Sizing of power cables for circuit breaker controlled feeders (technical article by mr. Asif Eqbal)

Continued from article Sizing of power cables for circuit breaker controlled feeders (part 2)

3. Criteria Starting and running voltage drops in cable

This criterion is applied so that the cross sectional area of the cable is sufficient to keep the voltage drop (due to impedance of cable conductor) within the specified limit so that the equipment which is being supplied power through that cable gets at least the minimum required voltage at its power supply input terminal during starting and running condition both.

Cables shall be sized so that the maximum voltage drop between the supply source and the load when carrying the design current does not exceed that which will ensure safe and efficient operation of the associated equipment. It is a requirement that the voltage at the equipment is greater than the lowest operating voltage specified for the equipment in the relevant equipment standard.

So before starting with calculation for voltage drop let us first analyze that what is the permissible voltage drop as per relevant standards and guidelines and what is the possible logic behind selecting these values as the permissible values.

Indian standard 1255- CODE OF PRACTICE FOR INSTALLATION AND MAINTENANCE OF POWER CABLES UP TO AND INCLUDING 33 kV RATING in its clause 4.2.3.4 mentions the permissible value for different cross sectional sizes of Aluminium conductor in volts/kM/Ampere for cables from voltage grade of 1.1kV till 33kV. Since we calculate voltage drop in terms of percentage of source voltage, this clause is not very widely used in basic as well as detailed engineering fraternity.

Its complex unit requires to be multiplied by cable length and ampacity. However one can definitely check for any cable size and length, what value is obtained in terms of percentage?

IEEE standard 525 – Guide for the Design and Installation of Cable Systems in Substations in its annexure C, clause number C3 mentions that Voltage drop is commonly expressed as a percentage of the source voltage. An acceptable voltage drop is determined based on an overall knowledge of the system. Typical limits are 3% from source to load center, 3% from load center to load, and 5% total from source to load. These values are indicated diagrammatically below.

6.6kV substation layout

So far we have understood:

1. What are primary and secondary feeders?
2. What are the permissible values of voltage drop in cables for different types of feeder?
3. What are the governing standards for permissible voltage drop values?

Well answer to this lies in the fact that there is a rule of thumb that 2 percent of voltage is lost at terminations and other points like cable joints in a circuit between the power source and the load. Such voltage loss are not indicated and accounted for in cable sizing calculation. The cable sizing calculation only considers the voltage drop in cable conductor from source to load. It is prudent to make certain that the designed voltage drop does not exceed 5% to avoid problems after installation.

It is much more costly to remove and replace an existing cable or piece of equipment that is under rated versus the cost of equipment and cables designed with a degree of extra size and avoid problems due to inadequate voltage at the load.

The NEC recommends or requires a maximum voltage drop of 5%, but realistically connection impedances, deterioration of terminals due to heat and age, etc; add resistance to the total circuit.

Difference between voltage drop and voltage dip?

A voltage dip is a decrease in the magnitude of a supply voltage having the duration of some cycles to seconds. A voltage dip is a power quality problem which occurs due to:

Sudden change in the load, such as suddenly switching ON the large inductive load or any temporary fault in the utility side of the system and impedance of source (Transformer)

Voltage dip is a sort of transient negative side fluctuation of bus voltage which is experienced by all other loads connected to that bus, however it is caused by switching ON of any one single load of large magnitude. It is mainly experienced as a decrease in bus voltage due to starting of large motor. Since bus voltage decreases so other loads connected to that bus experience a fluctuation of voltage. We often come across this phenomenon at our home also when due to sudden switching ON of refrigerator or an air condition the voltage fluctuates.

Even in case of utility the addition of a large load will normally be scheduled with the utility so they can project the time of day that a load, such as an office or industrial plant, is turned on. Whereas the voltage drop is the drop in supply voltage before it reaches to the load. It is totally because of impedance of the connecting cable. It is because of this reason that for checking the adequacy of transformer MVA capacity and suitability of its percentage impedance that we conduct voltage dip calculation after sizing of transformer. Same can also be done by motor starting studies.

Now let us come back to the original topic that is voltage drop and its calculation. As we already know about the permissible values of voltage drop so let us calculate and derive an expression for the same in terms of impedance of cable, cable length and source voltage.

Let us consider a reference phasor as V. Direction of V as X axis and perpendicular to V as Y axis. Approximation OC = OF which is almost equal to OE as EF can be neglected because EF << OF

X component of voltage drop:
= Vdx = AE = AD + DE = AD + BG
= IRCosф + IX Sinф (Equation-1)

Y Component of voltage drop:
= Vdy = CE = CG-EG
= CG-BD
= IXCosф – IRSinф (Equation-2)

X component of VS:
VSx = OE = √ (OC2 –CE2)

VSx = √ VS2 – Vdy2 (Equation-3)

V = OE –AE = VSx – Vdx (Equation-4)

Now Voltage drop Vd is:
Vd = VS – V = VS – (VSx –Vdx) (Putting the value of V from equation-4)
Vd = VS + Vdx – VSx
Vd = VS + Vdx – VS2 – Vdy2 Equation -5 (Putting the value of VSx from equation-3)

Now substituting the values of Vdy and Vdx from equation-2 and equation-1 respectively:

Vd = VS + (IRCosф + IX Sinф) – √ (VS2 – (IXCosф – IRSinф)2 (Equation -6)

Equation-6 is the final expression for voltage drop where:

VS = the supply voltage
I = the load current
R = the resistance of cable conductor in Ohms/kM
X = the reactance of cable conductor in Ohms/kM

The above equation for voltage drop is recommended for exact calculation as per IEEE-241, Recommended Practice for Electric Power Systems in Commercial Buildings, clause number 3.6.1 and IEEE-141, Recommended Practice for Electric Power Distribution for Industrial Plants, clause number 3.11.1

Many consultants recommend the use of above formula for exact calculation of voltage drop in cables meant for power plants. However as per IEEE-525, Guide for the Design and Installation of Cable Systems in Substations, equation number C.2b of Annexure C recommends the use of following formula:

Vd = IRCosф + IXSinф (Equation-7)

Since cable length is usually expressed in meters so before substituting in above expression proper unit conversion should be done.

