# Advanced DC Voltage Control Technique for Converters

Farrukh Zeb, Mobina Pouresmaeil, Edris Pouresmaeil, Jorma Kyyra

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Farrukh Zeb, Mobina Pouresmaeil, Edris Pouresmaeil, Jorma Kyyra. Advanced DC Voltage Control Technique for Converters. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0005. hal-05069523

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# Main Title: Advanced DC Voltage Control Technique for Converters: Achieving Superior Speed and Stability with Model Predictive Control

Farrukh Zeb, Mobina Pouresmaeil, Edris Pouresmaeil, Jorma Kyyra

Electrical engineering department, Aalto University

P.O. Box 11000 (Otakaari 1B)

FI-00076 AALTO

Espoo, Finland

Tel.: +358 9 47001.

E-Mail: farrukh.zeb@aalto.fi, Mobina.Pouresmaeil@aalto.fi, edris.pouresmaeil@aalto.fi, jorma.kyyra@aalto.fi

URL: https://www.aalto.fi/en

()

**Index Terms**—Model Predictive control, Active front-end, Proportional Integral (PI control), DC voltage, AC-DC converter, Weighting function.

**Abstract**—Among different converter topologies, the active front-end (AFE) rectifier has been widely used in recent research for generating controlled output DC power. Simultaneously, model predictive control (MPC) has emerged as a prominent and actively researched topic, particularly for its applications in development of advanced control strategies. In this paper, a control method is presented that leverages the predictive capability of MPC to achieve the desired reference power through the DC power generated by the AFE rectifier. A new exponential function has been introduced in the proposed control method as a dynamic reference power for the MPC. This reference power can be updated according to the DC-link voltage requirements for an effective DC voltage regulation. Finally, the performance of the proposed control method is compared with the performance of the conventional PI-based control method and preceding MPC-based control techniques, to validate its superiority over the existing control methods. Implemented and verified in Matlab Simulink, this technique shows five-time faster recovery and zero steady state error.

## I. INTRODUCTION

Green hydrogen, produced from renewable energy sources (RES), has attracted considerable attention as a prominent and clean source of energy [1] Hydrogen pro-

duction from electricity involves the electrolysis process. The market offers two major options for electrolysis: (i) the proton exchange membrane and (ii) the alkaline electrolysis technologies [2]. The implementation of these technologies as a suitable solution to produce green hydrogen from RES requires high-quality DC voltages and currents that are precisely set according to the needs of these electrolyzers. Thereby necessitating AC-DC converters to convert the AC power to the required DC form in minimum amount of time [3]. To achieve the desired regulated DC voltage, several advanced rectifier topologies have been employed in various applications, including the 12-pulse thyristor rectifier, the 12-pulse diode rectifier with multiphase chopper, the hybrid 12-pulse thyristor rectifier with active shunt power filter, and the active front-end (AFE). Among these topologies, AFE stands out due to its superior power quality, high efficiency and reliability [4]. A properly designed AFE rectifier can effectively control the DC-Link pulsation even under presence of an unregulated voltage sources [5]. The advantages of AFE rectifier extend to evaluating active and reactive power [6], with the control mechanism implemented aimed at effectively managing losses within the system [7]. Numerous control strategies have been proposed to effectively regulate the AFE rectifier output. These control strategies are generally categorized as voltage-oriented control (VOC) and direct power control (DPC) [8]. In [9], the classical control technique of VOC is presented using proportional-integral (PI)
controllers. Moreover in [10], MPC and VOC based controller were compared to show the efficiency of MPC over VOC where MPC was used with PI. A DPC method is employed in [11] to control the DC voltage through direct control of active and reactive power. However, the tuning process for the PI controller poses significant challenges due to its inherent difficulty, resulting in a delayed response [12]. Nowadays, controllers with high-performance computing are required in power electronics as per the demand of renewable industries [13]. Utilizing MPC for industries can be more beneficial if the computational complexity is dealt with [14]. Different strategies for generating the desired active power reference for the FSMPC-based control technique are presented [12], [15], [16] that are elaborated in the following. In [16], the reference DC voltage along with future reference values is utilized to derive the desired active power reference. The adoption of this method is accompanied by the occurrence of steady-state errors, primarily due to its sensitivity to changes in reactive power and system parameters. To avoid the steady-state error, [12] presents a method to control the output DC voltage using input active power which is measured from output power and stored energy on the DC side. However, it has a slow dynamic response as compared with the previous method. In most cases a trade-off is observed among the robustness, efficiency, and complexity of the system. The focus of this paper is to ensure the obtained voltage follows the reference voltage efficiently while keeping the system simple, robust, and fast. Consequently, a function that facilitates the use of MPC on the output DC voltage of the rectifier is introduced in this paper. By using the proposed exponential function, the obtained power follows the reference power and effectively regulates the DC link voltage. The rest of the paper is organized as follows. Section 2 describes the mathematical model of AFE rectifier while the proposed control is discussed in Section 3. The proposed model is simulated in MATLAB/Simulink and the simulation results, along with comparisons to other PI-based and MPC-based models, are provided in Section 4, followed by conclusion in Section 5.

