In the context of modern power systems, the integration of renewable energy sources such as photovoltaic (PV) systems has become increasingly prevalent. Among the critical components in these systems, the inverter plays a pivotal role in converting DC power from solar panels into AC power that can be fed into the utility grid. However, the output voltage of distribution network inverters often suffers from significant fluctuations, which can degrade power quality and affect the stability of the grid. To address this challenge, this paper presents a deadbeat control method for distributed photovoltaic power distribution network inverters based on the Space Vector Pulse Width Modulation (SVPWM) algorithm. By leveraging the characteristics of SVPWM, the method accurately synthesizes voltage vectors and employs a deadbeat controller to achieve rapid and precise voltage regulation. Experimental results demonstrate that the proposed approach effectively reduces total harmonic distortion (THD) to 0.04% and significantly suppresses output voltage fluctuations, thereby improving the performance of types of solar inverter in grid-connected applications.
Keywords: SVPWM algorithm; distributed photovoltaic power source; inverter; deadbeat control; controller; discrete processing
1. Introduction
Photovoltaic inverter grid-connected systems are essential for converting direct current (DC) electricity generated by solar panels into alternating current (AC) electricity suitable for the utility grid. Among the various types of solar inverter, the string inverter, microinverter, and central inverter are commonly used in distributed PV systems. However, the control of inverters in distribution networks poses significant challenges due to the fluctuating nature of solar irradiance and load conditions. Traditional control algorithms often suffer from high modulation errors and harmonic content, leading to poor power quality and potential grid disturbances. The deadbeat control strategy, which aims to achieve zero-error tracking within one sampling period, offers a promising solution for high-performance inverter control. When combined with SVPWM, which provides superior voltage utilization and reduced harmonics, the overall system can achieve fast dynamic response and high steady-state accuracy.
Several studies have explored inverter control techniques. For instance, a hierarchical control method based on the IEC 61499 standard has been proposed for distributed PV inverters, but its compatibility limitations affect control precision. Another approach using LADRC and quasi-PR controllers for wind power inverters shows sensitivity to parameter tuning, which can degrade performance. In contrast, the proposed method integrates SVPWM with deadbeat control to overcome these drawbacks. This paper describes the design and implementation of a deadbeat controller for types of solar inverter in a distributed PV distribution network, focusing on the mathematical modeling, state analysis, and discrete-time control.
2. Inverter Model and SVPWM-Based State Adjustment
2.1 Dynamic Model of the Inverter
To establish the control framework, it is necessary to derive the dynamic equations of the inverter. The voltage dynamics in a three-phase inverter can be expressed as follows:
$$ U_n = \begin{bmatrix} -\frac{R_n}{L_n} & 0 & 0 \\ 0 & -\frac{R_n}{L_n} & 0 \\ 0 & 0 & -\frac{R_n}{L_n} \end{bmatrix} \begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix} + \frac{1}{L_n} \begin{bmatrix} u_a – e_a \\ u_b – e_b \\ u_c – e_c \end{bmatrix} $$
where \(U_n\) represents the voltage dynamic vector, \(R_n\) is the resistance, \(L_n\) is the inductance, \(i_a, i_b, i_c\) are the phase currents, \(u_a, u_b, u_c\) are the phase voltages, and \(e_a, e_b, e_c\) are the back electromotive forces. The output power of the inverter can be calculated using:
$$ P_z = \delta_y (U_n^d i_d + U_n^q i_q) + \delta_w P_w $$
where \(U_n^d\) and \(U_n^q\) are the d-q axis voltages, \(i_d\) and \(i_q\) are the d-q axis currents, \(P_w\) is the reactive power, and \(\delta_y\) and \(\delta_w\) are the active and reactive power distribution coefficients, respectively. This model provides the foundation for designing the control system.
2.2 SVPWM Voltage Vector Synthesis
SVPWM is a modulation technique that controls the switching states of a types of solar inverter to generate a desired voltage vector. By dividing the space vector plane into six sectors, SVPWM synthesizes the reference voltage vector using the nearest two active vectors and zero vectors. The voltage vector can be expressed as:
$$ V_s = \frac{U_\alpha^n + k_s U_\beta^n}{P_z} $$
where \(U_\alpha^n\) is the commanded voltage in the α-axis, \(U_\beta^n\) is the actual voltage in the β-axis, and \(k_s\) is the voltage fluctuation coefficient. The resultant synthesized vector is:
$$ V_h = \sum_{s=1}^{h} V_s \times p_s $$
where \(p_s\) denotes the duty cycle of each voltage vector. The state equation of the inverter in the αβ frame is:
$$ Z_t = \begin{bmatrix} 0 & \frac{1}{C_k} I_t \\ \frac{1}{L_s} I_t & \frac{r_c}{L_s} I \end{bmatrix} \begin{bmatrix} U_t \\ i_L \end{bmatrix} + \begin{bmatrix} 0 & -\frac{1}{C_k} I_t \\ \frac{1}{L_s} I_t & 0 \end{bmatrix} \begin{bmatrix} V_h \\ i_0 \end{bmatrix} $$
where \(C_k\) is the filter capacitance, \(U_t\) is the grid nominal voltage, \(i_L\) is the nominal current, \(I_t\) is the current variation function, and \(i_0\) is the initial current. The transfer function used for state adjustment is given by:
$$ D_c = Q_c \times \frac{1 – e_p}{s_c} \times \frac{1}{s_c L_n} $$
$$ T_z = Z_t \times D_c \times \left(1 – \frac{1}{h_c}\right) + y_z $$
These equations form the basis for adjusting the inverter’s operating state using SVPWM.
3. Deadbeat Controller Design
The deadbeat control strategy aims to achieve zero steady-state error in a finite number of sampling steps. To implement this, the state modulation function is discretized. The discrete form is:
$$ u_k = \frac{1}{m_k} \left( r_{k+1} – g_c u_c – g_b I_k – m_z i_k + \kappa_m T_z \right) $$
where \(u_k\) is the discrete control output, \(m_k\) is the discretization parameter, \(r_{k+1}\) is the reference state, \(u_c\) is the voltage variation, \(g_c\) is the voltage variation gain, \(I_k\) is the instantaneous current, \(g_b\) is the current variation gain, \(m_z\) is the grid current variation parameter, \(i_k\) is the grid current variation function, and \(\kappa_m\) is the operating state discretization coefficient.
The final deadbeat controller for the types of solar inverter is formulated as:
$$ Q_k = g_f \left( f_0 + k_u q_u \right) + g_u \left( U_z – k_r P_f \right) + g_m u_k + h_w $$
where \(Q_k\) is the controller output, \(f_0\) is the filter parameter, \(q_u\) is the cutoff frequency, \(U_z\) is the instantaneous voltage, \(P_f\) is the state feedback function, \(k_u\) and \(k_r\) are droop coefficients, \(g_f\), \(g_u\), and \(g_m\) are control gains, and \(h_w\) is the control error compensation. This controller ensures the inverter tracks the reference voltage with minimal overshoot and fast response.
4. Experimental Verification
4.1 Experimental Setup
To validate the proposed method, an experimental platform was built using a 20 kW PV array as the DC source, a 10 kW three-phase inverter with a switching frequency of 10 kHz, and a 5 kW resistive load. The sampling frequency was set to 10 kHz. The SVPWM parameters are listed in Table 1.
| Parameter | Value |
|---|---|
| Carrier frequency (Hz) | 100 |
| Sampling period (s) | 1 |
| Modulation index | 0.4 |
| Switching frequency (kHz) | 10 |
| Number of sectors | 6 |
| Reference voltage coefficient \(k_s\) | 0.44 |
| Transfer coefficient \(e_p\) | 1.36 |
| State adjustment coefficient \(h_c\) | 2.12 |
4.2 Harmonic Content Analysis
Figure 1 (represented by the hyperlink image) shows the harmonic content before and after applying the proposed deadbeat control. It is evident that the method significantly reduces the harmonic distortion compared to the uncontrolled scenario. The lower the harmonic content, the better the inverter’s output voltage quality.
4.3 Voltage Fluctuation Comparison
Table 2 compares the voltage fluctuation rate for three methods: the proposed method, the IEC 61499-based method (Control 1), and the LADRC+PR method (Control 2). The proposed method achieves an average fluctuation rate of 0.41%, which is substantially lower than 5.44% for Control 1 and 11.26% for Control 2.
| Test No. | Proposed Method | Control 1 | Control 2 |
|---|---|---|---|
| 1 | 0.25 | 5.62 | 12.23 |
| 2 | 0.36 | 5.34 | 10.25 |
| 3 | 0.44 | 5.87 | 13.25 |
| 4 | 0.54 | 5.12 | 11.25 |
| 5 | 0.26 | 5.96 | 14.15 |
| 6 | 0.35 | 5.24 | 12.26 |
| 7 | 0.45 | 5.12 | 13.25 |
Table 3 shows the total harmonic distortion (THD) values. The proposed method achieves a THD of 0.04%, well below the standard threshold of 0.1%, indicating superior harmonic suppression capability.
| Method | THD (%) |
|---|---|
| Proposed Method | 0.04 |
| Control 1 | 0.15 |
| Control 2 | 0.22 |
5. Conclusion
This paper presents a deadbeat control method for distributed photovoltaic power distribution network inverters based on the SVPWM algorithm. By accurately modeling the inverter dynamics and implementing a discrete-time deadbeat controller, the proposed method effectively regulates the output voltage, minimizes harmonic distortion, and achieves rapid dynamic response. Experimental results confirm that the method reduces THD to 0.04% and voltage fluctuation to below 0.5%, outperforming existing approaches. This work contributes to the advancement of high-performance control for various types of solar inverter, enhancing the reliability and efficiency of grid-connected PV systems.
References (simplified for brevity):
[1] Li Qingxi, et al. (2025). Deadbeat Control for Distributed PV Inverters Based on SVPWM. Micromotors, 58(11), 37-41.