the ctr_Ih adjusts with a constant offset due to initial resistance differences and controls variations of . The exact measurement of the initial differences in the full-bridges of the prototype is very difficult and also vary due to temperature effects. Therefore, there is a difference between simulated duty offset and prototype offset. However, the difference does not affect the functionality of the ctr_Ih. The magnetizing current in Figure 13(a) oscillates around its DC-offset while the ctr_Ih shows a better performance on . This difference results from measuring voltage offset due to operational amplifier and is the main drawback of the control scheme. Therefore, the measuring offset must be minimized by using offset compensated operational amplifiers. Compared to simulation the magnitude of magnetizing current is reduced. In real prototype there are also parasitic resistances in the PCB-Layout and in the supply lines from the source. As consequence the given input voltage drops till the transformer with and decreases the slope of magnetizing current . The magnitude of observer and magnetizing current vary each time the operating point changes, as the controlling parameter for PI-controller PI_IL depend on and were not modified during the experiment. Nevertheless, the effect on average values of or observer current is negligible and saturation can be prevented. Therefore, the experimental results confirm the results of simulation and prove the functionality of ctr_Ih for observed disturbances.

7. Conclusion

This paper presents a digital control scheme ctr_Ih for preventing saturation of the transformer due to flux imbalances in isolated PSFB converters. As the magnetizing current of a transformer, which is responsible for the saturation problem, cannot be measured directly, the proposed ctr_Ih uses a Luenberger observer for estimating the magnetizing current. Conventional methods overcome this problem either with increased costs and system size due to additional passive devices or need for lossy and bandwidth limited current measuring. As measuring inputs, the proposed ctr_Ih only needs the average values of transformer voltages and that can be measured with simple operational amplifiers with low self-consumption and naturally high bandwidth. The digital design of ctr_Ih allows for flexible implementation in the main control unit MCU of PSFB converters. Therefore, the MCU includes the ctr_Ih with Luenberger observer model and PI-controller, the output regulator ctr_IL as well as a phase-shift calculator and directly interventions the PWM signals for all power switches S₁–S₈ via driver.

The paper identifies two inevitable effects as main reasons for increased magnetizing DC-offset current . First, initial resistance differences due to manufacturing tolerances of devices and second dynamic changes of duty cycle for regulating the output power. It is shown that without any control both effects would lead to transformer saturation and threaten system reliability. The proposed ctr_Ih with Luenberger observer model is evaluated by simulation and experimental results on a PSFB prototype with power for the identified effects. The ctr_Ih is able to compensate initial resistance differences within by independently controlling the duty cycles of leading and lagging leg of the full-bridge. Also dynamic changes in duty cycle can be controlled out and guarantee a stable continuous operation with an magnetizing DC-offset at . The differences between simulation and experiment can be explained through the additional voltage drop in the supply lines and PCB-layout that result in a smaller magnitude of for the real prototype. The main drawback of the proposed scheme can be eliminated by using offset compensated operational amplifiers.

Data Availability

The datasets supporting the research are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgments

The authors would like to thank Hochschule Karlsruhe-University of Applied science and ads-tec Energy GmbH for facilitating this research.

References

https://www.statista.com/statistics/222066/projected-global-energy-consumption-by-source/.
J. Liu, W. Yao, J. Wen et al., “Impact of power grid strength and PLL parameters on stability of grid-connected DFIG wind farm,” IEEE Transactions on Sustainable Energy, vol. 11, pp. 545–557, 2020.
View at: Google Scholar
A. Coester, M. W. Hofkes, and E. Papyrakis, “Economic analysis of batteries: impact on security of electricity supply and renewable energy expansion in Germany,” Applied Energy, vol. 275, 2020.
View at: Publisher Site | Google Scholar
P. Chatterjee and M. Hermwille, “Befeuern der DC-Ladeinfrastruktur-leistungsbausteine für schnelles Laden,” Emolility Tec Jan, vol. 34–37, 2019.
View at: Google Scholar
J. M. Zhang, X. G. Xie, X. K. Wu, and Qian, “Zhaoming Comparison study of phase-shift full bridge ZVS converters,” IEEE 35th Annual Power Electronics Specialists Conference, vol. 1, pp. 533–539, 2004.
View at: Google Scholar
Y.-Do Kim, K.-M. Cho, D. Y. Kim, and G. W Moon, “Wide-range ZVS phase-shift full-bridge converter with reduced conduction loss caused by circulating current,” IEEE Transactions on Power Electronics, vol. 28, no. 7, pp. 3308–3316, 2013.
View at: Publisher Site | Google Scholar
H. Cha, L. Chen, R. Ding, Q. Tang, and Peng, “Fang zheng an alternative energy recovery clamp circuit for full-bridge PWM converters with wide ranges of input voltage,” IEEE Transactions on Power Electronics, vol. 23, pp. 2828–2837, 2008.
View at: Google Scholar
J. A. Sabaté, V. Vlatkovic, R. B. Ridley, F.-C.- Lee, and B.-H.- Cho, Design Considerations for High-Voltage High-Power Full-Bridge Zero-Voltage-Switched PWM Converter, IEEE, Piscataway, NJ, USA, 1990.
Norm IEC 69/523/CD, Electric Vehicle Conductive Charging System Part 23: DC Electric Vehicle Charging Station, Beuth-Verlag, Berlin, Germany, 2017.
J. A. Claassens and I. W. Hofsajer, “A flux balancer for phase shift ZVS DC-DC converters under transient conditions,” Twenty-First Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Phoenix, AZ, USA, vol. 19, p. 5, 2006.
View at: Google Scholar
L. H. Mweene, C. A. Wright, and M. F. Schlecht, “A 1 kW 500 kHz front-end converter for a distributed power supply system,” IEEE Transactions on Power Electronics, vol. 6, pp. 398–407, 1991.
View at: Publisher Site | Google Scholar
J.-H. Ko, S.-W. Baek, K.-M. Lee, H.-W. Kim, K.-Y. Cho, and J.-M. Kim, “Hybrid current-mode control of PSFB converter to compensate slew interval and prevent magnetic saturation of transformers,” Electronics, vol. 9, 2020.
View at: Publisher Site | Google Scholar
T.-H. Kim, S.-J. Lee, and W. Choi, “Design and control of the phase shift full bridge converter for the on-board battery charger of the electric forklift,” in Proceedings of the 8th International Conference on Power Electronics-ECCE, pp. 2709–2716, Asia, Jeju, Korea, 2011.
View at: Google Scholar
J.-H. Cho, K.-B. Park, J.-S. Park, G.-W. Moon, and M.-J. Youn, “Design of a digital offset compensator eliminating transformer magnetizing current offset of a phase-shift full-bridge converter,” IEEE Transactions on Power Electronics, vol. 27, no. 1, pp. 331–341, 2012.
View at: Publisher Site | Google Scholar
H. Schmidt-Walter and R. Kories, Caption 2 Electric Field in Electrical Engineering-A Pocket Reference, Springer-Verlag, Heidelberg, Germany, 2003.
F. Taeed and M. Nymand, “Adaptive slope compensation for high bandwidth digital current mode controller,” in IEEE 2015 IEEE 11th International Conference on Power Electronics and Drive Systems, Piscataway, NJ, USA, 2012.
View at: Google Scholar
Y. Sun and B. Jiao, “Design of a soft-switched phase-shift full bridge converter,” in 3rd International Conference on Systems and Informatics, pp. 230–234, ICSAI), Shanghai, China, 2016.
View at: Google Scholar
R. Sheehan, Understanding and Applying Current-Mode Control Theory, National Semiconductor Corporation, Santa Clara, CA, USA, 2007.
N. Kondrath and M. K. Kazimierczuk, “Slope compensation and relative stability of peak current-mode controlled PWM dc-dc converters in CCM,” in IEEE 56th International Midwest Symposium on Circuits and Systems, pp. 477–480, MWSCAS), Columbus, OH, USA, 2013.
View at: Google Scholar
J. Chen, A. Prodic, R. W. Erickson, and D. Maksimovic, “Predictive digital current programmed control,” IEEE Transactions on Power Electronics, vol. 18, no. 1, pp. 411–419, 2003.
View at: Publisher Site | Google Scholar
Y. Panov, M. M. Jovanovic, and B. T. Irving, “Novel transformer-flux-balancing control of dual-active-bridge bidirectional converters 2015,” IEEE Applied Power Electronics Conference and Exposition (APEC), 2015.
View at: Google Scholar
K. H. Andersen and M. Nymand, “Fast Digital estimating and balancing of transformer magnetizing current in an isolated full bridge converter 2017,” IEEE Southern Power Electronics Conference (SPEC), vol. 1–6, 2017.
View at: Google Scholar
Y. Panov, M. M. Jovanovic, L. Gang, and M. Yueyong, “Transformer-flux-balancing control in isolated bidirectional DC-DC converters 2014,” IEEE Applied Power Electronics Conference and Exposition-APEC, pp. 49–56, 2014.
View at: Google Scholar
K. Umetani, Y. Itoh, and M. Yamamoto, “Adetection method of dc magnetization utilizing local inhomogeneity of flux distribution in power transformer core,” IEEE Energy Conversion Congress and Exposition (ECCE), pp. 3739–3746.
View at: Google Scholar
F. Naseri, Z. Kazemi, M. M. Arefi, and E. Farjah, “Fast discrimination of transformer magnetizing current from internal faults: an extended kalman filter-based approach,” IEEE Transactions on Power Delivery, vol. 33, no. 1, pp. 110–118, 2018.
View at: Publisher Site | Google Scholar
M. Schühle, M. Beltle, S. Tenbohlen, and BonmannD, “Development of a simulation model to inspect magnetic flux in power transformer components in case of saturation,” VDE-Hochspannungstechnik, vol. 14, 2016.
View at: Google Scholar
N. Kutkut and G. Luckjiff, “Current mode control of a full bridge DC-to-DC converter with a two inductor rectifiers,” in Proceedings of the 28th Annual IEEE Power Electronics Specialists Conference. Formerly Power Conditioning Specialists Conference 1970-71. Power Processing and Electronic Specialists Conference 1972 (PESC97), pp. 203–209, St. Louis, MO, USA, 1997.
View at: Google Scholar
J.-G. Cho, J. A. Sabate, G. Hua, and F. C. Lee, “Zero-voltage and zero-current-switching full bridge PWM converter for high-power applications,” IEEE Transactions on Power Electronics, vol. 11, no. 4, pp. 622–628, 1996.
View at: Publisher Site | Google Scholar
R. G. Raj, S. Palani, and H. H. Sait, “State space modeling and implementation of a new transformer based multilevel inverter topology with reduced switch count,” Circuits and Systems, vol. 07, no. 04, pp. 446–463, 2016.
View at: Publisher Site | Google Scholar
J. Lunze, Regelungstechnik 2: MehrgröSSzensysteme Digitale Regelung, Springer-Verlag, Heidelberg, Germany, 2008.
O. Föllinger, Regelungstechnik, Einführung in die Methoden und ihre Anwendung, Hüthig Verlag, Heidelberg, Germany, 1994.
C.-T. Chen, State-Space Solutions and Realizations in Linear System Theory and Design, Oxford University Press, Oxford, US, pp. 90–96, 1993.
J. Ackermann, Der Entwurf linearer Regelungssysteme im Zustandsraum, M.I.T. Press, Cambridge, MA, USA, pp. 90–96, 1972.

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