As the integration of photovoltaic (PV) systems into power grids accelerates, understanding the fault characteristics of inverters becomes crucial for grid stability. Unlike traditional synchronous generators, PV inverters exhibit highly controllable fault behaviors dictated by their control strategies. This article explores the steady-state short-circuit current characteristics and equivalent negative sequence impedance of PV inverters under asymmetrical faults, with a focus on different negative sequence control strategies. The analysis covers various types of solar inverter configurations and their responses to faults, emphasizing how control objectives influence output currents and impedances. By deriving analytical expressions and validating them through simulations, this study highlights the similarities and differences in fault behaviors across control strategies and fault types. The findings underscore the need to account for negative sequence control in protection system design for renewable-rich grids.
Photovoltaic inverters, as key interfaces between PV arrays and the grid, convert DC power to AC and manage power quality. Under asymmetrical faults, such as single-phase-to-ground or phase-to-phase faults, inverters can control both positive and negative sequence currents to meet grid codes. However, the impact of negative sequence control strategies on fault characteristics is often overlooked. This article addresses this gap by analyzing three common negative sequence control objectives: suppressing negative sequence current, eliminating double-frequency oscillations in reactive power, and mitigating double-frequency oscillations in active power. These strategies are applied to various types of solar inverter systems, including grid-following inverters, to demonstrate their effects on short-circuit currents and equivalent impedances.
The steady-state short-circuit current of an inverter can be derived from its control references. Assuming a dual-loop control structure with power outer loops and current inner loops, the output currents quickly track their references. Let \( i^{+*} = i^{+*}_d + j i^{+*}_q \) represent the positive sequence current reference in the forward synchronous rotating frame, and \( i^{-*} = i^{-*}_d + j i^{-*}_q \) denote the negative sequence current reference in the reverse synchronous rotating frame. The steady-state currents are given by:
$$ i^+ = i^{+*} $$
$$ i^- = i^{-*} $$
Transforming these to phase quantities yields the output currents. For instance, the phase-a current is:
$$ i_a = |i^+| \cos(\omega_1 t + \phi^+) + |i^-| \cos(\omega_1 t – \phi^-) $$
where \( \phi^+ = \arctan(i^{+}_q / i^{+}_d) \) and \( \phi^- = \arctan(i^{-}_q / i^{-}_d) \). The magnitudes and phases depend on the control strategy and fault conditions. This formulation applies to all types of solar inverter systems, highlighting their controllable nature.
Under fault conditions, inverters follow low-voltage ride-through (LVRT) requirements. The positive sequence current references are set based on voltage sag levels. For example, the reactive current reference \( i^{+*}_q \) is increased to support grid voltage, while the active current reference \( i^{+*}_d \) is adjusted within current limits. The negative sequence current references are determined by the chosen control objective. Let \( e^+_d \) and \( e^+_q \) be the positive sequence grid voltages, and \( e^-_d \) and \( e^-_q \) the negative sequence voltages in the respective frames. The negative sequence references for different objectives are:
| Control Objective | Description | Negative Sequence Current Reference |
|---|---|---|
| Objective I | Suppress negative sequence current | \( i^{-*} = 0 \) |
| Objective II | Eliminate reactive power oscillations | \( i^{-*}_d = \rho \frac{e^-_d i^{+*}_d + e^-_q i^{+*}_q}{e^+_d}, \quad i^{-*}_q = \rho \frac{e^-_q i^{+*}_d – e^-_d i^{+*}_q}{e^+_d} \) with \( \rho = 1 \) |
| Objective III | Mitigate active power oscillations | Same as Objective II but with \( \rho = -1 \) |
Here, \( \rho \) is a parameter that defines the control strategy. This unified approach allows for consistent analysis across various types of solar inverter configurations.
