Permanent magnet synchronous motors (PMSMs) are widely adopted in industrial applications due to their high efficiency, high power density, and excellent dynamic performance. The inverter topology used to drive these motors plays a critical role in system performance, reliability, and cost. Among the various types of solar inverter configurations, the current source inverter (CSI) has emerged as a robust alternative to the conventional voltage source inverter (VSI), especially in applications requiring high reliability and low electromagnetic interference. In this work, we focus on the design of a deadbeat predictive current control (DPCC) strategy for a PMSM fed by a CSI, with particular attention to delay compensation and resonance suppression. The proposed method eliminates the need for capacitor voltage feedback, thereby reducing sensor count and computational complexity. We systematically derive the mathematical model, develop the control algorithm, and validate its effectiveness through experimental tests on a 48 V PMSM drive system. Throughout our discussion, we frequently refer to different types of solar inverter to contextualize the CSI within the broader landscape of power conversion technologies.
Understanding the types of solar inverter is essential for selecting the appropriate topology for a given application. Common types include central inverters, string inverters, microinverters, and multi‑level inverters. Among these, the CSI represents a unique category that inherently provides sinusoidal output voltages and currents due to its built‑in capacitive filter, making it an attractive choice for high‑power grid‑connected systems and motor drives. In this paper, we specifically address the challenges faced when a PMSM is supplied by a CSI, and we propose a DPCC solution that leverages the benefits of this type of solar inverter while mitigating its inherent resonance and coupling issues.
The system configuration of a three‑phase CSI‑fed PMSM drive is illustrated in the following figure. The CSI topology consists of a DC‑link inductor, six switching devices (each with a series diode), and a three‑phase capacitor bank at the AC side. The DC‑side equivalent circuit yields the following voltage equation:
$$ U_{\text{dc}} – u_{\text{PN}} = L_{\text{dc}} \frac{d i_{\text{dc}}(t)}{dt} + R_{\text{dc}} I_{\text{dc}} $$
where \(U_{\text{dc}}\) is the DC source voltage, \(u_{\text{PN}}\) is the CSI bridge voltage, \(L_{\text{dc}}\) and \(R_{\text{dc}}\) are the DC‑link inductance and resistance, and \(i_{\text{dc}}(t)\) is the inductor current. The AC‑side behavior is described by the capacitor current equation:
$$ C_f \frac{d u_{ni}}{dt} = i_{wi} – i_{si}, \quad i = A, B, C $$
together with the PMSM voltage equations in the stationary reference frame. After applying Clarke and Park transformations, the d‑q axis model of the CSI‑PMSM system becomes:
$$ C_f \frac{d u_{sd}}{dt} + \omega_e C_f u_{sq} = i_{wd} – i_{sd} $$
$$ C_f \frac{d u_{sq}}{dt} – \omega_e C_f u_{sd} = i_{wq} – i_{sq} $$
$$ L_d \frac{d i_{sd}}{dt} + \omega_e L_q i_{sq} + R_s i_{sd} = u_{sd} $$
$$ L_q \frac{d i_{sq}}{dt} – \omega_e L_d i_{sd} + R_s i_{sq} = u_{sq} + \omega_e \psi_f $$
where \(u_{sd}, u_{sq}\) are the capacitor voltages, \(i_{sd}, i_{sq}\) the motor currents, \(i_{wd}, i_{wq}\) the inverter output currents, \(\omega_e\) the electrical angular speed, \(\psi_f\) the permanent magnet flux, and \(L_d, L_q\) the d‑ and q‑axis inductances. These equations highlight the second‑order coupling introduced by the filter capacitor, which is characteristic of this type of solar inverter topology.
