Impact of different harmonic loads on distribution transformers

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Procedia Engineering 202 (2017) 76–87

4th International Colloquium "Transformer Research and Asset Management”

Impact of different harmonic loads on distribution transformers Dejan Pejovskia*, Krste Najdenkoskib, Mihail Digalovskic Rade Koncar – Service and Repairs of Electrical Products, Bul. “3ta Makedonska brigada” no. 52, 1000 Skopje, Republic of Macedonia ”Ss. Cyril and Methodius” University, Faculty of Electrical Engineering and Information Technologies, ul. “Rugjer Boshkovikj” no. 18, 1000 Skopje, Republic of Macedonia a a

b,c b,c

Abstract The increased usage of electrical load devices causes non-sinusoidal waveforms of currents and voltages in the power system. These harmonic loads have a significant impact on distribution transformers. The primary effect of harmonic currents are the additional power losses in transformer components, which result in increase in generated heat, as well as reduction of transformer’s life-expectancy. This study examines the effects of different nonlinear loads on а dry-type three phase distribution transformer with rated power of 4.5kVA and rated voltage 440/380V. Measurements are done to several relevant parameters, such as: current and voltage high order harmonics, active and reactive power, power factor, total harmonic distortion etc. with sophisticated instruments in laboratory conditions. Using the measurement data, additional power losses are calculated according to the mathematical model proposed in the IEEE Std. C57.110-1998. This study shows an experimental confirmation of theoretically expected results. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of ICTRAM 2017. Peer-review under responsibility of the organizing committee of ICTRAM 2017. Keywords: Nonlinear loads; Transformer losses; Transformer’s capability equivalent

1. Introduction In todays electricity distribution system has been noticed a sudden increase in nonlinear loads, such as: computers, fluorescent lights, adjustable electromotor drives, power converters etc. These loads draw non-sinusoidal currents from the utility and cause distortion in the sinusoidal current and voltage waveforms, which are known as ‘harmonics’ [1]. According to Fourier, distorted waveforms can be represented as an infinite sum of pure sine waves

* Corresponding author. Tel.: +389-75-335-142 E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of ICTRAM 2017.

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of ICTRAM 2017. 10.1016/j.proeng.2017.09.696

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in which the frequencies are integer multiples of the fundamental frequency of the distorted wave [2]. Since power system components are designed to operate at rated frequency and conditions, harmonics cause various problems: additional power losses and overheating in the electrical machines, excessive neutral currents, uncontrolled relay actions, possible resonance etc. The most common effects of nonlinear loads on distribution transformers are [3,4]: • • • • •

Saturation of transformer’s core by changing its operating point towards the knee of the nonlinear B-H curve, Increase in core (hysteresis and eddy current) power losses, Increase in fundamental and harmonic copper losses, Increase in the temperature of windings, cleats, leads, insulation and oil, which can cause overheating, Bushings, tap changers and cable-end connections will also be exposed to higher stresses, which can result in transformer’s failure, • Transformer’s efficiency reduction and power factor decrease, • Transformer’s derating, • Reduction of transformer’s life-expectancy etc.

Transformers are designed to deliver the required power to the load with minimum losses at the fundamental frequency. These losses are generally classified as no-load loss (excitation loss) and load loss (impedance loss). The sum of those two components forms transformer total loss [5]: PTL = PNL + PLL

(1)

The no load losses occur due to the voltage excitation of the core and losses due to magnetic hysteresis and eddy currents. Load loss is subdivided into I2R loss and “stray loss”. Stray loss is determined by subtracting the I2R loss (calculated from the measured resistance) from the measured load loss (impedance loss). Stray loss can be defined as the loss due to stray electromagnetic flux in the windings, core, core clamps, magnetic shields, enclosure or tank walls etc. Thus, the stray loss is subdivided into winding stray loss (PEC) and stray loss in components other than windings (POSL). The winding stray loss includes winding conductor strand eddy-current loss and loss due to circulating currents between strands or parallel winding circuits. All of this loss may be considered to constitute winding eddy-current loss. The total load loss can be calculated as [5]:

PLL = P + PEC + POSL Nomenclature I I1 Ih IR I1-R I2-R PEC PEC-R P PLL PLL-R PNL POSL POSL-R PTSL-R

RMS load current [A] RMS fundamental load current [A] RMS current at harmonic h [A] RMS fundamental current under rated frequency and rated load conditions [A] High voltage rms fundamental line current under rated frequency and rated load conditions [A] Low voltage rms fundamental line current under rated frequency and rated load conditions [A] Winding eddy-current loss [W] Winding eddy-current loss under rated conditions [W] I2R loss portion of the load loss [W] Load loss [W] Load loss under rated conditions [W] No load loss [W] Other stray loss [W] Other stray loss under rated conditions [W] Total stray loss under rated conditions [W]