For asymmetrical faults, the short-circuit current characteristics vary significantly with the control objective. Consider a single-phase-to-ground fault on phase A, where the voltage drops to a fraction \( \lambda \) (0 ≤ λ < 1). The negative sequence voltage components are \( e^-_d = (\lambda – 1)/3 \) and \( e^-_q = 0 \). The phase currents can be expressed as:
$$ i_a = \sqrt{ |i^+|^2 + |i^-|^2 + 2 |i^+||i^-| \cos(\phi^+ + \phi^-) } \cos(\omega_1 t + \phi_a) $$
$$ i_b = \sqrt{ |i^+|^2 + |i^-|^2 + 2 |i^+||i^-| \cos(\phi^+ + \phi^- + 120^\circ) } \cos(\omega_1 t + \phi_b) $$
$$ i_c = \sqrt{ |i^+|^2 + |i^-|^2 + 2 |i^+||i^-| \cos(\phi^+ + \phi^- – 120^\circ) } \cos(\omega_1 t + \phi_c) $$
The key parameter \( \phi^+ + \phi^- \) depends on the control objective and fault type. For Objective I, \( i^- = 0 \), so currents are balanced. For Objective II, \( \phi^+ + \phi^- = 180^\circ \), leading to reduced current in the faulted phase. For Objective III, \( \phi^+ + \phi^- = 0^\circ \), resulting in increased current in the faulted phase. Similar analyses apply to phase-to-phase faults, where the characteristics may mirror those of other fault types under different objectives. This behavior is consistent across many types of solar inverter designs, emphasizing the need for strategy-specific protection settings.
The equivalent negative sequence impedance, crucial for protection schemes, is derived from the negative sequence voltage and current:
$$ Z^- = – \frac{e^-_d + j e^-_q}{i^-_d + j i^-_q} $$
Substituting the negative sequence current references gives:
$$ Z^- = – \frac{e^+_d}{\rho (i^{+}_d – j i^{+}_q)} $$
This shows that the impedance magnitude is the ratio of positive sequence voltage to current, while the phase angle depends on the active and reactive currents and the control objective. For Objective I, \( Z^- \) is infinite. For Objective II, the impedance angle lies between -90° and -180°, and for Objective III, it ranges from 0° to 90°. These characteristics can affect directional elements and fault detection in systems with multiple types of solar inverter installations.
To validate the theoretical analysis, a simulation model of a 1 MW PV inverter connected to a 110 kV grid via transformers and lines was developed. The system parameters include transformer leakages and line impedances. Asymmetrical faults were applied at the midpoint of the grid connection line. For a single-phase-to-ground fault on phase A, the output currents and equivalent impedances were recorded under different control objectives. The results confirm the theoretical predictions: with Objective I, currents are symmetrical; with Objective II, the faulted phase current is minimal; and with Objective III, it is maximal. The impedance angles align with the derived expressions, demonstrating the strategy-dependent behavior.
Similarly, for a phase-to-phase fault between phases B and C, the current characteristics under Objective II resemble those of a single-phase fault under Objective III, and vice versa. This interchangeability highlights the complexity of fault analysis in networks with diverse types of solar inverter controls. The simulation waveforms and impedance plots match the analytical calculations, reinforcing the importance of considering negative sequence strategies in protection studies.
In conclusion, the fault characteristics of PV inverters are highly influenced by negative sequence control strategies. Objectives such as suppressing negative sequence current or mitigating power oscillations lead to distinct short-circuit current profiles and equivalent impedances. These differences can result in similar behaviors for different fault types under varying strategies, challenging traditional protection schemes. Therefore, it is essential to incorporate negative sequence control effects in the design and setting of protection systems for grids with high penetration of renewable sources. Future work could explore adaptive protection methods that account for the dynamic control of various types of solar inverter systems.
The analysis presented here provides a foundation for understanding inverter fault responses. By leveraging mathematical derivations and simulations, this study illuminates the critical role of control strategies in shaping fault characteristics. As the deployment of PV systems grows, accounting for these factors will enhance grid reliability and facilitate the integration of renewable energy. Engineers and researchers should prioritize the evaluation of negative sequence controls when developing new protection principles for modern power systems.