The electrical properties of a connection point to the public electrical power supply network are characterised by the applied mains voltage and the internal resistance, which is also referred to as the network impedance. The grid voltage at a grid connection point (NVP) is usually known and can also be measured relatively easily. However, an exact determination of the mains impedance is much more complex. For the nominal frequency of the network, an approximate estimation of the equivalent longitudinal impedance of a connection can be carried out using equipment characteristics. In this context, the amount of impedance at the nominal network frequency is of great interest, as this, together with the network voltage, defines the maximum short-circuit power and thus the capacity of a connection. In addition to the maximum short-circuit power, however, the ratio of resistance and reactance (R/X) or the resulting phase angle of the mains impedance is also important. The magnitude and R/X ratio determine the voltage changes generated by power flows at an NVP and are important parameters especially for the design and control of grid-connected power electronic converter systems. The grid impedance determines the maximum possible active and reactive power injection or withdrawal of the systems and thus also their ability to regulate the voltage at an NVP. In addition, the complex grid impedance is a relevant parameter when designing filter and compensation systems of generators and consumers, as the impedance ratios of the connection point should always be taken into account when precisely adjusting them (fine-tuning).

If exact data are available, the modelling and analysis of grids at grid frequency, such as load flow or short circuit calculations, can be carried out with satisfactory accuracy by analytical considerations or numerical calculations in simulation programs. In most cases, even a low modelling depth is sufficient to produce acceptable results. An approximate determination of the grid impedance can be made by estimating the short-circuit power at the grid frequency. The grid impedance is mainly determined by the short-circuit power of the upstream grid, the rated power of the connected transformer and the type and length of the line to an NVP. Based on these characteristics, the approximate longitudinal impedances of the equipment can be determined and added to a resulting short-circuit impedance.

**Determination of the longitudinal impedance of the upstream network:**

The approximate amount of the internal impedance of a feeding network results from the simple relation

with the nominal grid voltage in kV and the short-circuit power in MVA at the coupling point Q to the grid. The short-circuit power depends strongly on the structure of the grid The short-circuit power depends strongly on the structure of the grid (beam or mesh grid) as well as on the number of feed-in points. The factor 1.1 is used for short-circuit observations. For investigations in normal operation, such as load flow calculations, on the other hand, the current and voltage behaviour is better described without the factor 1.1.

**Determination of the longitudinal impedance of the transformer:**

The longitudinal impedance of a transformer can also be estimated.

Here, the short-circuit voltage in percent related to the rated voltage in kV and the rated power of the transformer in MVA. The ohmic resistance can usually be neglected ( ≈ ).

Determination of the longitudinal impedance of lines:

The largest contribution to the equivalent longitudinal impedance at an NVP is usually made by the lines. The longitudinal impedance of a line results from

and

with the corresponding inductive and resistive loadings and in Ω/km as well as the circuit length in km.

Conversion of the longitudinal impedance to a respective voltage level:

The longitudinal impedances of the equipment refer to the respective voltage level and can be converted from the high voltage side (OS) to the low voltage side (US) by the transformer transmission ratio:

**Example of estimating the mains impedance at a medium voltage connection:**

The following figure shows an estimation of the short-circuit impedance at the end of a 10 kV cable based on characteristic data. The cable is fed via a transformer from a superimposed 110 kV network. With the simplification Z(Q) = X(Q) and Z(T) = X(T), this gives the resulting longitudinal impedance at the NVP.

**Illustration**: Estimation of the grid impedance (b) at a 10 kV connection based on equipment characteristics (a).

In practice, however, other equipment has an influence on the mains impedance at an LVP. These include, above all, longitudinal elements of protective and switching devices such as current-limiting reactors, circuit breakers or fuses. These increase the short-circuit impedance and reduce the short-circuit current accordingly. In addition, the impedance at an NVP is also determined by loads and generators at the nominal network frequency. The characteristics are often not known exactly and also vary over time. Loads and generators are cross-admittances and, like capacitive and ohmic cross-couplings in equipment, lead to a slight reduction in the resulting impedance at the grid frequency. However, cross-admittances mainly affect the frequency response of the impedance above 50/60Hz through resonance effects.

**Conclusion**:

The longitudinal impedance of an electrical connection point can be estimated with relatively little effort if there is sufficient information about the equipment. However, due to many unknown parameters, the estimation of the longitudinal impedance is often subject to large uncertainties.

**Measurement solutions by morEnergy GmbH:**

In many cases, an exact identification of the mains impedance can only be done by measurement. For this purpose, morEnergy GmbH has developed the ONIS systems. ONIS stands for Online-Network-Impedance-Spectrometer. The systems can be used to measure impedances of network connection points as well as of electrical consumers and generators during operation under voltage. The systems are also fully-fledged transient recorders and power quality analysers. The ONIS systems can be purchased or rented. Furthermore, in addition to measurement services with the ONIS systems, morEnergy GmbH also offers grid simulations and many other technical consulting and services. Further information on the ONIS systems and the services of morEnergy GmbH can be found at www.morEnergy.net.

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