# T-type Inverter as a Power-Pulsation Buffer for a PMSM with Large Load Variation

Pelle Weiler, Toshiyuki Fujita, Hiroshi Fujimoto, Takayuki Miyajima, Yoshiko Yasuda, Akio Yamagiwa

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## To cite this version:

Pelle Weiler, Toshiyuki Fujita, Hiroshi Fujimoto, Takayuki Miyajima, Yoshiko Yasuda, et al., T-type Inverter as a Power-Pulsation Buffer for a PMSM with Large Load Variation. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0218. hal-05095875

HAL Id: hal-05095875

https://utc.hal.science/hal-05095875v1

Submitted on 3 Jun 2025

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# T-type Inverter as a Power-Pulsation Buffer for a PMSM with Large Load Variation

Pelle Weiler

Department of Advanced Energy
The University of Tokyo

Chiba, Japan

pelle.weiler@edu.k.u-tokyo.ac.jp

Toshiyuki Fujita

Department of Advanced Energy
The University of Tokyo

Chiba, Japan

t-fujita@edu.k.u-tokyo.ac.jp

Hiroshi Fujimoto

Department of Advanced Energy
The University of Tokyo

Chiba, Japan
fujimoto@k.u-tokyo.ac.jp

Takayuki Miyajima

Daikin Industries Ltd.

Osaka, Japan

takayuki.miyajima@daikin.co.jp

Yoshiko Yasuda

Daikin Industries Ltd.

Osaka, Japan

yoshiki.yasuda@daikin.co.jp

Akio Yamagiwa

Daikin Industries Ltd.

Osaka, Japan

akio.yamagiwa@daikin.co.jp

**Index Terms**—Energy Management System, Modulation strategy, T-type inverter, Three-phase motor drive

**Abstract**—This paper presents a modulation strategy for a three-level T-Type inverter to utilize the neutral point as a power-pulsation buffer. The pulsating power of a swing compressor is compensated by the buffer, resulting in dc input power of the motor inverter, despite the varying load. Consequently, the overall drive system can be designed with significantly reduced dc-link capacitance, saving cost and size. Next to theoretical derivation, the proposed modulation strategy is verified in simulation and experiment.

## I. INTRODUCTION

With the rise of private solar energy, many households convert their heating systems to air conditioners to fully utilize their generated electricity. To further maximize energy savings and profitability, these systems can utilize batteries to store excess production during the day and support consumption outside peak production [1]. These type of systems are commonly referred to as energy management systems (EMS) [2], [3]. An example implementation is depicted in Fig. 1a, with a photovoltaic inverter, battery storage, grid inverter and a heat pump. The swing compressor of the heat pump is driven by a permanent magnet synchronous machine (PMSM), integrated into the pump housing.

The grid and motor inverter both present highly varying loads, at twice the grid frequency and rotational frequency of the compressor respectively. Left uncompensated, those two systems will forward this load ripple into the dc-link. In presence of these load variations, large and bulky buffer capacitance is required to keep the voltage within specified limits.

Instead of using a large dc-link capacitance, several types of auxiliary converters allow to remove the load ripple from the dc-link entirely, commonly referred to as power-pulsation buffers (PPB). A parallel current injector (PCI) is connected in parallel to the dc-link and compensates the load current flow, by storing and releasing the excess energy in a separate capacitor [4]. In contrast to the dc-link capacitance, the storage capacitor is allowed to fluctuate between the dc-link voltage and zero, immensely increasing the energy storage capability. However, due to the magnitude of the current load current, the PCI has to process the same power as the main inverter it is compensating. Another option is a series connected approach, isolating the load ripple entirely. The advantage is that only a fraction of the load power needs to be processed, at the cost of higher passive and active part count. An overview and comparison between the two approaches is presented in [5].

Next to electric energy storage, the approach presented in [6] utilizes the inertia of the motor as mechanical energy storage. The speed of the connected scroll pump is varied to compensate the pulsating power of the grid inverter. This is possible due to the low torque ripple of the scroll compressor, as well as permitting a varying rotational speed. For a swing compressor, as used in the proposed EMS, this approach likely becomes infeasible, as the torque variation is too large, and requires power pulsation buffering itself, as depicted in Fig. 1b.

