A Harmonic Suppression Method for the Single Phase PWM Rectifier in the Hydrogen Production Power Supply

Abstract

In renewable and sustainable hydrogen production energy systems (RSHPES), the presence of harmonics gives rise to fluctuations in the voltage and current of the electrolysis cell (EC). This, in turn, results in an unstable electrolysis process, a reduction in hydrogen production efficiency, and an escalation in electrode corrosion. This paper puts forward a novel harmonic suppression control method (HSCM), which is devised for the single phase PWM rectifier in hydrogen production rectifiers (HPR) with the aim of alleviating the adverse impacts caused by harmonics. Initially, a highly meticulous harmonic model is constructed, which lays solid groundwork for understanding the existing problems. Subsequently, a comprehensive and detailed explanation of the HSCM is provided, accentuating its novel and inventive strategy for harmonic suppression. Thereafter, a comparison is drawn between the HSCM and traditional methods, thereby manifesting its enhanced suitability and superiority within the context of RSHPES. In conclusion, the simulation and experimental results vividly demonstrate the advantages, effectiveness, and practicality of HSCM under four conditions of power grids containing integer multiples of harmonics, interharmonics, ultraharmonics, and voltage disturbances.

1. Introduction

Electrolysis of water is an environmentally friendly and efficient method for hydrogen production, which uses renewable energy to decompose water into hydrogen and oxygen. This process not only achieves zero carbon emissions during production but also contributes to energy transition and reduces dependence on fossil fuels. Therefore, hydrogen is also considered a carrier for energy transition [1,2,3]. The renewable energy sources (RES) in RSHPES are wind power and photovoltaic (PV) [4,5,6]. Wind turbine generators connect to the AC bus via an AC-AC converter, and solar panels do the same via a DC-AC converter. The AC bus supplies electrical energy to the EC through the HPR [7,8,9]. A schematic diagram of the RSHPES is depicted in Figure 1.

With the increasing power generated by renewable energy sources, the power electronic devices of water’s electrolysis to hydrogen system have also increased accordingly. However, power electronic devices within RSEHPE are primarily responsible for generating harmonics [10,11]. These harmonics are very deleterious for the EC. They will accelerate the corrosion of the electrodes, decrease the efficiency of hydrogen production, and disrupt the balance of the electrolysis process [12]. With this threat in mind, numerous researchers have begun to investigate strategies for harmonic suppression through the control methods of the HPR. The topology of the HPR is shown in Figure 2.

The HPR is composed of a PWM full-bridge rectifier and a phase-shift full-bridge converter. The HSCM is adopted in the PWM full-bridge rectifier. Because the HSCM aims to reduce the harmonic content in the input current, the phase-shift full-bridge converter can be ignored in this paper.

Passive and active power filters are usually used for harmonic suppression. However, extra hardware will increase the system cost and the difficulty of operation and maintenance [13]. Therefore, digital filters have become the mainstream. A low pass filter is processed in Ref. [14] to solve the impact of the twice-frequency power pulsation of DC voltage; however, the bandwidth will be diminished. Ref. [15] introduces an additional resonant element to eliminate the third harmonic. However, control mechanisms that rely on small-signal linearized models may not guarantee stability across the entire operating range. The one-sampling-ahead-preview (OSAP) control scheme is used to suppress the harmonic in Ref. [16], although the harmonics of the AC bus will distort the reference current. Ref. [17] reduces the modulation level by reducing the output power. Therefore, the operating region is the linear modulation region. The distortion of the input current is avoided, but the efficiency decreases. A control strategy based on reactive power compensation is proposed. The power factor will be changed in this way [18,19].

As solar panels and wind turbines become more prevalent, the harmonic content will also increase, causing greater damage to EC. The amplitude and phase of the harmonics will both increase. This could potentially lead to system instability. Therefore, suppressing harmonics is an urgent priority [20,21]. At present, there is a plethora of research papers on harmonic suppression. However, few methods are capable of dealing with the ever-increasing harmonic content in RSHPES.

In this paper, the author proposes a harmonic suppression strategy for the single-phase PWM rectifier (SPR) in HPR. The proposed method solves the influence of harmonics by eliminating the harmonics of AC bus current. In addition, the challenge of increasingly growing harmonic amplitude and phase can be addressed.

The paper is organized as follows. Section 2 details the topology and control of SPR. Section 3 discusses two reasons for AC current distortion caused by grid voltage harmonics. Section 4 shows the proposed harmonic current suppression strategy. Finally, the simulation and experimental results are displayed and analyzed in Section 5 and Section 6, respectively. Section 7 concludes this paper.

2. Topology and Control

2.1. Topology

The topology of the SPR is shown in Figure 3. u_s is the AC bus voltage, L_s is a filter inductance, R_s is the line equivalent resistance, S₁~S₄ is switches on the rectifier bridge, C is a side filter capacitor, R_o is the equivalent impedance of the subsequent circuit., i_s is the current at AC side, i_dc is the output current, i_c is the capacitance current, i_o is the load current, u_dc is the output voltage, and u_AB is the AC side voltage of rectifier bridge.

The working modes of the SPR under the unipolar modulation are illustrated in Figure 4.

The equivalent circuit of the SPR is described in Figure 5.

2.2. Control

The control block diagram of the SPR is shown in Figure 6. The common control is voltage and current double closed-loop based on the average current control mode. In Figure 6, u_or is the reference of u_o, i_sr is the reference of is, G_V(s) is the controller of the outer voltage loop, G_I(s) is the controller of the inner current loop, and k_pwm is the modulation coefficient. 1/(sL + r) is the model of L_s and R_s. m is modulating voltage. 1/sC is the model of C.

The voltage outer loop is responsible for maintaining the stability of the DC voltage, while the current inner loop is responsible for precisely controlling the input current to track the given current command. G_V(s) is the proportional-integral (PI) controller. G_I(s) is the quasi proportional resonant (QPR) controller.

3. Harmonic Model in RSHPES

This section analyzes the mechanism of harmonic current generated in the AC bus, The expression of u_s is shown in (1).

$$\left\{\begin{array}{l}{u}_{\mathrm{s}}(t)=u_{\mathrm{so}}(t)+u_{\mathrm{sh}}(t)\hfill \\ u_{\mathrm{so}}(t)=\sqrt{2}{U}_{\mathrm{so}}\cos (\omega t)\hfill \\ u_{\mathrm{sh}}(t)={\displaystyle \sum _{k=2}^n\sqrt{2}{U}_{\mathrm{s}k}\cos (k\omega t)}\hfill \end{array}\right.$$

(1)

where, u_so is the fundamental frequency AC bus voltage, and U_so is the root mean square (RMS) of the fundamental frequency AC bus voltage. u_sh is the AC bus harmonic voltage. U_sk is the RMS of the AC bus harmonic voltage. AC bus voltage harmonics can generate AC bus current harmonics from both topological and control aspects.

3.1. The Topology Aspect

From Figure 5, the AC bus current in this aspect i_st can be calculated. The R_L is ignored

$$i_{\mathrm{st}}(t)={\displaystyle \frac{1}{L}}{\displaystyle \int u_s(t)\mathrm{d}t}-{\displaystyle \frac{1}{L}}{\displaystyle \int u_{\mathrm{AB}}(t)\mathrm{d}t}$$

(2)

According to the superposition theorem, it is known the expression of u_AB in the topology aspect is presented in

$$u_{\mathrm{AB}}(t)=\sqrt{2}{U}_{\mathrm{AB}}\cos (\omega t+\phi )$$

(3)

where U_AB is the RMS, φ is the phase of the u_AB. According to (2), i_st is expressed as

$$i_{\mathrm{st}}(t)={\displaystyle \int \frac{\sqrt{2}{U}_{\mathrm{s}}\cos (\omega t)-\sqrt{2}{U}_{\mathrm{AB}}\cos (\omega t+\phi )}{L}\mathrm{d}t}+{\displaystyle \int \frac{{\displaystyle \sum _{k=2}^n\sqrt{2}{U}_{\mathrm{s}k}\cos (k\omega t)}}{L}}\mathrm{d}t$$

(4)

From Equation (4), the AC bus current harmonics of the topology aspect is i_sht and it is as indicated in (5)

$$i_{\mathrm{sht}}(t)={\displaystyle \int \frac{{\displaystyle \sum _{k=2}^n\sqrt{2}{U}_{\mathrm{s}k}\cos (k\omega t)}}{L}}\mathrm{d}t={\displaystyle \frac{{\displaystyle \sum _{k=2}^n\sqrt{2}{U}_{\mathrm{s}k}\sin (k\omega t)}}{k\omega L}}$$

(5)

3.2. The Control Aspect

Figure 6 indicates that harmonics is introduced into the controller because u_o and u_s/U_s is sampled.

