### Power And Distribution Transformers Sizing Calculations – Part Seven

 Subject Of Previous Articles Article Glossary of Sizing Power and Distribution Transformers, Resources used to calculate basic ratings of power and distribution transformers the selection factors for the Power and Distribution Transformers Applicable calculations procedures for sizing of power and distribution transformers 1- Applicable procedures for calculating power and distribution transformer ratios, 2- Applicable procedures for calculating power transformer efficiency, 3- Applicable procedures for calculating power transformer voltage regulation, 4- Special Cases In Transformers Sizing Calculations: Secondary Unit Substations Special Cases In Transformers Sizing Calculations: Paralleled Transformers Note: I’d like from all of you to review our course “EP-3: Electrical Procurement – Transformers Course” to be more familiar with the contents of our new articles about the Power and Distribution Transformers sizing calculations. Today, we will explain other special cases for Power and Distribution Transformers sizing calculations; K-Factor Transformers.

 Special Cases In Transformers Sizing Calculations     3- K-Factor Transformers

 Linear Vs. Nonlinear Loads     Linear Loads:   A load that does not affect the input waveform, which is a pure sinewave, composed of a fundamental frequency (e.g. 60 hz) component with no multiple frequencies. Typical linear loads are resistive heating and induction motors.   Nonlinear Loads:   A load that distorts the input sinewave such that the resultant waveform is composed of a fundamental frequency (e.g. 60 hz) component and multiple frequency components (e.g. 120 hz, 180 hz,..etc) called harmonics. Examples of these loads used in offices are: computers, fax machines, copiers, printers, cash registers, UPS systems, and solid-state ballasts. In industrial plants, nonlinear loads are such as variable speed drives, HID lighting, solid-state starters and solid-state instruments. See Fig.1       Fig.1: voltage and current waveforms for nonlinear loads.

Harmonics

As defined by ANSI / IEEE Std. 519, Harmonics are voltages or currents at frequencies that are integer multiples of the fundamental (60 Hz) frequency: 120 Hz, 180 Hz, 240 Hz, 300 Hz, etc. which called odd harmonics (3rd, 5th, 7th ,..., 25th,...). See Table-1.

 Harmonic Frequency in Hz fundamental 60 3rd 180 5th 300 7th 420 9th 540 11th 660 etc. etc.

Table-1: Harmonics

 The Effect of Nonlinear Loads on the Electrical Power Systems   Nonlinear loads produce harmonic currents which flow from the load towards the power source following the path of least impedances result in harmonic voltage drops which are observed as harmonic voltage distortion. The voltage distortions could become very severe when the power systems inductive and capacitive impedances become equal, a condition of parallel resonance.   The Problems Caused By Harmonic Currents Include:   Overheating of cables, especially the neutral conductor, but if normal wiring sizing methods are employed, then the derating for wiring for harmonics is minimal and can be ignored, Overheating and vibration in induction motors, Increased losses in transformers due to stray magnetic losses in the core, and eddy current and resistive losses in the windings. eddy current losses are of most concern when harmonics are present, because they increase approximately with the square of the frequency, Where power factor capacitors are fitted, harmonic currents can damage them and care must be taken to avoid resonance with the supply inductance.

 Diversity of Harmonics   Each non-linear load generates harmonics independently with the magnitude and phase angle of each harmonic depending on the design of the circuit and the instantaneous loading. When several loads are connected in parallel, for example, a number of personal computers on an office floor, the overall sum of each harmonic will be less than the sum of the individual magnitudes. See Fig.3.       Fig.3: Diversity of Harmonics   In other words, the K-factor of the overall load is less than that which would be expected from measurement of all the individual items. Similarly, when there are linear loads present, the overall K-factor is reduced because the harmonic load is a smaller proportion of the total load.

Sizing Methods of Transformers for Non-Linear Loads

We have three methods for Sizing Transformers for Non-Linear Loads as follows:

Method#1: ANSI / IEEE C57.110 has a procedure for de-rating standard distribution transformers for non-linear loading but We will explain this method later since it is more complicated.

Method#2: Underwriters’ Laboratories method where the appropriate K-Factor for a transformer with non-linear loads can be calculated as follows:

K = Σ (Ih)2 (h)2

Where:
Ih = RMS Current at Harmonic h
h = Harmonic Order, i.e. 3rd, 5th, 7th, etc.

Fig.4: K-factor calculations by UL

Method#3: Estimating K-Factor from Tables

1- List the kVA value for each load category to be supplied. Next, assign a K-factor designation that corresponds to the relative level of harmonics drawn by each type of load. Refer to Table-2.

2- Multiply the kVA of each load or load category times the Index of Load K-rating (ILK) that corresponds to the assigned K-factor rating. This result is an indexed kVA-ILK value.

KVA x ILK = kVA-ILK

2- Tabulate the total connected load kVA for all load categories to be supplied.

4- Next, add-up the kVA-ILK values for all loads or load categories to be supplied by the transformer.

5- Divide the grand total kVA-ILK value by the total kVA load to be supplied. This will give an average ILK for that combination of loads.

Total kVA-ILK/ Total kVA = average ILK

6- From Table-2 find the K-factor rating whose ILK is equal to or greater than the calculated ILK.

 Description K-Factor ILK Incandescent Lighting Electric Resistance Heating Motors (without solid state drives) Control Transformers / Electromagnetic Control Devices Motor-Generators (without solid state drives) K1 0.00 Standard Distribution Transformers Electric Discharge Lighting (HID) UPS with Optional Input Filter Welders Induction Heating Equipment PLCs and Solid State Controls K4 25.82 Telecommunications Equipment (PBX) UPS without Input Filtering Multiwire Receptacle Circuits in General Care Areas of Health Care Facilities, Schools, etc. Multiwire Receptacle Circuits Supplying Testing Equipment on an Assembly Line K13 57.74 Main-Frame Computer Loads Solid State Motor Drives (variable speed drives) Multiwire Receptacle Circuits in Critical Care Areas in Hospitals K20 80.94 Multiwire Receptacle Circuits in Industrial, Medical and Educational Laboratories Multiwire Receptacle Circuits in Commercial Office Spaces Small Main-Frames (mini and micro) K30 123.54

Table-2: Estimating K-Factor

Notes:

• The problem associated with calculating K- Factor is selecting the range of harmonic frequencies that should be included. Some use up to 15th harmonic, others up to 25 th harmonic, and still others include up to 50th harmonic.
• For the same load, each of these calculations can yield significantly different K-Factors, because even very small current levels associated with higher harmonics, when multiplied by the harmonic number squared, can yield significantly to the K-Factor.
• Based on the underlying assumptions of ANSI / IEEE C57.II0, it seems reasonable to limit the K-Factor calculation to harmonic currents less than 25 th harmonic.
• In establishing standard transformer K-Factor rating; UL chose ratings of 1, 4, 9, 13, 20, 30, 40 and 50. From a practical viewpoint individual loads with K-Factors greater than 20 are infrequent.
• For example, At best office areas with some nonlinear loads and large computer rooms normally have observed K-Factors of 4 to 9. Areas with high concentrations of single phase computers and terminals have observed K- Factors of 13 to 17.

In the next article, we will explain K-Factor/Factor K Calculators used in sizing transformers with non-linear loads. So, please keep following.

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