## II. ACTIVE FRONT END RECTIFIER MODEL

Fig. 1 illustrates the AFE rectifier, connecting the DC load to the AC grid. (1) represents the dynamics of the system in continuous time:

$$ \bar{v} = L_f \frac{d\bar{i}}{dt} + R_f \bar{i} + \bar{v}_R \quad (1) $$

where $\bar{v} = v_\alpha + jv_\beta$ and $\bar{i} = i_\alpha + ji_\beta$ represent AC grid voltage and current, and $R_f$, and $L_f$ are the parasitic

<figure><img src="image_2.png" /><figcaption>Fig. 1. AFE Rectifier</figcaption></figure>

<table><caption>TABLE I
THE POSSIBLE SWITCHING STATES FOR A TWO-LEVEL CONVERTER AND THE EQUIVALENT VOLTAGE VECTORS.</caption><thead><tr><th>Index</th><th>Switching states in abc</th><th>Voltage vectors</th></tr></thead><tbody><tr><td>0</td><td>0 0 0</td><td>0</td></tr><tr><td>1</td><td>1 0 0</td><td><sup>2V<sub>dc</sub></sup>&frasl;<sub>3</sub></td></tr><tr><td>2</td><td>1 1 0</td><td><sup>V<sub>dc</sub></sup>&frasl;<sub>3</sub> + j<sup>&radic;3V<sub>dc</sub></sup>&frasl;<sub>3</sub></td></tr><tr><td>3</td><td>0 1 0</td><td>-<sup>V<sub>dc</sub></sup>&frasl;<sub>3</sub> + j<sup>&radic;3V<sub>dc</sub></sup>&frasl;<sub>3</sub></td></tr><tr><td>4</td><td>0 1 1</td><td>-<sup>2V<sub>dc</sub></sup>&frasl;<sub>3</sub></td></tr><tr><td>5</td><td>0 0 1</td><td>-<sup>V<sub>dc</sub></sup>&frasl;<sub>3</sub> - j<sup>&radic;3V<sub>dc</sub></sup>&frasl;<sub>3</sub></td></tr><tr><td>6</td><td>1 0 1</td><td><sup>V<sub>dc</sub></sup>&frasl;<sub>3</sub> - j<sup>&radic;3V<sub>dc</sub></sup>&frasl;<sub>3</sub></td></tr><tr><td>7</td><td>1 1 1</td><td>0</td></tr></tbody></table>

resistance and the filter inductance respectively. $\bar{v}_R = v_{R\alpha} + jv_{R\beta}$ represent the converter AC terminal voltage, which is employed as the control action in the model predictive control. For a two-level converter there are eight possible values for the terminal voltage, which are listed in Table. 1 and are employed in the MPC for prediction purpose.