P_in is the input instantaneous power, and the expression of P_in is shown in (6).

$$P_{\mathrm{in}}(t)=u_{\mathrm{s}}{i}_{\mathrm{s}}=[{\displaystyle \frac{U_{\mathrm{so}}^2\sin (2\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin (2\omega t+\phi )}{\omega L}}+{\displaystyle \sum _{k=2}^n\frac{U_{\mathrm{s}k}^2\sin (2kwt)}{k\omega L}}]+{\displaystyle \frac{U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin (\phi )}{\omega L}}$$

(6)

P_out is output instantaneous power, which is expressed as (7)

$$P_{\mathrm{out}}=u_{\mathrm{o}}{i}_{\mathrm{dc}}=u_{\mathrm{o}}{i}_{\mathrm{o}}+u_{\mathrm{o}}{i}_{\mathrm{c}}=U_{\mathrm{o}}{I}_{\mathrm{o}}+C{U}_{\mathrm{o}}{\displaystyle \frac{d{u}_{\mathrm{ore}}(t)}{dt}}$$

(7)

where Uo and Io are the DC components, and u_ore represents the ripple component. When the line loss is ignored, P_in = P_out, the expression of u_ore can be obtained as (8).

$$u_{\mathrm{or}e}(t)={\displaystyle \frac{U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (2\omega t+\phi )-U_{\mathrm{AB}}^2\cos (2\omega t)}{2{\omega }^{2}CL{U}_{\mathrm{o}}}}$$

(8)

As can be seen from Figure 6, i_sr can be obtained as (9).

$$\begin{array}{ll}{i}_{\mathrm{sr}}(t)& =k_{\mathrm{p}}[\cos (\omega t)+{\displaystyle \sum _{k=2}^{n}m\cos (k\omega t)}\left]\right\{(U_{\mathrm{or}}-U_{\mathrm{o}})-{\displaystyle \frac{U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (2\omega t+\phi )-U_{\mathrm{AB}}^2\cos (2\omega t)}{2{\omega }^{2}CL{U}_{\mathrm{o}}}}\}\\ & +k_{\mathrm{i}}[\cos (\omega t)+{\displaystyle \sum _{k=2}^{n}m\cos (k\omega t)}]{\displaystyle \int \left\{\right(U_{\mathrm{or}}-U_{\mathrm{o}})-\frac{U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (2\omega t+\phi )-U_{\mathrm{AB}}^2\cos (2\omega t)}{2{\omega }^{2}CL{U}_{\mathrm{o}}}\}}\end{array}$$

(9)

where m = U_sk/U_so. When U_dc reaches the reference, U_dcr − U_dc = 0. The simplification results of (9) is

$$\begin{array}{ll}{i}_{\mathrm{sr}}(t)& ={\displaystyle \frac{k_{\mathrm{p}}}{4{\omega }^{2}CL{U}_{\mathrm{o}}}}[U_{\mathrm{AB}}^2\cos (\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (\omega t+\phi )+U_{\mathrm{AB}}^2\cos (3\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (3\omega t+\phi )]\\ & +{\displaystyle \frac{k_{\mathrm{p}}m}{4{\omega }^{2}CL{U}_{\mathrm{o}}}}{\displaystyle \sum _{k=2}^{\mathrm{n}}\begin{array}{l}\{U_{\mathrm{AB}}^2\cos [(k-2)\omega t]-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos [(k-2)\omega t+\phi ]+U_{\mathrm{AB}}^2\cos [(k+2)\omega t]\\ \hspace{1em}\hspace{1em}-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos [(k+2)\omega t+\phi ]\}\end{array}}\\ & +{\displaystyle \frac{k_{\mathrm{i}}}{8{\omega }^{3}CL{U}_{\mathrm{o}}}}[U_{\mathrm{AB}}^2\sin (\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin (\omega t+\phi )+U_{\mathrm{AB}}^2\sin (3\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin (3\omega t+\phi )]\\ & +{\displaystyle \frac{k_{\mathrm{i}}m}{8{\omega }^{3}CL{U}_{\mathrm{o}}}}{\displaystyle \sum _{k=2}^{\mathrm{n}}\begin{array}{l}\{U_{\mathrm{AB}}^2\sin [(k-2)\omega t]-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin [(k-2)\omega t+\phi ]+U_{\mathrm{AB}}^2\sin [(k+2)\omega t]\\ \hspace{1em}\hspace{1em}-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin [(k+2)\omega t+\phi ]\}\end{array}}\end{array}$$

(10)

From (10), we can deduce that the input current will contain the 3th, (k − 2)th and (k + 2) th harmonic. When stability is achieved in the system, the expression of i_s is presented in (11)

$$\begin{array}{ll}{i}_{\mathrm{s}}(t)& =i_{\mathrm{sr}}(t)+i_{\mathrm{st}}(t)\\ & ={\displaystyle \frac{k_{\mathrm{p}}}{4{\omega }^{2}CL{U}_{\mathrm{o}}}}[U_{\mathrm{AB}}^2\cos (\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (\omega t+\phi )+U_{\mathrm{AB}}^2\cos (3\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos (3\omega t+\phi )]\\ & +{\displaystyle \frac{k_{\mathrm{p}}m}{4{\omega }^{2}CL{U}_{\mathrm{o}}}}{\displaystyle \sum _{k=2}^{\mathrm{n}}\begin{array}{l}\{U_{\mathrm{AB}}^2\cos [(k-2)\omega t]-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos [(k-2)\omega t+\phi ]+U_{\mathrm{AB}}^2\cos [(k+2)\omega t]\\ \hspace{1em}\hspace{1em}-U_{\mathrm{AB}}{U}_{\mathrm{so}}\cos [(k+2)\omega t+\phi ]\}\end{array}}\\ & +{\displaystyle \frac{k_{\mathrm{i}}}{8{\omega }^{3}CL{U}_{\mathrm{o}}}}[U_{\mathrm{AB}}^2\sin (\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin (\omega t+\phi )+U_{\mathrm{AB}}^2\sin (3\omega t)-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin (3\omega t+\phi )]\\ & +{\displaystyle \frac{k_{\mathrm{i}}m}{8{\omega }^{3}CL{U}_{\mathrm{o}}}}{\displaystyle \sum _{k=2}^{\mathrm{n}}\begin{array}{l}\{U_{\mathrm{AB}}^2\sin [(k-2)\omega t]-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin [(k-2)\omega t+\phi ]+U_{\mathrm{AB}}^2\sin [(k+2)\omega t]\\ \hspace{1em}\hspace{1em}-U_{\mathrm{AB}}{U}_{\mathrm{so}}\sin [(k+2)\omega t+\phi ]\}\end{array}}\\ & +{\displaystyle \frac{\sqrt{2}{U}_{\mathrm{s}k}}{k\omega L}}{\displaystyle \sum _{k=2}^n\sin (k\omega t)}+{\displaystyle \frac{\sqrt{2}{U}_{\mathrm{s}}}{\omega L}}\sin (\omega t)-{\displaystyle \frac{\sqrt{2}{U}_{\mathrm{AB}}}{\omega L}}\sin (\omega t+\phi )\end{array}$$

(11)

This implies that the harmonic voltages on the AC bus not only generate harmonic currents but also cause a phase shift in the fundamental current.

4. Harmonic Suppression Method

4.1. The Traditional Harmonic Suppression Method

The main methods to counteract the impact of harmonic voltages in the AC bus on rectifiers include the use of the PI controllers, resonant elements, and quasi-PR(QPR) controllers [22,23,24,25,26,27,28,29]. According to Figure 6, their transform function of the inner current loop controllers G_PI(s), G_RE(s) and G_QPR(s) are, respectively, presented in (12), (13) and (14).

$$G_{\mathrm{PI}}(s)=k_{\mathrm{p}}+{\displaystyle \frac{k_i}{s}}$$

(12)

$$G_{\mathrm{RE}}(s)=k_{\mathrm{pRE}}+{\displaystyle \sum _{i=2}^l\frac{k_{\mathrm{rRE}l}{\omega }_i^2}{s^2+{\omega }_i^2}}$$

(13)

$$G_{\mathrm{QPR}}(s)=k_{\mathrm{pQPR}}+{\displaystyle \frac{2k_{\mathrm{rQPR}}{\omega }_{\mathrm{c}}s}{s^2+2{\omega }_{\mathrm{c}}s+{\omega }_n^2}}$$

(14)

where ω_n is the resonant frequency, ω_k is kth harmonic, k_p k_pRE and k_pQPR are proportional coefficients, k_i is an integral coefficients, and k_rREl and k_rQPR are resonance coefficients. ω_c is the cut-off frequency of the QPR controller. When using the inner current loop with the aforementioned three types of controllers, their diagrams of the inner current loop are shown in Figure 7, Figure 8 and Figure 9, respectively.

