A Study on Novel Current Controller for Improving Transient Characteristics in Direct Current Power Systems

Abstract

This study proposes a novel current controller to enhance the transient response characteristics and control responsiveness of energy storage systems (ESSs) in DC power systems. To achieve this, an Enhanced Transient High-Speed Controller (ETHSC) is introduced, which improves upon the conventional Transient High-Speed Controller (THSC) by incorporating real-time error compensation for excitation voltage application time. The ETHSC calculates the inductor’s flux linkage $\lambda$ in real-time and corrects errors caused by the nonlinear characteristics of inductance, ensuring more stable control performance. This study further analyzes the limitations of the conventional THSC and mathematically formulates the ETHSC architecture, introducing a real-time inductance correction algorithm to enhance transient response and stability. The proposed controller was implemented in a boost converter topology and compared with the conventional THSC. Through PSIM simulations and a 500 W prototype experiment, the ETHSC demonstrated its ability to maintain fast transient response while significantly reducing overshoot caused by inductor nonlinearity. These results confirm that the ETHSC provides a more stable and efficient control strategy compared to conventional transient controllers, making it a promising solution for high-performance DC power systems.

1. Introduction

Recently, with the increase in distributed power sources such as solar power, wind power, energy storage systems (ESSs), and fuel cells, there has been a growing interest in DC power systems like LVDC (Low-Voltage Direct Current) and MVDC (Medium-Voltage Direct Current) that can easily integrate with these systems [1,2]. These DC power systems are especially advantageous for applications with low DC power requirements, such as data centers and DC homes, enabling high-efficiency energy delivery, as shown in Figure 1 [3,4,5,6]. Using DC power allows for the delivery of more power through the same electrical pathway compared to AC systems, and it reduces the number of power conversion stages, thus enabling the construction of high-efficiency power grids [7,8,9]. This can reduce the volume, weight, and cost of power systems [10,11]. Additionally, there is no need for phase and frequency synchronization between various power sources, and concerns about harmonics or reactive power control are minimized, making it easier to integrate system components [12,13]. Furthermore, power quality management and fault monitoring or isolation become easier as the power systems are interconnected and integrated through power conversion circuits [14,15].

However, despite these advantages, strategic control methods are required to supply high-quality DC power systems [16,17]. Since various power sources and nonlinear loads are integrated into the DC bus, even if each subsystem is designed to be stable, the integration can cause mutual interference, leading to performance degradation or instability of the overall system [18,19,20]. In particular, with the advancement of power electronic devices and control technologies, the dynamic characteristics of power conversion circuits at the load end have improved, causing electronic loads or motor loads driven by inverters to operate as constant power loads. Unlike constant resistance and constant current loads, constant power loads exhibit nonlinearity, which is a major factor contributing to system instability [21,22,23].

Various methods such as sliding-mode control (SMC), state-feedback control, and gain-scheduling have been proposed for stable and high-speed control in the transient state of the bidirectional DC/DC converter [24,25,26,27]. However, although these methods can improve performance, their designs are complicated. Consequently, peak current mode control (PCMC), which has a relatively simple control architecture, is sometimes applied to bidirectional DC/DC converters. However, PCMC suffers from control instability when the duty cycle exceeds 50% due to the inherent time delay of the control loop, resulting in sub-harmonic oscillation [28,29,30]. And recent research has explored simplified digital logic-based compensation methods that can be applied independently of modulation or control schemes, reducing implementation complexity while enhancing transient response and stability [31,32]. Accordingly, a THSC with fast and stable control in the transient state that can compensate for the disadvantages of the aforementioned controller was proposed [33]. The THSC has a simple architecture, is immune to duty cycles, and effectively reduces overshoots that may occur in transient states. However, the THSC has a significant limitation in that it operates as an open-loop controller, meaning it cannot correct errors caused by parameter variations when the system is running. This can lead to overshoot or undershoot due to inaccuracies in system parameters. Therefore, this study analyzes the structural limitations of the conventional THSC and proposes an ETHSC to compensate for parameter variation errors that occur during system operation.

While existing transient controllers, such as PCMC and SMC, each offer certain advantages, they also suffer from fundamental limitations.

Table 1. Comparison of ETHSC with conventional transient control methods.

Controller Type	Advantages	Limitations
PCMC	Simple design	Bandwidth limitation, sub-harmonic oscillation
SMC	Robust performance	Complex design, computational burden
THSC	Fast transient response	Open-loop, parameter dependency leads to overshoot/undershoot
ETHSC (Proposed)	Fast transient response, real-time error correction	Additional computational step for correction

summarizes these limitations and how the proposed ETHSC (Enhanced Transient High-Speed Controller) overcomes them.

