# Multiple generator's stator windings as voltage sources for a multilevel converter

T Tayar, D Shmilovitz

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T Tayar, D Shmilovitz. Multiple generator's stator windings as voltage sources for a multilevel converter. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0025. http://epe2025.org

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Multiple generator’s stator windings as voltage sources for a multilevel
converter

T. Tayar and D. Shmilovitz

Tel-Aviv University
Israel

Contact: [shmilo@tauex.tau.ac.il](mailto:shmilo@tauex.tau.ac.il)
**Keywords**

Multilevel, generator, frequency matching

**Abstract**

It is proposed to use a generator's stator windings to create multiple, isolated voltage sources for multilevel converters (MC). Under this approach the generator windings are viewed as transformer windings, with multiple secondary windings. Thus, we propose to redesign the stator windings as multiple transformers hence turning a single 3-phase output multiple 3-phase outputs. After rectifying the outputs, they function as separate isolated DC voltage sources, which are applied to an MC's input. Taking advantage of the readily existing generator's magnetics, no additional magnetic components are required under the proposed method.

The proposed method was validated experimentally.

**Introduction**

For the past few years Modular Multilevel Converters (MMC) are becoming increasingly common, particularly in industrial applications and high-power systems [1],[2]. The MMC is a converter comprised almost solely of switches. These switches control the connection among multiple submodules (SM) and build a required AC signal at its output [3]. Each SM requires an individual DC source, and multiple switches, which are mostly arranged in an H-bridge configuration. This arrangement is responsible for the series connection of the SMs one to the other [4]. The momentary connection either adds or subtracts the DC source in combination with other DC sources from other SMs, which together form the required output signal. In this topology all SMs are identical, facilitating optimized design and manufacturing process. This makes the converter easy to scale to various voltage ratings [5],[6]. Moreover, repairs of such converters are also simplified as failing SMs can be replaced with other SMs. In addition, redundant modules kept in bypass until a failed module requires replacement can also be applied. However, since all the SM's DC sources must be isolated, the power must come from independent sources such as batteries, PV panels [7], etc.

Another option is isolation using dedicated hardware, typically by using high frequency transformers [8]-[10]. This dedicated hardware increases the converter's complexity and footprint. This is intensified as the amount of SMs is increased in an application.

In this work we propose using the stator windings of a generator to create isolated DC sources for an MMC. This approach is based on the idea that a generator can be used as a transformer, with multiple output windings. Our main approach is to redesign a generator's stator windings as a transformer with multiple secondary windings, replacing a single 3-phase output with multiple 3-phase outputs. Rectifying each output allows it to function as an individual isolated DC voltage source. This DC source can connect directly to the MMC. Additionally, this topology enables the use of Selective Harmonic Elimination (SHE) modulation [11],[12]. This technique uses the half-wave symmetry of the harmonics to eliminate the same harmonic [13]-[17]. The proposed approach offers several advantages:

1. All magnetic components are integrated into the stator eliminating the need for additional magnetic components, which simplifies the converter. The MMC is only comprised of switches, which makes it exceptionally small. As a result, this converter may be fitted directly on the generator.

2. The switching frequency is 50/60Hz, resulting in low switching losses and a slow control system, which leads to a robust and low-cost design.

3. Using the SHE modulation can eliminate the low harmonics, allowing a simple output filter.

4. The design can be scalable for different voltage and power ratings. More SMs can also eliminate additional harmonics, as required for complying with the utility grid's standards.

5. Adding more SMs to the design enables redundancy in the converter, allowing for a failed SM to be bypassed until it is replaced. This allows for continuous operation during a fault in the converter.
The proposed system is also cost effective compared to other conventional methods. First, due to the usage of thinner gauge copper wire in its construction, the generator itself would use less copper than conventional generators. Second, each SM in the system operates at a low switching frequency and under a lower voltage than the required output voltage. In addition, since the switches only conduct for a short interval during the switching period, their average power rating is also lower. This allows for the use of simple, cheap, and common switching components which operate at less demanding. Also, splitting the power between parallel submodules can result in a better heat evacuation. This lowers the need for complex and expensive cooling solutions for the system. Thus, the cost of operation is also reduced. And finally, by adding parallel redundancy modules in this system, maintenance can be performed while the system is in operation. This allows for continuous operation with no down time, lowering the cost of maintenance during the life cycle of the system.