As model predictive control requires the discrete mathematical model of the system to predict future behavior, Euler's forward estimation introduced in (2), utilized to discretize the model. In (2), T is the sample time for discretization, and $\bar{i}(k)$, and $\bar{i}(k+1)$ represent the current and the next samples of the AC grid current, respectively.

$$ \frac{d\bar{i}}{dt} = \frac{\bar{i}(k+1) - \bar{i}(k)}{T} \quad (2) $$

By placing (2) in (1), the discrete model of the system can be described as:

$$ \bar{i}(k+1) = \left(1 - \frac{R_f}{L_f}\right) \bar{i}(k) + \frac{T}{L_f} \left(\bar{v}(k) - \bar{v}_R(k)\right) \quad (3) $$

The instantaneous active and reactive power of the AC source in alpha-beta frame are defined by (4) and (5),
using the measured AC source voltage and the predicted current in the AC side. In these equations the AC source voltage in the next sample time is approximated to be equal to the voltage at the current sample time, i.e., $\bar{v}(k+1) = \bar{v}(k)$

$$P(k+1) = V_{\alpha}(k+1)i_{\alpha}(k+1) + V_{\beta}(k+1)i_{\beta}(k+1) \quad (4)$$

$$Q(k+1) = V_{\beta}(k+1)i_{\alpha}(k+1) - V_{\alpha}(k+1)i_{\beta}(k+1) \quad (5)$$

### III. THE PROPOSED CONTROL

The model predictive control employs all eight possible control actions as shown in Table. 1 to predict the state variables at the next sampling time, then the optimal control action and the equivalent switching function are extracted for switching purpose. The optimal control action is chosen based on the minimum cost function of the proposed control at each sample time. The cost function of the MPC control is defined in (6), with the objectives of active and reactive power reference tracking. At each sample time, the switching state resulting in the minimum tracking error is extracted as the optimal switching state of the AFE rectifier.

$$g_R = (P'(k+1) - P(k+1))^2 + (Q'(k+1) - Q(k+1))^2 \quad (6)$$

$P'(k+1)$ represents the reference power at next interval and $P(k+1)$ represents the obtained power. Subtraction in between the reference power and obtained power gives the next path for switching sequence with addition of reactive power where $Q'(k+1)$ represents the reference reactive power and $Q(k+1)$ represents the obtained reactive power.

The main objectives of the AFE rectifier are to regulate the DC-link voltage and to control the reactive power on the AC side. As the DC voltage and the active power in the AC side are linked together, the cost function is defined to follow the reference active and reactive power. Then the reference active power is generated in a way to regulate the DC link voltage to its reference value.

This paper introduces a novel methodology for obtaining the active power reference value for the cost function of the MPC technique. Moreover, this approach ensures that the resultant power aligns with the reference power through the utilization of the MPC technique. This method removes the need for a PI controller for

DC voltage regulation and the difficulty of parameter tuning. The proposed control technique mitigates the complexity of the system and can provide a fast and accurate dynamic as well as the desired steady-state behavior. Consequently, the system becomes simple, fast, and robust. To fulfill this objective, an exponential function, represented by $W$, has been introduced in (7):

$$W = e^{\frac{V_{dc}}{V_{dc}}} \quad (7)$$

The proposed MPC-based control technique is depicted in Fig. 2. The presented diagram features parameter $W$, utilized for the purpose of eliminating differences between the obtained power and reference power. This function aligns the input power with output dc power and eliminated the need of modulator. Moreover, this function serves to maintain the obtained DC voltage ($V_{dc}$) in accordance with the reference voltage ($V'_{dc}$) while simultaneously minimizing the difference between the $V'_{dc}$ and the $V_{dc}$. $e$ is used because it is more common in natural exponential growth models, physics, and systems involving continuous exponential dynamics.