Therefore, in this study, we propose an ETHSC based on the THSC that maintains a simple control structure, stability in transient states, and fast response. Unlike conventional control methods that rely on complex feedback loops and adaptive tuning mechanisms, the ETHSC achieves simplicity by utilizing system parameters determined in the initial design stage. The ETHSC determines the inductor’s excitation voltage application time in the same manner as the THSC, utilizing pre-determined topology equations, designed inductor values, and real-time sensor data from voltage and current sensors. Since the system parameters, such as inductance and circuit topology, are known in advance, the ETHSC only needs to compute the excitation voltage duration for the inductor based on these fixed values and measured signals. This approach eliminates the need for sophisticated real-time adjustments, making the controller computationally efficient and easy to implement while ensuring fast transient response and stability. Therefore, this study analyzes the structural limitations of the conventional THSC and proposes an ETHSC to compensate for parameter variation errors that occur during system operation. Then, the ETHSC further enhances the THSC by introducing a real-time inductance nonlinearity compensation mechanism. In real applications, the inductance value is not constant but varies depending on the magnitude of the current due to core saturation and other nonlinear effects. This variation introduces errors in excitation voltage application time, leading to potential overshoot or deviations from the desired control trajectory. The ETHSC compares the calculated flux linkage with the actual flux linkage in each control cycle to extract errors and dynamically adjust the excitation voltage application time. By continuously compensating for these errors, the ETHSC improves overall system stability and reliability, ensuring precise current tracking even under varying inductance conditions.

Through simulation and experimental validation, the proposed ETHSC demonstrates superior transient performance compared to conventional methods. The remainder of this paper details the ETHSC architecture, performance evaluation, and comparison with existing transient controllers.

The remainder of this paper is organized as follows. Section 2 describes the bidirectional DC/DC converter topology and its control methods, providing a foundation for the proposed ETHSC. Section 3 introduces the Enhanced Transient High-Speed Controller (ETHSC), detailing its theoretical formulation and real-time inductance compensation algorithm. Section 4 presents simulation and experimental results, comparing the performance of the ETHSC with conventional controllers such as PI, SMC, and the THSC. Finally, Section 5 concludes the study by summarizing the findings and discussing potential directions for future research.

2. Bidirectional Boost Converter

2.1. Hardware Description

Figure 2 shows a conventional bidirectional boost converter applicable to the ESS and SC configured for fuel cell applications. The interpretation of a bidirectional boost DC/DC converter can be expressed as inductor voltage $v_L$, inductor current $i_L$, and flux linkage $\lambda$ depending on the switch state. $v_L$, $i_L$, and flux linkage $\lambda$ have the following relationship [1,2].

$$v_L\left(t\right)=L{\displaystyle \frac{d{i}_L\left(t\right)}{dt}}={\displaystyle \frac{d\lambda \left(t\right)}{dt}}$$

(1)

The inductor voltage $v_L$ according to the switch state can be calculated by applying Kirchhoff’s voltage law (KVL): The inductor voltage based on the operation state of Q1, which is the subject of bidirectional boost converter control, is expressed as follows:

$$\left\{\begin{array}{cc}{\displaystyle v_{L\left(on\right)}=V_{in}-V_{out}}\hfill & \left(Q1\text{:} ON,Q2\text{:} OFF\right)\hfill \\ {\displaystyle v_{L\left(off\right)}=-V_{out}}\hfill & \left(Q1\text{:} OFF,Q2\text{:} ON\right)\hfill \end{array}\right.$$

(2)

Depending on the switch state, inductor current ripple $∆i_L$ can be expressed using Equation (2), and the increases and decreases of the current are expressed by $∆i_{Lp}$ and $∆i_{Ln}$.

$$\left\{\begin{array}{cc}{\displaystyle ∆i_{Lp}=\frac{V_{in}-V_{out}}{L}\times D{T}_s}\hfill & \left(Q1\text{:} ON\right)\hfill \\ {\displaystyle ∆i_{Ln}=\frac{V_{out}}{L}\times \left(1-D\right)T_s}\hfill & \left(Q1\text{:} OFF\right)\hfill \end{array}\right.$$

(3)

In Equation (3), D is the duty ratio, and $T_s$ is the sampling time. According to the voltage second balance law (VSBL), the relationship between the input voltage $V_{in}$, output voltage $V_{out}$, and duty ratio D can be represented by $V_{out}$=$V_{in}$$/(1-D)$. The inductor design is possible using Equations (1)–(3), and it is assumed that the value of the inductor is set such that it can be a current continuous mode (CCM). Generally, in bi-directional boost converters, $V_{in}$, $V_{out}$, $T_s$, L, and C are determined in the design condition; and in converter control, the inductor current and output voltage ripple are determined only by the duty ratio D.

2.2. Bidirectional Converter Controllers

The bi-directional converters applied to the DC power system require active power-control technology to stabilize the DC-bus voltage, respond to rapid power changes, and recover regenerative energy. The duty ratio D, which is a bidirectional converter control element, is determined by the relationship between the input and output voltages in the average steady-state operation, in which the energy charged and discharged in the inductor are the same. The voltage second balance law (VSBL) was established in the average steady-state operation; however, it was not established in the transient state, where the voltage or current changes. Therefore, voltage and current controls are performed using a feedback controller, such as a PI controller. The most common method applied to a bidirectional converter is the proportional–integral (PI) controller.

The PI controller is a control technique used by integrating error signals and creating control signals in parallel with proportional control and has excellent control responsiveness. Moreover, it has the advantage of minimizing the vibration of the system at the control target point and controlling errors under normal conditions. However, it is difficult to guarantee control stability owing to the overshoot characteristics of the transient state caused by changes in system parameters or loads; therefore, the THSC has recently been studied to reduce the overshoot that may occur in transient states and to increase the responsiveness of control.

A THSC is a controller that can increase reactivity by calculating the flux linkage of an inductor configured in a bidirectional converter and applying an excitation voltage without PWM switching to instantly settle the control current target point in a transient state. The configuration of the THSC is shown in Figure 3. The structure of the THSC is divided into a control block with fast responsiveness in the transient state and a PI controller with a feedforward term that can perform stable control in the normal state.

The operation of the THSC operates when a delta current command $∆i^{\ast }$ is generated more than a specific current level in the upper controller based on the change in power or load. The delta current command value $∆i^{\ast }$ is generated by as much as the difference between the real current command value $i_n^{\ast }$ and command value $i_{n-1}^{\ast }$ of the previous sampling, which determines whether or not the THSC should be operated. To operate the THSC stably, it should operate when $∆i^{\ast }$ is greater than inductor current ripple $∆i_L$, that is, when duty = 1 or duty = 0. Under this condition, $mod{e}^{\ast }$ is set to 1, and if the THSC operation condition is not satisfied, $mod{e}^{\ast }$ is set to 0. The inductor current ripple $∆i_L$, which changes to the maximum for one cycle when duty = 1 or duty = 0, can be set using Equation (3). The THSC calculates the flux linkage ${\lambda }^{\ast }$ shown in Equation (1) using the aforementioned information and operates by calculating the target arrival time $∆T_t^{\ast }$ for applying the excitation voltage. The inductor voltage should be classified based on the Q1 switch ON/OFF state, which is the control subject of the boost converter, and these are divided into $∆T_{t\left(on\right)}$ and $∆T_{t\left(off\right)}$, respectively.

$$\left\{\begin{array}{cc}{\displaystyle ∆T_{t\left(on\right)}=\frac{L∆i^{\ast }}{v_{L\left(on\right)}}}\hfill & \left(Q1\text{:} ON\right)\hfill \\ \\ {\displaystyle ∆T_{t\left(off\right)}=\frac{L∆i^{\ast }}{v_{L\left(off\right)}}}\hfill & \left(Q1\text{:} OFF\right)\hfill \end{array}\right.$$

(4)

As shown in the above equation, the target arrival time $∆T_t^{\ast }$ is affected by the input and output voltages depending on the operating state, which is expressed in the form of a multiple sampling time $T_s$.

The calculated $∆T_t^{\ast }$ was reduced by $T_s$ in each control cycle, and the resulting value operation remained as time $T_c$, which is the remaining time for reaching the target current in the current control loop. If $T_c/T_s>1$, then the duty $d_s\left(n\right)$ is recognized as a transient state, and the applied system maintains a value based on whether $∆i^{\ast }$ is increasing or decreasing. In this case, if $d_s\left(n\right)=1$, it means that Q1 is ON ($Q1=1$), and if $d_s\left(n\right)=0$, it means that Q1 is OFF ($Q1=0$). Contrarily, if the condition is $T_c/T_s>1$, it is switched to enable the PI controller with the feedforward term for stable control near the control target point. In conclusion, the THSC can ensure fast responsiveness by calculating the target arrival time through hardware components and input and output specifications known in the design stage, and by keeping the switch state on or off to reach the control current target point.

However, the THSC does not correct errors using real-time voltage or current data, and errors in the target arrival time may occur because of inductors with nonlinear characteristics. Errors in the target arrival time caused by inductors with nonlinear characteristics occur when the value of the inductor set for calculating the target arrival time is large or small, as shown in Figure 4.

The value of the inductor input to the THSC is expressed as $L_{set}$, $L_L$ when the value of the actual inductor is large, and $L_S$ when it is small. If the characteristics of the actual inductor are larger than those of the set inductor (blue dotted line), the THSC ends before the target current point and switches to the PI+Feedforward control, which can lead to undershoots. However, if the actual inductor value is smaller than the applied value of the set inductor (green dotted line), the operating time of the THSC is maintained even after the target current point, which is fatal because an overshoot may occur. Accordingly, a simple architecture, which is an advantage of existing THSCs, along with a method to maintain high speed in transient conditions and ensure stability are essential.

3. Enhanced Transient High-Speed Controller (ETHSC)

The existing THSC can improve responsiveness in transient conditions because it calculates the amount of flux linkage and applies an excitation voltage to the inductor for a certain period of time without PWM to settle instantaneously from the transient state to the average steady state. However, the THSC is more similar to an open-loop-type controller because it uses only various parameter information made in the design stage and does not compensate for errors occurring in the output. Furthermore, because the input parameter information is assumed to have linear characteristics, errors owing to nonlinear characteristics in the system can cause problems such as overshoot or undershoot. Accordingly, this study proposes an improved THSC that can maintain the advantages of existing THSCs and ensure stability. Figure 5 shows a block diagram of the controller proposed in this study.

Similar to the THSC, the overall controller configuration can be divided into an ETHSC block that can operate in a transient state and a PI controller with a feedforward term that can operate stably in the average steady state. Similar to the THSC, the proposed ETHSC determines whether the transient state starts through the command value change $∆i^{\ast }$ and selects the ETHSC block or PI+Feedforward block. If it is recognized as a transient state and indicates the order in which the ETHSC operates, then it is as follows.

Step1: The target linkage flux amount ${\lambda }^{\ast }$ is calculated using the initially designed inductor value L, input voltage $V_{in}$, output voltage $V_{out}$, and current command value $∆i^{\ast }$. Through this, $∆T_t^{\ast }$ can be calculated, and the resulting value can be obtained using Equation (4) according to the $∆i^{\ast }$.

Step 2: The calculated $∆T_t^{\ast }$ can be reduced by $T_s$ at every sampling period to calculate the ETHSC operation’s remaining time $T_c$. In the case of the existing THSC method, mode changes are made based on condition $T_c/T_s>1$ or $T_c/T_s<1$ using only the parameter value at the time when the THSC begins. However, the ETHSC proposed in this study integrates the actual current $i_{real}$, predicts current value $i_{Ts}$ for every cycle to detect errors, and calculates the operating error time $T_e$. Through this, lambda errors can be improved by compensating $T_e$ to target arrival time $∆T_t^{\ast }$, which can be expressed as Equation (5):

$$\left\{\begin{array}{cc}{\displaystyle ∆T_{e\left(on\right)}=\frac{L(i_{Ts\left(on\right)}-i_{real})}{v_{L\left(on\right)}}=\frac{{\lambda }_{e\left(on\right)}^{\ast }}{v_{L\left(on\right)}}}\hfill & \left(Q1\text{:} ON\right)\hfill \\ \\ {\displaystyle ∆T_{e\left(off\right)}=\frac{L(i_{Ts\left(off\right)}-i_{real})}{v_{L\left(off\right)}}=\frac{{\lambda }_{e\left(off\right)}^{\ast }}{v_{L\left(off\right)}}}\hfill & \left(Q1\text{:} OFF\right)\hfill \end{array}\right.$$

(5)

where $i_{Ts}$ is the predicted current value that changes for each sampling and can be calculated using Equation (3) depending on the switch state, and $i_{Ts}$, according to the switch state, is divided into $i_{Ts\left(on\right)}$ and $i_{Ts\left(off\right)}$. Consequently, the difference between $i_{Ts}$ and the actual current $i_{real}$ is the same as the difference between the predicted linkage flux ${\lambda }_{Ts}(=L\times i_{Ts})$ and linkage flux ${\lambda }_{real}(=L\times i_{real})$ of the inductor exhibiting actual nonlinear characteristics. This can compensate for the time required to apply the excitation voltage through the error generated by comparing the predicted magnetic flux amount ${\lambda }_{Ts}$ with the actual magnetic flux amount ${\lambda }_{real}$ for every control cycle. Figure 6 shows the operation of the ETHSC with the lambda error compression block added (yellow highlight), as shown in Equation (5) and Figure 5.

Figure 6 shows the process of compensation when the operation remain-time $T_c$ according to $∆i^{\ast }$ is greater or less than value $L_{set}$ of the inductor input by the ETHSC. The red waveform in Figure 6 represents $T_c$ of the existing THSC without $T_e$ compensation when it is the $L_{set}$, and the blue waveform represents the operation remain-time $T_c$ of the ETHSC with $T_e$ compensation. Figure 6a shows $T_c$ when the value of the applied inductor is smaller $(L_{real}<L_{set})$ than that of the $L_{set}$. When the controller operates while $∆i^{\ast }$ occurs, the target arrival time $∆T_t^{\ast }$ by $L_{set}$ is calculated, and the decrease in $T_c$ by $T_s$ is calculated for each sampling. This means that under the $L_{real}<L_{set}$ condition, $∆T_t^{\ast }$ by $L_{set}$ is longer than the actual control target arrival time by $L_{real}$, which can cause overshoot.

Contrarily, in the $L_{real}>L_{set}$ condition, ${∆}_t^{\ast }$ by $L_{set}$ is shorter than the actual control target time, resulting in an undershoot or reducing the effect of improving the responsiveness of the transient state. Therefore, the ETHSC compares the difference between the predicted current $i_{Ts}$ from the $L_{set}$ and actual current $i_{real}$ to compensate $T_c$ for the operating error time $T_e$ to prevent overshoot or undershoot. Because this is the same as compensating for the lambda characteristics that vary depending on the current size in the actual inductor, the stability and reliability can be significantly improved by reducing the overshoot that may occur in the transient state.