## The proposed system

The fundamental design of the suggested system is presented in Figure 1. The modified generator is represented by a generator excitation coil viewed as a transformer with a single primary winding and multiple individual secondary windings for each one of the three phases. All secondary windings are the same and interchangeable. This transformer secondary represents the stator windings. Each transformer secondary is rectified, and functions as a DC source for each SM in the MMC. For simplicity, the rectification we present is a simple diode bridge, though it may be done by any method. Each SM is implemented using four switches in an H-bridge configuration. All the SMs are divided into three groups, where the outputs of each individual SM in the group are then connected in series. The H-bridge's switching operation in each SM is set using the SHE method. This complete MMC configuration produces three individual outputs which form the required 3-phase output. This 3-phase output may not require additional filtration, due to the utilization of the SHE method. Thus, the complete MMC can be connected directly to the utility grid or a load. Denoting the number of the multiple windings for each phase as N, and the required MMC's output voltage amplitude as V_pk, the turn ratio of the stator is determined such that the

<figure><img src="image_2.png" /><figcaption>Figure 1: The proposed system</figcaption></figure>

rectified voltage amplitude of each of the individual windings is

$$V_{DC} = \frac{V_{pk}}{N}, \qquad (1)$$

where $V_{DC}$ is the required SM's rectified voltage.

The MMC controls the switching of each SM in the sequence such that it shapes the required output waveform. For each phase, all SMs are connected in series to form the output. And the switching operation either adds, subtracts, or bypasses the DC source. Table 1 details the switches' states for each operation.

<table><caption>Table 1: SM switches operation scheme.</caption><thead><tr><th>Operation</th><th>S<sub>1</sub></th><th>S<sub>2</sub></th><th>S<sub>3</sub></th><th>S<sub>4</sub></th><th>Output</th></tr></thead><tbody><tr><td>Addition</td><td>ON</td><td>OFF</td><td>OFF</td><td>ON</td><td>V<sub>DC</sub></td></tr><tr><td>Bypass</td><td>OFF</td><td>OFF</td><td>ON</td><td>ON</td><td>0</td></tr><tr><td>Subtraction</td><td>OFF</td><td>ON</td><td>ON</td><td>OFF</td><td>-V<sub>DC</sub></td></tr></tbody></table>
For a single phase, the MMC's output voltage is

$$V_o(t) = \sum_{i=1,2,...}^{N} V_{SM,i}(t). \qquad (2)$$

Where $V_{SM,i}(t)$ is the output voltage of a single SM. The approximate a sinusoidal waveform is

$$V_{SM,i}(t) = \begin{cases} V_{DC} & \sin(\omega_g t + \varphi_i) > \sin(\pi(0.5 - d)) \\ -V_{DC} & \sin(\omega_g t + \varphi_i) < \sin(\pi(0.5 - d)) \\ 0 & \text{otherwise} \end{cases} \quad (3)$$

Where $\omega_g$ is the utility grid's frequency, $\varphi_i$ is the individual SM phase angle, and $d$ is the duty-cycle, for each output state. This function creates a square-wave function with a dead-time between switching from a positive voltage to a negative voltage. Additionally, to eliminate the 3rd harmonic in all SMs we select $d = \frac{1}{3}$ [18]. The Fourier decomposition the SM's function is.

$$V_{SM,i} = \frac{2\sqrt{3}V_{DC}}{\pi} \sum_{k=1,5,7,11...}^{\infty} \frac{c_k \sin(k(\omega_g t + \varphi_i))}{k}, \quad (4)$$

where $C_k$ is a coefficient representing the function's sign,

$$C_k = (-1)^{\frac{k-1}{2}} \sin(\frac{kn}{3}), \forall k = 1,5,7, \dots \quad (5)$$

Using the SHE modulation, to eliminate the harmonic component $k$, we first define the phase angle $\varphi_\omega(k)$ as

$$\varphi_{\omega}(k) = \frac{\pi}{k} \qquad (6)$$

Using this phase angle in $\varphi_i$ for half the SMs ensures a $\pi \frac{\text{rad}}{s}$ phase difference for the $k^{th}$ harmonic between the SMs, leading to a negative sign for the $k^{th}$ harmonic in half of the SMs, and a positive sign in the others. Thus, when summing the output voltages of all SMs, the $k^{th}$ harmonic is eliminated. For example, Table 2 presents the $\varphi_i$ values for eliminating the 5$^{th}$, 7$^{th}$ and 11$^{th}$ harmonics. Applying the $\varphi_i$ values from Table 2 to (2) and (4), the resulting output voltage is:

$$V_o(t) = \frac{2\sqrt{3}V_{DC}}{\pi} \left( \sum_{i=1}^{N} \sin(\omega_g t + \varphi_i) + \sum_{i=1}^{N} \sum_{k=13,17,...}^{\infty} \frac{c_k \sin(k(\omega_g t + \varphi_i))}{k} \right) \quad (7)$$

<table><caption>Table 2: SHE modulation $\varphi_i$ values</caption><thead><tr><th>i</th><th>φ<sub>i</sub></th><th>i</th><th>φ<sub>i</sub></th></tr></thead><tbody><tr><td>1</td><td>0</td><td>5</td><td>φ<sub>ω</sub>(11)</td></tr><tr><td>2</td><td>φ<sub>ω</sub>(5)</td><td>6</td><td>φ<sub>ω</sub>(11) + φ<sub>ω</sub>(5)</td></tr><tr><td>3</td><td>φ<sub>ω</sub>(7)</td><td>7</td><td>φ<sub>ω</sub>(11) + φ<sub>ω</sub>(7)</td></tr><tr><td>4</td><td>φ<sub>ω</sub>(7) + φ<sub>ω</sub>(5)</td><td>8</td><td>φ<sub>ω</sub>(11) + φ<sub>ω</sub>(7) + φ<sub>ω</sub>(5)</td></tr></tbody></table>

Where we can see that converter's the output voltage contains the required utility grid signal and additional harmonics which begins at the 13th harmonic, which is simpler to filter.

Figure 2 presents the waveforms of two SMs in the MMC. These SMs utilizes SHE modulation, to eliminate the 5th harmonic when added to each other.

Figure 3 presents the harmonics of both a single SM, and the two SMs MMC connected in series.

<figure><img src="image_3.png" /><figcaption>Figure 2: SHE modulation with two SMs: (a) $V_{SM,1}$; (b) $V_{SM,2}$; (c) $V_{SM,1} + V_{SM,2}$, the dashed line presents the approximate sine wave.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>(a) Harmonics of a single SM.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>(b) Harmonics of an MMC with two SMs.</figcaption></figure>

<caption>Figure 3: MMC and SM harmonics.</caption>

## The control system

The converter's control system's main function is to reach utility grid synchronization. It controls both the frequency and phase angle of the output voltage. Whereas the peak voltage is predetermined from (1). As noted in the previous section, the SM's switching frequency is the same as the output voltage frequency. The SM's phase angle is predetermined by its place in the series according to the SHE modulation algorithm. Thus, the control system must compensate for the variations in the utility grid's frequency and phase angle by setting the SMs according to their transient changes. Therefore, the control system would only control the modulated switching frequency $\omega_m$, and apply the variations in phase angle to each SM in the 3-phase converter, all according to its position in the series, while retaining the synchronization with the utility grid. Figure 4 presents the design of the converter's closed loop control system. To construct the control system, we assume a utility grid PLL signal is available. This signal is denoted here as $\theta_{\text{ref}} = \omega_{\text{ref}} \cdot t + \varphi_{\text{ref}}$. The input voltages to the system are the N isolated and rectified voltages from the generators, each having a voltage amplitude of $V_{\text{DC}}$.

<figure><img src="image_6.png" /><figcaption>Figure 4: Closed loop system.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5: Control system - single SM.</figcaption></figure>

Each of these voltages is fed individually to an SM, where it is multiplied by the modulation signal and creates the square wave as denoted in (3). Applying $d = \frac{1}{3}$ the required SM signal is produced, as depicted in (4). This signal is summed in series with all the other SMs in the chain, and then filtered. Figure 5 presents the mathematical representation of the working principle and the control of an individual SM. Where SM begins with an isolated AC power supply from the generator's stator. Next, the AC voltage is rectified, which is depicted by the next block. This block represents the conversion of the input voltage from AC to DC with no specific method. The rectified isolated DC voltage denoted as $V_{\text{DC}}$. This voltage enters the multiplication block. This block has two inputs: $V_{\text{DC}}$ and $x_{\text{sw}}$. The $x_{\text{sw}}$ signal is the output of the $f_{\text{sw}}$ block which performs the function which creates the approximated sinusoidal waveform; thus, the output of the multiplication block is (3). Finally, this result feeds into the summation block which represents the series connection of all the SMs in the MMC.

## Generator construction

To construct the generator for the experiments we modified an existing alternator. First, we bypassed the alternator's regulator and attached wires directly to the excitation coil. This was done to allow for direct control on the excitation current. This allows us to adjust and set the output
voltage level for the experiments. Next, we modified the stator coils. We removed the existing windings from the stator and wound up the new windings in the same path. The stator had 36 slotted positions for winding the copper wires. For the new windings we used a smaller gauge enamel wire. Instead of the single wire that was originally placed in the path of each phase, we placed two wires for each path. Thus, for each one of the three-phases we had two identical and isolated voltage outputs, which ultimately means that we had a stator with six individual isolated voltages sources as needed for our MMC. The finished generator had six pole pairs and 11 turns for each of the stator's output coils. Figure 6 is an illustration describing the modification made to the alternator's stator. It presents both the alternator before and after the modification.

An image of the modified alternator and its stator's output is presented in Figure 7. For the rectification we chose a simple diode bridge rectification. Hence, when connected to the converter, each output of the modified stator is individually fitted with a diode bridge and a capacitor, as previously presented in Figure 1.

The capacitor value is selected to be high enough for both compensating for ripple in the DC voltage created by the diode bridge creating a constant DC voltage, and to function as the intermediate energy storage, otherwise known

<figure><img src="image_8.png" /><figcaption>Figure 6: Alternator before and after modification.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 7: The modified alternator's stator output.</figcaption></figure>

as the DC-link. Also, additional capacitors were attached to the input of each SM to further attenuate the ripple when needed.

## Experimental Verification

In this section, we present the results of the experiments conducted with the prototype generator and converter circuit that we designed and built. In these experiments, the system's performances were tested. The experiments we performed focus on frequency matching and load performance, as they are the generator's and converter's main functions. Therefore, the generator's output voltage is controlled manually, and it reached its steady state before the converter was turned on. The manual control of the generator does not affect the experiment's results. This is because the generator would still produce the required individual isolated voltages as designed to do, and as it was the main purpose in this work. The generator's velocity was set and maintained by an external motor controlled by a VFD connected to the generator's shaft using a timing belt. The generator's excitation field was set by an external voltage source, which was adjusted until the generator reached the required output voltage. Table 3 presents the main parameters for the experiments.

<table><caption>Table 3: Experimental parameters</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>V<sub>DC</sub></td><td>{~80V (@N = 2)<br/>~40V (@N = 4)</td></tr><tr><td>v<sub>o</sub></td><td>~115 V<sub>RMS</sub></td></tr><tr><td>ω<sub>o</sub></td><td>2π60 rad/s</td></tr><tr><td>R<sub>Load</sub></td><td>53Ω</td></tr></tbody></table>

Figure 8 and Figure 9 present the main experimental waveforms at the converter's output. Both figures show the modulated output $v_o(t)$ of the system and its FFT analysis. Figure 8 shows a 3-phase output signal of the MMC which incorporate two SMs. In this arrangement, the 5th harmonic is eliminated. This can be seen in the bottom waveform, which presents the voltage's FFT analysis, where the 5th harmonic is missing.
<figure><img src="image_10.png" /><figcaption>Figure 8: 3-phase, two SMs experiment: (Top) 3-phase output voltage; (Bottom) output voltage FFT.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 9: Single-phase, four SMs experiment: (Top) Single-phase output voltage; (Bottom) output voltage FFT.</figcaption></figure>

Figure 9 shows a single-phase output signal of the MMC which incorporate four SMs. In this arrangement, both the 5^th^ and 7^th^ harmonics are eliminated. Again, the output voltage's FFT analysis shows that both the 5th and 7th harmonics are missing. As can be seen in both figures, the results match in good agreement with both the theoretical output voltage from (7), and the theoretical graphs presented in Figure 2 and Figure 3.

An experiment of measuring the input current to each SM in The MMC was also performed. In this experiment we used the MMC with two SM levels, and individually measured their input currents. Figure 10 presents the results of this experiment. The figure shows a single phase of the MMC's outputs, as well as the input current for each one of the individual SMs. The current was measured from the positive of the SM's individual DC power supply. Therefore, we can see that each SM's current input is positive DC current while the complete MMC outputs is an AC voltage. We also can see the different current draw at each stage where the SMs connect in the

<figure><img src="image_12.png" /><figcaption>Figure 10: input current of two SMs: (Top) output voltage; (Middle) input current $SM_1$; (Bottom) input current $SM_2$.</figcaption></figure>

sequence. The connection sequence is as follows: SM No.2 is the first in the sequence and begins to power the load, until SM No.1 is also connected. At this point the current draw is doubled as both SMs are connected in series. Then, SM No.2 disconnects, the current is halved, and only SM No.1 supplies the current until the end of the sequence. The same sequence is performed for both the positive and the negative parts of the output voltage, where the control system determines both when each connection occurs and the direction of the connection. Thus, creating both positive and negative voltages. This in turn constructs the required output AC voltage.

## Conclusion

A method for creating multiple isolated voltage sources for an MMC by adding multiple windings to a generator's stator is introduced. The generator itself can be utilized as both a power source, and an isolating transformer. With the added windings the resulted isolated voltages are rectified and used as the input voltages for individual SMs in an MMC.

The proposed method uses no additional magnetic components other than the ones that already exist inside the modified stator. Therefore, it minimizes the overall system size. In addition, this method uses a low switching frequency, as low as the utility grid's frequency which results in low switching losses. Moreover, by using a larger number of SMs stages the output filter can be considerably simplified as there are less and less harmonics to filter.
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