Grid Impedance Ratio and Short Circuit Ratio (SCR)

Normally the power grid or utility system consists of many machines and high-power renewables that are interconnected with transmission and distribution systems. Knowing the system strength is very important for the power grids when the high-power renewables (like wind or PV plants) are interconnected with the network to avoid stability related issues. The strength of the power grid can be defined by the short circuit ratio (SCR) and grid impedance (or X/R) ratio.

1. Grid Impedance (X/R) Ratio

The grid impedance or X/R ratio is the ratio of equivalent inductive reactance (XS) to the equivalent resistance (RS) of the system. The X/R ratio indicates the characteristics of the power grid. The impedance of the network (Zs) and X/R ratio are given by,

For transmission systems, the X/R ratio is in the range of 5 to 20. For distribution systems, the X/R ratio is much lower.

Short circuit fault current consists of an AC component (symmetrical short circuit current) and a decaying DC component which makes the fault current asymmetrical. The decay rate of the DC component depends on the X/R or (L/R) ratio. If the X/R ratio is high, the decay time of the DC component is longer. Also, the X/R ratio helps to select the proper protection devices.

2. Short Circuit Ratio (SCR)

Short circuit ratio (SCR) is the ratio of available system strength measured in short circuit MVA to the rated capacity of the wind or PV plant. (or) The SCR is the ratio of the short circuit capacity at the connection point to the rated capacity of the power electronic equipment connected to that point. Where, short circuit capacity is the short circuit current multiplied with rated voltage.

The SCR of the power grid can be calculated by,

where, SMVA is the short circuit MVA capacity.

VLL is the line-to-line voltage in kV.

Zs is the equivalent impedance of the network in Ω.

PMW is the power rating in MW.

Based on the range of SCR, the system strength can be classified as follows,

• SCR>3 is a strong system that can have lesser operating problems.

• 2<SCR<3 is a weak system that has some operating problems can be expected.

• SCR<2 is a very weak system which can increase the operating problems. It is very sensitive to active and reactive power injections or absorptions and very difficult to stabilize the system voltage.

For example, the sample calculation for short circuit ratio (SCR) is given below,

If short circuit MVA and power rating are known,

Short circuit MVA = 1534 MVA

Wind power rating = 300 MW

The short circuit ratio is calculated by,

Suppose if the line voltage and equivalent impedance of the network are known from Thevenin’s equivalent circuit. Then,

Line to line voltage or Thevenin’s voltage = 300 kV

Wind power rating = 300 MW

Equivalent impedance of the network, Zs = (2.54+j58.6) Ω = 58.66∠87.51° Ω

The short circuit ratio is calculated by,

References

• Dragan Jovcic, High voltage direct current transmission: converters, systems, and DC grids, John Wiley & Sons, 2019.

• IEEE Std 3002.3™-2018 - IEEE Recommended Practice for Conducting Short-Circuit Studies and Analysis of Industrial and Commercial Power Systems.

• IEC 60909 - Short-circuit currents in three-phase a.c. systems.

• NERC, Short circuit modeling and system strength, 2018.

• Yu, Lin, et al. "A Critical System Strength Evaluation of a Power System with High Penetration of Renewable Energy Generations." CSEE Journal of Power and Energy Systems, 2021.