Figure 7 shows a flowchart of the EHTSC operation based on the set sampling period. The basic configuration inputs the inductor value initially determined during the design stage, similar to the existing THSC configuration. The analog sensing signal for control is then read by the ADC, and the current command value based on the power is adjusted at each set period. As aforementioned, to drive the controller stably, it is set to operate when $∆i^{\ast }$ is larger than inductor current ripple $∆i_L$, that is, when duty = 1 or duty = 0. If $∆i^{\ast }$ occurs above the $∆i_L$, the target arrival time $∆T_t^{\ast }$ is calculated according to the increase or decrease in the amount of power, and the duty at this time is kept at one or zero. Thereafter, unlike the existing THSC, the operation error time $T_e$ is compensated by comparing the predicted linkage flux ${\lambda }_{Ts}$ with the actual linkage flux ${\lambda }_{real}$ at the operation remain-time $T_c$ calculated for each sampling. Subsequently, when $T_c$ is less than one, that is, less than the sampling time $T_s$, it is determined that the control target point has almost been reached, and the system is operated using a PI controller that includes a feedforward term for stable control in a normal state.

4. Simulation and Experiment

4.1. Simulation

Figure 8 shows a simulation circuit diagram used to verify the validity of the ETHSC proposed in this study. The simulation was conducted using PSIM 9.0 from Powersim Corporation. To verify the validity of ETHSC in simulation, we compared it with SMC, PI, and THSC. The simulation circuits were configured identically, and the battery was modeled using the Randles equivalent circuit. To accurately compare the transient characteristics of each controller, a simulation was performed with the same gain as that of the PI+feedforward controller. Simulations were performed for two cases: ideal and actual inductors configured in the simulation system.

A simulation was conducted by applying the results obtained through 3D electromagnetic finite element analysis to confirm the operational characteristics of the controller based on the nonlinearity of the actual inductor. The magnetic core used the “MF060” ferrite core and the B-H curve reflected in the simulation is shown in Figure 9a. Figure 9b–d show the results of the inductance analysis based on the magnitude of the input current, magnetic flux–density distribution, and actual inductor.

The inductor value $L_{real}$ used in the simulation was based on 620 $\mathsf{\mu }$H applied in the experiment. In addition, $L_{set}$, which provides an error in calculating the target linkage flux amount ${\lambda }^{\ast }$ of the controller, was inputted as ±100 $\mathsf{\mu }$H based on $L_{real}$. In addition, in order to confirm the operation of the nonlinearity of the inductor, the raw data of Figure 9b were inputted and the simulation for $L_{real\left(act\right)}$ was also performed. The battery voltage configured in the system was set to 24 and 48 V when duty = 0.5, in which the current ripple of the system was maximized. Accordingly, it can be confirmed through Equation (4) that the target arrival time $∆T_t^{\ast }$$(∆T_{t\left(on\right)},∆T_{t\left(off\right)})$ for applying the excitation voltage was the same. The following

Table 2. Specifications and parameters of the simulation circuit.

Note	Symbol	Value
Converter input voltage	$V_{in}$	24 V
Battery voltage	$V_{bat}$	48 V
Inductor set value	$L_{set}$	620 ± 100 $\mathsf{\mu }$H
Inductor value in simulation circuit	$L_{real}$	620 $\mathsf{\mu }$H
Actual inductor value	$L_{real\left(act\right)}$	Figure 9b data
Max. current command value variation	$∆i_{max}^{\ast }$	20.0 A
System requirements’ response time	$∆T_{target}$	600 $\mathsf{\mu }$s
Switching frequency	$f_s$	20 kHz

summarizes the parameters used in the simulations.

Figure 10 and Figure 11 show the simulation result waveform based on the state of the ideal inductors $L_{real}$ and $L_{set}$$(L_{real}=L_{set},L_{real}>L_{set},L_{real}<L_{set})$ fixed.

First, the simulation waveform in Figure 10 shows the current command $i^{\ast }$ and the current waveform according to it, which confirms the transient state of each controller, including the ETHSC when the condition is $L_{real}=L_{set}$. At this time, the THSC and ETHSC can be expected to output the same form, so the resulting waveforms are shown separately. It can be seen through Equation (4) that it takes about 516.6 $\mathsf{\mu }$s when the current command $i^{\ast }$ changes from 0 to 20 A, and it can be confirmed that stable control is achieved through the PI controller after reaching the steady state. In contrast, it can be confirmed that the PI controller and SMC controller take about 1.3 ms when the current command $i^{\ast }$ changes from 0 to 20 A, and that overshoot occurs. Then, from $+∆i_{max}^{\ast }$ to $-∆i_{max}^{\ast }$ and from $-∆i_{max}^{\ast }$ to $+∆i_{max}^{\ast }$, the current command value $i^{\ast }$ is 40 A. It can be observed that it takes approximately 1033.3 $\mathsf{\mu }$s to reach the steady state when changing, and this can also be verified through Equation (4). Moreover, we can see that SMC takes about 1.8 ms from $+∆i_{max}^{\ast }$ to $-∆i_{max}^{\ast }$, and the PI controller takes about 2.6 ms. We can also see that these two controllers have overshoot.

Figure 11 shows the result waveforms of each controller under the conditions $L_{real}>L_{set}$ and $L_{real}<L_{set}$, and the $T_c$ waveforms of THSC and ETHSC. In simulations to compare the transient characteristics with other controllers, the PI controller and SMC controller were set to a control gain that did not cause overshoot or chatter in the steady state.

First, in Figure 11a, which is the resulting waveform under the condition $L_{real}>L_{set}$ ($L_{real}=720\mathsf{\mu }$H, $L_{set}=620\mathsf{\mu }$H), in the case of the THSC, the controller is terminated before the current reference value is reached due to the inductor error that occurs in the initial setup stage, which reduces the advantage of fast transient response. However, in the case of the ETHSC, the difference between the predicted current $i_{Ts}$ and the actual current $i_{real}$ is compared at each sampling, and the operation error time $T_e$ is calculated through Equation (5) and this is compensated for $T_c$. As a result, it can be confirmed that the inductor current stably reaches the steady state while maintaining the high-speed characteristic in the transient state. And in the case of SMC, it showed a response time of about 1.3 ms for the rising time and about 2.2 ms for the falling time until reaching the current command value. It was confirmed that overshoot hardly occurred after reaching the current command value. The reason for these results is that the actual inductance value is larger than the inductance reflected for control gain design, which results in a worse transient response. Finally, the PI controller showed a response time of about 1.5 ms for the rising time and about 3.0 ms for the falling time until reaching the current command value, and it was confirmed that overshoot occurred. This is the result of conducting the simulation by changing the value of the actual inductor value $L_{real}$ to 720 $\mathsf{\mu }$H.

Figure 11b shows the resulting waveforms of the THSC and ETHSC under the condition of $L_{real}<L_{set}$ ($L_{real}=520\mathsf{\mu }$H, $L_{set}=620\mathsf{\mu }$H). In the case of the THSC, it can be confirmed that the operation maintenance time $T_c$ due to the inductor error generates an error, and the controller is not terminated even after reaching the steady state, causing overshoot. However, in the case of ETHSC, it can be confirmed that by compensating the operation error time $T_e$ for the operation maintenance time $T_c$, it is stably switched to the PI controller after reaching the steady state without overshoot. In addition, the PI controller and SMC controllers showed characteristics almost similar to the previous conditions. As the inductor decreased, the PI controller showed a response of about 1.1 ms and 2.2 ms for the rising time and falling time, respectively, and the SMC showed a response of 0.9 ms and 1.6 ms. The red box in Figure 11 represents the operating error time $T_e$ caused by the lambda error. When using ETHSC, we can see that the operating error time caused by the lambda error is compensated.

Finally, Figure 12 shows the simulation result’s waveforms using an inductor with nonlinearity applied to the results obtained through the 3D electromagnetic finite element analysis. First, based on the simulation result’s waveforms applied with the ETHSC, when the current command value $i^{\ast }$ is changed to $\pm ∆i_{max}^{\ast }$, $T_e$ is compensated for $T_c$. Therefore, it can be confirmed that the high-speed characteristics in the transient state can be maintained and the overshoot can be effectively prevented. However, in the case of the THSC, it was confirmed that an overshoot of about 2.5 A occurred during the rising time and about 4.1 A occurred during the falling time. As we can see from the resulting waveform, even one sampling difference can cause an overshoot. This can be easily predicted through the inductance analysis results according to the input current size shown in Figure 9b. Since the value of the inductor current decreases as the inductor current increases, the size of the overshoot also increases as the current increases. This means that the DC bus voltage stability of the DC power system deteriorates, causing fatal damage to the load configured in the system. As a result, it was verified that operating the system using the ETHSC can maintain high-speed characteristics under transient conditions and effectively reduce overshoot compared to the THSC, thereby ensuring system stability.

A summary of the simulation results conducted under various inductor conditions is presented in

Table 3. Performance comparison of PI, SMC, THSC, and the ETHSC under different inductor conditions.

Test Condition	Controller	Rising Time	Falling Time	Deviation (R/F)
$L_{real}=L_{set}$	PI	1.3 ms	2.6 ms	4.7 A/4.7 A
	SMC	1.2 ms	1.8 ms	0.9 A/0.9 A
	THSC	516 $\mathsf{\mu }$s	1.03 ms	2.5 A/4.1 A
	ETHSC	516 $\mathsf{\mu }$s	1.03 ms	0.3 A/0.2 A
$L_{real}>L_{set}$	PI	1.5 ms	3.0 ms	4.5 A/4.5 A
	SMC	1.3 ms	2.2 ms	0.8 A/0.8 A
	THSC	1.1 ms	1.8 ms	1.0 A/1.7 A
	ETHSC	751 $\mathsf{\mu }$s	1.5 ms	0.2 A/0.1 A
$L_{real}<L_{set}$	PI	1.1 ms	2.2 ms	5.1 A/5.1 A
	SMC	975 $\mathsf{\mu }$s	1.6 ms	0.9 A/0.9 A
	THSC	500 $\mathsf{\mu }$s	1.0 ms	4.0 A/8.5 A
	ETHSC	500 $\mathsf{\mu }$s	1.0 ms	0.2 A/0.1 A
nonlinear L	PI	1.2 ms	2.4 ms	5.3 A/5.3 A
	SMC	960 $\mathsf{\mu }$s	1.9 ms	0.9 A/0.9 A
	THSC	432 $\mathsf{\mu }$s	1.2 ms	2.5 A/4.1 A
	ETHSC	432 $\mathsf{\mu }$s	1.2 ms	0.4 A/0.2 A

. This table provides a comparative analysis of the rise time, fall time, and deviation (R/F) for PI, SMC, the THSC, and the proposed ETHSC. Here, deviation (R/F) represents the overshoot occurring during the rising time (R) and falling time (F), respectively. As shown in the results, the ETHSC demonstrates excellent transient stability with minimal deviation, effectively mitigating overshoot and undershoot caused by inductor nonlinearity.

