ELECTRIC MACHINERY

PART 5
TRANSFORMERS

  Types of cores for power transformer (both types are constructed from thin laminations electrically isolated from each other - minimize eddy currents)

power transformer
power transformer

  The primary and secondary windings are wrapped one on top of the other with the low-voltage winding innermost, due to 2 purposes:
    It simplifies the problem of insulating the high-voltage winding from the core.
    It results in much less leakage flux.

  Types of transformers:
    Step up/Unit transformers - Usually located at the output of a generator. Its function is to step up the voltage level so that transmission of power is possible.
    Step down/Substation transformers - Located at main distribution or secondary level transmission substations. Its function is to lower the voltage levels for distribution 1st level purposes.
    Distribution Transformers - located at small distribution substation. It lowers the voltage levels for 2nd level distribution purposes.
    Special Purpose Transformers - E.g. Potential Transformer (PT) , Current Transformer (CT)

Special Purpose Transformers

  The transformer has Np turns of wire on its primary side and Ns turns of wire on its secondary sides. The relationship between the primary and secondary voltage is as follows:

Special Purpose Transformers


where a is the turns ratio of the transformer.
  The relationship between primary and secondary current is:

relationship between primary and secondary current


  Note that since both type of relations gives a constant ratio, hence the transformer only changes ONLY the magnitude value of current and voltage. Phase angles are not affected.
  The dot convention in schematic diagram for transformers has the following relationship:
    If the primary voltage is +ve at the dotted end of the winding wrt the undotted end, then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same wrt the dots on each side of the core.
    If the primary current of the transformer flows into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding.
  The necessity to control the power flow rose early in the history of the development of electrical power systems. When high-voltage grids were superimposed on local systems, parallel-connected systems or transmission lines of different voltage levels became standard. Nowadays large high-voltage power grids are connected to increase the reliability of the electrical power supply and to allow exchange of electrical power over large distances. Complications, attributed to several factors such as variation in powergeneration output and/or power demand, can arise and have to be dealt with to avoid potentially catastrophic system disturbances. Additional tools in the form of phase-shifting transformers (PSTs) are available to control the power flow to stabilize the grids. These may be justified to maintain the required quality of the electrical power supply. To transfer electrical power between two points of a system, a difference between source voltage (VS) and load voltage (VL) in quantity and/or in phase angle is necessary. Using the notation of figure:

phase angle

it follows that:

transformer equation

transformer equation

  Because of the predominantly inductive character of the power system, an active power flow between source and load must be accomplished with a phase lag between the terminals. Phase-shifting transformers are a preferred tool to achieve this goal. Two principal configurations are of special interest: (1) the power flow between transmission systems operating in parallel where one system includes a PST and (2) where a single transmission line which includes a PST is connecting two otherwise independent power systems. The latter is in fact a special case of the first, but it has become more important nowadays for the interconnection of large systems. For the following considerations, it is assumed that the ohmic resistance R is small compared with the reactance X and thus has been neglected.

transformer


  One practical basic situation is that a location where power is needed (load side) is connected to the source side through two systems that need not necessarily have the same rated voltage level. Without any additional measure, the currents I1 and I2 would be distributed in proportion to the ratio of the impedances of the systems,

transformer equation


Total Power Transfer


  The voltages at the source side (VS) and at the load side (VL) are considered constant, i.e., not influenced by the transferred power, and operating synchronously but not necessarily of the same value and phase angle. To calculate the power flow it has been assumed that the voltages at source side (VS) and load side (VL) and the impedance (Z) are known.

transformer equation

transformer equation


Then the current becomes:

transformer equation


and the power at source (SS) and load (SL) side can be calculated by multiplying the respective voltage with the conjugate complex current:

transformer equation


Because a mere inductive impedance has been assumed, only the reactive power changes.
Symmetrical conditions :

transformer equation


are very common:

transformer equation


This solution can be considered as a basic load (SL0 = P0 + jQ0) that exists only when the magnitude and/or phase angle of the source and load voltages are different. If a PST is installed in this circuit with an advanced phase-shift angle , the transferred load can be calculated by substituting + as angle and adding the PST impedance XT to X. By introducing the basic load in the result, the power flow can be calculated as a function of :

transformer equation