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Learning goals:
• To refresh basic electrical concepts
• To define basic concepts of transformer
• To refresh single-phase power concepts
• To refresh three-phase power concepts.
1. Introduction
A significant proportion of industrial electricity is about single-phase and three-phase transformers, AC and DC machines. In this context, we will study the electrical circuits and their construction, design, testing, operation, and maintenance.
For troubleshooting electrical equipment and control circuits, it is important to understand the basic principles on which the electrical equipment works. The following sections will outline the basic electrical concepts.
1.1 Basic electrical concepts
In each plant, the mechanical movement of different equipments is caused by an electric prime mover (motor). Electrical power is derived from either utilities or internal generators and is distributed through transformers to deliver usable voltage levels.
Electricity is found in two common forms:
• AC (alternating current)
• DC (direct current).
Electrical equipments can run on either of the AC/DC forms of electrical energies. The selection of energy source for equipment depends on its application requirements. Each energy source has its own merits and demerits.
Industrial AC voltage levels are roughly defined as LV (low voltage) and HV (high voltage) with frequency of 50-60 Hz.
An electrical circuit has the following three basic components irrespective of its electrical energy form:
• Voltage (volts)
• Ampere (amps)
• Resistance (ohms).
Voltage is defined as the electrical potential difference that causes electrons to flow.
Current is defined as the flow of electrons and is measured in amperes.
Resistance is defined as the opposition to the flow of electrons and is measured in ohms. All three are bound together with Ohm's law, which gives the following relation between the three:
V =IR
Where,
V= Voltage
I= Current
T= Resistance.
(a) Power In DC circuits, power (watts) is simply a product of voltage and current.
P =VI
For AC circuits, the formula holds true for purely resistive circuits; however, for the following types of AC circuits, power is not just a product of voltage and current.
Apparent power is the product of voltage and ampere, i.e., VA or kVA is known as apparent power. Apparent power is total power supplied to a circuit inclusive of the true and reactive power. Real power or true power is the power that can be converted into work and is measured in watts.
Reactive power If the circuit is of an inductive or capacitive type, then the reactive component consumes power and cannot be converted into work. This is known as reactive power and is denoted by the unit VAR. (b) Relationship between powers Apparent power (VA) = VA × True power (Watts) = VA cosf × Reactive power (VAR) = VA sinf × (c) Power factor Power factor is defined as the ratio of real power to apparent power. The maximum value it can carry is either 1 or 100(%), which would be obtained in a purely resistive circuit.
True power:
Power factor = Apparent power Watts kVA
(d) Percentage voltage regulation
(No load voltage Full load voltage)
% Regulation = 100 Full load voltage
(e) Electrical energy
This is calculated as the amount of electrical energy used in an hour and is expressed as follows: Kilowatthour = kW x h
Where:
kW = kilowatt
h = hour.
(f) Types of circuits
There are only two types of electrical circuits - series and parallel.
A series circuit is defined as a circuit in which the elements in a series carry the same current, while voltage drop across each may be different.
A parallel circuit is defined as a circuit in which the elements in parallel have the same voltage, but the currents may be different.
1.2 Transformer
A transformer is a device that transforms voltage from one level to another. They are widely used in power systems. With the help of transformers, it is possible to transmit power at an economical transmission voltage and to utilize power at an economic effective voltage.
Basic principle
Transformer working is based on mutual emf induction between two coils, which are magnetically coupled.
When an AC voltage is applied to one of the windings (called as the primary), it produces alternating magnetic flux in the core made of magnetic material (usually some form of steel). The flux is produced by a small magnetizing current which flows through the winding. The alternating magnetic flux induces an electromotive force (EMF) in the secondary winding magnetically linked with the same core and appears as a voltage across the terminals of this winding. Cold rolled grain oriented (CRGO) steel is used as the core material to provide a low reluctance, low loss flux path. The steel is in the form of varnished laminations to reduce eddy current flow and losses on account of this.
Typically, the coil connected to the source is known as the primary coil and the coil applied to the load is the secondary coil.
A schematic diagram of a single-phase transformer is shown in the FIG. 1.
A single-phase transformer consists mainly of a magnetic core on which two windings, primary and secondary, are wound. The primary winding is supplied with an AC source of supply voltage V1. The current I? flowing in the primary winding produces flux, which varies with time. This flux links with both the windings and produces induced emfs. The emf produced in the primary winding is equal and opposite of the applied voltage (neglecting losses). The emf is also induced in the secondary winding due to this mutual flux. The magnitude of the induced emf depends on the ratio of the number of turns in the primary and the secondary windings of the transformer.
FIG. 1 Schematic diagram of a single-phase transformer
Potential-induced
There is a very simple and straight relationship between the potential across the primary coil and the potential induced in the secondary coil.
The ratio of the primary potential to the secondary potential is the ratio of the number of turns in each and is represented as follows:
11 22 NV NV
==
The concepts of step-up and step-down transformers function on similar relation.
A step-up transformer increases the output voltage by taking 21 > NN and a step-down transformer decreases the output voltage by taking
21 >. NN
Current-induced
When the transformer is loaded, then the current is inversely proportional to the voltages and is represented as follows:
12 1 21 2 VI N VIN
==
EMF equation of a transformer:
rms value of the induced emf in the primary winding is:
11m 4.44 EfN f =×××
rms value of the induced emf in the secondary winding is: 22m 4.44 EfN f =×××
Where:
N1 = Number of turns in primary
N2 = Number of turns in secondary
m f = Maximum flux in core and
f = Frequency of AC input in Hz.
1.3 Ideal transformer
The following assumptions are made in the case of an ideal transformer:
• No loss or gain of energy takes place.
• Winding has no ohm resistances.
• The flux produced is confined to the core of the transformer, which links fully both the windings, i.e., there is no flux leakage.
• Hence, there are no I 2 R losses and core losses.
• The permeability of the core is high so that the magnetizing current required to produce the flux and to establish it in the core is negligible.
• Eddy current and hysteresis losses are negligible.
1.4 Types of transformers
1. As per the type of construction (a) Core type: Windings surround a considerable part of the core.
(b) Shell type: Core surrounds a considerable portion of the windings.
2. As per cooling type (a) Oil-filled self-cooled: Small- and medium-sized distribution transformers.
(b) Oil-filled water-cooled: High-voltage transmission line outdoor transformers.
(c) Air Cooled type: Used for low ratings and can be either of natural air circulation (AN) or forced circulation (AF) type.
3. As per application
(a) Power transformer: These are large transformers used to change voltage levels and current levels as per requirement. Power transformers are usually used in either a distribution or a transmission line.
(b) Potential transformer (PT): These are precision voltage step-down transformers used along with low-range voltmeters to measure high voltages.
(c) Current transformer (CT): These transformers are used for the measurement of current where the current-carrying conductor is treated as a primary transformer. This transformer isolates the instrument from high-voltage line, as well as steps down the current in a known ratio.
(d) Isolation transformer: These are used to isolate two different circuits without changing the voltage level or current level.
A few important points about transformers:
• Used to transfer energy from one AC circuit to another
• Frequency remains the same in both the circuits
• No ideal transformer exists
• Also used in metering applications (current transformer, i.e., CT, potential transformers, i.e., PT)
• Used for isolation of two different circuits (isolation transformers)
• Transformer power is expressed in VA (volt amperes)
• Transformer polarity is indicated by using dots. If primary and secondary windings have dots at the top and bottom positions or vice versa in diagram, then it means that the phases are in inverse relationship.
1.5 Connections of single-phase transformer
Depending on the application's requirement, two or more transformers have to be connected in a series or parallel circuits. Such connections can be undertaken as depicted in the following diagram examples: (a) Series connection of two single-phase transformers
As shown in FIG. 2, two transformers can be connected in a series connection. If both are connected as in FIG. 2 then voltage twice that of voltage rating of the individual transformer can be applied. Their current rating must be equal and high enough to carry load current. Precaution should be taken to connect transformers windings, keeping in mind the polarity. In the above example, primary total turns to secondary total turns are in the 2:1 ratio, leading to half voltage.
Sec. side (200 turns) (400 turns) Pri. side H2 H3 H1 H4 480 V AC (200 turns) Xmer 1 X3 X2 X4 X1 240 V AC (100 turns) (100 turns) (200 turns) Xmer 2
FIG. 2 Series connection of two single-phase transformers
(b) Parallel connection of two single-phase transformers As shown in FIG. 3, two transformers are connected in series on the primary side while the secondary sides are connected in parallel.
X3 X2 H2 H3 X4 X1 120 V AC H1 H4 480 V AC Sec. side (100 turns) (400 turns) Pri. side (200 turns) Xmer 2 (200 turns) Xmer
FIG. 3 Parallel connection of two single-phase
Transformers
On the primary side, the number of turns is added while on the secondary side they remain as it is due to their parallel condition.
LVDT (linear voltage differential transformer) is the best practical example of the basic transformer and its series connection. Use of transformers with such connections can pose problems of safety and load sharing and are hardly used in practical power circuits. It is possible to deploy these connections while designing control transformers if such use will have any specific advantage. Parallel operation of two separate transformers is possible under specific conditions to meet an increased load requirement but the risks involved must be properly evaluated.
1.6 Three-phase transformers
Large-scale generation of electric power is generally three-phasic with voltages in 11 or 32 kV. Such high three-phasic voltage transmission and distribution requires use of the three-phase step-up and step-down transformers.