4.2. Experiment

Figure 13 shows a prototype of the non-insulated boost converter to confirm the characteristics of the controller proposed in this study. The configuration of a charging system was conducted with an inductor “MF060” fragment core and a 24 V LiFePO₄ analyzed in the simulation. A 24 V LiFePO₄ was configured as a single input, and the output-side battery was configured as a series of 24 V LiFePO₄ 2Ea. To accurately compare only the characteristics of the THSC and ETHSC, the controller composition was determined by applying the same gain of the PI controller operating in the steady-state area. The parameters configured for the system, including the inductor, are listed in

Table 4. Specifications and parameters of experiment.

Note	Symbol	Value
Converter input voltage	$V_{in}$	22.4 to 29.2 V
Battery voltage	$V_{bat}$	44.8 to 58.4 V
System inductor’s inductance	$L_{real}$	620 $\mathsf{\mu }$H
Inductance	$L_{set}$	620 ± 100 $\mathsf{\mu }$H
Max. current command value variation	$∆i_{max}^{\ast }$	20.0 A
System requirements response time	$∆T_{target}$	600 $\mathsf{\mu }$s
Switching frequency	$f_s$	20 kHz
System P gain	$k_p$	0.003
System I gain	$k_i$	1.2

.

First, an experiment was conducted to compare the operating characteristics of the THSC based on the state of $L_{real}$ and $L_{set}$$(L_{real}=L_{set},L_{real}>L_{set},L_{real}<L_{set})$, and the resulting waveform is shown in Figure 14. The experiment analyzed the transient-state characteristics by setting the current command value $i^{\ast }$ to 20 A to confirm the nonlinear characteristics of the inductor at the rated power. Channel 1 (yellow) in Figure 14 represents the inductor current $I_L$, and Channel 4 (green) represents the waveform that outputs the operation maintenance time $T_c$ of the THSC using a 16-bit digital-to-analysis converter IC (DAC8532). $T_c$ was decreased by $T_s$ for each sampling; the size of $T_s$ was set to 5000 as a digital value; and the analog voltage output was approximately 381 mV.

Figure 14a is an experimental results waveform under the $L_{real}=L_{set}$ condition, and it can be observed that the inductor current $I_L$ reached the current command value $i^{\ast }$ within approximately 467 $\mathsf{\mu }$s stably without overshoot. It can be confirmed that the normal-state arrival time measured in the experiment represents a value that is close to that of Equation (4). Furthermore, the operation holding time Tc was reduced from 3.57 to 381 mV while the THSC was operating, which can be confirmed to be normally outputted to 9.36 × 381 mV ≈ 3.57 V, which can be calculated as follows: $∆T_t^{\ast }/T_s=467\mathsf{\mu }\mathrm{s}/50\mathsf{\mu }\mathrm{s}=9.36$.

Figure 14b shows the experimental results waveform when $L_{real}>L_{set}$. The experiment was conducted by setting the set inductance value to 520 $\mathsf{\mu }$H, which is 100 $\mathsf{\mu }$H lower than the actual inductor value $L_{real}$. Under the $L_{real}>L_{set}$ condition, the inductor current $I_L$ ends at 16.8 A, and the operation is switched to the PI+Feedforward controller, and it takes approximately 392 $\mathsf{\mu }$s.

Finally, in Figure 14c, the experiment was conducted by setting the value $L_{s}et$ of the inductance set to 720 $\mathsf{\mu }$H to confirm the transient characteristics under the $L_{real}<L_{set}$ condition. As mentioned, the THSC has an open-loop form. Therefore, it can be observed that the THSC is maintained even after the current command value $i^{\ast }$ reaches the target arrival time $∆T_t^{\ast }$ under the $L_{real}<L_{set}$ condition, resulting in an overshoot. At this time, the THSC maintenance time was approximately 543 $\mathsf{\mu }$s, and the magnitude of the current in which the overshoot occurred was measured to be approximately 23.2 A.

The results of the experiment are summarized in

Table 5. Experimental comparison of the THSC and ETHSC operations.

Test Condition	Controller	Arrival Time	Deviation Value
$L_{real}=L_{set}$	THSC	467 $\mathsf{\mu }$s	+0.1 A
	ETHSC	452 $\mathsf{\mu }$s	−0.1 A
$L_{real}>L_{set}$	THSC	1.5 ms	−3.2 A
	ETHSC	453 $\mathsf{\mu }$s	+0.1 A
$L_{real}<L_{set}$	THSC	467 $\mathsf{\mu }$s	+3.2 A
	ETHSC	455 $\mathsf{\mu }$s	+0.1 A

. In this case, the actual inductor value remained unchanged, while the set value of the inductor was varied in the program. As a result, the rising slopes are all identical. However, the time mentioned above represents the duration for which the THSC operates.

