Three-Phase Short-Circuit Current Calculation at Arbitrary Time Using MATLAB

In power system analysis, three-phase short-circuit current calculation plays a vital role in evaluating system transient stability and protection device operating characteristics. Traditional manual calculations often rely on symmetrical component methods and complex differential equations. Leveraging MATLAB's powerful numerical computation and simulation capabilities, we can efficiently achieve precise short-circuit current solutions at arbitrary time instants.

### Core Methodology System Modeling: The first step involves constructing an equivalent circuit model of the power network, including parameterized representations of components such as generators (using subtransient reactance models), transformers, and transmission lines. In MATLAB implementation, this typically involves creating impedance matrices using functions like `sparse` for efficient large-scale system handling.

Differential Equation Solving: Three-phase short circuits represent symmetrical faults whose transient processes can be described by generator electromagnetic transient equations. MATLAB's ODE solvers (such as `ode45` or `ode15s` for stiff systems) automatically handle time-domain differential equations without requiring manual separation of periodic and aperiodic components. The solver parameters like relative tolerance (`RelTol`) and absolute tolerance (`AbsTol`) can be optimized for accuracy.

Arbitrary Time Current Extraction: By setting simulation time steps through the `tspan` vector in ODE functions, instantaneous current values at specific post-fault moments can be output. To account for decay time constant effects, damping coefficients can be incorporated into the model using exponential decay functions or custom differential equation modifications.

### Extended Applications Asymmetric Fault Extension: By modifying the impedance matrix using sequence component transformations, this method can be extended to analyze asymmetric faults like single-phase grounding and two-phase short circuits. The `sym2abc` and `abc2sym` functions facilitate symmetrical component conversions.

Protection Verification: Combining short-circuit current results with circuit breaker interrupting capacity data enables validation of protection relay setting合理性. Custom MATLAB scripts can automate comparison between calculated currents and device ratings.

MATLAB's flexibility and visualization tools (such as the `plot` function with customizable time-axis formatting) make current waveform analysis more intuitive, particularly suitable for teaching demonstrations and rapid engineering validation scenarios. Additional features like `simulink` integration allow for hybrid modeling approaches combining numerical and block-based simulations.