As shown in (11) and Figure 7, as long as there are harmonics present, m will not be zero. No matter how the k_p and k_i are adjusted, the harmonic components cannot be eliminated. Therefore, the PI controller is not suitable for suppressing the impact of harmonic voltages in the AC bus on the HPR.

Based on Figure 8, the open-loop transfer function of the inner current loop with the resonance coefficients is

$$H_{\mathrm{RE}}(s)={\displaystyle \frac{k_{\mathrm{pRE}}}{sL+r}}+{\displaystyle \sum _{i=2}^l\frac{k_{\mathrm{rRE}l}{\omega }_i^2}{(s^2+{\omega }_i^2)(sL+r)}}$$

(15)

The performance of the resonant elements controller is affected by k_pRE and k_rREl. Therefore, it is necessary to plot the Bode diagrams for three different values of k_pRE and k_rREl to analyze. Set the filter order n = 8, the first value set k_pRE = 1, k_rRE2 = k_rRE3 = k_rRE4 = k_rRE5 = k_rRE6 = k_rRE7 = k_rRE8 = 1, the second value set k_pRE = 0.35, k_rRE2 = 1, k_rRE3 = 0.1, k_rRE4 = 0.5, k_rRE5 = 0.7, k_rRE6 = 2, k_rRE7 = 1.3, k_rRE8 = 1.9, the third value set k_pRE = 10, k_rRE2 = 10, k_rRE3 = 3.1, k_rRE4 = 3.2, k_rRE5 = 1.3, k_rRE6 = 2.6, k_rRE7 = 1.8, k_rRE8 = 0.3. The bode diagram is presented in Figure 10.

From Figure 10, it can be seen that the high gain at the harmonic frequencies indicates that the resonant elements have a good suppression effect on harmonics. However, in the case of the first and third values, the fundamental frequency will experience a leading phase shift, which is detrimental to the stability of the system. Therefore, the selection of coefficients has become a rather critical issue. Small deviations can cause the system to become unstable. The harmonic spectrum in RSHPES is very rich [30,31,32], including integer multiple harmonics, interharmonics, and ultraharmonics. Figure 10 only illustrates the suppression capability of the resonant elements on integer multiple harmonics, and cannot eliminate the impact brought by interharmonics and ultraharmonics.

According to Figure 9, the open-loop transfer function of the inner current loop with the QPR is

$$H_{\mathrm{QPR}}(s)={\displaystyle \frac{k_{\mathrm{pQPR}}{s}^2+2(k_{\mathrm{pQPR}}+k_{\mathrm{rQPR}}){\omega }_{\mathrm{c}}s+k_{\mathrm{pQPR}}{\omega }_n^2}{(s^2+2{\omega }_{\mathrm{c}}s+{\omega }_n^2)(sL+r)}}$$

(16)

The performance of the resonant elements controller is affected by k_pQPR and k_rQPR. Taking the k_pQPR and k_rQPR in three different scenarios allows for the analysis of the QPR controller’s characteristics. The first value is set as k_pQPR = 1, k_rQPR = 100, the second value is set as k_pQPR = 100, k_rQPR = 1, and the third value is set as k_pQPR = 100, k_rQPR = 100. The bode diagram is described in Figure 11.

In Figure 11, ω_c1 ω_c2 and ω_c3 are the cut-off frequencies of the H_QPR(s) under the three different values. A conclusion can be drawn by ω_c1 > ω_c3 that reducing k_pQPR will increase the system’s bandwidth and response speed, but it will also decrease the phase margin, increasing the probability of system instability. It can be obtained through ω_c2 < ω_c3 that diminishing k_rQPR will enhance the system’s phase margin, but it will cut down the system’s bandwidth, resulting in slower system response.

The fundamental gain and phase margin do not differ significantly under the three scenarios, therefore, employing a QPR controller will enhance the system’s stability. However, the QPR controller only has a suppressive effect on high-frequency harmonics and cannot eliminate the impact of low-frequency harmonics.

4.2. HSCM

The HSCM takes harmonics as the control object. The harmonic amplitude of the AC bus current is controlled to be 0, so as to eliminate the influence of harmonics.

The method for extracting harmonic components from input current is to use a 50 Hz notch filter to eliminate the fundamental component, and the rest is the harmonic component. The expression of the notch filter is shown in (17).

$$G_{\mathrm{n}}(s)={\displaystyle \frac{s^2+{({\omega }_{0\mathrm{n}})}^2}{s^2+(\frac{{\omega }_{0\mathrm{n}}}{Q_{\mathrm{n}}})s+{({\omega }_{0\mathrm{n}})}^2}}$$

(17)

where Q_n is the quality factor.