Figure 15 shows the experimental results waveform used to confirm the operational characteristics of the ETHSC. For the experimental conditions, when the current command value $i^{\ast }$ was set to 20 A, the results according to the states of $L_{real}=L_{set}$, $L_{real}>L_{set}$, and $L_{real}<L_{set}$ were confirmed. For the configuration of the experimental results waveform, Channels 1 (yellow) and 4 (green) are the DAC outputs of the inductor current $I_L$ and operation maintenance time $T_c$, respectively, as in the previous experiment. Furthermore, to confirm the operation of the ETHSC, Channel 3 (blue) shows a DAC output waveform in which the operation error time $T_e$ was compensated for the operation remaining time $T_c$. For an accurate comparison between the ETHSC and THSC, DAC was output by giving a delay of approximately 10 $\mathsf{\mu }$s compared to Channel 4 (green). The experimental results show that the ETHSC performs a stable operation by compensating $T_e$ with $T_c$ regardless of the state of $L_{real}$ and $L_{set}$. This is similar to compensating for the lambda characteristics that change depending on the current size of the actual inductor. Consequently, the ETHSC secures high responsiveness in transient conditions, which is an advantage of the existing THSC and effectively reduces overshoots or undershoots that can be caused by inductors with nonlinear characteristics, which means that the stability and reliability can be significantly improved.

Based on the analysis of the experimental results waveforms in Figure 14 and Figure 15, Table 5 summarizes the operational comparison between the THSC and ETHSC. This table presents a comparison of the arrival time and deviation value of the two controllers under various inductor conditions. As shown in the results, the ETHSC maintains a more consistent arrival time compared to the THSC and exhibits minimal deviation variations. This indicates that the ETHSC effectively suppresses overshoot and undershoot caused by the nonlinear characteristics of the inductor, contributing to improved system stability and reliability.

5. Conclusions

This study proposed an Enhanced Transient High-Speed Controller (ETHSC) to overcome the limitations of the conventional Transient High-Speed Controller (THSC). The ETHSC incorporates real-time error compensation to effectively suppress overshoot and undershoot caused by the nonlinear characteristics of inductance, thereby improving transient response performance and system stability.

To achieve this, the limitations of the conventional THSC were analyzed, and the ETHSC was mathematically formulated to enable real-time inductance compensation. A new control algorithm was developed to dynamically correct errors caused by inductance nonlinearity, ensuring precise current tracking and enhanced system stability.

To validate the proposed ETHSC, PSIM-based simulations and a 500 W prototype experiment were conducted, and its performance was compared with the conventional proportional–integral (PI) controller, Sliding Mode Control (SMC), and THSC. The experimental and simulation results demonstrated that the ETHSC maintains the same transient response speed as the THSC while effectively suppressing overshoot and undershoot. Moreover, compared to PI control, the ETHSC reduces transient response time and improves current tracking accuracy. When compared to SMC, the ETHSC achieves similar transient performance but with lower computational complexity and easier implementation. These results confirm that ETHSC provides an effective control strategy that ensures both fast response and high stability compared to existing control methods.

Although ETHSC has shown excellent performance, further validation and improvements are necessary to enhance its applicability across various conditions. First, the performance of the ETHSC can be influenced by inductor core materials and magnetic characteristics. Therefore, experimental data on different inductor types (e.g., ferrite cores, powdered cores) should be collected to develop an advanced compensation algorithm for improved accuracy. Second, the ETHSC relies on real-time voltage and current measurements, making it susceptible to sensor errors and measurement noise, which may degrade the accuracy of error compensation. Future research should explore applying Kalman filtering or adaptive estimation techniques to enhance the reliability of sensor data. Third, while the ETHSC has been validated in bidirectional DC/DC converters, additional evaluation is required for its applicability to multi-phase converters and grid-connected inverters. Experimental verification in various power conversion topologies should be conducted to ensure stable operation across different system configurations.

Future research should explore various directions to further enhance the performance and applicability of the ETHSC. One approach is by integrating machine learning-based control techniques to predict system parameter variations and optimize transient response. Additionally, developing a self-tuning ETHSC capable of automatically adjusting its parameters in response to real-time load variations could improve system robustness. Moreover, experimental validation in large-scale energy storage systems (ESSs) and electric vehicle (EV) power management systems is needed to assess the practical feasibility of the ETHSC. Finally, further studies should investigate its implementation in AC/DC hybrid microgrids to explore its potential for broader applications.

The proposed ETHSC effectively improves transient response characteristics and enhances system stability by minimizing the impact of nonlinear inductance variations, thus addressing the limitations of the THSC. Furthermore, comparative experimental analysis with PI, SMC, and the THSC has demonstrated that the ETHSC offers superior stability and faster response compared to conventional methods. The simulation and experimental results confirm the high performance and reliability of the ETHSC, indicating its potential for practical application in next-generation high-speed power conversion systems.