Fig. 2a represents the proposed MPC-based control method. MPC controlled by PI-based generated active power reference is represented in Fig. 2(b). Comparing these two figures highlights the differences in generating the reference power in these two control methods. The proposed MPC based design using the $W$ function is shown and which replaces the PI controller. Instead of PI controller, $W$ is utilized to obtain the reference power. The reference active power for the step ahead ($P'_{dc}(k+1)$) in the proposed control is generated with the purpose of regulating the DC link voltage without the tracking error, as:

$$P'_{dc}(k+1) = P'_{dc}(k) + M \quad (8)$$

where the term $M$, defined in (9), is used to minimize the error for getting the next desired step. $P_E$ is defined as error between the measured active power, $P_{dc}(k)$, and the reference power in DC side, $P'_{dc}(k)$, defined in (10). The proposed function $W$ is applied to $P_E$ for minimizing the difference between $P_{dc}(k)$ and $P'_{dc}(k)$.

$$M = P_E W \quad (9)$$

$$P_E = P'_{dc}(k) - P_{dc}(k) \quad (10)$$

$P'_{dc}(k)$ and $P_{dc}(k)$ at time instant $k$, can be calculated as

$$P'_{dc}(k) = V'_{dc} I_{dc}(k) \quad (11)$$
<figure><img src="image_3.png" /><figcaption>Fig. 2. Diagram of the MPC-based control technique. (a) MPC with PI-based. (b) The proposed method.</figcaption></figure>

$$P_{dc}(k) = V_{dc}(k) I_{dc}(k) \quad (12)$$

Where $V'_{dc}$ represents the reference DC-link voltage. (9) shows the significance of $W$. As $V_{dc}$ approaches to its minimum value, $W$ leans to unity, and $M$ becomes equivalent to $P'_{dc}$, thereby reaching its maximum value while remaining free from errors. When $V_{dc}$ becomes equal to $V'_{dc}$, $W$ reaches its maximum value, while $M$ converges towards its minimal value, thus keeping the error near zero and removing the differences between $P'_{dc}$ and $P_{dc}$. Through this method, the error is significantly mitigated.

Within a well-established electrical grid input framework, the resultant $P_{dc}$ becomes same to the active power originating from the input source $P_s$. To achieve the unity power factor in the AC side, the reference reactive power of $Q'(k+1) = 0$ is considered in the proposed control.

# IV. SIMULATION RESULTS AND DISCUSSION

## A. Methodology

The proposed system is implemented using MATLAB/Simulink, designed to handle a power of 2kW. It aims to maintain stable operation, with voltage ($V_s$) of 400V observed during simulations. To facilitate the conversion of AC power to DC power, a 6-pulse Active Front End (AFE) rectifier is integrated into the system, as depicted in Fig. 1. This rectifier is crucial for achieving the necessary DC output from the AC input. A Model Predictive Controller (MPC) is used to control the output voltage of the AFE rectifier as shown in Fig. 2a. The MPC replaces the traditional Proportional-Integral (PI) controller typically used in rectifier control systems. The key component of the MPC is the block that calculates the weighting function based on the rectifier voltage ($V_{dc}$) and the reference voltage ($V'_{dc}$). This innovative

approach allows for more accurate and dynamic control of the rectifier's output, improving system stability and performance. In this closed-loop system, the AFE rectifier is connected to a stable grid, ensuring that the DC power ($P_{dc}$) is equal to the power supplied ($P_s$). The output from the AFE is fed into the MPC block, which calculates the future steps for both active and reactive power. These calculations are used to optimize the cost function, which in turn determines the switching sequence of the AFE rectifier. This process ensures that the system operates efficiently and maintains a stable output voltage, essential for the subsequent stages of hydrogen production. Detailed system components include a stable AC voltage source of 400V, the 6-pulse AFE rectifier for AC to DC conversion, the MPC for dynamic control, the weighting function calculation block for real-time voltage adjustments, and cost function optimization for efficient power conversion. The use of MATLAB/Simulink for modeling and simulation ensures that the system's performance can be tested and optimized before real-world deployment.

## B. Results of the proposed control technique

To evaluate the functionality and performance of the proposed control method, a series of simulations in MATLAB/Simulink are conducted across various scenarios. These results enable a comprehensive assessment of the system's capabilities under diverse conditions, showing its robustness and effectiveness. Parameters of the model and control are listed in Table.2.

