With the increasing integration of solar inverters into power systems, understanding their fault characteristics under asymmetrical conditions becomes critical. This paper analyzes steady-state short-circuit current behavior and equivalent negative sequence impedance characteristics of solar inverters under different negative sequence control strategies.
Steady-State Short-Circuit Current Calculation
The output current of solar inverters during asymmetrical faults can be expressed as:
$$i_a = |\boldsymbol{i}^+| \cos(\omega_1 t + \phi^+) + |\boldsymbol{i}^-| \cos(\omega_1 t – \phi^-)$$
$$i_b = |\boldsymbol{i}^+| \cos(\omega_1 t – 120^\circ + \phi^+) + |\boldsymbol{i}^-| \cos(\omega_1 t + 120^\circ – \phi^-)$$
$$i_c = |\boldsymbol{i}^+| \cos(\omega_1 t + 120^\circ + \phi^+) + |\boldsymbol{i}^-| \cos(\omega_1 t – 120^\circ – \phi^-)$$
where $|\boldsymbol{i}^+|$ and $|\boldsymbol{i}^-|$ represent positive and negative sequence current magnitudes, respectively.
Negative Sequence Control Strategies
Three primary control objectives for solar inverters under unbalanced conditions:
| Control Objective | Mathematical Representation |
|---|---|
| Suppress Negative Sequence Current | $\boldsymbol{i}^- = 0$ |
| Eliminate Reactive Power Oscillation | $Q_{c2} = Q_{s2} = 0$ |
| Eliminate Active Power Oscillation | $P_{c2} = P_{s2} = 0$ |
Fault Current Characteristics
The phase relationship between sequence components varies with control strategies:
$$ \phi^+ + \phi^- = \arg[\rho(\boldsymbol{e}^-)] $$
where $\rho$ takes values 0, 1, or -1 depending on the control objective.
| Control Objective | Fault Type | |
|---|---|---|
| Single-Phase Ground | Phase-Phase Fault | |
| Objective I | $|i_{fault}| = |\boldsymbol{i}^+|$ | $|i_{fault}| = |\boldsymbol{i}^+|$ |
| Objective II | $|i_{fault}| = \big||\boldsymbol{i}^+| – |\boldsymbol{i}^-|\big|$ | $|i_{fault}| = \sqrt{|\boldsymbol{i}^+|^2 + |\boldsymbol{i}^-|^2 – |\boldsymbol{i}^+||\boldsymbol{i}^-|}$ |
| Objective III | $|i_{fault}| = |\boldsymbol{i}^+| + |\boldsymbol{i}^-|$ | $|i_{fault}| = \sqrt{|\boldsymbol{i}^+|^2 + |\boldsymbol{i}^-|^2 + |\boldsymbol{i}^+||\boldsymbol{i}^-|}$ |
Equivalent Negative Sequence Impedance
The equivalent negative sequence impedance of solar inverters is calculated as:
$$ Z^- = -\frac{\boldsymbol{e}^+}{\rho(\boldsymbol{i}^+)} $$
where $\rho$ determines the impedance angle characteristics:
| Control Objective | Impedance Angle Range |
|---|---|
| Objective I | Infinite impedance |
| Objective II | $-90^\circ$ to $-180^\circ$ |
| Objective III | $0^\circ$ to $90^\circ$ |
Simulation Verification
A 1MW solar inverter model was simulated in PSCAD/EMTDC to validate theoretical analysis:
$$ \text{Grid Parameters: } Z_{pos} = 0.19 + j2.68\Omega, \ Z_{zero} = 1.78 + j8.6\Omega $$
Key observations from phase-ground fault simulations:
- Objective I produces symmetrical currents with zero negative sequence components
- Objective II minimizes fault phase current magnitude
- Objective III maximizes fault phase current magnitude
Practical Implications
The distinct fault characteristics of solar inverters under different negative sequence control strategies require:
- Adaptive protection setting calculations
- Enhanced fault detection algorithms
- Control strategy-aware grid planning
$$ \text{Current Limitation: } i_{max} = 1.2I_N \text{ (during voltage dips)} $$
Modern solar inverters demonstrate flexible fault response characteristics that differ fundamentally from synchronous generators, requiring new approaches for power system protection and stability analysis.