To avoid auxiliary circuits, as well as variation of the motor speed, this paper presents a power pulsation buffer integrated into the motor inverter. Using a three-level T-type inverter, the power flow into the neutral point capacitor is controlled to achieve power pulsation buffer-
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 1: (a) Energy management system with photovoltaic energy generation, battery storage, air conditioning and battery storage. Next to the ac grid, the swing compressor of the air conditioner presents a large load ripple. (b) Torque profile of a swing compressor and resulting motor power (black). To achieve dc input power (dashed), a buffer with corresponding power can be added to the air conditioning inverter (gray).</figcaption></figure>

ing. Section II covers the derivation of the proposed modulation scheme based on an idealized analytic model of the machine and inverter. Following the derivation, the concept is verified in section III using circuit simulation tools. Section IV covers the setup and experimental verification. Lastly, section V concludes the paper.

## II. POWER BUFFERING USING A T-TYPE INVERTER

This section presents the derivation of the proposed modulation scheme to buffer the varying load ripple in the neutral point of the T-type inverter. The schematic is depicted in Fig. 2a. The center switch of the T-type inverter is selectively used to control the current flow into the buffer capacitor. To achieve sufficient current flow at any point in time, additional reactive power is injected into the motor.

### A. Motor model

Starting with the operating point of the PMSM, the produced torque $T_m$ is given by

$$T_m = N_p (\Psi + (L_d - L_q)i_d) i_q, \quad (1)$$

where $i_d$ and $i_q$ are the quadrature stator currents in the power invariant reference frame, $L_d$ and $L_q$ the motor inductances, $\Psi$ the motor flux linkage scaled to the absolute reference frame, and $N_p$ the number of pole pairs. The machine parameters are listed in Table I. For increased operating efficiency in compressor applications a salient PMSM is used [7]. With the machine rotating at an angular velocity of $\omega_m$, the dq-reference frame rotates at a frequency of

$$\omega_e = N_p \omega_m, \quad (2)$$

<table><caption>TABLE I: Motor and inverter specification</caption><thead><tr><th>Parameter</th><th>Variable</th><th>Value</th></tr></thead><tbody><tr><td>Motor inductance</td><td>L<sub>d</sub>|L<sub>q</sub></td><td>11.2 mH | 21.2 mH</td></tr><tr><td>Flux linkage</td><td>Ψ</td><td>0.107 Wb</td></tr><tr><td>Motor resistance</td><td>R<sub>s</sub></td><td>0.380 Ω</td></tr><tr><td>Number of pole pairs</td><td>N<sub>p</sub></td><td>2</td></tr><tr><td>Maximum torque</td><td>Ṫ<sub>m</sub></td><td>1.5 N m</td></tr><tr><td>Maximum speed</td><td>ω̇<sub>m</sub></td><td>2500 rpm</td></tr><tr><td>DC supply voltage</td><td>v<sub>dc</sub></td><td>300 V</td></tr><tr><td>Switching frequency</td><td>f<sub>sw</sub></td><td>20 kHz</td></tr><tr><td>Buffer capacitance</td><td>C<sub>n</sub></td><td>75 μF</td></tr></tbody></table>

proportional to the number of pole pairs. The resulting motor voltages are obtained through

$$v_d = R_s i_d + L_d \frac{di_d}{dt} - \omega_e L_q i_q \quad (3)$$

and

$$v_q = R_s i_q + L_q \frac{di_q}{dt} + \omega_e (L_d i_d + \Psi), \quad (4)$$

where $R_s$ is the winding resistance. The corresponding phase currents and voltages in the stationary reference frame $i_{a,b,c}$ and $v_{a,b,c}$ are obtained using the power-invariant inverse Park-Clarke transform. The inverter must be modulated in such a way to supply the required voltages and currents to the motor.