Sometimes multiple runs of cable are used so number of runs should come as division factor in above expression for equivalent resistance. Multiplying factor of √3 is to be taken for 3 phase system.

Resistance of cable conductor

Resistance of cable conductor is calculated from resistivity value of conductor material at 20 C, which is a standard temperature for testing adopted by all cable manufacturers. Resistivity is concerted into resistance by following formula:

Rdc = ρ X L / A

Where:
ρ = Resistivity at 20 C
L= 1 kM length
A = Cross sectional area of conductor.

This resistance is DC resistance at 20C. It is converted to DC resistance at 90 C by the following conversion formula:

Rt = R₂₀ (1 + αT)

Where:
R₂₀ = Resistance at 20 C
α = Coefficient of linier expansion of Aluminium
T = Temperature at which resistance is to be calculated

For sizing of cables for AC system the resistance of conductor to be selected should be AC resistance at 90 C and not DC resistance. DC resistance is selected for sizing of cables for DC system like battery, battery charger etc….

A conductor offers a greater resistance to a flow of alternating current than it does to direct current. When the term “ac resistance of a conductor” is used, it means the DC resistance of that conductor plus an increment that reflects the increased apparent resistance in the conductor. This increment is mainly caused by:

Skin effect

This results in a decrease of current density toward the center of a conductor. A longitudinal element of the conductor near the center is surrounded by more magnetic lines of force than is an element near the rim.

Thus, the counter-emf is greater in the center of the element. The net driving emf at the center element is thus reduced with consequent reduction of current density. In simple terms the current tends to crowd toward the outer surface.

Proximity Effect

In closely spaced ac conductors, there is a tendency for the current to shift to the portion of the conductor that is away from the other conductors of that cable. This is called proximity effect. The flux linking the conductor current in one conductor is distorted by the current in a nearby conductor which in turn causes a distortion of the cross-sectional current distribution.

The above mentioned two factors are for increased resistance is generally expressed as the AC/DC resistance ratio. There are other magnetic effects can also cause an additional increase in AC/DC resistance ratios. However we are not going to discuss them in this article. ac/dc ratio is determined by skin effect factor and proximity effect factor.

Rac = (AC/DC) ratio x Rdc

For frequencies higher than 60 hertz, a correction factor for the values of resistance is applied as follows:

x = 0.027678 √  f/Rdc

Where:
f = frequency in hertz
Rdc = conductor DC resistance at operating temperature, in ohms per 1000 feet. The inductance of a multi-conductor cable mainly depends on the thickness of the insulation over the conductor.

Inductive reactance of cable conductor

The inductive reactance of an electrical circuit is based on Faraday’s law. That law states that the induced voltage appearing in a circuit is proportional to the rate of change of the magnetic flux that links it. The inductance of an electrical circuit consisting of parallel conductors, such as a single-phase concentric neutral cable may be calculated from the following equation:

XL = 2π f (0.1404 log S/r + 0.153) x 10^-3

Where:
XL = Ohms per 1000 feet
S = Distance from the center of the cable conductor to the center of the neutral
r = Radius of the center conductor
S and r must be expressed in the same unit, such as inches.

Now, in technical articles part-2 and part-1 we had considered the sizing of cable for DOL motor feeder rated at 160kW supplied by 415V. Minimum required area was calculated as 3CX240 Sq mm Al, XLPE, however due to continuous current requirement the cable cross section required was calculated as 3CX300 Sq mm.

Now let us check the running and starting voltage drop for the same using exact equation-6 as well as approximated equation-7.

• Resistance of conductor of 3CX300 mm Sq Al, XLPE cable = 0.128 Ohms/kM (From manufacturers catalog)
• Reactance of conductor of 3CX300 mm Sq Al, XLPE cable = 0.071 Ohms/kM (From manufacturers catalog)
• Cable length = 150Mtr (assumed for this calculation)
• Running power factor of motor = 0.85
• Starting power factor of Motor = 0.3
• Starting current of motor = 6 times rated current

Assuming a drop of 1.5% in the cable for incomer feeder, that is from (source) to load center (PCC) which we have not calculated here for sake of simplicity and space limitation.

Modifying equation-6 for proper units:

L = length of cable = 150 Mtr
N = Number of parallel runs of cable = 1

Substituting the values all the values in the above equation:

Now we can verify the above obtained result by the approximate formula so that we can analyze the amount of approximation involved in using that formula.

Modifying equation-7 for proper units:

L = length of cable = 150 Mtr
N = Number of parallel runs of cable = 1

Substituting the values all the values in the above equation

Hence we can see that even the approximate formula does give accuracy till one place of decimal and can be used. We can do a small case study by varying the cable length from 50 Mtrs to 150 Mtrs in steps of 15 Mtrs and analyze the difference in voltage drop by the use of two formulas.

Hence we can observer that voltage drop only after one place of decimal as obtained by exact formula is on lesser side where as approximate formula till the route length of 100 Mtrs gives voltage drop on higher side. For route length above 100 Mtrs both the formulas almost converge to give same value of running voltage drop.

Hence it is advisable to go for exact formula as far as possible however the approximate formula also gives the fairly accurate result.

With the completion of third and final criteria of voltage drop we come to the end of sizing of power cables for breaker controlled motor feeders supplied by 415V supply. With this methodology readers can develop a formulated excel sheet for sizing of power cables for circuit breaker controlled feeders.

GE Watthour Meter

Power measurement in AC circuits can be quite a bit more complex than with DC circuits for the simple reason that phase shift complicates the matter beyond multiplying voltage by current figures obtained with meters.

What is needed is an instrument able to determine the product (multiplication) of instantaneous voltage and current. Fortunately, the common electrodynamometer movement with its stationary and moving coil does a fine job of this.

Three phase power measurement can be accomplished using two dynamometer movements with a common shaft linking the two moving coils together so that a single pointer registers power on a meter movement scale. This, obviously, makes for a rather expensive and complex movement mechanism, but it is a workable solution.

An ingenious method of deriving an electronic power meter (one that generates an electric signal representing power in the system rather than merely move a pointer) is based on the Hall effect.

Figure 1 - Hall effect: Voltage is proportional to current and strength of the perpendicular magnetic field.

The voltage generated across the width of the flat, rectangular conductor is directly proportional to both the magnitude of the current through it and the strength of the magnetic field. Mathematically, it is a product (multiplication) of these two variables.

The amount of “Hall Voltage” produced for any given set of conditions also depends on the type of material used for the flat, rectangular conductor. It has been found that specially prepared “semiconductor” materials produce a greater Hall voltage than do metals, and so modern Hall Effect devices are made of these.

It makes sense then that if we were to build a device using a Hall-effect sensor where the current through the conductor was pushed by AC voltage from an external circuit and the magnetic field was set up by a pair or wire coils energized by the current of the AC power circuit, the Hall voltage would be in direct proportion to the multiple of circuit current and voltage.

Having no mass to move (unlike an electromechanical movement), this device is able to provide instantaneous power measurement: (Figure 2)

Figure 2 - Hall effect power sensor measures instantaneous power.

Not only will the output voltage of the Hall effect device be the representation of instantaneous power at any point in time, but it will also be a DC signal! This is because the Hall voltage polarity is dependent upon both the polarity of the magnetic field and the direction of current through the conductor.

If both current direction and magnetic field polarity reverses - as it would ever half-cycle of the AC power – the output voltage polarity will stay the same.

If voltage and current in the power circuit are 90o out of phase (a power factor of zero, meaning no real power delivered to the load), the alternate peaks of Hall device current and magnetic field will never coincide with each other: when one is at its peak, the other will be zero. At those points in time, the Hall output voltage will likewise be zero, being the product (multiplication) of current and magnetic field strength. Between those points in time, the Hall output voltage will fluctuate equally between positive and negative, generating a signal corresponding to the instantaneous absorption and release of power through the reactive load.

The net DC output voltage will be zero, indicating zero true power in the circuit. Any phase shift between voltage and current in the power circuit less than 90o will result in a Hall output voltage that oscillates between positive and negative, but spends more time positive than negative. Consequently there will be a net DC output voltage.

Conditioned through a low-pass filter circuit, this net DC voltage can be separated from the AC mixed with it, the final output signal registered on a sensitive DC meter movement. Often it is useful to have a meter to totalize power usage over a period of time rather than instantaneously. The output of such a meter can be set in units of Joules, or total energy consumed, since power is a measure of work being done per unit time.

Or, more commonly, the output of the meter can be set in units of Watt-Hours.

The “motor” used in these meters has a rotor made of a thin aluminum disk, with the rotating magnetic field established by sets of coils energized by line voltage and load current so that the rotational speed of the disk is dependent on both voltage and current.

Resource: Lessons in electric circuits – volume II

Instrument transformers - ABB

Instrument transformers (ITs) are designed to transform voltage of current from the high values in the transmission and distribution systems to the low values that can be utilized by low voltage metering devices. There are three primary applications for which ITs are used: metering (for energy billing and transaction purposes); protection control (for system protection and protective relaying purposes); and load survey (for economic management of industrial loads).

Depending on the requireinents for those applications, the IT design and construction can be quite different. Generally the metering ITs require high accuracy in the range of normal operating voltage and current. Protection ITs require linearity as a wide range of voltages and currents. During a disturbance, such as system fault or overvoltage transients, the output of the IT is used by a protective relay to initiate an appropriate action (open or close a breaker, reconfigure the system, etc) to mitigate the disturbance and protect the rest of the power system.

Instrument transformers are the most common and economic way to detect a disturbance. Typical output levels of instrument transformers are 1-5 amperes and 115-120 volts for CTs and VTs, respectively. There are several classes of accuracy for instrument transformers defined by the IEEE, CSA, IEC, and ANSI standards.

Figure 1: Current and Voltage Transformer Symbols and Simplified Concepts

Figure 1 presents a conceptual design of CTs and VTs.

Figure 2 shows how the polarity markers are used to keep the direction of current flow as the meters exactly the same, as if the primary circuit was carried through the meters. Grounding of the secondary circuit is most important, but in complicated three-phase connections, the best point to ground is not always easily determined.

Figure 2: Instrument Transformer Connections

A The current transformer is designed to connect in series with the line to transform the line current to the standard 5 amperes suitable for the meter or relay. The voltage transformer is designed to connect in parallel with the line to transform the line voltage to 115 or 120 volts suitable for the meter or relay.

To keep the voltage at the meters and relays at a safe value, the secondary circuit must be grounded.

B The polarity markers indicate the relative instantaneous directions of current in the windings. The polarity, or instantaneous direction of current, is of no significant difference for current-operated or voltage-operated devices.

Correct operation of current-current, voltage-voltage, or current-voltage devices usually depends on the relative instantaneous directions.

Instrument Transformers

Instrument transformers are special types of transformers intended to measure currents and voltages. The common laws for transformers are valid.

Current transformers

For a short-circuited transformer the following valid:

This equation gives current transformation in proportion to the primary and secondary turns. A current transformer is ideally a short-circuited transformer where the secondary terminal voltage is zero and the magnetizing current is negligible.