Previously, it was common practice to use three single-phase transformers in place of a single three-phase transformer. However, the consequent evolution of the three-phase transformer proved space saving and economical as well.
Still, construction-wise a three-phase transformer is a combination of three single-phase transformers with three primary and three secondary windings mounted on a core having three legs.
Commonly used three-phases are:
• Three-phase three-wire (delta)
• Three-phase four-wire (star).
1. Delta connection It consists of three-phase windings (FIG. 4) connected end-to-end and are 120° apart from each other electrically. Generally, the delta three-wire system is used for an unbalanced load system. The three-phase voltages remain constant regardless of load imbalance.
V_L = Vph
Where,
V_L= line voltage
V_ph= phase voltage.
Relationship between line and phase currents:
I_L = _/3 I_ph
Where L ph
I_L = line current
Iph= phase current.
2. Three-phase four-wire star connections
The star type of construction (FIG. 5) allows a minimum number of turns per phase (since phase voltage is 1_/3 of line voltage) but the cross section of the conductor will have to be increased as the current is higher compared to a delta winding by a factor of _/3 . Each winding at one end is connected to a common end, like a neutral point - therefore, as a whole there are four wires.
FIG. 4 Three-phase transformer delta connection on primary side.
A three-wire source as obtained from a delta winding may cause problems when feeding to a star connected unbalanced load. Because of the unbalance, the load neutral will shift and cause change of voltage in the individual phases of the load. It is better to use a star connected four-wire source in such cases. Three-wire sources are best suited for balanced loads such as motors.
FIG. 5 Three-phase four-wire transformer star connection
Relationship between line and phase voltages:
V_L = _/3 Vph
Where:
V_L = line voltage
V_ ph = phase voltage.
Relationship between line and phase currents:
I_L = I_ph
Where
I_L = line current
Iph= phase current.
Output power of a transformer in kW:
Where
V_L= line voltage
I_L= line current
cos Φ = power factor.
3. Possible combinations of star and delta
The primary and secondary windings of three single-phase transformers or a three-phase transformer can be connected in the following ways:
• Primary in delta - secondary in delta
• Primary in delta - secondary in star
• Primary in star - secondary in star
• Primary in star - secondary in delta.
FIG. 6 shows the various types of connections of three-phase transformers. On the primary side, V is the line voltage and I the line current. The secondary sideline voltages and currents are determined by considering the ratio of the number of turns per phase (a = N1/N2) and the type of connection. Table 1 gives a quick view of primary-line voltages and line currents and secondary-phase voltages and currents. The power delivered by the transformer in an ideal condition irrespective of the type of connection = 1.732 VL, IL assuming cosf = 1.
1.7 Testing transformers
The following tests are carried out on transformers:
• Measurement of winding resistance
• Measurement of Voltage ratio
• Test phasor voltage relationship
• Measurement of impedance voltage, short-circuit impedance and load loss
• Measurement of no load loss and no load current
• Measurement of insulation resistance
• Dielectric test
• Temperature rise.
FIG. 6 Types of connections for three-phase transformers: (a) Delta-delta
connection; (b) Delta-star connection; (c) Star-star connection; (d) Star-delta
connection
Table 1 Voltage and current transformation for different three-phase transformer connections Why is transformer rating defined in kVA?
A transformer, unlike a motor, has no mechanical output (expressed in kW). The current flowing through it can vary in power factor, from zero PF lead (pure capacitive load) to zero PF lag (pure inductive load) and is decided by the load connected to the secondary.
The conductor of the winding is rated for a particular current beyond which it will exceed the temperature for which its insulation is rated irrespective of the load power factor.
Similarly, the voltage that can be applied to a transformer primary winding has a limit.
Exceeding this rated value will cause magnetic saturation of the core leading to distorted output with higher iron losses.
It is therefore usual to express the rating of the transformer as a product of the rated voltage and the rated current (VA or kVA). This however does not mean that you can apply a lower voltage and pass a higher current through the transformer. The VA value is bounded individually by the rated voltage and rated current.
Why is power transmitted at higher voltages?
When a particular amount of power has to be transmitted over a certain distance the following aspects need to be considered to decide the best voltage.
A lower voltage the need higher size conductors to withstand the high current involved.
There is a physical limitation to the size of conductor. Also, the percentage voltage drop may become excessive. A higher voltage will make the conductor size manageable and reduce the voltage drop (% value) but the cost of the line becomes high due to larger clearances needed.
The best voltage will be one in which the total operational cost which the sum of the annualized capital cost (of the line) and the running cost due to power loss in the line is the lowest. In practice, it is found that transmitting bulk power over long distances is economical if done in the HV range. The actual voltage will vary based on the distance and quantum of power. Distribution circuits where typically the amount of power and distance involved are both lower, the best voltage is in the MV range (11, 22 or 33 kV). For the same reason, low voltage circuits are found only in local sub-distribution circuits.