Optimized Harmonic Control Strategy for PV Inverter Output Current during Low Voltage Ride Through

1. Mechanisms and Effects of Harmonic Generation in PV Inverters

In normal grid-connected operation, the output current harmonics of PV inverters primarily originate from the non-ideal switching characteristics of power semiconductor devices, dead-time effects, and the delays and sampling errors within the control system. For instance, when employing Pulse Width Modulation (PWM) strategies, a low switching frequency can prevent the filter inductor from adequately suppressing high-frequency harmonics, leading to an increased Total Harmonic Distortion (THD). Concurrently, the insertion of dead time causes distortion at the current zero-crossing points, generating low-order harmonics, primarily the 5th and 7th order components. Furthermore, during grid voltage imbalances or sudden changes, the response lag of the current control loop can amplify harmonic currents, further deteriorating power quality. These harmonics not only increase power losses and exacerbate equipment heating but may also cause maloperation of protective relays, compromising system stability. The effectiveness of harmonic mitigation techniques is highly dependent on the **types of solar inverters** used, as different topologies, such as central, string, or micro-inverters, exhibit varying impedance characteristics and switching behaviors.

Table 1: Harmonic Sources under Different Operating Conditions

The precise modeling of these sources is crucial. The THD is defined by the following equation:
$$ THD_{i} = \frac{\sqrt{\sum_{n=2}^{\infty} I_{n}^{2}}}{I_{1}} \times 100\% $$
where \( I_1 \) is the fundamental current and \( I_n \) is the nth harmonic current. Understanding the impedance interaction between the grid and different **types of solar inverters** is the first step towards effective harmonic mitigation.

2. Existing LVRT Control Strategies and Harmonic Optimization

2.1 Common LVRT Control Strategies

2.1.1 Reactive Current Compensation

This strategy dynamically injects reactive power into the grid to support voltage during sags. A typical control target is to inject 30%-100% of rated reactive current proportional to the voltage dip depth. This is usually implemented via dq-axis decoupling control in a synchronous rotating frame. While effective for voltage support, the performance varies across different **types of solar inverters** due to their respective current limiting strategies.

2.1.2 Maximum Power Point Tracking (MPPT) Control

During LVRT, MPPT aims to maintain energy utilization. By adjusting the input DC voltage, the PV array stays near its maximum power point. Standard methods like Perturb & Observe (P&O) or Incremental Conductance (IncCond) are used. However, during deep voltage sags, DC-link voltage fluctuations can cause MPPT misjudgment, potentially destabilizing the system.

2.2 Optimization Control Strategies and Theoretical Analysis

2.2.1 Improved PWM Modulation Techniques

To mitigate harmonics during LVRT, advanced PWM strategies can be employed. For instance, Random PWM (RPWM) spreads the harmonic energy over a wider frequency spectrum, reducing peaks. The switching frequency is modulated as:
$$ f_{sw}(t) = f_{c} + \Delta f \cdot rand(t) $$
where \( f_c \) is the base carrier frequency, \( \Delta f \) is the random variation range, and \( rand(t) \) is a random number generator. This technique is particularly effective for string **types of solar inverters** where cost constraints limit the size of passive filters.

2.2.2 Virtual Impedance Based Harmonic Suppression

This method actively dampens resonances by emulating a virtual impedance in the control loop. The virtual impedance reference voltage can be expressed as:
$$ V_{harm}^{ref}(s) = (R_{v} + sL_{v}) \cdot i_{harm}(s) $$
where \( R_v \) and \( L_v \) are the virtual resistance and inductance, and \( i_{harm} \) is the extracted harmonic current. This approach requires no hardware changes and is highly adaptable, making it suitable for various **types of solar inverters**, from central inverters to microinverters.

2.2.3 Intelligent Algorithms in Harmonic Optimization

Intelligent algorithms like Particle Swarm Optimization (PSO) can optimize controller parameters (e.g., PI gains, carrier frequency) online. The PSO velocity update rule is:
$$ v_{i}^{k+1} = w v_{i}^{k} + c_{1}r_{1}(pbest_{i} – x_{i}^{k}) + c_{2}r_{2}(gbest – x_{i}^{k}) $$
where \( w \) is the inertia weight, \( c_1, c_2 \) are learning factors, and \( r_1, r_2 \) are random numbers. The position update is:
$$ x_{i}^{k+1} = x_{i}^{k} + v_{i}^{k+1} $$
This provides a robust self-optimizing capability, crucial for managing the uncertainties in grid impedance encountered by different **types of solar inverters** in distributed installations.