When ω_0n = 100π, the fundamental component of the current will be filtered out and the harmonic component will be retained. The harmonic suppression control loop is shown in Figure 12.

Where i_sh is the AC bus current harmonics. i_shr is the reference value of i_sh, u_ph is the voltage harmonic of the inductor, and G_h(s) is the controller of the harmonic suppression. When i_shr = 0, the controller will reduce the harmonic amplitude to 0 by adjusting the duty cycle.

The harmonic suppression loop is added to the inner current loop [29,30]. The proposed harmonic suppression method is presented in Figure 13.

In Figure 13, i_sr is the reference value of i_s. The current loop should have a high gain for 50 Hz current. The output of G_I(s) is

$$u_{\mathrm{p}}=u_{\mathrm{pb}}-u_{\mathrm{ph}}$$

(18)

where u_p is the voltage of the inductor, and u_pb is the fundamental component of u_p. When the output of G_h(s) is -u_ph, the harmonic component of u_p will be offset. Thus, HSCM is more suitable for application in HPR connected to the RSHPES with a rich frequency spectrum. It can effectively suppress the impact of integer multiple harmonics, interharmonics, and ultraharmonics. G_h(s) and G_I(s) can use exactly the same controller, and a PI controller will suffice.

To highlight the superiority and reliability of the HSCM, the methods mentioned above are listed in

Table 1. Comparison of four methods.

Methods	Indicator a	Indicator b	Indicator c	Indicator d
The PI controller	×	√	√	×
The resonant elements controller	√	√	×	×
The QPR controller	×	√	√	×
The HSCM	√	√	√	√

for comparison, with performance indicators including (a) low-frequency filtering performance, (b) high-frequency filtering performance, (c) stability, and (d) whether they can be applied to the HPR in the RSHPES.

The control structure diagram of the SPR in this paper is shown in Figure 14.

5. Simulation

In this section, it is proved by simulation with MATLAB/Simulink that the proposed harmonic suppression strategy can effectively suppress the harmonic current. The simulation model of HPR is shown in Figure 15. S₅~S₈ form thee inverter bridge of the PSFB. C_r is the blocking capacitor, and T is the high frequency transformer. D₁~D₄ are high frequency diode rectifier bridges. L_o and C_o constitute the output filtering circuit.

The simulation parameters are displayed in

Table 2. Simulation parameters of the HPR.

Parameter	Value
us	$110\sqrt{2}$cos(100πt)V
Ls	1 mH
rs	0.04 Ω
Ci	470 μF
fs	10 kHz
uo	60 V
Pout	1500 W
Ro	2.4 Ω
Co	220 uF
T	2:1
Cr	10 uF
udc	400 V

.

In Table 2, f_s is the switching frequency. P_out is the output power. To verify the correctness and effectiveness of the proposed method, analysis will be conducted from two aspects: the presence of harmonics in the grid voltage and the disturbance injection into the grid voltage.

Injecting harmonics into the power grid can be done in two ways: injecting harmonics of a single frequency and injecting a mixture of harmonics at multiple frequencies. The kinds of harmonic injection are shown in

Table 3. The kinds of harmonic in u_s.

Harmonics	Value
Integer multiple harmonics	−0.0018cos(2ωt + 94.9°) − 0.0318cos(3ωt + 9.9°) −0.0035cos(4ωt + 92.9°) − 0.0023cos(5ωt − 64.1°) −0.0009cos(6ωt + 86.4°) − 0.0072cos(7ωt − 2.7°) −0.0016cos(8ωt + 26.3°) − 0.0098cos(9ωt + 110.1°) V
Interharmonics	−0.0018cos(2.5ωt + 94.9°) − 0.0318cos(3.5ωt + 9.9°) −0.0035cos(4.5ωt + 92.9°) − 0.0023cos(5.5ωt − 64.1°) −0.0009cos(6.5ωt + 86.4°) − 0.0072cos(7.5ωt − 2.7°) −0.0016cos(8.5ωt + 26.3°) − 0.0098cos(9.5ωt + 110.1°) V
Supraharmonics	−0.318cos(3500ωt + 9.9°) − 0.18cos(4500ωt + 94.9°) V

.

When the power grid contains only the fundamental frequency, the simulation results of u_s and i_s are shown in Figure 16.

Figure 16 only shows the results of the steady state and does not display the transient process. THD(u_s) is THD (total harmonic distortion) of u_s, THD(i_s) is THD of i_s and PF is the power factor. These notations are the same for the subsequent simulation results and experimental results.

From Figure 16, it can be seen that, when there is no harmonic voltage in the power grid, both u_s and i_s are sine waves. THD(u_s) = 0%, THD(i_s) = 1.25% and PF = 1. The FFT of Figure 16 is presented in Figure 17.

In Figure 17, FFT of u_s is free of harmonic components. i_s contains only a small amount of 2nd, 3rd, and 5th harmonics. The conclusion that can be drawn is that, when the power grid voltage is a standard sine wave, the AC-side current is harmonics-free. At the same time, the simulation results in Figure 16 and Figure 17 serve as a control experiment.

When the integer multiple harmonics are injected, the simulation results of u_s and i_s are displayed in the time period of 0.3–0.4 s in Figure 18a. Under the influence of the 3rd harmonic voltage, the current exhibits significant distortion, with THD(u_s) = 2.43%, and THD(i_s) = 32.74%. FFT(u_s) is demonstrated in Figure 18b. FFT(i_s) before 0.4 s is depicted in Figure 18c. At t = 0.4, the HSCM is applied. In Figure 18a, during the time period of 0.4–0.5 s, the current waveform is significantly improved, with the THD(i_s) = 1.35%, and the value of PF has changed from 0.963 to 0.998. FFT(i_s) after 0.4 s is shown in Figure 18d. From this, it can be seen that the harmonic content is significantly reduced.

From Figure 19a and Figure 16, it can be seen that, when the interharmonics are present, the sinusoidal quality of i_s is very low. Figure 17 and Figure 19c illustrate that the harmonic content of i_s is relatively high with THD(i_s) = 35.03%. After the action of HSCM, the current waveform becomes a sine wave, with THD(i_s) = 1.43%. PF has improved from 0.947 to 0.998. The harmonic components in Figure 19d are minimal.

From Figure 16 and Figure 20a, it can be seen that, when supraharmonics are added to u_s, they do not cause distortion in i_s. Regardless of whether HSCM is in action or not, i_s always presents as a sine wave. In Figure 20b, u_s contains only high-frequency harmonics. Comparing Figure 17 with Figure 20c,d, it is evident that before the action of HSCM, THD(i_s) = 1.53%, and after the action of HSCM, THD(i_s) = 0.24%. Therefore, supraharmonics exert a minor influence on i_s, and HSCM has improved the situation of low-frequency harmonics in i_s.

When the circuit is in a steady state, a voltage disturbance of u_s1 = 50$\sqrt{2}$cos(100πt) is introduced at t = 0.3 s, followed by another voltage disturbance of u_s2 = −100$\sqrt{2}$cos(100πt) at t = 0.5 s. The simulated waveform is shown in Figure 21.

In Figure 21, the intervals are set as follows. Interval I: from t = 0.1 s to t = 0.3 s, Interval II: from t = 0.3 s to t = 0.5 s, Interval III: from t = 0.5 s to t = 0.7 s. In Figure 21a, before the effect of HSCM, when u_s1 is superimposed on u_s, i_s drops and distortion occurs. The addition of u_s2 causes i_s to overshoot. Figure 21b shows the waveform of u_s and i_s after the disturbance is added with HSCM in effect. Whether influenced by u_s1 or u_s2, the transition of i_s is smoother compared to that in Figure 21a, without overshoot or distortion. Not only that, but the PF and Total THD in Figure 21b are both better than those in Figure 21a. FFT(i_s) with u_s1 and u_s2 are shown in Figure 22.

By comparing Figure 22b with Figure 22e, it can be seen that HSCM can prevent u_s1 from causing DC components and second-harmonic distortion in i_s. Similarly, HSCM can also prevent the damage caused by u_s.

From the above simulation results, we can conclude that HSCM can effectively suppress the impact of harmonic currents in the power grid on the AC-side current, including the effects of integer multiple harmonics, interharmonics, and also improve THD(i_s) in the case where u_s contains superharmonics. Additionally, HSCM can eliminate the effects of grid voltage disturbances. This ensures the integration of HPR into RSHPES.

6. Experiment

Figure 23 is a photograph of the experimental prototype. A 1500 W experimental platform was built for verifying the simulation results. The BOM (bill of materials) used in the experiment is shown in

Table 4. The BOM of the HPR.

