In the calculation of short circuit current, the principle formula includes:

where U_k is the open circuit voltage of short circuit point, in BPA it’s often fixed to 1.05 U_n, Z_k is equivalent impedance of short circuit point, other hypotheses and conditions includes whether or not consider standard ratio of transformer, charging power of lines, high voltage impedance, low voltage reactive power compensation, actual transformation ratio, static load, induction motor load and etc.

In the calculation of short circuit current of the algorithm, the principle formula is as same as the above algorithm. Where U_k is the open circuit voltage of short circuit point, in BPA it comes from the result of power flow calculation. Z_k is equivalent impedance of short circuit point, other hypotheses and conditions are as same as the above algorithm based on schemes.

At present, the main relevant international standards of calculation of short circuit current includes IEC60909 series standards and ANSI/IEEE/UL series standards. Furthermore, in order to guide the calculation of short circuit currents in DC auxiliary installations in power plants and substations, IEC 61660 series standards are setup. Many countries or enterprises developed their own national standards, industry standards or enterprise standards based on these series standards and combined with their actual situation. In china, the national standards, industry standards or enterprise standards of short circuit current calculation are no exception, all based on the IEC60909 or IEC 61660 series standards, combined with the actual situation of the specific application areas, is almost equivalent to utilize the two series of standards, but a slight modification.

The general approach is divided into two steps. At first the short circuit currents of the individual sources are calculated separately. Subsequently, the individual currents are superposed resulting in an overall short circuit current of the system.

The international simulation software of calculation of short circuit current includes BPA of Bonneville Power Administration, PSS/E and NETOMAC of Siemens, ARENA of EDF, PSAPAC/ LISP of EPRI, NEPLAN of ABB, EXTAB of TEPCO. In china, the main software includes PSD-BPA and PSASP. They all abide by these above series standards by and large. In the paper, PSD-BPA is adopted, and all kinds of hypotheses and conditions are based on PSD-BPA [2] [3].

HVDC can be distinguished into two types by converter: Current source converters (CSC) and voltage source converters (VSC). CSCs are also called line- commutated converters (LCC), because they rely on a synchronous voltage for proper operation. The thyristor is the key element of a CSC, which allows very high transmission powers. CSC-HVDC systems with voltages of ±800 kV and powers of more than 8000 MW are possible [4]. VSCs are referred as self-com- mutated converters because of the ability to operate independently from the power grid. The AC/DC-conversion is accomplished by insulated gate bipolar transistors (IGBTs) with turn-on and turn-off capability. Because of the high complexity of the control system, there are only a few realizations by far now. In this paper, UHVDC based on LCC is considered. The Equivalent circuit of a six-pulse bridge at a short circuit on the DC side is shown as Figure 1.

The six-pulse bridge is the basic element of a CSC-HVDC, which is shown in Figure 1 at a short circuit on the DC side. The largest short circuit current of a single bridge can be expected, if a line-to-line short circuit occurs directly at the terminal (R_DC = 0, L_DC = 0). For this particular case the DC short circuit current can be derived according to the loops I and II shown in Figure 1. In this instant the diodes D1, D3 and D2 are conducting.

The resistance R_DC and the inductance L_DC of the DC system comprise the parameters of the rectifier, the smoothing reactor and the line. The calculation of the characteristic parameters of the short circuit current is based on the corresponding values of the AC and DC system. The quasi-steady-state short circuit current of a rectifier in a three-phase bridge connection is

where U_N is the nominal voltage of the AC system, Z_N the system impedance, U_rTLV/U_rTHV the ratio of the rated voltages of the secondary and primary transformer side and λ_D considers the influence of the DC side resistance.

The peak short circuit current i_pD is calculated using:

The factor k_D depends on the ratio of the inductances L_DC/L_N and the parameters R_N, R_DC and X_N.

The calculation of the time constantsτ_1D, τ_2Dand the time to peak t_pD is described in the reference [2].

The equivalent circuit diagram of the capacitor is depicted in Figure 2. The resistance R_CBr and the inductance L_CBr include the resistances and inductances of the capacitor and of the connection to the line.

The quasi-steady-state short circuit current of the capacitor is zero:

The peak short circuit is calculated by using

where k_C depends on the eigen-frequency ω₀ and the decay coefficient δ. The corresponding calculation of ω₀ respectively δ and the equations for τ_1C, τ_2C and t_pC are specified in the reference [2].