Voltage transformers

For a transformer in no bad the following is valid:

This equation gives voltage transformation in proportion to the primary and secondary turns. A voltage transformer is deally a transformer under no-load conditions where the load current is zero and the voltage drop is only caused by the magnetizing current and is thus negligible.

Types of Instrument Transformer Construction

Types of Instrument Transformer Construction

Resources:

• ABB Instrument Transformers - Technical Information and Application Guide
• INSTRUMENT TRANSFORMERS – PART-1 CURRENT & VOLTAGE TRANSFORMERS (FOR ELECTRIC T&D, POWER PLANTS &, INDUSTRIAL APPLICATIONS)

Sizing of power cables for circuit breaker controlled feeders (part 2)

Continued from article Sizing of power cables for circuit breaker controlled feeders (part 1)

2. Criteria-2 Continuous current capacity (Ampacity)

This criterion is applied so that cross section of the cable can carry the required load current continuously at the designed ambient temperature and laying condition. Ampacity is defined as the current in amperes a conductor can carry continuously under the conditions of surrounding medium in which the cables are installed. An ampacity study is the calculation of the temperature rise of the conductor in a cable system under steady-state conditions.

Cable ampacity, if required to be calculated than it is calculated as per the following equation givenin IEEE -399, section 13.

This equation is based on Neher-McGrath method where,

• Tc’ – allowable conductor temperature (ºC)
• Ta’ – ambient temperature (either soil or air) (ºC)
• ∆Td – temperature rise of conductor due to dielectric heating (ºC)
• ∆Tint – temperature rise of the conductor due to interference heating from adjacent cables (ºC)
• Rac – electrical ac resistance of conductor including skin effect, proximity and temperature effects (µ_/ft)
• R’ca – effective total thermal resistance of path between conductor and surrounding ambient to include the effects of load factor, shield/sheath losses, metallic conduit losses, effects of multiple conductors in the same duct etc (thermal- Ωft, ºC-cm/W).

However please note that while sizing a power cable we never calculate the ampacity. The above equation is used to analyze the cable ampacities of unique installations. Standard ampacity tables are available for a variety of cable types and cable installation methods and can be used for determining the current carrying capacity of a cable for a particular application.

These standards provide tabulated ampacity data in manufacturers catalog for cables installed in air, in ductbank,  directly buried or in trays for a particular set ofconditions clearly defined.

It is because of this reason that we need to give the reference of manufacturers catalog from where the ampacity  values are picked up.

Now once the current carrying capacity of a cable is found from standard catalog; we convert that rated capacity (Ampacity) into actual laying condition. The standard current ratings for cables are modified by the application of suitable multiplying factors to account for the actual installation conditions. Hence we define one more term here called ampacity deration factor.

Ampacity duration factor is defined as the product of various factors which accounts for the fraction decrease in the ampacity of the conductor. Those factors and physical condition deriving them are as follows:

1. K1= Variation in ambient air temperature for cables laid in air / ground temperature for cables laid underground.
2. K2 = Cable laying arrangement.
3. K3 = Depth of laying for cables laid direct in ground.
4. K4 = Variation in thermal resistivity of soil.

Now from where do we get these multiplying factors to find the overall ampacity deration factor? Againwe get these values from manufacturers catalog because manufacturer of the cable is in best position to conduct thepractical experiments and test on the cables and find the percentage/fractional decrease in current carrying capacity of the cable in various conditions.

For better understanding of the ampacity deration factor the following pictorial representation is provided below.

Table for ampacity deration factor along with pictorial representation is provided below.

Rating factors for variation in ambient air temperature:

Rating factors for variation in ground temperature:

Rating factors for multicore cables laid on open racks in air:

No. of rocks	No of cables per rack
	1	2	3	6	9
1	1.00	0.98	0.96	0.93	0.92
2	1.00	0.95	0.93	0.90	0.89
3	1.00	0.94	0.92	0.89	0.88
6	1.00	0.93	0.90	0.87	0.86

No. of rocks	No of cables per rack
	1	2	3	6	9
1	1.00	0.84	0.80	0.75	0.73
2	1.00	0.80	0.76	0.71	0.69
3	1.00	0.78	0.74	0.70	0.68
6	1.00	0.76	0.72	0.68	0.66

Rating factors for single core cable in trefoil circuits laid on open racks in air:

No. of rocks	No of circuits per rack
	1	2	3
1	1.00	0.98	0.96
2	1.00	0.95	0.93
3	1.00	0.94	0.92
6	1.00	0.93	0.90

Rating factors for groups of multicore cables laid direct in ground, in horizontal formation:

Spacing	No. of cables in group
	2	3	4	6	8
Cables touching	0.79	0.69	0.62	0.54	0.50
15 cm	0.82	0.75	0.69	0.61	0.57
30 cm	0.87	0.79	0.74	0.69	0.66
45 cm	0.90	0.83	0.79	0.75	0.72
60 cm	0.91	0.86	0.82	0.78	0.76

Rating factors for grouping of multicore cables laid direct in ground in tier formation:

Rating factors for grouping of single core cable laid in trefoil circuits laid direct in ground in horizontal formation:

Spacing	No. of circuits in group
	2	3	4	6	8
Cables touching	0.78	0.68	0.61	0.53	0.48
15 cm	0.81	0.71	0.65	0.58	0.54
30 cm	0.85	0.77	0.72	0.66	0.62
45 cm	0.88	0.81	0.76	0.71	0.67
60 cm	0.90	0.83	0.79	0.76	0.72

Rating factors for depth of laying for Cables laid direct in the ground:

Rating factors for variation in thermal resistivity of soil:

(multicore cables laid direct in ground)

Rating factors for variation in thermal resistivity of soil, three single core cables laid direct in the ground:

(three cables in trefoil touching)

Now let us apply the ampacity criteria for sizing the cable of a motor. The minimum required size as per criteria-1 is already determined in part-1 of this article.

Rated Load current for 160kW motor = 160 x 1000/ (1.732 x 415 x 0.85 x motor efficiency)
Rated load current for motor = 275.66 Ampere

Now assuming that cable is laid in open racks in air the applicable ampacity deration factor will be:

K = K1 X K2 (K3 and K4 will not be applicable in this case)
K1 = 0.89
K2 = 0.70 (assuming 3 Nos. of cable rack with number of cables/rack to be 6 and cables are laid touching each other)

K = 0.89 x 0.70 = 0.623

Now K x Cable Ampacity should be greater than or equal to the required load current.
Aluminum, XLPE, 3C x 300 Sq mm cable has ampacity in air = 461 Amperes (From Manufactures catalog)

Applying ampacity deration factor = 461 * 0.623 = 287.203 Amperes which is greater than required load current of 275.6 Amperes.

Hence cable size selected on the basis of continuous current requirement is single run of 3C x 300 Sq mm, Aluminum, XLPE.

Low voltage switchboard with circuit breakers (incomers, feeders)

The following three criteria apply for the sizing of cables for circuit breaker controlled feeders:

I. Short circuit current withstand capacity

This criteria is applied to determine the minimum cross section area of the cable, so that cable can withstand the short circuit current.

Failure to check the conductor size for short-circuit heating could result in permanent damage to the cable insulation and could also result into fire. In addition to the thermal stresses, the cable may also be subjected to significant mechanical stresses.

II. Continuous current carrying capacity

This criteria is applied so that cross section of the cable can carry the required load current continuously at the designed ambient temperature and laying condition.

III. Starting and running voltage drops in cable

This criteria is applied to make sure that the cross sectional area of the cable is sufficient to keep the voltage drop (due to impedance of cable conductor) within the specified limit so that the equipment which is being supplied power through that cable gets at least the minimum required voltage at its power supply input terminal during starting and running condition both.

1. Criteria-1 Short circuit capacity

The maximum temperature reached under short circuit depends on both the magnitude and duration of the short circuit current. The quantity I2t represents the energy input by a fault that acts to heat up the cable conductor. This can be related to conductor size by the formula:

A = Minimum required cross section area in mm2
t = Operating time of disconnecting device in seconds
Isc = RMS Short Circuit current Value in Ampere
C = Constant equal to 0.0297 for copper & 0.0125 for aluminum
T2 = Final temp. ° C (max. short circuit temperature)
T1 = Initial temp. ° C (max. cable operating temperature – normal conditions)
T0 = 234.5° C for copper and 228.1° C for aluminum

Equation-1 can be simplified to obtain the expression for minimum conductor size as given below in equation-2:

Now K can be defined as a Constant whose value depends upon the conductor material, its insulation and boundary conditions of initial and final temperature because during short circuit conditions, the temperature of the conductor rises rapidly. The short circuit capacity is limited by the maximum temperature capability of the insulation. The value of K hence is as given in Table 2.

Boundary conditions of initial and final temperature for different insulation is as given under in Table 1 below.

Table 1

Table 2

In the final equation-2 we have determined the value of constant K. Now the value of t is to be determined. The fault current (ISC) in the above equation varies with time. However, calculating the exact value of the fault current and sizing the power cable based on that can be complicated. To simplify the process the cable can be sized based on the interrupting capability of the circuit breakers/fuses that protect them.

This approach assumes that the available fault current is the maximum capability of the breaker/fuse and also accounts for the cable impedances in reducing the fault levels.

Alternatively let us consider that feeder is for any large motor which is being fed from LV 415V or 400V switchgear having a circuit breaker with separate multifunction motor protection relay (For this calculation it is assumed to be SIEMENS made 7SJ61).

The instantaneous protection feature of this relay will be turned ON as and when any fault occurs. However, the selected cable shall have the capacity to withstand the maximum fault current for a finite duration (that is fault clearing time of the circuit breaker).

The minimum faults withstand duration necessary (for the instantaneous setting) for cable is calculated as under:

Therefore the cable selected for a circuit breaker controlled motor feeder in 415V or 400V switchgear shall be suitable to withstand the maximum rated fault current of 50kA for at least 120msec. However taking allowance of 40 Mili seconds in the opening time of circuit breaker due to aging, frequent number of operation, increase in contact resistance of circuit breaker and finally to cover the variation due from manufacturer to manufacturer.

Hence the cable selected for a circuit breaker controlled motor feeder in 415V or 400V switchgear shall be suitable to withstand the maximum rated fault current of 50kA for at least (120+40) 160msec. Many consultants recommend for use operating time of disconnecting device as 200msec also. Value of “t” more than 160 seconds is a conservative design.

Although it may appear that selection of minimum cross sectional area of cable conductor as 240 mm² is only just large enough for the duty, the actual fault current in the motor circuit is generally less than the switchboard fault withstand rating of 50kA, hence the selection of cable of cross sectional area 240 mm2 in practice offers sufficient design margin.

The minimum cross sectional area of cable required for 415V or 400V switchgear motor feeder from fault withstand point of view shall be 240mm².

We have considered for circuit breaker controlled motor feeder and analyzed the duration of short circuit/fault withstanding time in seconds for the same. Exactly the Same holds true for Circuit breaker controlled (Please see the below figure) outgoing transformer feeder.

However operating time of disconnecting device is slightly different for circuit breaker controlled incomer and tie feeders. Duration of fault withstanding/operating time of disconnecting device for incomer and tie feeder is 1 and 0.5 second respectively. This is because of additional presence of inverse definite minimum time delay protection relays along with instantaneous protection. The inverse definite time delay protection has time settings greater than 0.5 for incomer feeders and about 0.5 for tie feeders.

For all different type of feeders the operating time of disconnecting device is indicated in figure below:

Typical value of t (fault clearing time). All the connecting cables has to be sized for short circuit duration (t) indicated in the diagram above

The final cable size shall be selected considering the other two criteria that is continuous current carrying capacity & voltage drop criteria which would be continued in part-2 and part-3.

Overvoltages Caused by Indirect Lightning Strokes

A direct stroke is defined as a lightning stroke when it hits a shield wire, a tower, or a phase conductor. An insulator string is stressed by very high voltages caused by a direct stroke. An insulator string can also be stressed by high transient voltages when a lightning stroke hits the nearby ground.

An indirect stroke is illustrated in Figure 1 below.

Figure 1 - Illustration of direct and indirect lightning strokes

Voltage Components

The voltage induced on a line by an indirect lightning stroke has four components:

1. The charged cloud above the line induces bound charges on the line while the line itself is held electrostatically at ground potential by the neutrals of connected transformers and by leakage over the insulators. When the cloud is partially or fully discharged, these bound charges are released and travel in both directions on the line giving rise to the traveling voltage and current waves.

2. The charges lowered by the stepped leader further induce charges on the line. When the stepped leader is neutralized by the return stroke, the bound charges on the line are released and thus produce traveling waves similar to that caused by the cloud discharge.

3. The residual charges on the upper part of the return stroke induce an electrostatic field in the vicinity of the line and hence an induced voltage on it.

4. The rate of change of current in the return stroke produces a magnetically induced voltage on the line. If the lightning has subsequent strokes, then the subsequent components of the induced voltage will be similar to one or the other of the four components discussed above.

The magnitudes of the voltages induced by the release of the charges bound either by the cloud or by the stepped leader are small compared with the voltages induced by the return stroke. Therefore, only the electrostatic and the magnetic components induced by the return stroke are considered in the following analysis. The initial computations are performed with the assumption that the charge dis-tribution along the leader stroke is uniform, and that the return-stroke current is rectangular.

However, the result with the rectangular current wave can be transformed to that with currents of any other waveshape by the convolution integral (Duhamel’s theorem).

Figure 2 - Return stroke with residual charge column

It was also assumed that the stroke is vertical and that the overhead line is lossfree and the earth is perfectly conducting.

The vertical channel of the return stroke is shown in Figure 2, where the upper part consists of a column of residual charge that is neutralized by the rapid upward movement of the return-stroke current in the lower part of the channel.

Figure 3 - Coordinate system of line conductor and lightning stroke

Figure 3 shows a rectangular system of coordinates where the origin of the system is the point where lightning strikes the surface of the earth.

The line conductor is located at a distance yo meters from the origin, having a mean height of hp meters above ground and running along the x-direction. The origin of time ( t ¼ 0) is assumed to be the instant when the return stroke starts at the earth level.

Resource: Pritindra Chowdhuri – Tennessee Technological University

An AC digital clamp meter

Clamp-on ammeter or simply ‘clamp meter’ is an instrument that is used to measure the current flowing through a conductor. An AC Clamp meter basically consists of a current transformer in its jaws, bar CT usually. Utilizing the principle of current transformer, the reading will be displayed.

Whereas a DC clamp meter is quite different. It uses a Hall Effect sensor for measuring the current.

How does an AC clamp meter work?

When the instrument is ‘clamped’ on a conductor, the conductor itself acts as primary and the magnetic flux due to current flowing through the conductor cuts the secondary of CT.

The current in the secondary of the CT is converted to voltage using a current-to-voltage converter. This signal is fed to an analogue to digital converter. A micro controller is usually employed and it will drive the display circuit for the current reading.

Block diagram of an AC clamp meter

How does a DC clamp meter work?

Unlike AC, current transformers cannot be used for measuring direct current. So Hall Effect sensor is used for this purpose. The Hall element used responds to the magnetic flux due to direct current in the conductor which produces voltage across the element.

The developed voltage is proportional to the current in the conductor. So by measuring voltage, current can be determine.

Block diagram of a DC clamp meter

Hall Effect and Hall Effect sensor

Hall effect sensor

The Hall effect is the production of potential difference across an electrical conductor, transverse to current in conductor and a magnetic field perpendicular to the current. This effect was discovered by Edwin Hall in 1879.

A Hall Effect sensor is a transducer that produces a voltage when kept under the influence of magnetic field. The charge carriers experience a force called Lorentz force. Due to this force the charges gets distributed on the surface of material leaving equal and opposite charges on the opposite surface which constitutes a potential difference that exists as long as magnetic field is steady.

In a DC clamp meter Hall Effect sensor is used as a magnetometer. The voltage so developed is proportional to magnetic field and hence to the current.

Even though a clamp meter is mainly used for measuring current, these instruments are added with feature to measure voltage, resistance, frequency etc.

Medium Voltage Air Insulated Metal-Clad Switchgear (AIS)

Various factors affect the reliability of a substation, one of which is the arrangement of the switching devices. Arrangement of the switching devices will impact maintenance, protection, initial substation development, and cost.

1. Single Bus Configuration

Single bus configuration

This arrangement involves one main bus with all circuits connected directly to the bus. The reliability of this type of an arrangement is very low. When properly protected by relaying, a single failure to the main bus or any circuit section between its circuit breaker and the main bus will cause an outage of the entire system. In addition, maintenance of devices on this system requires the de-energizing of the line connected to the device.

Maintenance of the bus would require the outage of the total system, use of standby generation, or switching to adjacent station, if available. Since the single bus arrangement is low in reliability, it is not recommended for heavily loaded substations or substations having a high availability requirement.

Reliability of this arrangement can be improved by the addition of a bus tiebreaker to minimize the effect of a main bus failure.

2. Double Bus, Double Breaker Configuration

Double Bus, Double Breaker Configuration

This scheme provides a very high level of reliability by having two separate breakers available to each circuit. In addition, with two separate buses, failure of a single bus will not impact either line. Maintenance of a bus or a circuit breaker in this arrangement can be accomplished without interrupting either of the circuits.

This arrangement allows various operating options as additional lines are added to the arrangement; loading on the system can be shifted by connecting lines to only one bus. A double bus, double breaker scheme is a high-cost arrangement, since each line has two breakers and requires a larger area for the substation to accommodate the additional equipment. This is especially true in a low profile configuration.

The protection scheme is also more involved than a single bus scheme.

3. Main and Transfer Bus Configuration

Main and Transfer Bus Configuration

This scheme is arranged with all circuits connected between a main (operating) bus and a transfer bus (also referred to as an inspection bus). Some arrangements include a bus tie breaker that is connected between both buses with no circuits connected to it.

Since all circuits are connected to the single, main bus, reliability of this system is not very high. However, with the transfer bus available during maintenance, de-energizing of the circuit can be avoided. Some systems are operated with the transfer bus normally de-energized. When maintenance work is necessary, the transfer bus is energized by either closing the tie breaker, or when a tie breaker is not installed, closing the switches connected to the transfer bus. With these switches closed, the breaker to be maintained can be opened along with its isolation switches. Then the breaker is taken out of service. The circuit breaker remaining in service will now be connected to both circuits through the transfer bus.

This way, both circuits remain energized during maintenance. Since each circuit may have a different circuit configuration, special relay settings may be used when operating in this abnormal arrangement.

When a bus tie breaker is present, the bus tie breaker is the breaker used to replace the breaker being maintained, and the other breaker is not connected to the transfer bus. A shortcoming of this scheme is that if the main bus is taken out of service, even though the circuits can remain energized through the transfer bus and its associated switches, there would be no relay protection for the circuits. Depending on the system arrangement, this concern can be minimized through the use of circuit protection devices (reclosure or fuses) on the lines outside the substation.

This arrangement is slightly more expensive than the single bus arrangement, but does provide more flexibility during maintenance. Protection of this scheme is similar to that of the single bus arrangement. The area required for a low profile substation with a main and transfer bus scheme is also greater than that of the single bus, due to the additional switches and bus.

4. Double Bus, Single Breaker Configuration

Double Bus, Single Breaker Configuration

This scheme has two main buses connected to each line circuit breaker and a bus tie breaker. Utilizing the bus tie breaker in the closed position allows the transfer of line circuits from bus to bus by means of the switches. This arrangement allows the operation of the circuits from either bus. In this arrangement, a failure on one bus will not affect the other bus.

However, a bus tie breaker failure will cause the outage of the entire system. Operating the bus tie breaker in the normally open position defeats the advantages of the two main buses. It arranges the system into two single bus systems, which as described previously, has very low reliability. Relay protection for this scheme can be complex, depending on the system requirements, flexibility, and needs.

With two buses and a bus tie available, there is some ease in doing maintenance, but maintenance on line breakers and switches would still require outside the substation switching to avoid outages.

5. Ring Bus Configuration

Ring Bus Configuration

In this scheme, as indicated by the name, all breakers are arranged in a ring with circuits tapped between breakers. For a failure on a circuit, the two adjacent breakers will trip without affecting the rest of the system. Similarly, a single bus failure will only affect the adjacent breakers and allow the rest of the system to remain energized. However, a breaker failure or breakers that fail to trip will require adjacent breakers to be tripped to isolate the fault.

Maintenance on a circuit breaker in this scheme can be accomplished without interrupting any circuit, including the two circuits adjacent to the breaker being maintained. The breaker to be maintained is taken out of service by tripping the breaker, then opening its isolation switches. Since the other breakers adjacent to the breaker being maintained are in service, they will continue to supply the circuits. In order to gain the highest reliability with a ring bus scheme, load and source circuits should be alternated when connecting to the scheme.

Arranging the scheme in this manner will minimize the potential for the loss of the supply to the ring bus due to a breaker failure. Relaying is more complex in this scheme than some previously identified. Since there is only one bus in this scheme, the area required to develop this scheme is less than some of the previously discussed schemes. However, expansion of a ring bus is limited, due to the practical arrangement of circuits.

6. Breaker-and-a-Half Configuration

Breaker-and-a-Half Configuration

The breaker-and-a-half scheme can be developed from a ring bus arrangement as the number of circuits increases. In this scheme, each circuit is between two circuit breakers, and there are two main buses. The failure of a circuit will trip the two adjacent breakers and not interrupt any other circuit. With the three breaker arrangement for each bay, a center breaker failure will cause the loss of the two adjacent circuits. However, a breaker failure of the breaker adjacent to the bus will only interrupt one circuit.

Maintenance of a breaker on this scheme can be performed without an outage to any circuit. Further- more, either bus can be taken out of service with no interruption to the service. This is one of the most reliable arrangements, and it can continue to be expanded as required. Relaying is more involved than some schemes previously discussed.

This scheme will require more area and is costly due to the additional components.

Comparison table of configurations:

Resource: CsanyiGroup – Air Insulated Substations – Bus/Switching Configurations

Using AC and DC together in electrical system?

There are a number of issues to using AC and DC together in the same electrical system. Briefly, they are: circuit boxes and hardware, outlets, wiring schemes and sizes, and switches.

Circuit boxes

The Electrical Code prohibits AC and DC in the same box. You’ll need two distribution boxes – one for AC and one for DC.

Circuit breakers rated for AC won’t work for DC. Expect to pay more for DC breakers. On the other hand, fuses are mostly indifferent to AC or DC, or even differences in voltage. Older-style circuit boxes employing fuses that no longer meet Code for AC wiring will work fine for DC circuits. Up to ratings of 30 Amps, the new style of automotive fuses are also great for DC systems.

Outlets

Standard receptacles will work for DC or AC. You must exercise caution in using both in the same household. Plugging a 12V DC load into a 120V AC socket may fry the load if the circuit breaker/fuse doesn’t pop first.

Plugging a 120V AC load into a 12V DC circuit may hurt the load or blow a fuse or simply do nothing. Still, who needs this worry. Amateur electricians have many
ways to handle this situation. One scheme uses the same type of receptacle for AC and DC circuits but colorcodes or labels the receptacle plate itself. This works okay for hermits but it’s lousy for guests, children, and the uninformed.

A second scheme is to wire AC and DC into the same receptacle, with a shared common (bad idea). Another scheme is to wire the 12V appliances to a unique auto cigarette
lighter plug/receptacle (light loads only, please). Or a plug/receptacle of the style found in older RVs (recreational vehicles) for 12V circuits (mostly inadequate).

Polarity is another issue with DC. Incandescent lights and simple heating circuits don’t really care about polarity, but you must observe proper polarity (pos. or neg.) for LEDs, high-frequency fluorescent lamps, stereos, and many other DC loads. This is easily handled by the newer style of plugs and receptacles that permit insertion in only one way. These will ensure correct polarity in wiring plug and receptacle, as will the use of 3-prong plugs.

Wiring

Overall, 12V DC wiring will require a larger gauge of wire for even modest loads. Wire size increases rapidly with any length. Here, preparation and creativity go a long way
toward minimizing the expense and labor while retaining full capability.

What do you want to do and where? Special low-voltage wiring tables will assist you in sizing wire for specific loads at varying distances.

There is also merit in the idea of running a branch line of large wire to the far side of the house where it can be distributed from a second, smaller fuse box to loads in that area. Large-gauge wire is stiff and awkward to route; plan accordingly. Use 12-gauge wire “fingers” from a bigger gauge wire to ease connections to receptacles and switches.

Use junction boxes for wire gauges of #8 and larger. Relatively short lengths of #12 wire leading from these to loads and receptacles will incur only small losses.

Switches

Switches designed to handle 120V AC may fail in use with 12V DC. The arc produced when a standard AC lightswitch opens (turns off) a DC circuit will be hotter and last longer.

Figure 1 - A capacitor will reduce arcing in a switch in a DC circuit

Absolutely avoid “silent” switch types; they open way too slow. Either way, the DC arc will eventually (if not immediately) burn a switch’s contacts. It is possible to add a capacitor across the switch to suppress this arc (Figure 1).

Figure 2 - Series-wiring of multiple-pole switches reduces arcing

Or to wire a switch with multiple poles in series (not parallel; see Figure 2) to help it survive this arc. Of course, you may also find and install switches rated to switch DC current.

Resource: January/February 2000 Backwoods Home Magazine

Disassembled residual current device RCD; I=40A, ΔI=30mA

For domestic applications only the first five of the below listed residual current devices (RCD) need to be considered. For industrial and commercial buildings all of the classifications need to be considered.

Table below aims to identify where each type of RCD can be used, together with the benefits provided. However, before looking at Table 2 there are two other classifications of RCD that need to be considered – general and time-delayed operation each having Type a.c., A or B characteristics.

RCCB

(Residual Current Operated Circuit Breaker without Integral Overcurrent Protection)

A mechanical switching device designed to make, carry and break currents under normal service conditions and to cause the opening of the contacts when the residual current attains a given value under specified conditions.

It is not designed to give protection against overloads and/or short-circuits and must always be used in conjunction with an overcurrent protective device such as a fuse or circuit breaker.

RCBO

(Residual Current Operated Circuit Breaker with Integral Overcurrent Protection)

A mechanical switching device designed to make, carry and break currents under normal service conditions and to cause the opening of the contacts when the residual current attains a given value under specified conditions.

In addition it is designed to give protection against overloads and/or short-circuits and can be used independently of any other overcurrent protective device within its rated short-circuit capacity.

SRCD

(Socket-Outlet incorporating a Residual Current Device)

A socket-outlet for fixed installations incorporating an integral sensing circuit that will automatically cause the switching contacts in the main circuit to open at a predetermined value of residual current.

FCURCD

(Fused Connection Unit incorporating a Residual Current Device)

A fused connection unit for fixed installations incorporating an integral sensing circuit that will automatically cause the switching contacts in the main circuit to open at a predetermined value of residual current

PRCD

(Portable Residual Current Device)

A device comprising a plug, a residual current device and one or more socket-outlets (or a provision for connection). It may incorporate overcurrent protection.

CBR

(Circuit Breaker incorporating Residual Current Protection)

A circuit breaker providing overcurrent protection and incorporating residual current protection either integrally (an Integral CBR) or by combination with a residual current unit which may be factory or field fitted.

NOTE – The RCBO and CBR have the same application, both providing overcurrent and residual current protection. In general, the term RCBO is applied to the smaller devices whereas CBR is used for devices throughout the current range, with ratings up to several thousand amperes, single and multi-phase.

The RCBO and CBR are more strictly defined by the relevant standards.

RCM

(Residual Current Monitor)

A device designed to monitor electrical installations or circuits for the presence of unbalanced earth fault currents. It does not incorporate any tripping device or overcurrent protection.

MRCD

(Modular Residual Current Device)

An independently mounted device incorporating residual current protection, without overcurrent protection, and capable of giving a signal to trip an associated switching device.

Suitability of different types of RCD for different applications

Suitability of different types of RCD for different applications

Application Notes:

(1) Only if used in conjunction with suitable overcurrent protection (e.g. Fuse/circuit breaker)
(2) 10 mA RCDs are associated with highly sensitive equipment and high risk areas such as school laboratories and in hospital areas
(3) Yes provided 30mA or less, but not normally used
(4) With time delay
(5) CU – Consumer unit to BS EN 60439-3
(6) Must provide double pole isolation
(7) DB – Distribution Board; PB – Panel Board; SB – Switch Board

Resource: eama – The RCD Handbook | BEAMA Guide to the Selection and Application of Residual Current Devices