Power Density Enhancement of Three-Phase Rectifier Using Higher Frequency Solid State Transformer

Nowadays, worldwide the demand on DC power supplies is increasing rapidly, especially for automotive, railway, aircraft, and data center applications. The value of the global semiconductor rectifiers market is predicted to hit $6.6 billion by 2026 [1]. Three phase conventional diode rectifier is one of the most trusted and popular converters due to its high reliability and durability [2-6]. However, the conventional three-phase rectifier utilizes conventional line frequency transformer (50/60) Hz for isolation purposes. The use of a conventional transformer has a negative consequence on the total power density of the three-phase rectifier. The power density is given by Eq. (1) [7]. It is ratio of the total power process through a converter to the total volume occupied by that power converter. Figure 1 illustrated the relationship between the occupied by transformer’s core with its running frequency [7]. High power density implies less footprint of power electronics converters [8]. For automotive and aircraft applications, high power density means reduced transport fuel consumption. Magnetic components such as transformers and inductors have the major footprint for the power electronics converter [9]. A higher power density is achieved by increasing the transformer's running frequency. Despite its smaller core cross-section area, the transformer core still produces the same amount of flux lines. Figure 1 shows A 1MVA silicone steel (Si) core transformer's volume shrinks from (2000 to 200) liter if the transformer’s core running frequency is raised from (50 to 1 kHz) respectively [7]. Renewable energy resources such as solar and wind turbines are the most promising energies worldwide. For more than a century, transformers have formed the backbone of electrical grids. However, as the world seeks to address the issue of climate change by expanding the utilization of renewable energy sources such as wind turbine farms and solar photovoltaic stations, new developments in transformer technology will play a significant role in this effort. In ocean depths where fixed-foundation turbines are impractical, floating wind farms, which comprise of wind turbines installed on floating structures, are ideally suited. They may vastly expand the amount of ocean that can be used for offshore wind farms across the world. If a wind farm has to have transformers, the best place for them to be inside the wind turbine tower, as shown in Figure 2 [10].

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Figure 1. Transformers' core occupied with operation frequency [7]

The U.S. Department of Energy presented a vision 20% wind energy by 2030 to motivate the developing wind power [11]. Three-phase, six-pulse and multi-pulse converters are extensively used for high-power applications such as wind turbine and high voltage direct current HVDC [12-16]. However, the major drawback of these topologies is the low power density due to the use of a hefty line frequency transformer. Moreover, the traditional transformers such as the On-Load Tap OLTC Changing have some sort of low response [17].

Power Density $=\frac{\text { Total power process }(w)}{\text { Total volume ocupied }(\text { Liter })}$    (1)

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Figure 2. Off-shore rooftop wind turbine transformer proposed by ABB [10]

A solid-state transformer combines a power electronics converter with high-frequency transformer to perform voltage transformation, isolation, and extra regulation. The use of solid-state transformers reduces the hefty of magnetic components and allows for finer levels of control. However, these functionalities are unavailable from line frequency transformers. The solid-state transformers have become more popular due to the use of advanced power semiconductors such as Silicon Carbide SiC and Gallium Nitride Gan. Many applications can be benefited from solid-state transformers because of their adaptability and ease of control [18-23]. General Electric GE proposed and designed 1 MVA, 20 kHz solid state transformer. Their proposal was compared with a regular transformer in size and weight. The proposed is illustrated in Figure 3 [24]. The outcome results proved better power density for their proposal. In response to the power density concerns, the presented study presents an isolated six-pulse diode converter with the use of solid-state transformer, as shown in Figure 4.

The proposed idea indicates that the power density can be enhanced without sacrificing the performance of the six-pulse rectifier. In this paper, a design example for three phase six-pulse rectifier using a high frequency (2 kHz) solid state transformer is discussed. Extensive Matlab simulation analysis is explained in details. The presented concept offers advantages as listed below:

-The presented topology is robust and performed as a regular isolated three-phase rectifier.

-The input utility current has the same quality as a regular six-pulse rectifier.

-Using a frequency boost converter can give more resilience to control the power flow.

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Figure 3. General Electric prototype comparison between solid-state transformer and traditional one [24]

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Figure 4. Proposed concept of three phase six-pulse rectifier using high frequency solid state transformer

The major harmonics content of electrical input currents (i_a, i_b, i_c) for the conventional six-pulse diode rectifier is well known (5^th, 7^th, 11^th, 13^th, etc.) [2, 4]. In this section, depth analysis and math derivation show that the current grid quality for the presented idea and a conventional six-pulse rectifier with the use of a regular transformer are totally identical. In order to derive mathematical equations for the input current i_a, the output load current I_{L DC} for the rectifier is assumed to be smooth DC (see Figure 6). The comprehensive mathematical analysis is applied to the first phase, as shown in Figure 6. I_PA is the primary transformer winding current, and S_FBC is the frequency boost converter switching function (see Figure 5). To acquire the relationship between I_PA and the secondary side currents of the transformer I_SA, the transformer volt-ampere balanced between the primary and secondary sides should be used, as explained in Eq. (2). From Figure 6, it can be observed that I_SA and I_SB as written in Eqs. (3) and (4):