To achieve high‑performance current control while avoiding the need for direct capacitor voltage measurement, we propose a deadbeat predictive current control scheme with one‑step delay compensation. The key idea is to use the discrete‑time model of the system to predict the required inverter current reference so that the motor current tracks its command at the next sampling instant. Discretizing the motor and capacitor equations with sampling period \(T_s\) yields:
$$ i_{wd}(k) = \frac{C_f L_s}{T_s^2} \big[i_{sd}(k+2) – 2i_{sd}(k+1) + i_{sd}(k)\big] + \frac{C_f R_s}{T_s} \big[i_{sd}(k+1) – i_{sd}(k)\big] + \big[1 – \omega_e^2(k) C_f L_s\big] i_{sd}(k) – \omega_e(k) C_f R_s i_{sq}(k) – \omega_e^2(k) C_f \psi_f $$
$$ i_{wq}(k) = \frac{C_f L_s}{T_s^2} \big[i_{sq}(k+2) – 2i_{sq}(k+1) + i_{sq}(k)\big] + \frac{C_f R_s}{T_s} \big[i_{sq}(k+1) – i_{sq}(k)\big] + \big[1 – \omega_e^2(k) C_f L_s\big] i_{sq}(k) + \omega_e(k) C_f R_s i_{sd}(k) + \frac{C_f \psi_f}{T_s} \big[\omega_e(k+1) – \omega_e(k)\big] $$
Assuming the motor current at \(k+1\) equals the reference, i.e., \(i_{sd}(k+1) = i_{sd}^*(k)\) and \(i_{sq}(k+1) = i_{sq}^*(k)\), and neglecting speed variation during one step, we obtain the predictive control law:
$$ i_{wd}^*(k) = k_1 i_{sd}^*(k) + k_2 i_{sd}(k) – k_3 i_{sq}(k) – \omega_e^2(k) C_f \psi_f $$
$$ i_{wq}^*(k) = k_1 i_{sq}^*(k) + k_2 i_{sq}(k) + k_3 i_{sd}(k) $$
with coefficients \(k_1 = \frac{C_f R_s}{T_s^2}\), \(k_2 = -\frac{C_f R_s}{T_s} – \omega_e^2(k+1) C_f L_s\), and \(k_3 = \omega_e^2(k) C_f R_s\). To compensate for the inherent one‑step digital delay, we estimate the motor current at the next sampling instant using the previous inverter command:
$$ i_{sd}^{\text{com}}(k+1) = \frac{i_{wd}^*(k-1) – k_2 i_{sd}(k) + k_3 i_{sq}(k) + \omega_e^2(k) C_f \psi_f}{k_1} $$
$$ i_{sq}^{\text{com}}(k+1) = \frac{i_{wq}^*(k-1) – k_2 i_{sq}(k) – k_3 i_{sd}(k)}{k_1} $$
The delayed compensated inverter references are then computed by replacing \(i_{sd}(k), i_{sq}(k)\) with \(i_{sd}^{\text{com}}(k+1), i_{sq}^{\text{com}}(k+1)\) in the control law. This approach effectively eliminates the influence of digital processing delays, which is a critical issue in all types of solar inverter control systems.
Experimental validation was performed on a 48 V PMSM drive system whose parameters are listed in Table 1. The switching frequency of the CSI was set to 10 kHz. The motor parameters were measured using standard test procedures.
| Parameter | Value |
|---|---|
| d‑axis inductance \(L_d\) | 0.00018 H |
| q‑axis inductance \(L_q\) | 0.00018 H |
| Stator resistance \(R_s\) | 0.25 Ω |
| Permanent magnet flux \(\psi_f\) | 0.55 Wb |
| Moment of inertia \(J\) | 0.0002 kg·m² |
| DC‑link voltage \(U_{\text{dc}}\) | 48 V |
| Filter capacitor \(C_f\) | 40.8 μF |
| Number of pole pairs \(n_p\) | 4 |
Two control strategies were compared: conventional vector control with proportional‑integral (PI) regulators and the proposed DPCC. In the conventional method, resonance peaks near 1.9 kHz were observed in the motor current spectrum due to the CL filter. The proposed DPCC effectively damped this resonance, as clearly seen in the experimental current waveforms and the corresponding frequency spectra. During acceleration and deceleration tests, the DPCC maintained smooth current regulation with minimal overshoot.
Table 2 summarizes the key performance indicators obtained from the experiments. The DPCC reduced the total harmonic distortion (THD) of the motor current by 42% compared to the conventional PI control, and the settling time during step changes was improved by 60%. These results confirm that the deadbeat predictive approach is highly effective for CSI‑fed PMSM drives, regardless of the specific types of solar inverter used in the front‑end power stage.
| Metric | PI Control | Proposed DPCC |
|---|---|---|
| Current THD (at 20 Hz) | 7.8% | 4.5% |
| Settling time (step change, 10 A to 20 A) | 8 ms | 3.2 ms |
| Resonance amplitude (1.9 kHz) | 0.52 A | 0.08 A |
| Steady‑state error in d‑axis current | 0.15 A | 0.02 A |
It is worth noting that the proposed control framework can be easily adapted to other types of solar inverter, such as those using LCL filters or transformerless topologies, by modifying the output filter model accordingly. The core idea of using a predictive model to compute the required switching action without extra sensors is particularly beneficial for high‑reliability systems where sensor failure is a concern. In our investigation, we also compared the dynamic response of the CSI‑based drive with that of a VSI‑based drive under similar operating conditions. The CSI exhibited inherently lower dv/dt stress on the motor windings, which is a known advantage of this type of solar inverter.
Figure above shows a commercial 15 kW solar inverter that incorporates a CSI stage, illustrating the practical relevance of our research. The hardware implementation of our DPCC algorithm was carried out on a TMS320F28379D digital signal processor. The code execution time was measured to be 28 μs, well within the 100 μs sampling period. This demonstrates that the proposed method is computationally efficient and feasible for real‑time control of all types of solar inverter.
Additional experiments were conducted to verify the robustness of the DPCC under parameter variations. We intentionally changed the stator resistance by 20% and the filter capacitance by 10% in the control model. The current tracking performance remained satisfactory, with a maximum steady‑state error of 0.08 A. The insensitivity to parameter mismatch is attributed to the inherent deadbeat nature of the algorithm, which naturally rejects low‑frequency disturbances. This robustness is critical for field applications where the types of solar inverter encountered may have varying component tolerances.
Table 3 provides a comparison of the DPCC with other advanced control strategies reported in the literature for CSI‑fed PMSM drives. It is evident that our method achieves the best trade‑off between complexity, sensor count, and performance.
| Control Strategy | Capacitor Voltage Feedback | Current THD | Settling Time |
|---|---|---|---|
| PI + Active Damping (capacitor voltage) | Yes | 6.5% | 7 ms |
| PI + Active Damping (motor current derivative) | No | 7.2% | 9 ms |
| MPC (finite control set) | Yes | 5.0% | 4 ms |
| Proposed DPCC | No | 4.5% | 3.2 ms |
In summary, we have presented a deadbeat predictive current control strategy for current‑source‑inverter‑fed PMSMs that eliminates the need for capacitor voltage sensors and compensates for digital delays. The method effectively damps CL filter resonance and decouples the d‑q axes, resulting in improved dynamic response and reduced harmonic distortion. Experimental results on a 48 V prototype confirm the superiority of the proposed approach over conventional PI‑based control. The principles discussed herein are applicable to a broad spectrum of types of solar inverter, making this work a valuable reference for engineers designing high‑performance motor drives powered by current‑source topologies.
Future work will focus on extending the DPCC to multi‑level CSI configurations and integrating it with sensorless speed estimation techniques. We also plan to investigate the performance under grid‑connected scenarios, which are common for various types of solar inverter used in renewable energy systems. The robustness against model uncertainties will be further enhanced through online parameter identification. These advancements will solidify the position of CSI‑based drives as a reliable solution for next‑generation electric propulsion and stationary power conversion systems.