PART 5 TRANSFORMERS
Types of cores for power transformer (both types are constructed from thin laminations electrically isolated from each other  minimize eddy currents)
The primary and secondary windings are wrapped one on top of the other with the lowvoltage winding innermost, due to 2 purposes:
It simplifies the problem of insulating the highvoltage 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)
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:
where a is the turns ratio of the transformer.
The relationship between primary and secondary current is:
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 highvoltage grids were superimposed on local systems, parallelconnected systems or
transmission lines of different voltage levels became standard. Nowadays large highvoltage 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 phaseshifting 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 (V_{S})
and load voltage (V_{L}) in quantity and/or in phase angle is necessary. Using the notation of figure:
it follows that:
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. Phaseshifting 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.
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 I_{1} and I_{2} would be distributed in proportion to the ratio of the impedances of the systems,
Total Power Transfer
The voltages at the source side (V_{S}) and at the load side (V_{L}) 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 (V_{S}) and load side
(V_{L}) and the impedance (Z) are known.
Then the current becomes:
and the power at source (S_{S}) and load (S_{L}) side can be calculated by multiplying the respective voltage
with the conjugate complex current:
Because a mere inductive impedance has been assumed, only the reactive power changes.
Symmetrical conditions :
are very common:
This solution can be considered as a basic load (S_{L0} = P_{0} + jQ_{0}) 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 phaseshift angle ,
the transferred load can be calculated by substituting +
as angle and
adding the PST impedance X_{T} to X. By introducing the basic load in the result, the power flow can be
calculated as a function of :