As a preliminary measure, the reference DC-link voltage is raised from $V'_{dc} = 630V$ to $V'_{dc} = 660V$. This adjustment aims to facilitate a comprehensive observation and analysis of the system's response to voltage fluctuations and allow us to understand its operational
<figure><img src="image_4.png" /><figcaption>Fig. 3. Simulation result when the reference voltage changed from 630V to 660V. (a) dc link voltage . (b) Power. (c) Reactive power</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Simulation result when the reactive power reference increased from 0 to 2.762kVar. (a) dc link voltage . (b) Power. (c) Reactive power</figcaption></figure>

dynamics. Simulation result of the first scenario is shown in Fig. 3.

Algorithm 1 MPC controlled Rectifier

Calculate $v_s, i_s, V_{dc}, I_{dc}$

Evaluate Eq.No.(7)(8)(9)(10)

$$F = e^{10}$$

$$For n = 1 : 8$$

$$Eq.(3), (4), (5)$$

Defining Cost Function

$$Eq. (6)$$

if(cost < F) then

$$F = cost$$

$$nopt = n$$

end

end

$$nold = nopt$$

The DC-link voltage $V_{dc}$ aligns itself with the reference voltage $V'_{dc}$, effecting a rapid adjustment within a

time span of less than 0.01s. As the $V_{dc}$ changes on 0.2s a spike appears in Power diagram at same moment but it can be observed from Fig. 3 that the power $P_{dc}$ promptly tracks the reference power $P'_{dc}$, swiftly reaching a stabilized state. This response indicates the system's adeptness in generating the right reference active power and converging towards the desired reference value. During this whole period, the reactive power remains zero and follows to the reference reactive power. Although the system follows the reference values almost perfectly still small spikes can be observed. These disturbances come due to switching of the rectifier. These can be removed by applying separate filters for harmonics [15]. These results are phenomenon when looking at recovery speed and shape of the signal

In the context of the second scenario, as illustrated in Fig. 4, a change in the $Q'$ is observed while keeping $V'_{dc}$ at 630V. The initial value of $Q'$ is zero which indicates unity power factor and raised to 2762 [Var], at time 0.2s. This change is considered to subject our system to a substantial reactive load, thus assessing its performance and resilience under such demanding conditions.

The results shown in Fig. 4 specifically reveals some very minor disturbances in both voltage $V_{dc}$ and power $P_{dc}$ at 0.2s, due to the introduction of this high variation in reactive power. However, the system promptly recovers from this transient distress. Notably, the system exhibits remarkable resilience, rapidly restoring equilibrium and effectively modifying the effects of the introduced reactive power. This rapid response features the system's robustness and its capacity to rapidly respond
<figure><img src="image_6.png" /><figcaption>Fig. 5. Simulation results when a parallel resistance of $R = 100\Omega$ added to the DC Load. (a) dc link voltage. (b) Power. (c) Reactive power.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. Simulation comparison when Voltage increased from 630V to 660V. (a) Proposed control technique. (b) Dynamic references. (c) PI controller.</figcaption></figure>

variations induced by changes in reactive power.

Fig. 5 defines the third scenario wherein modifications were implemented in the load configuration. Specifically, at $0.2s$ a parallel resistor with a resistance of $R = 100\Omega$ was introduced in conjunction with the preexisting load resistor. It is noteworthy that despite this dynamic change in the load, the system demonstrates a rapid response by restoration of power to its respective stable states in a remarkably instant duration.

### C. Comparison of the proposed control method with other methods

To validate the results, two control methods were selected for comparison. One is MPC with PI-based active power reference generation, and the other is MPC with dynamic references presented in [17]. Different research papers were investigated, among which the high-speed MPC was found in MPC with dynamic references. In [10] the speed of predictive controller was sacrificed over non-zero steady-state error. As written earlier that high-speed regulation is required for industries, and that is one of the most important reasons why MPC has gained popularity over PI controller, therefore the control system should regulate the output of AFE very fast. Fig. 6 compares the proposed control technique with the other two control methods when a change in dc voltage reference from 630V to 660V is considered. In this scenario the dc load $R_{dc}$ and reactive power $Q$ are kept constant.

The reference dc voltage was changed from 630V to 660V at $0.2s$ to compare the transient response of

all three controllers. The MPC with dynamic references comes to steady state at $0.215s$ and PI-based control method reaches the steady state at $0.246s$ while this paper shows much faster response by coming into the steady-state at $0.205s$. Moreover, non-zero steady-state error can be seen from dynamic references while the proposed control method follows the reference voltage without any steady-state error. To check the stability and robustness of the system, an additional resistance of $100\Omega$ in parallel has been added to the system at $0.2s$ while keeping $V'_{dc}$ and $Q'$ constant.

Fig. 7 depicts the robustness of the system. In Fig. 7 (b) the voltage in dynamic references recovers to its steady state at $0.211s$ but it clearly shows the non-zero steady-state error with somewhat noise added to the system after the addition of that extra load and in Fig. 7(c) the voltage of PI controller comes near to steady state around $0.25s$. The proposed system on other hand shows its significance in this scenario. The voltage recovers to steady state at $0.25s$ and follows the reference precisely. Fig. 8 illustrates the effect of voltage on power in all the three scenarios. Fig. 8(a) shows the result of the proposed control method in this paper in which the power recovers very quickly to steady-state without any significant overshoot. On the other hand, as depicted in Fig. 8(b), the control method with dynamic references follows the reference power smoothly, although it exhibits a non-zero steady state error in power, and as shown in Fig. 8(c), the PI controller recovers near steady state at $0.25s$ while showing non-zero steady state error.
<figure><img src="image_8.png" /><figcaption>Fig. 7. Simulation comparison when a parallel resistance of 100Ω added (a) Proposed control technique. (b) Dynamic references. (c) PI controller</figcaption></figure>

<table><caption>TABLE III
PARAMETERS OF THE MODEL AND THE PROPOSED CONTROL.</caption><thead><tr><th>Reference</th><th>V<sub>dc</sub></th><th>C<sub>dc</sub></th><th>L<sub>f</sub></th></tr></thead><tbody><tr><td>[10]</td><td>120V</td><td>1000μF</td><td>50mH</td></tr><tr><td>Dynamic references</td><td>22V</td><td>15000μF</td><td>15mH</td></tr><tr><td>[15]</td><td>480V</td><td>368μF</td><td>5.77mH</td></tr><tr><td>Proposed design</td><td>630V</td><td>250μF</td><td>0.4mH</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Comparison of Effect on Power by increasing voltage from 630V to 660V. (a) Proposed control technique. (b) Dynamic references. (c) PI controller</figcaption></figure>

Table. III represents comparison of different systems with the proposed design and showing its significance in controlling the DC link voltage with minimum resources and simple approach. The values of filters are far more

than the proposed model in similar papers. Although the proposed model stream line the obtain voltage with reference voltage yet still there can be seen very small ripples as explained earlier. This is due to switching nature of the rectifier. As it can be illustrated that signal itself has maintained its shape but the transition period becomes very short. This will be next step towards fast processing and new fast switching rectifiers like Gallium Nitride (GaN) can play a significant role in future conversion of energy.

## V. CONCLUSION

The integration of the W function with Active Front-End (AFE) technology within Model Predictive Control (MPC) demonstrates highly promising results. The achieved voltage accurately follows the reference voltage and quickly recovers from various disturbances, indicating rapid response capabilities. The proposed model system exhibits a fast dynamic response, robustness, superior disturbance rejection, and zero steady-state errors, outperforming traditional PI control and previous MPC-based techniques. These characteristics eliminate the need for a proportional-integral (PI) controller and avoid complex calculations. Compared to other MPC and PI controllers, the proposed method not only recovers from disturbances in less than 2ms which in other scenarios was more than 10ms but also maintains zero steady-state error. The current work aims to control the DC link voltage in a fast and simple manner. This approach provides a regulated DC voltage for various applications such as electrolysis and energy storage systems, as well as scenarios requiring rapid processing, including Electric Vehicle (EV) charging, Uninterruptible Power Supplies (UPS), and other industrial needs. Given the necessity for additional control and regulation of power, a DC-DC converter is typically used. However, the future direction of this research is to eliminate the need for a DC-DC converter without adding any further controllers, thereby simplifying the system and improving its compactness and robustness.

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