Multimachine Stability

In an N-bus power system with M synchronous machines, loads are modeled as constant admittances, and network nodal equations are formulated.

The admittance matrix is partitioned to include load admittances and inverted generator impedances.

With known machine voltages, the bus voltage equation is solved to find machine currents and electrical power.

Transient stability analysis requires solving swing equations for machines and power-flow equations for the network.

First, run a pre-fault power-flow program to determine initial bus voltages, machine currents, and electrical outputs.

Set mechanical power outputs equal to electrical outputs and initialize the frequency to the synchronous angular frequency.

Next, compute the load admittances, internal machine voltages, and the power-flow bus admittance matrix.

Adjust the admittance matrix for events like switching operations, load changes, or faults.

At each time step t plus delta t, calculate machine electrical power, power angles, and speeds.

Repeat this process until the desired time horizon is reached, ensuring the step size balances solution accuracy and computation time.