### B. Inverter modulation

Symmetric space vector modulation is used to extend the inverter output voltage to an amplitude of $v_{dc}/\sqrt{3}$. The
<figure><img src="image_5.png" /><figcaption>Fig. 2: (a) Schematic of the T-type inverter. In addition to the standard two-level inverter, a bi-directional switch connects the switching nodes to a third voltage level. T-type inverters typically keep this midpoint voltage to half of the dc-link. With the proposed power buffering method, the midpoint voltage is allowed to fluctuate, utilizing the capacitor as energy storage. (b) two-level (gray) and three-level (black) pulse-width modulation. Typical two-level modulation utilizes the dutycycle d to generate the desired average output voltage. In case of three-level modulation, the midpoint switch requires a set of two dutycycles. As the on-time of the center switch directly corresponds to midpoint current, the duration of the center dutycycle can be varied to control the power flow into the buffer capacitor.</figcaption></figure>

average inverter output voltage over one switching period then corresponds to

$$v_{sx} = v_x - \frac{\max(v_a, v_b, v_c)}{2} - \frac{\min(v_a, v_b, v_c)}{2} + \frac{v_{dc}}{2}, \quad (5)$$

where max and min select the largest and smallest phase voltage respectively. The index x acts as a placeholder for all three phases a, b, c. Figure 2b depicts the pulse-width modulation operation of a single phase leg.

In regular two-level modulation, the duty cycle $d_x$ in a range of 0 to 1 determines the on-time of the corresponding high-side switch. The low-side switch conducts for a period proportional to $1 - d_x$ and the average phase output voltage corresponds to $d_x v_{dc}$.

For three-level modulation, the dutycycles $d_{px}$ and $d_{nx}$ are used, indicating the on-time of the high-side switch and midpoint switch respectively. The lowside switch conducts during the remainder of the switching period. With both dutycycles in a range of 0 to 1, the constraint of

$$d_{px} + d_{nx} \le 1 \qquad (6)$$

is imposed to restrict the entire duration to the switching period. The dutycycles need to be selected such that

$$v_{sx} = d_{px}v_{dc} + d_{nx}v_{n}. \qquad (7)$$

Compared to two-level modulation, multiple solutions are possible for the same output voltage. Combining Eq. (6) and Eq. (7) yields

$$d_{nx} \le \begin{cases} \frac{v_{dc}-v_{sx}}{v_{dc}-v_{n}}, & \text{if } v_{sx} > v_{n} \\ \frac{v_{sx}}{v_{n}}, & \text{otherwise} \end{cases} \qquad (8)$$

as a constraint. Regular three-level operation of a T-type inverter maximizes $d_{nx}$ to reduce output current ripple. Instead of maximizing $d_{nx}$, the proposed modulation scheme uses this degree of freedom to control the current into the midpoint, given by

$$i_n = d_{na}i_a + d_{nb}i_b + d_{nc}i_c. \qquad (9)$$

The largest possible current can be obtained by maximizing the dutycycles of the phases where the direction of the output current matches the desired midpoint current, and setting the dutycycle to zero where the output current opposes the desired midpoint current. Using the midpoint current, the buffer power can be controlled to absorb the power fluctuation generated by the load torque.

### C. Buffer power

The power the inverter can inject into the buffer capacitor is

$$P_n = v_n i_n. \qquad (10)$$
<figure><img src="image_6.png" /><figcaption>Fig. 3: (a) Operation under MTPA current trajectory. During low torque, the available buffer power (black, dashed) does not meet the required buffer power (black, solid). (b) Proposed trajectory generation. Adding d-axis current during low torque allows for sufficient power to be fed into the buffer to achieve complete power pulsation buffering.</figcaption></figure>

To achieve power buffering, it must equal the AC component of the load, given by the difference of instantaneous and average power

$$P_n(t) = P_m(t) - \overline{P_m(t)}, \qquad (11)$$

where is the instantaneous power of the motor equal to

$$P_m = v_a i_a + v_b i_b + v_c i_c, \qquad (12)$$

given ideal components and ignoring effects such as dead-time. In a real world implementation the average power will include inverter losses and output voltage deviations, which complicates measurement or calculation. Instead, the value will be adjusted by a low-bandwidth control loop, which is trying to keep the cycle-average buffer voltage stable by requesting a certain average power. Given the required buffer power, the buffer voltage is equal to

$$v_n(t) = \frac{1}{C_n} \int_{0}^{\frac{2\pi}{\omega_m}} i_n(t) dt = \frac{1}{C_n} \int_{0}^{\frac{2\pi}{\omega_m}} \frac{P_n(t)}{v_n(t)} dt. \quad (13)$$

### D. Trajectory generation

Using the established principles of modulation and requirements for motor torque and buffer current, the required trajectory of the motor currents can be calculated. Rearranging Eq. (1) to

$$i_q = \frac{T_m}{N_p (\Psi + (L_d - L_q)i_d)} \qquad (14)$$

yields the constant torque line. Regular motor control would try to minimize the total RMS current and follow the path of maximum torque per amp (MTPA) for any load torque. However, the proposed power buffering scheme also needs to maintain the buffer current, so at times it becomes necessary to deviate from the minimum current.

For example, during zero output torque, the buffer would need to store energy as indicated in Fig. 1b. However, following MTPA would result in $i_d = i_q = 0$. Instead, some value of $i_d$ can be chosen to allow sufficient current to flow into the buffer, while maintaining an output torque of zero. For any operating point, a set of $i_d$ and $i_q$ along the constant torque line are evaluated for the maximum possible power $\hat{P}_n$ available to the neutral point. Then, the set with sufficient power and minimum rms current is chosen.

To calculate the maximum possible buffer power for a given set, $i_d$ and $i_q$ are transformed into the stationary frame. The motor voltages are obtained following Eq. (3)-(4) and the maximum possible dutycycles for
<figure><img src="image_7.png" /><figcaption>Fig. 4: Buffer voltage, motor currents and buffer current of the proposed modulation scheme. The dashed lines indicate the contribution of each phase to the buffer current.</figcaption></figure>

all midpoint siwtches are calculated using Eq. (8) and denoted as $\hat{d}_{nx}$. Each midpoint switch will contribute to the buffer current proportional to its dutycycle and its respective phase current.

Any phase current that matches the desired buffer current in direction is referred to as matching phase, any that opposes it as opposing phase. Next, the largest possible midpoint current $\hat{i}_n$ is calculated, by only summing the phases with matching current, such that

$$ \hat{i}_n = \sum_{x=a,b,c} \begin{cases} \hat{d}_{nx}i_x, & \text{if } \operatorname{sgn}(i_x) = \operatorname{sgn}(i_n) \\ 0, & \text{otherwise} \end{cases} \qquad (15) $$

The maximum achievable buffer power $\hat{P}_n$ follows from equation (10). For a full rotation, the maximum possible buffer power and motor current trajectory are depicted in Fig. 3. For all operating points sufficient buffer power can be maintained. During high output torque, the current trajectory follows the MTPA curve. At low output torque, the amplitude of $i_d$ is raised to maintain the available power above the required buffer power. The power at a given point can always be reduced to match $P_n$ by scaling the midpoint dutycycle, without affecting the produced load torque.

### E. Dutycycle scaling

The power into the neutral point is scaled down to the desired buffer power by adjusting the midpoint dutycycles and subsequently the midpoint current $i_n$. To maximize utilization of the midpoint switches, and thus benefits of three-level modulation, the midpoint dutycycles of any matching phase are maximized and the opposing phases are scaled to achieve the desired buffer current.

To obtain the required scaling factors, the total combined neutral point current $\bar{i}_n$ is calculated, by combining all three phases at maximum dutycycle, such that

$$ \bar{i}_n = \sum_{x=a,b,c} \hat{d}_{nx}i_x. \qquad (16) $$

The corresponding scaling factor for opposing phases is then given by

$$ s_{-} = \min \left( \frac{i_{n} - \hat{i}_{n}}{\bar{i}_{n} - \hat{i}_{n}}, 1 \right). \qquad (17) $$

In case this factor equals one, the dutycycles of any matching phase are scaled down by a factor of

$$ s_{+} = \min \left( \frac{i_{n} - \bar{i}_{n} + \hat{i}_{n}}{\hat{i}_{n}}, 1 \right). \qquad (18) $$
<figure><img src="image_8.png" /><figcaption>Fig. 5: Simulation results of standard three-level modulation (a) compared to the proposed PPB operation (b). The gray waveforms depict the motor and inverter currents including the switching ripple. The black lines depict the values sampled synchronously to the PWM carrier, which represents the quantity visible to a control system.</figcaption></figure>

The scaling operation can thus be written as

$$d_{nx} = \begin{cases} s_+ \hat{d}_{nx}, & \text{if } \operatorname{sgn}(i_x) = \operatorname{sgn}(i_n) \\ s_- \hat{d}_{nx}, & \text{otherwise} \end{cases} \quad (19)$$

The resulting operation is depicted in Fig. 4, with the motor currents drawn in solid, colored lines. Their contribution towards the midpoint current, given by $d_{nx}i_x$, is plotted with dashed lines.

### III. SIMULATION

The concept is verified in open loop using the circuit simulation tool PLECS, by applying the calculated ducycles to a T-type inverter and PMSM. The proposed

modulation method is compared to standard three-level operation, where the center switches are always fully utilized. The results are depicted in Fig. 5 for two full rotations of the compressor. During high output power, both $i_d$ and $i_q$ match the standard operation. To achieve power buffering during low output power, $i_d$ diverges from the MTPA curve. Regular three-level modulation maintains the midpoint current near zero, with only slight ripple during high-load operation. The midpoint voltage remains balanced around half the supply voltage. The average input current shows significant peaks during high torque operation and drops significantly during low output torque. For the presented modulation scheme, the
<figure><img src="image_9.png" /><figcaption>Fig. 6: Experimental setup. (a) T-type inverter. The bidirectional switches are implemented as an additional PCB that plugs on top of a commercially available two-level SiC inverter. The heatsink is removed for visibility. (b) Motor test bench. Device-under-test PMSM (right) and induction machine set to constant speed (left).</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7: Control loop concept for the proposed modulation scheme.</figcaption></figure>

midpoint current $i_n$ contains the desired ac ripple, such that energy is stored and released accordingly. The ac ripple of the midpoint current is reflected in the capacitor voltage, showing a large variation. With the input current $i_{dc}$ at a near constant value, the power buffering works as intended.

## IV. EXPERIMENTAL VERIFICATION

The experimental setup, consisting of a three-level inverter and a motor testbench with controllable speed, is depicted in Fig. 6. The motor parameters are listed in Table I. The inverter is a combination of a commercial two-level silicon-carbide (SiC) inverter and a custom plug-in board with three bidirectional switches, realized with drain-to-drain connected SiC devices.

Figure 7 depicts the proposed control loop implementing the trajectory generation and dutycycle scaling presented in the previous section. The trajectory generator is fed by the reference torque $T_m^*$ and the required buffer power $P_n$. The generated current request $i_{dq}^*$ is fed into a current controller, determining the required motor voltage in the rotating reference frame. Lastly, the dutycycle scaling takes place, generating the neutral point dutycycles to achieve the requested buffer power. The buffer current is determined by the sum of expected

compressor power and the output of the neutral point voltage controller.

To test the power buffering modulation, the motor is spun at 2000 rpm and the torque is modulated in a sinusoidal shape from 0 N m to 1.5 N m. The switch from regular to power buffer operation is shown in Fig. 8. During regular operation, the input current ripple corresponds to the varying motor torque and the neutral point voltage remains at half the supply voltage. After enabling the power buffer modulation, the input ripple reduces significantly, and the neutral point begins to fluctuate. The high frequency oscillation on the input current likely results from the LC resonance between the remaining dc-link capacitance on the inverter and the long cable connection to the dc supply.

## V. CONCLUSION

The presented selective three-level modulation scheme for a T-type inverter allows to effectively implement power-pulsation buffering in motor drives, using the midpoint capacitor as the buffer. The end result is a near dc input current despite a large varying load torque. Compared to a conventional approach with a two-level inverter and auxiliary circuits, no additional magnetic components or current sensing are required. The theory
<figure><img src="image_11.png" /></figure>

Fig. 8: Measurement results for pulsating load torque of 1.5 N m at 2000 rpm. Switch between normal operation (left half) and power buffer operation (right half). As soon as the buffering is enabled, the neutral point voltage begins to fluctuate and energy is stored and released within the buffer capacitor. Consequently, the input current ripple decreases significantly.

of operation was derived analytically and verified by simulation as well as experiment. Using the presented modulation scheme, the overall required capacitance in a drive system can be reduced significantly. Furthermore, the resulting dc input current simplifies control design of other components, as they are isolated from the varying load ripple. As the presented approach injects additional reactive current into the motor, slightly larger inverter and motor losses are expected. Future research will address the size and efficiency compared to regular T-type operation.

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