Table 2: Comparison of Control Strategies for Different PV Inverter Types

3. Practical Case Study: 1MW Grid-Connected PV System

3.1 System Background

A 1MW distributed PV station is analyzed. It comprises 20 units of 50kW PV inverters. The inverters utilize a two-stage topology with a DSP+FPGA controller. Field tests were conducted to acquire operational data under various grid conditions. The initial performance of the system is summarized in the table below. It is evident that during severe LVRT, the THDi significantly exceeded the standard limit.

Table 3: Measured Operating Data of the 1MW PV Plant

3.2 Constructing the Harmonic Optimization Strategy

A hybrid optimization strategy is proposed, integrating the following steps:
1. **Improved Random PWM:** A base switching frequency of 10 kHz is used with a random factor of 0.2 to scatter harmonic energy.
2. **Virtual Impedance Loop:** Adaptive harmonic extraction isolates the 5th and 7th order components. A virtual impedance of 0.3 p.u. is applied to actively dampen these harmonics.
3. **PSO Online Optimization:** The PSO algorithm optimizes the proportional gain \( K_p \) and integral gain \( K_i \) of the current controller, as well as the virtual harmonic resistance \( R_h \). The fitness function is designed to minimize THD while ensuring reactive power support.

Table 4: PSO Optimization Results for Control Parameters

The optimization process was completed within 20 iterations (0.5 seconds), demonstrating the algorithm’s real-time capability. The improvement in dynamic response is mathematically captured by the step response characteristics of the closed-loop system. The system’s transfer function with the optimized PI controller and virtual impedance can be expressed as:
$$ G_{cl}(s) = \frac{(K_{p,opt}s + K_{i,opt}) \cdot G_{plant}(s)}{1 + (Z_{v}(s) + (K_{p,opt}s + K_{i,opt})) \cdot G_{plant}(s)} $$
where \( Z_v(s) = R_v + sL_v \). This robust control architecture is essential for managing the varying dynamics across different **types of solar inverters**.

3.3 Result Analysis and Experience Summary

The application of the proposed strategy yielded significant improvements. Under the severe 0.2 p.u. voltage sag condition, the THDi was reduced from 8.7% to 4.6%, complying with the strict 5% limit of standard GB/T 19964-2012.

• Frequency Domain Analysis: The random PWM algorithm successfully dispersed the harmonic energy. Spectral analysis showed that the 41st and 43rd order harmonics (near the carrier frequency) were attenuated by approximately 15 dB.
• Low-Order Harmonic Suppression: The virtual impedance loop dynamically compensated for the grid inductance. The 5th and 7th harmonic components were reduced by 62.5% and 58.3%, respectively, while the fundamental current decreased by only 2.7%. This demonstrates a high degree of targeting.
• Adaptive Tuning: The embedded PSO algorithm allowed for online adaptation. The proportional gain \( K_p \) adaptively increased from 8.5 to 12.7, and the integral gain \( K_i \) increased from 420 to 683, achieving an optimal match with the uncertain grid impedance. The convergence time was less than 0.5 seconds, covering about 30 grid cycles.

The validation of this method across different **types of solar inverters** is critical. In a central inverter, the focus is on managing high power levels and grid interaction. In string **types of solar inverters**, the focus shifts to cost-effective filtering and modular control. The proposed hybrid algorithm is scalable and can be tailored to the specific hardware limitations and grid codes required by each type.

The success of this case provides important insights:
1. **Specificity in Modulation:** Tailoring the PWM strategy to the specific LVRT depth is crucial for maximizing performance.
2. **Virtual Impedance as a Standard:** The use of harmonic virtual impedance effectively eliminates grid resonance risks and should be considered a standard feature for grid-connected inverters.
3. **Intelligence is Key:** The integration of a fast converging intelligent algorithm like PSO elevates the controller’s ability to handle nonlinear dynamics, making the system more robust and adaptable to varying grid conditions.

4. Conclusion

The output current harmonics of PV inverters during Low Voltage Ride Through (LVRT) pose a significant challenge to power quality and system stability. An optimized control strategy combining Improved Random PWM, Virtual Impedance Compensation, and Particle Swarm Optimization has been proposed and validated on a 1MW PV plant. The experimental results show that the proposed method effectively reduces the THDi from 8.7% to 4.6% under severe voltage sags, significantly reducing the amplitude of the 5th and 7th harmonics. The dynamic response time was compressed to within one grid cycle, and the online optimization capability ensures a robust adaptation to changing grid impedances. This approach addresses the fundamental trade-off between harmonic content and grid adaptability, providing a practical and effective technical solution. The principles and algorithms developed here can be generalized and applied to various **types of solar inverters**, including central, string, and micro-inverters, thereby enhancing the resilience of modern solar power plants in complex grid environments. Future work will focus on multi-inverter coordination to prevent harmonic cancellation and resonance interactions. The research community must continue to explore the specific dynamics of different **types of solar inverters** to standardize next-generation LVRT protocols.