When a fault or an operation happens, electromagnetic transient procedure and electromechanical transient procedure occur in power system. Usually we analyze the two procedures individually, because uniform analysis is very complex and impractical. We use electromechanical transient simulation to analyze electromechanical transient procedure and electromagnetic transient simulation to analyze electromagnetic transient procedure. Electromechanical transient procedure varies slowly compared with electromagnetic transient procedure, therefore the integration time step of electromechanical transient simulation is much larger than that of electromagnetic transient simulation. Usually the integration time step of electromechanical transient simulation is 10 milliseconds while that of electromagnetic transient simulation is about 20 - 200 microseconds.

Electromechanical transient simulation can simulate quite large power system, based on three-sequence phasor model with much larger time step. While, Electromagnetic transient simulation, based on three-phase instant value model, can analyze electromagnetic transient procedure and represent those power electronic devices very easily, while the scale of the system simulated is very limited for its much larger computation amount. Hybrid simulation combines the advantages of the both. With hybrid simulation, we can analyze the electromagnetic transient procedure appearing in a special small network under the background of a large power system.

In hybrid simulation, Norton equivalent circuit of electromechanical transient network is connected to the electromagnetic transient network. If there are generators in electromechanical transient network, Norton equivalent admittance matrix becomes asymmetric when transformed from three sequences to ABC three phases. PSD-BPAFDS (Full Dynamic Process Simulation Software) provides the performance.

DFIG can be described as an induction machine model in space vector notation. The space vector model is subjected to a reference frame transformation to get decoupled d-q model. The reference frame is usually aligned with stator flux reference frame. This facilitates in decoupling the active and reactive power of the machine. The terminal rotor voltage vector which is a control input in case of a DFIG will then be able to decide i_dr and i_qr independently. The detailed model of a DFIG is a fifth order model having two voltage equations for stator and rotor each.

The typical structure of a DFIG system with crowbar protection using a wound rotor induction machine is shown as below Figure 3 [6].

In the procedure of calculation, crowbar resistance is often assumed to be connected to rotor winding throughout the duration of the fault. The assumption is valid because crowbar activation is fast and completed in few milliseconds. It also assumes constant generator speed during fault conditions. The above assumption can cause errors in fault current prediction but is considered for simplification. The magnetic nonlinearities are neglected in this analysis. Considering the effect of saturation on leakage reactance may increase the fault current levels.

The decaying stator natural flux will induce an emf in rotor of frequency, then the emf induced in rotor winding will cause a current to flow limited by crowbar resistance. This current will in tum produce a flux which will oppose the stator flux. This will be the case in a steady state condition if stator natural flux persists. Thus DFIG fault current analysis is governed by crowbar resistance. Due to introduction of crowbar the AC component present during the fault decays at much faster rate. This causes the stator fault current to be entirely DC component. The interruption of DC current may be a problem for AC circuit breaker. This could become even more hazardous as we move towards DFIGs with higher MVA ratings as they have a higher stator time constant.

The short-circuit current of an idle running machine will be determined. Neglecting the mechanical losses, the machine rotates at the synchronous rotational speed ω_s. The stator resistance can be neglected in steady state. Before the occurrence of the short circuit, the rotor current is zero: I_r = 0. The stator current is:

The maximum stator current of an induction machine in case of a short circuit at the stator terminals is:

The time constant for the damping of the dc components in stator and rotor are defined as below:

Due to asymmetry of fault, the stator flux will have positive and negative sequence components. The magnitude and phase angle of these components depends on the type of fault.

The initial value of the current is determined under the assumption that the stator and rotor resistance can be neglected. When the bypass resistors are connected to protect the converter in case of a fault, (6) becomes:

And the transient time constant of the rotor becomes:

The two exponential functions inside the brackets in (7) are based on the assumption that the rotor and stator flux are 180˚ out of phase after half a period, implying that the current reaches its maximum value at t = T/2. This assumption is approximately valid for an induction machine, where the slip is small and where the stator and rotor flux are approximately in phase with each other, at the moment the fault occurs. A DFIG can however operate at a much larger slip. This implies that at the moment of the fault, the two flux vectors are not in phase with each other.

Taking into account these differences between an induction machine and a DFIG, then (7) becomes:

A larger bypass resistance will result in a smaller. At the same moment, Δt decreases. As a result, the term inside the brackets in (12) stays approximately constant. As a rough approximation, the maximum stator current is then given as: