System of relative units

To simplify calculations when calculating parameters in power transmission systems, a system of relative units is used. This method involves expressing the current value of the system value in terms of the base (base) value taken as a unit.

So the relative value is expressed as a multiplier of the base value (current, voltage, resistance, power, etc.) and does not depend, expressed in relative units, on the voltage level. In English literature, relative units are denoted pu or p.u. (from system of unit — system of relative units).

For example, for transformers of the same type, voltage drop, impedance and losses differ in absolute value at different applied voltages. But in relative sizes they will remain roughly the same. When the calculation is done, the results are easily converted back to system units (in amperes, in volts, in ohms, in watts, etc.) because the base values ​​to which the current values ​​are compared are known initially.

As a rule, relative units are convenient for calculating transmitted power, but it often happens that the parameters of motor generators and transformers are specified in relative units, so every engineer should be familiar with the concept of relative units. The units of power, current, voltage, impedance, admittance are used in the relative unit system. Power and voltage are independent quantities, dictated by the properties of real energy systems.

All network values ​​of the system can be expressed as multiples of selected base values. So, if we talk about power, then the rated power of the transformer can be chosen as the base value. It happens that the power obtained at a certain moment in the form of a relative value greatly facilitates calculations. The basis for the voltage is the nominal bus voltage, etc.

In general, the context always allows you to understand what relative value is being discussed, and even the presence of the same symbol "pu" in English literature will not confuse you.

So all system physical quantities are named. But when we translate them into relative units (actually into percentages), the nature of theoretical calculations is generalized.

The relative value of some physical quantity is understood as its relationship with some base value, that is, with the value chosen as a unit for a given measurement. The relative value is marked with an asterisk below.

Often, the following basic values ​​are taken in the calculations: basic resistance, basic current, basic voltage and basic power.

The subscript «b» indicates that this is a base value.

Then the relative units of measurement will be called relative basic:

The asterisk indicates the relative value, the letter «b» - the base. EMF is relatively fundamental, current is relatively fundamental, etc. And the relative base units will be determined by the following expressions:

For example, to measure angular velocities, the angular synchronous velocity is taken as unity and therefore the synchronous angular velocity will be equal to the fundamental angular velocity.

Then an arbitrary angular velocity can be expressed in relative units:

Accordingly, the following relations may be taken as basic for flux linkage and for inductance:

Here, the principal flux linkage is the flux linkage that induces the principal stress at the principal angular velocity.

So, if the synchronous angular velocity is taken as the basis, then:

in relative units, emf is equal to flux and inductive resistance is equal to inductance. This is because the base units are chosen appropriately.

Then consider the phase voltage in relative and fundamental units:

It is easy to see that the phase voltage in relative fundamental units turns out to be equal to the linear relative fundamental voltage. Similarly, the value of the stress amplitude in relative units turns out to be equal to the effective:

From these dependences it is evident that in relative units even the power of three phases and the power of one phase are equal, and the excitation currents, fluxes and emf of the generator - also turn out to be equal to each other.

It is important to note here that for each element of the circuit, the relative resistance will be equal to the relative voltage drop under the conditions of the rated power supplied to the circuit.

When calculating short-circuit currents, four main parameters are used: current, voltage, resistance and power. The fundamental values ​​of voltage and power are taken as independent, and through them the fundamental resistance and current are then expressed. From the power equation of a three-phase network — current, then Ohm's Law — resistance:

Since the base value can be chosen arbitrarily, the same physical quantity can, expressed in relative units, have different numerical values. Therefore, the relative resistances of generators, motors, transformers are set in relative units by entering relative nominal units. Sn — nominal power. Un — nominal voltage. Relative nominal values ​​are written with an index «n»:

To find the nominal resistances and currents, the standard formulas are used:

To establish the relationship between relative units and named quantities, we first express the relationship between the relative base and the base quantities:

Let's write the base resistance in terms of power and substitute:

So you can translate the specified value into a relative base value.

And in a similar way you can establish a relationship between relative nominal units and nouns:

To calculate the resistance in named units with known relative nominal values, use the following formula:

The relationship between relative nominal units and relative base units is established by the following formula:

Using this formula, relative nominal units can be converted to relative base units.

In power systems, to limit short-circuit currents, set current limited reactors, actually — linear inductors. They get rated voltage and current but not power.

Given that

and transforming the above expressions for the relative nominal and relative base resistance, we obtain:

Relative values ​​can be expressed as a percentage: