Method for calculating power flow solution of a power transmission network that includes unified power flow controllers

A method for calculating power flow solution of a power transmission network that includes unified power flow controllers, said method being adapted to analyze a power transmission network that includes at least one unified power flow controller, at least one power generating device, at least one load device, a first transmission line, a sending-end bus, and a receiving-end bus, the unified power flow controller being embedded between the sending-end and receiving-end buses, the first transmission line being connected electrically to the receiving-end bus, the unified power flow controller including a series transformer, a series converter, a direct current coupling capacitor, a shunt converter, and a shunt transformer, the shunt transformer being connected electrically to the sending-end bus, the series transformer being connected electrically to the sending-end bus and the receiving-end bus, the direct current coupling capacitor being connected electrically to the shunt converter and the series converter, the series converter being connected electrically to the shunt converter and the series transformer, the shunt converter being connected electrically to the shunt transformer, the unified power flow controller being expressible using an equivalent model, the equivalent model including a series voltage source, a series impedance, a shunt voltage source, and a shunt impedance, the series voltage source having one end connected electrically to the receiving-end bus, the series impedance being connected electrically to the other end of the series voltage source and the sending-end bus, the shunt impedance being connected electrically to the sending-end bus and the shunt voltage source, said method comprising the steps of:

• (A) giving an initial vector value x(k) to a state vector x, elements in the state vector x including a direct-axis component IshD of an output current of the shunt voltage source of the equivalent model, and voltage magnitude and phase angle at each of said buses of the power transmission network;
• (B) performing orthogonal decomposition of a voltage Vr at the receiving-end bus such that the voltage Vr has a direct-axis component VrD and a quadrature-axis component VrQ;
• (C) according to the value of the state vector x, calculating the value of a mismatch vector f of the power transmission network while neglecting the unified power flow controller;
• (D) according to the value of the state vector x, calculating the value of a Jacobian matrix J of the power transmission network while neglecting the unified power flow controller;
• (E) according to the value of the state vector x, calculating an equivalent active load demand Pr′(x(k)) and an equivalent reactive load demand Qr′(x(k)) of the unified power flow controller on the receiving-end bus;
• (F) according to the values Pr′(x(k)), Qr′(x(k)) calculated in step (E), calculating current values IserD(x(k)), IserQ(x(k)) of the series voltage source in the equivalent model;
• (G) calculating an equivalent active load demand Ps′(x(k)) and an equivalent reactive load demand Qs′(x(k)) of the unified power flow controller on the sending-end bus;
• (H) according to active power losses of the transformers and the converters in the unified power flow controller, calculating the mismatch of an active power balance equation Pdc′(x(k));
• (I) calculating the value f′(x(k)) of a mismatch vector of the power transmission network that includes the unified power flow controller;
• (J) calculating the value of a Jacobian matrix J′(x(k)) of the power transmission network that includes the unified power flow controller;
• (K) according to the following equation, updating the state vector x(k+1):
• x(k+1)=x(k)−J′−1(x(k))f′(x(k))
• where f′(x(k)) and J′(x(k)) were respectively obtained in steps (I) and (J);
• (L) determining whether f′(x(k)) is smaller than a tolerable error and proceeding to step (M) if f′(x(k)) is smaller the tolerable error, and otherwise using x(k+1) to update the state vector x, and skipping back to step (B) to repeat steps (B) to (L);
• (M) calculating voltages Vser, Vsh of the series voltage source and the shunt voltage source according to the convergence value of the state vector x;
• and
• (N) setting the converters of the unified power flow controller according to the voltages Vser, Vsh obtained in step (M).