CA2627 Building Science Instructor: Jiayu Chen Ph.D. Lecture 06 Transformers, three phase AC...

CA2627 Building Science

Instructor: Jiayu Chen Ph.D.

Lecture 06 Transformers, three phase AC circuits, building power distribution

© Jiayu Chen, Ph.D. 2

Learning Objectives

1. Analyze the ideal transformer; compute primary and secondary currents and voltages and turns ratios. Calculate reflected sources and impedances across ideal transformers.

2. Understand maximum power transfer.3. Learn three-phase AC power notation; compute load currents and voltages for

balanced wye and delta loads.4. Understand the basic principles of residential electrical wiring and of electrical

safety.


Electricity supply in Hong Kong

Ref.: Supply rules from CLPhttps://www.clponline.com.hk/MyHome/CustomerService/OpenAccount/SupplyRules/Pages/Default.aspx?lang=enSupply rules from HK Electrichttp://www.heh.com/NR/rdonlyres/F98E0121-03CA-4C4F-B2DA-F77774833876/0/SupplyRule_en_2008.pdf

Power Distribution

https://www.clponline.com.hk/MyHome/CustomerService/OpenAccount/SupplyRules/Pages/Default.aspx?lang=en

https://www.clponline.com.hk/MyHome/CustomerService/OpenAccount/SupplyRules/Pages/Default.aspx?lang=en

http://www.heh.com/NR/rdonlyres/F98E0121-03CA-4C4F-B2DA-F77774833876/0/SupplyRule_en_2008.pdf

http://www.heh.com/NR/rdonlyres/F98E0121-03CA-4C4F-B2DA-F77774833876/0/SupplyRule_en_2008.pdf


EMSD Code of PracticeEMSD Code of Practice for Electricity (Wiring) Regulations, 2009 Edition(http://www.emsd.gov.hk/emsd/e_download/pps/pub/COP_E.pdf)

Power Distribution

http://www.emsd.gov.hk/emsd/e_download/pps/pub/COP_E.pdf


Electricity is supplied by the HKE or CLP in Hong Kong. The nominal values are:

• Frequency • Phase supply

o for a single phase supply, a nominal voltage of 220 volts (root mean square value) plus or minus 6% between a phase conductor and neutral conductor;

o for a 3 phase supply, using a 3 phase 4 wire system, a nominal voltage of 380 volts plus or minus 6% (root mean square value) between phase conductors and 220 volts (root mean square value) plus or minus 6% between phase and neutral conductors;

o for a 3 phase supply, a nominal voltage of 11,000 volts (root mean square value) plus 10% or minus 2% between phase conductors; and

o for a 3 phase supply, a nominal voltage of 132,000 volts (root mean square value) plus 10% or minus 2% between phase conductors.

Power Distribution


Beyond the generation plant, an electric power network distributes energy to several substations. This network is usually referred to as the power grid.

Power Distribution


Transformers

A transformer is a device that couples two AC circuits magnetically rather than through any direct conductive connection and permits a “transformation” of the voltage and current between one circuit and the other (for example, by matching a high-voltage, low-current AC output to a circuit requiring a low-voltage, high current source).


Transformers

The ideal transformer consists of two coils that are coupled to each other by some magnetic medium. There is no electrical connection between the coils. The coil on the input side is termed the primary, and that on the output side the secondary.

Let us assume the primary coil is wound so that it has turns, while the secondary has turns. We define the turns ratio N as

An ideal transformer multiplies a sinusoidal input voltage by a factor of N and divides a sinusoidal input current by a factor of N.


Transformers

If N is greater than 1, the output voltage is greater than the input voltage and the transformer is called a step-up transformer.

If N is less than 1, then the transformer is called a step-down transformer. A transformer with N = 1 is called an isolation transformer and may perform a

very useful function if one needs to electrically isolate two circuits from each other.

Note: • Any DC currents at the primary will not appear at the secondary coil.• An important property of ideal transformers is conservation of power• We can easily verify an ideal transformer by


Example:We require a transformer to deliver 500 mA at 24 V from a 120 V rms line source. How many turns are required in the secondary? What is the primary current?

Assume we have the first coil with 3000 turns,

We will have

Knowing the turns, we can now compute the primary current,

Transformers


TransformersIn many practical circuits, the secondary is tapped at two different points, giving rise to two separate output circuits. The most common configuration is the center-tapped transformer, which splits the secondary voltage into two equal voltages. The most common occurrence of this type of transformer is found at the entry of a power line into a household, where a high-voltage primary is transformed to 240 V, and split into two 120-V lines.

110 V vs 220 V ?


Transformers

Impedance Reflection

A very common and rather general situation is that where an AC source, represented by its Thévenin equivalent, is connected to an equivalent load impedance by means of a transformer.

At the primary connection, we can have


Impedance Reflection

Transformers

We will have

And apply Thévenin equivalent

Thus the load sees the source impedance multiplied by a factor of , this is called impedance reflection.


Maximum power transfer

Transformers

The power transfer efficiency is defined as:

Recall that the maximum power to be transferred form the source to the load, the impedance must be matched (Proof was omitted)Conclusion: We know

That is

Where is the conjugate of the source impedance

When the load impedance is equal to the complex conjugate of the source impedance, the load and source impedances are matched and maximum power is transferred to the load.


Example:Find the transformer turns ratio and load reactance that results in maximum power transfer in the circuit. ; ; ; ;

For the maximum power transfer, we will require

Thus,

Further, to cancel the reactive power we require that

And

Thus the load reactance should be a capacitor with the value of

Transformers


TransformersA substantial amount, 20% of the power from the source, is lost in the line if no transformers are used. Since power goes into heating up the line (line has resistance), and P ~ I2R, the loss in the line can be reduced by reducing the current in the line, by using transformers. Transformers at the source step up the voltage and step down the current, keeping the power constant, before transmission. At the load, we use a step-down transformer to step down the voltage and step up the current.


TransformersExample:If the transformer delivers 50 A at 110 V rms with a certain resistive load, what is the power transfer efficiency between the source and the load?

The transformer primary voltage

The transformer primary current

The current through the inductance

The source current is (add phasor currents)

The source power is

Power transfer efficiency


3-phase AC circuits

Generation of Three Phase AC ElectricityThe generation of electrical power is more efficient in 3-phase systems. A 3-phase system employs three balanced voltages, equal in magnitude and differing in phase by 360°/3 = 120°.

http://www.fam-oud.nl/~plugsocket/Generator_3phase.html

http://ele.aut.ac.ir/~wind/en/tour/wtrb/syncgen.htm

http://www.launc.tased.edu.au/online/sciences/physics/3phase/threeph.htm








As the rotor rotates counterclockwise at 50 r/sec, its magnetic field cuts the armature windings, thereby inducing in them the sinusoidal voltages. These voltages have peaks at one-third of a period apart, or 120° apart, because the armature windings are displaced by 120° in space. As a result, the alternator produces three voltages of the same rms value, but with phase differences of 120°.

3-phase AC circuits

In HK: phase voltage = 220 V line voltage = 380 V


A three-phase circuit generates, distributes, and uses energy in the form of three voltages equal in magnitude and symmetric in phase. The three similar portions of a three-phase system are called phases. .Line voltage, abbreviated from line-to-line voltageBecause the voltage in phase aa' reaches its maximum first, followed by that in phase bb' and then by that in phase cc', we say the phase rotation is abc. The three voltages are said to be balanced voltages because they have identical amplitude, Vm, and frequency, ω, and are out of phase with each other by exactly 120°.

The positive phase sequence is abc; the sequence acb is called the negative phase sequence.

3-phase AC circuits


3-phase AC circuits

3-phase circuits and machines possess some unique advantages:

• The power transmitted in a three-phase circuit is constant or independent of time rather than pulsating, as it is in a single-phase circuit.

• Three-phase motors start and run much better than do single-phase motors.• The transmission of electrical power is more efficient in 3-phase systems

employing three sinusoidal voltages. For example, for the addition of one more conductor, a three-phase supply provides 73% more power than a single-phase supply. With a three-phase supply the voltage between two line or phase cables is √3 = 1.73 times that between the neutral and any one of the line cables, i.e. 220 volts x 1.73 =380 volts.


3-phase AC circuits

Y and Δ connectionsReferring to the generator, there are six terminals and three voltages, va, vb and vc. We use phasor notation and assume that each phase winding provides a source voltage in series with a negligible impedance. Under these assumptions, there are two ways of interconnecting the three sources.

Y connectionThe Y connection selects terminals a', b', and c' and connects them together as neutral. The common terminal is called the neutral terminal and is labeled n. The neutral terminal may or may not be available for connection. Balanced loads result in no current in a neutral wire, and thus it is often not needed.


3-phase AC circuits

Δ connectionThe Δ source connection is seldom used in practice because any slight imbalance in magnitude or phase of the three-phase voltages will not result in a zero sum. The result will be a large circulating current in the generator coils that will heat the generator and depreciate the efficiency of the generator.


3-phase AC circuits

The line-to-line voltage, , of the Y-connected sources is

And

Therefore, in a Y connection, the line-to-line voltage is times the phase voltage and is displaced in phase. The line current is equal to the phase current.The relation can also be obtained from the sine law,

Y-connected source


Example:The Y-connected three-phase voltage source V rms. Find the line-to-line voltage

Answer: V rms

3-phase AC circuits


3-phase AC circuitsY-to-Y circuitThis three-phase circuit consists of three parts: a three-phase source, a three-phase load, and a transmission line.

4-wire Y-to-YThe transmission line used to connect the source to the load consists of four wires, including a wire connecting the neutral node of the source to the neutral node of the load.

3-wire Y-to-YThe three-phase source is connected to the load using three wires, without a wire connecting the neutral node of the source to the neutral node of the load.


3-phase AC circuits

4-wire Y-to-YEach impedance of the three-phase load is connected directly across a voltage source of the three-phase source. Therefore, the voltage across the impedance is known, and the line currents are easily calculated as:

The current in the wire connecting the neutral node of the source to the neutral node of the load (the neutral wire) is:

The total average power delivered by the three-phase source to the three-phase load is calculated by adding up the average power delivered to each impedance of the load.

Where, eg. is the power absorbed by . Since we can calculate , we can then calculate .Denote the phase voltages of the Y-connected source as

Notice that we are using effective values because the units of are V rms


3-phase AC circuits4-wire Y-to-YFor a balanced load, , the load is said to be a balanced load. The currents are:

The line currents have equal magnitudes and differ in phase by 120°. The current in the neutral wire (which connects the neutral node of the source to the neutral node of the load) is:

This shows that the neutral wire has no current.Remember that we are using eff or rms values. The average power delivered to the load is

The average power delivered to the load can be determined by calculating PA and multiplying by 3


3-wire Y-to-YA 3-wire Y-Y circuit would not necessarily have the neutral current , and the node equation at node N needs to be solved. However, it can be shown that for a balanced 3-wire Y-Y circuit, the neutral current . The balanced three-wire Y-to-Y circuit acts like the balanced four-wire Y-to-Y circuit. The line currents and the average power delivered to the load are as given above.

The per-phase equivalent circuitFor balanced circuits, all 3 phases are similar, and we need only calculate one line current, say IaA. The per-phase equivalent circuit consists of the voltage source and impedances in the one of the phases. The neutral nodes, n and N, are connected by a short circuit in the per-phase equivalent circuit to indicate that VnN=0 in a balanced Y-to-Y circuit. The per-phase equivalent circuit can be used to analyze either 3-wire or 4-wire balanced Y-to-Y circuits, but it can only be used for balanced circuits.

3-phase AC circuits


3-phase AC circuits

The per-phase equivalent circuit

The Balanced Y-to-Y Circuit


3-phase AC circuits

Example:Determine the complex power delivered to the three-phase load of a four-wire Y-to-Y circuit. The phase voltages of the Y-connected source are V rms, V rms, and V rms. The load impedances are

We need to calculate only one line current, , and the complex power , delivered to only one of the load impedances, . The power delivered to the three-phase load is . We begin by calculating as

The complex power delivered to is

The complex power delivered to the three-phase load is


Example:Determine the complex power delivered to the three-phase load of a four-wire Y-to-Y circuit. The phase voltages of the Y-connected source are V rms, V rms, and V rms. The load impedances are

The line currents of an unbalanced four-wire Y-to-Y circuit are calculated using,

SoThe complex power delivered to is

Similarly we can find and

The total complex power is

3-phase AC circuits


3-phase AC circuits

Y-Δ transformations The Δ-to-Y and Y-to-Δ transformations convert Δ-connected loads to equivalent Y-connected loads and vice versa.


Y-Δ Circuit

3-phase AC circuits

We use the phasor diagram. In a Δ connection, the line current is √3 times the phase current and is displaced -30° in phase. The line-to-line voltage is equal to the phase voltage.Using sine law, We will have

Or


3-phase AC circuits

Balanced 3-phase circuitWe have only two possible practical configurations for three-phase circuits, Y-to-Y and Y-to-Δ and we can convert the latter to a Y-to-Y form. Thus, a practical three-phase circuit can always be converted to the Y-to-Y circuit.

Y-to-Δ circuit Y-to-Y circuit The per-phase equivalent circuit


3-phase AC circuits

Instantaneous and Average Power in a Balanced 3-Phase LoadOne advantage of three-phase power is the smooth flow of energy to the load. Consider a balanced load with resistance R. Then the instantaneous power is

Where , and the other two-phase voltage have a phase of .Furthermore,

Therefore,

The bracketed term is equal to zero for all time. Hence,

The instantaneous power delivered to a balanced three-phase load is a constant.


An electric connection to the general mass of earth, whose dimensions are very large in comparison to the electrical system being considered.The terms ‘Ground’ and ‘Grounding’ are synonymous with ‘Earth’ and ‘Earthing’ and are more prevalent in some countries like North America.

Earthing System - AdditionalEarthing System:


Earth Electrode 1 : • Electrical connect to earth• Independent earth electrode for each

system/equipment• Maintain sufficient distance, 3.5m or twice of

driven length, from on another without significant affect the potential of the others

Main Earthing Terminal 6 :• Connect group of protective conductors to the

earth electrode 1 through earth conductor 2

Protective / bonding Conductor 3 :• Exposed conductive parts• Conductive part of electrical installation - not a

live part• Extraneous conductive parts 4• Conductive part not forming part of the electrical

installation

Earthing System - Additional


Earthing System - AdditionalResidual Current Devices (RCDs)

The RCD is a circuit breaker which continuously compares the current in the phase with that in the neutral. The difference between the two will flow to earth, because it has left the supply through the phase and has not returned in the neutral.

The purpose of the residual current device is to monitor the residual current and to switch off the circuit quickly if it rises to a preset level.

When the amount of residual current, and hence of tripping current, reaches a pre-determined level, the circuit breaker trips, opening the main contacts and interrupting the circuit.

1

2

3


Lightning System - Additional

Thunder Cloud• Unstable upper atmosphere before lightning generation• Positive charge and negative charge of thunder cloud separated• Light weight positive charge at higher altitude, heavier negative charge at the base of the

cloud

Lightning Discharge• May be cloud to cloud or cloud to ground• Faintly luminescent leader channel from

cloud toward to ground into many fingers• Rapid escalating electric field at ground

cause streamer move upward• Discharge commenced the ionized channel

completed at the junction of the leader and streamer

Useful lighting projection system wiki:http://www.electrical-installation.org/enwiki/General_rules_of_lightning_protection

http://www.electrical-installation.org/enwiki/General_rules_of_lightning_protection

http://www.electrical-installation.org/enwiki/General_rules_of_lightning_protection


The Surge Protection Device (SPD) is a component of the electrical installation protection system.

This device is connected in parallel on the power supply circuit of the loads that it has to protect It can also be used at all levels of the power supply network. This is the most commonly used and most efficient type of overvoltage protection.

Lightning System - Additional

Note: Surge Protection Devices (SPD) are used for electric power supply networks, telephone networks, and communication and automatic control buses.

CA2627 Building Science Instructor: Jiayu Chen Ph.D. Lecture 06 Transformers, three phase AC...

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