$i_a=S_{F B C} \times I_{P A}$    (2)

$N_{P A} \cdot I_{P A}=N_{S A} \cdot I_{S A}+N_{S B} \cdot I_{S B}$    (3)

$I_{S A}=I_{D 1}$    (4)

$I_{S B}=-I_{D 6}$    (5)

Since the transformer turns ratio is one, so by substituting Eqs. (4) and (5) into Eq. (3) to get:

$I_{P A}=I_{D 1}-I_{D 6}$    (6)

The DC load current I_LDC goes through I_D1 and I_D6, shaping the primary current I_PA as a quasi-square wave written by Eq. (7):

$S_{q u s i}(w t)=\sum_{n=1,5,7,11,13, \ldots}^{\infty}\left(\frac{4 \times I_{L D C}}{n \pi} \cos \left(\frac{n \pi}{6}\right)\right) \sin (n w t)$    (7)

The frequency boost converter’s switching function S_FBC is equal to S_Rec multiplied by S_Inv (see Figure 5 and Eqs. (8)-(10)). The w_HF  is the boost frequency converter’s operating frequency 2 kHz:

$S_{\text {Rec }}=\left(\frac{4}{\pi}\right) \sum_{n=1,3,5, \ldots}^{\infty}\left(\frac{1}{n}\right) \sin (n w t)$    (8)

$S_{I n v}=\sum_{n=1,3,5, \ldots}^{\infty}\left(\frac{1}{n}\right) \sin \left(n w_{H F} t\right)$    (9)

$\begin{gathered}S_{F B C}=S_{R e c} \times S_{I n v}=\left(\frac{4}{\pi}\right) \sum_{n=1,3,5, \ldots}^{\infty}\left(\frac{1}{n}\right) \sin (n \pi D) \sin \left(n w_{H F} t\right)\end{gathered}$    (10)

Furthermore, I_PA has to respond to the whole switching function S_FBC. Due to the influence of S_FBC, the diode currents (I_D1, I_D6) would be written by Eqs. (11) and (12):

$I_{D 1}=S_{F B C} \times S_{\text {quai }}(w t)$    (11)

$I_{D 6}=S_{F B C} \times S_{\text {quai }}\left(w t-\frac{2 \pi}{3}\right)$    (12)

Substituting Eqs. (11) and (12) into Eq. (6) gives:

$I_{P A}=\left[S_{q u a i}(w t)-S_{q u a i}\left(w t-\frac{2 \pi}{3}\right)\right] \times S_{F B C}$    (13)

Substituting Eq. (11) into Eq. (2):

$\begin{gathered}i_a=\left[S_{F B C}\right]^2\left(\frac{2 \sqrt{3} I_{L D C}}{\pi}\left[\sin (w t)-\frac{1}{5} \sin (5 w t)-\right.\right. \left.\left.\frac{1}{7} \sin (7 w t)+\frac{1}{11} \sin (11 w t)+\cdots . e t c\right]\right)\end{gathered}$    (14)

When the duty ratio D of the frequency boost converter is (50%), this implies:

$\begin{gathered}{\left[S_{F B C}\right]^2=\left\lceil\frac{4}{\pi} \sum_{n=1,3,5, \ldots}^{\infty}\left(\frac{1}{n}\right) \sin (n \pi D) \sin \left(n w_{H F} t\right)\right]^2} =1.0\end{gathered}$    (15)

The phase ‘A’ input current i_a would be:

$i_a=\frac{2 \sqrt{3} I_{L D C}}{\pi}\left[\begin{array}{c}\sin (w t)-\frac{1}{5} \sin (5 w t) \\ -\frac{1}{7} \sin (7 w t)+\frac{1}{11} \sin (11 w t)-\cdots . e t c\end{array}\right]$    (16)

Evidently, the harmonics content of the input utility current i_a for the presented topology, similar to the regular six-pulse rectifier.

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Figure 6. Input current analysis i_a for the presented topology in Figure 4

When the transformer works at line frequency (50/60) Hz, that tends to have negative consequences for the power density. The transformer’s (volume/ weight) can be reduced by increasing its operating frequency. The higher frequency of operating, the higher power density. There will be a major role for recent developments in transformer technology. Floating wind farms, which consist of wind turbines installed on floating platforms, are well suited for offshore sites at ocean depths where fixed-foundation turbines are not feasible. If a wind farm has to use transformers, installing them in the turbine’s tower is preferable. Solid state transformer could be the perfect solution to reduce the structure cost of the wind turbine tower and increase it reliability to achieve high efficiency for the total converter. The results of the presented idea demonstrate that the three phase rectifier's output DC voltage and utility input current quality are not affected by the usage of the solid-state transformer. However, the proposed approach swaps out the traditional line frequency transformer with a smaller solid state version, resulting in more power density for the isolated three-phase rectifier.