- The load on an instrumentation transformer is frequently referred to as the burden on that transformer.
- A potential transformer should ideally accurately measure voltage while appearing as an open circuit to the system under measurement, i.e. drawing negligible current and power.
- Its load impedance should be “large” in some sense.
- An ideal current transformer would accurately measure current while appearing as a short circuit to the system under measurement, i.e. developing negligible voltage drop and drawing negligible power.
- Its load impedance should be “small” in some sense.
§2.9 The Per-Unit System
- Computations relating to machines, transformers, and systems of machines are often carried out in per-unit system.
- All pertinent quantities are expressed as decimal fractions of appropriately chose base values.
- All the usual computations are then carried out in these per unit values instead of the familiar volts, amperes, ohms, and so on.
- Advantages:
- The parameter values typically fall in a reasonably narrow numerical range when expressed in a per-unit system based upon their rating.
- When transformer equivalent-circuit parameters are converted to their per-unit values, the ideal transformer turns ratio becomes 1:1 and hence the ideal transformer can be eliminated.
- Actual quantities: V , I , P , Q ,VA , R , X , Z , G , B , Y
(2.40)
- To a certain extent, base values can be chosen arbitrarily, but certain relations between them must be observed. For a single-phase system:
(2.41)
(2.42)
- Only two independent base quantities can be chose arbitrarily; the remaining quantities are determined by (2.48) and (2.49).
- In typical usage, values of
and
and are chosen first; values of
and all other quantities in (2.48) and (2.49) are then uniquely established.
- The value of
must be the same over the entire system under analysis.
- When a transformer is encountered, the values of
differ on each side and should be chosen in the same ratio as the turns ratio of the transformer.
- The per-unit ideal transformer will have a unity turns ratio and hence can be eliminated.
- Usually the rated or nominal voltages of the respective sides are chosen.
- The procedure for performing system analyses in per-unit is summarized as follows:
- Select a VA base and a base voltage at some point in the system.
- Convert all quantites toper unit on the chosen VA base and with a voltage base that transforms as the turns ratio of any transformer which is encountered as one moves through the system.
- Perform a standard electrical analysis with all quantities in per unit.
- When the analysis is completed, all quantities can be converted back to real unit(e.g., volts, amperes, watts, etc.) by multiplying their per-unit values by their corresponding base values.
- Machine Ratings as Bases
When expressed in per-unit form on their rating as a base, the per-unit values of machine parameters fall within a relatively narrow range.
- The physics behind each type of device is the same and, in a crude sense, they can each be considered to be simply scaled versions of the same basic device.
- When normalized to their own rating, the effect of the scaling is eliminated and the result is a set of per-unit parameter values which is quite similar over the whole size range of that device. For power and distribution transformers,
- 0.06pu , R 0.005 - 0.02pu , and X 0.015 - 0.10pu.
- Manufacturers often supply device parameters in per unit on the device base.
- When performing a system analysis, it may be necessary to convert the supplied per-unit parameter values to per-unit values on the base chosen for the analysis.
(2.43)
(2.44)
(2.45)
(2.46)
Balanced Three-Phase System:
- Relations for base values:
(2.47)
- The three-phase volt-ampere base
and the line-to-line voltage base
are usually chosen first.
- The base values for the phase (line-to-neutral) voltage then is
(2.48)
- The base current for three-phase system is equal to the phase current, which is the same as the base current for a single-phase (per-phase) analysis.
(2.49)
- The three-phase base impedance is chosen to be the single-phase base impedance.
((2.50); (2.51); (2.52);(2.53)
Note that the factors of 3 and 3 are automatically taken care of in per unit by the base values. Three-phase problems can thus be solved in per unit as if they were single-phase problems.