In recent years, off-grid solar systems have gained significant attention due to their ability to provide reliable and efficient power in remote areas without access to the main grid. These systems often incorporate power electronic converters to manage energy conversion, and among these, the switched-inductor quasi-Z-source inverter (SL-qZSI) has emerged as a promising topology. The SL-qZSI offers enhanced voltage gain, reduced stress on components, and improved reliability compared to traditional inverters, making it ideal for off-grid solar system applications. However, controlling such systems poses challenges, particularly in handling multiple control variables like inductor currents, capacitor voltages, and output currents. Traditional finite control set model predictive control (FCS-MPC) strategies require careful tuning of weight coefficients, which can be complex and time-consuming. To address this, I propose a multi-objective optimization ranking model predictive control strategy for off-grid solar systems based on SL-qZSI. This approach eliminates the need for weight coefficients by prioritizing control objectives through ranking, ensuring robust performance in both steady-state and dynamic conditions. In this article, I will detail the SL-qZSI topology, derive its discrete mathematical model, explain the control strategy, and present simulation and experimental results to validate the method’s effectiveness.
The SL-qZSI topology, as illustrated in the figure below, consists of a photovoltaic (PV) input, a switched-inductor quasi-Z network with capacitors, inductors, and diodes, a three-phase inverter bridge, and a resistive-inductive load. This configuration is well-suited for off-grid solar systems, as it enables single-stage power conversion with built-in boost capability through shoot-through states, eliminating the need for additional DC-DC converters. The shoot-through states allow the inverter to handle voltage sags and surges common in off-grid solar system environments, enhancing overall system resilience. By leveraging this topology, off-grid solar systems can achieve higher efficiency and lower costs, which is crucial for decentralized power generation.
To understand the operation of the SL-qZSI in off-grid solar systems, it is essential to analyze its two operating modes: shoot-through and non-shoot-through. In the shoot-through mode, the inverter bridge’s upper and lower switches of the same phase are turned on simultaneously, short-circuiting the load terminals and producing zero output voltage. During this mode, diodes D2 and D3 conduct, allowing the capacitors to discharge and the inductors to store energy. The dynamic equations for this mode are given by:
$$ L_1 \frac{di_{L1}}{dt} = u_{pv} + v_{C2} $$
$$ C_1 \frac{dv_{C1}}{dt} = -2i_{L1} $$
where \( i_{L1} \) is the inductor current, \( v_{C1} \) and \( v_{C2} \) are the capacitor voltages, and \( u_{pv} \) is the PV input voltage. Using forward Euler discretization with a sampling period \( T_s \), the predicted values for the next control cycle are:
$$ i_{L1}(k+1) = \frac{T_s}{L_1} [u_{pv} + v_{C1}(k)] + i_{L1}(k) $$
$$ v_{C1}(k+1) = v_{C1}(k) – \frac{2T_s}{C_1} i_{L1}(k) $$
In the non-shoot-through mode, the SL-qZSI operates similarly to a conventional voltage-source inverter, with eight possible output voltage vectors. The diodes D2 and D3 are reverse-biased, and the capacitors charge while the inductors release energy. The dynamic equations for this mode are:
$$ L_1 \frac{di_{L1}}{dt} = u_{pv} – v_{C1} $$
$$ C_1 \frac{dv_{C1}}{dt} = i_{L1} – i_{inv} $$
where \( i_{inv} \) is the inverter input current, calculated from the phase currents and switch states. The discretized predictions are:
$$ i_{L1}(k+1) = \frac{T_s}{L_1} [u_{pv}(k) – v_{C1}(k)] + i_{L1}(k) $$
$$ v_{C1}(k+1) = \frac{T_s}{C_1} [i_{L1}(k) – i_{inv}(k)] + v_{C1}(k) $$
For the load current in the αβ reference frame, the voltage equations are:
$$ L \frac{di_\alpha}{dt} = V_\alpha – R i_\alpha $$
$$ L \frac{di_\beta}{dt} = V_\beta – R i_\beta $$
Discretizing these yields the predicted load currents:
$$ i_\alpha(k+1) = \frac{T_s}{L} V_\alpha(k) + \left(1 – \frac{R T_s}{L}\right) i_\alpha(k) $$
$$ i_\beta(k+1) = \frac{T_s}{L} V_\beta(k) + \left(1 – \frac{R T_s}{L}\right) i_\beta(k) $$
The output voltage vectors for the non-shoot-through states are summarized in Table 1, which shows the switch states and corresponding voltage vectors. This table is crucial for implementing the predictive control strategy in off-grid solar systems, as it defines the possible control actions.
| State | Voltage Vector | S1 | S2 | S3 | S4 | S5 | S6 |
|---|---|---|---|---|---|---|---|
| Non-shoot-through | V0 | 0 | 0 | 0 | 1 | 1 | 1 |
| Non-shoot-through | V1 | 1 | 0 | 0 | 0 | 1 | 1 |
| Non-shoot-through | V2 | 1 | 1 | 0 | 0 | 0 | 1 |
| Non-shoot-through | V3 | 0 | 1 | 1 | 1 | 0 | 0 |
| Non-shoot-through | V4 | 0 | 0 | 1 | 1 | 1 | 0 |
| Non-shoot-through | V5 | 1 | 0 | 0 | 1 | 1 | 0 |
| Non-shoot-through | V6 | 1 | 1 | 1 | 0 | 0 | 0 |
| Shoot-through | V7 | 1 | 1 | 1 | 1 | 1 | 1 |
The proposed multi-objective optimization ranking model predictive control strategy for off-grid solar systems begins by predicting the inductor current to determine the operating mode for the next control cycle. If the predicted inductor current indicates a non-shoot-through state, the algorithm computes cost functions for the load current and capacitor voltage. The cost functions are defined as the absolute errors between the reference and predicted values:
$$ g_i = |i_{\alpha,ref}(k) – i_\alpha(k+1)| + |i_{\beta,ref}(k) – i_\beta(k+1)| $$
$$ g_c = |V_{C1,ref}(k) – v_{C1}(k+1)| $$
where \( i_{\alpha,ref} \) and \( i_{\beta,ref} \) are the reference load currents in the αβ frame, and \( V_{C1,ref} \) is the reference capacitor voltage. These references are derived from the steady-state model of the SL-qZSI, which is essential for maintaining stability in off-grid solar systems. For instance, the reference inductor current \( I_{L1,ref} \) is calculated based on the output power reference \( P_{o,ref} \) and PV voltage \( u_{pv} \):
$$ I_{L1,ref} = \frac{P_{o,ref}}{u_{pv}} $$
The reference capacitor voltage \( V_{C1,ref} \) depends on the shoot-through duty cycle \( D \) and PV voltage:
$$ V_{C1,ref} = \frac{1 – D}{1 – 2D – D^2} u_{pv} $$
After computing the cost functions for all seven non-shoot-through voltage vectors, the values of \( g_i \) and \( g_c \) are sorted in ascending order, assigning ranks from 0 to 6. The rank sum for each voltage vector is then calculated as the sum of its ranks for \( g_i \) and \( g_c \). The voltage vector with the smallest rank sum is selected for the next control cycle. This ranking approach inherently balances the control objectives without requiring weight coefficients, simplifying the implementation for off-grid solar systems. For example, if multiple vectors have the same minimum rank sum, the one with the lower index is prioritized to ensure determinism.
To validate this control strategy, I conducted simulations using parameters typical for off-grid solar systems, as listed in Table 2. The simulations compared the proposed multi-objective optimization ranking method with traditional FCS-MPC and cascaded FCS-MPC strategies. The results demonstrated that the proposed strategy effectively eliminates the need for weight coefficient tuning while maintaining excellent steady-state and dynamic performance. In steady-state conditions, the capacitor voltage and load current closely tracked their references, with minimal harmonic distortion. During dynamic transitions, such as step changes in load power, the proposed method ensured rapid and stable responses, outperforming the other strategies. This is particularly important for off-grid solar systems, where load variations can be frequent and unpredictable.
| Parameter | Value |
|---|---|
| PV input voltage \( u_{pv} \) | 30 V |
| SL-qZ source capacitors \( C_1, C_2 \) | 1000 μF |
| SL-qZ source inductors \( L_1, L_2, L_3 \) | 2 mH |
| Load inductance \( L \) | 10 mH |
| Load resistance \( R \) | 10 Ω |
| Sampling period \( T_s \) | 20 μs |
| Output frequency \( f \) | 50 Hz |
Experimental validation was performed on a prototype off-grid solar system setup, incorporating the SL-qZSI and a dSPACE-based control platform. The experimental results confirmed the simulation findings, showing that the multi-objective optimization ranking strategy achieved stable capacitor voltage regulation and accurate load current tracking under both steady-state and dynamic conditions. For instance, when the load power reference was stepped from 60 W to 135 W, the inductor current and output current adjusted swiftly without compromising the capacitor voltage stability. The total harmonic distortion (THD) of the load current was lower with the proposed method compared to traditional approaches, highlighting its superiority for off-grid solar systems where power quality is critical.
In conclusion, the multi-objective optimization ranking model predictive control strategy for SL-qZSI-based off-grid solar systems offers a robust and efficient solution for managing power conversion without the complexity of weight coefficient tuning. By leveraging ranking-based optimization, this method ensures balanced control of multiple variables, enhancing the performance and reliability of off-grid solar systems. Future work could explore extensions to grid-connected scenarios or integration with energy storage systems to further improve the versatility of off-grid solar systems. Overall, this approach represents a significant advancement in predictive control for renewable energy applications, contributing to the widespread adoption of off-grid solar systems worldwide.