Parameter	Type	Number	Nrand
La,Lb,Lc	LGNE1 mH-30–100K-3P	1	LGNE
S1~S6	IKW30N60T	6	Infineon
Ci	C3D1U206JF0BC00/20uF	3	Faratronic
S7~S10	IKW30N60T	4	Infineon
Cr	C3D1U505KB00C00/5uF	2	Faratronic
T	GTF-60V 50A-100K	1	Wengudq
D1~D4	VS-E5PH6006L-N3	4	VISHAY
Lo	LGNE2uH-50–100K-CF3	1	LGNE
Co	450MXG470MEFCSN35X	2	Rubycon
us	61815-TC	1	Chroma
Ro	ZX-5-2.4	1	Tianjin Langwo

The input source selected in Table 4 is Chroma’s 61815-TC. This power supply can provide integer multiple harmonics, interharmonics, supraharmonics, and voltage disturbances, which is very useful for verifying the correctness and effectiveness of HSCM.

The experimental results when injecting integer multiple harmonics are shown in Figure 24, where Figure 24a is before the action of HSCM, and Figure 24b is after the action of HSCM.

In Figure 24a, THD(u_s) = 3.67%, THD(u_s) = 34.23% and PF = 0.963, and the distortion of i_s is quite severe. THD(u_s) = 3.67%, THD(u_s) = 1.83% and PF = 0.997 in Figure 24b, and i_s is a sine wave.

The experimental results when injecting interharmonics are shown in Figure 25, where Figure 25a is before the HSCM takes effect and Figure 25b is after the HSCM takes effect.

From Figure 25a, THD(u_s) = 3.53%, THD(i_s) = 36.13% and PF = 0.941, and i_s is not a sine wave. Under the influence of an interharmonic wave, the period of it is doubled. As shown in Figure 25b, THD(u_s) = 3.53%, THD(i_s) = 1.82% and PF = 0.997. The harmonics of i_s are eliminated.

Under the influence of ultraharmonics, the experimental waveform of u_s is shown in Figure 26.

As shown in Figure 26, the ultraharmonics have a relatively small impact on i_s. However, THD improved under the influence of HSCM, changing from 1.62% to 0.86%.

Figure 26 displays the experimental waveform with voltage disturbances applied to u_s. Disturbance u_s1 was introduced at time t₁, and disturbance u_s2 was introduced at time t₂.

When u_s1 is applied, the amplitude of u_s increases. When HSCM is not in effect, i_s drops and distortion occurs, after t = t₁ in Figure 27a. THD(i_s) = 5.13% and PF = 0.963. From Figure 27b, it can be seen that HSCM can cause u_s to change slowly under the influence of u_s1, without distortion. THD(i_s) = 1.24% and PF = 0.996. When u_s2 is applied, the amplitude of u_s decreases, i_s exhibits overshoot, and distortion occurs, as shown in Figure 27c. THD(i_s) = 4.43% and PF = 0.973. From Figure 27d, it is observed that the amplitude of u_s gradually increases under the influence of u_s2, without overshoot or distortion. THD(i_s) = 1.34% and PF = 0.997. Therefore, HSCM is also capable of mitigating the effects brought about by u_s2.

When HSCM is in effect, the change in i_s is more gradual, after t = t₁ in Figure 27b. u_s2 caused a reduction in the amplitude of u_s. Under the action of HSCM, i_s increased slowly, after t = t₂ in Figure 27b. However, without the action of HSCM, i_s exhibited overshoot, after t = t₂ in Figure 27a.

The voltage of C_i is u_dc and the voltage of C_o is u_o, as shown in Figure 28.

From Figure 28, it can be observed that the average value of u_dc is 400 V, and u_o is 62 V. Combined with the parameters provided in Table 2, it is evident that the HPR has achieved the rated power output and is operating stably. The waveform of u is a straight line, which is crucial for enhancing the performance of the electrolyzer.

The aforementioned experiment further demonstrates that HSCM can eliminate the effects of integer harmonics, interharmonics, and voltage disturbances, and can improve the THD(i_s) in the presence of superharmonics.

7. Conclusions

The spectrum in RSHPES is very rich, not only including integer multiples of harmonics but also interharmonics and ultraharmonics. There are also various disturbances present. Traditional harmonic suppression methods cannot guarantee that HPR will be immune to the harm caused by these harmonics and disturbances. Simulation and experimental results show that HSCM can effectively eliminate the damage caused by rich harmonics and disturbances. HSCM has made a contribution to the integration of HPR into RSHPES and has also prevented the harm of harmonics to EC.