IEEE 39-bus swing equations

Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.

def rhs(t: float, y: np.ndarray) -> np.ndarray:
    delta = y[:n_gen]
    omega = y[n_gen:]
    P_e = np.zeros(n_gen)
    for i in range(n_gen):
        for j in range(n_gen):
            if B[i, j] > 0:
                P_e[i] += E[i] * E[j] * B[i, j] * np.sin(delta[i] - delta[j])
    P_m_eff = P_m.copy()
    if fault_time <= t <= fault_time + fault_duration:
        P_m_eff[0] = 0.0
    ddelta = omega - omega_s
    domega = (P_m_eff - P_e - D * (omega - omega_s)) / M
    return np.concatenate([ddelta, domega])

Parameters

• B = [0, 5, 0, 0, 0, 0, …] [shape=(10, 10), min=0, max=5]
• D = [0.04, 0.04, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02]
• E = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
• M = [0.0265258238486, 0.0229713634529, 0.0237140865207, 0.0189394382279, 0.0229713634529, 0.0230774667483, 0.0200004711819, 0.018408921751, 0.0183028184556, 0.0222816920329]
• P_m = [2.5, 5.45, 6.5, 6.32, 5.6, 6.38, 2.8, 5.4, 0.7, 8.95]
• fault_duration = 0.1
• fault_time = 1
• n_gen = 10
• omega_s = 376.991118431

Initial condition

y(0) = [0.252680255142, 0.576389114736, 0.707584436725, 0.684131254766, 0.594385800001, 0.691898182137, …] [shape=(20,), min=0.0700572930881, max=376.991118431]

Horizon

t ∈ [0, 5]

Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.