(2)

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R1 R2 h hmax FHL FHL-OSL

3

DC resistance measured between two HV terminals [Ω] DC resistance measured between two LV terminals [Ω] Harmonic order Highest significant harmonic number (usually hmax=25) Harmonic loss factor for winding eddy currents Harmonic loss factor for othеr stray losses

2. Analysis and modelling The contribution made by harmonic currents to different loss components in the transformer is described in this section. Loss components affected by non-sinusoidal currents are: I2R loss, eddy current loss and the stray losses. • Harmonic current effect on I2R loss The ohmic losses are due to primary and secondary distorted currents flowing through the windings. If the root mean square value of the load current is increased due to harmonic components, the I2R loss will be increased accordingly [6]. • Harmonic current effect on eddy current loss Winding eddy current loss (PEC) in the power frequency spectrum tends to be proportional to the square of the load current and the square of frequency. This characteristic will cause excessive core losses and hence abnormal temperature rise in transformers supplying non-sinusoidal load currents [5]. • Harmonic current effect on other stray loss (POSL) Other stray loss in the core, clamps, and structural parts will also increase at a rate proportional to the square of the load current. However, studies by manufacturers and other researches show that eddy current losses in bus bars, connections and structural parts do not increase by the square of the frequency; they increase by a harmonic exponent factor of 0.8 [5]. • DC component of load current Harmonic load currents are frequently accompanied by a DC component in the load current. This component will increase the transformer core loss slightly, and it will increase the magnetizing current and audible sound level more substantially. Relatively small DC components are expected to have no effect on the transformer’s load carrying capability [5]. It is recommended to consider loss density in the windings on a per-unit basis (base current is rated current and base loss density is the I2R loss density at rated current). Thus Eq. (2) applied to rated load conditions can be rewritten on a per-unit basis as follows: PLL − R (pu ) = 1 + PEC − R (pu ) + POSL− R (pu )

(3)

As established in test codes in IEEE Standards, the stray loss component of the load loss is calculated by subtracting the I2R loss of the transformer from the measured load loss. Therefore,

(

PTSL − R = PLL − R − K ⋅ I12− R R1 + I 22− R R 2

)

(4)

where K=1 for single phase transformers and K=1.5 for three phase transformers. Based on the IEEE Standard, for the dry type transformer the eddy current loss can be assumed to be 67% of the total stray losses: PEC − R = 0,67 ⋅ PTSL − R

(5)

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POSL − R = PTSL − R − PEC − R

79

(6)

Given the eddy-current loss under rated conditions for transformer windings (PEC-R), the eddy-current loss due to any defined non-sinusoidal load current can be expressed as:

PEC = PEC − R

h =hmax

 h =1

 Ih   IR

2

 2  h 

(7)

In the same way the other stray losses can be calculated for any measured non-sinusoidal current:

POSL = POSL− R

h = hmax

 h =1

 Ih   IR

2

 0,8  h 

(8)

In harmonic presence, it is convenient to define a single number which may determine the capabilities of a transformer in supplying power to the load. Therefore, a proportionality factor (FHL) is applied to the winding eddy losses, which represents the effective RMS heating as a result of the harmonic load current. Similar factor can be derived for calculating the increase in the other stray losses due to harmonics (FHL-STR) [5].

h=hmax  I  h FHL =   h=1  I1 



2 h=h  2   max  I h   h  /    h=1  I1   

h=hmax  I  h FHL−STR =   h=1  I1 





  

2

  

2 h=h  0,8   max  I h   h  /    h=1  I1   



(9)

  

2

  

(10)

Considering the additional heating due to the increase in power losses when the transformer operates in nonlinear conditions, it is recommended to calculate its equivalent capability. In order for the transformer to maintain the same life-expectancy, the maximum load current can be calculated in per-units of the rated current as follows: I max ( pu) =

PLL − R ( pu) 1 + FHL ⋅ PEC − R ( pu)

(11)

Assuming that I2R losses are uniformly distributed within the winding, the maximum eddy current loss density is assumed to be 400% of the average value. For a distribution transformer with rated current lower than 1000A and turns ratio of 4:1 or less, the eddy current loss in per unit is [5]:

PEC− R (max) =

2,4 ⋅ PEC−R K ⋅ I 22−R R2

(pu)

(12)

3. Experimental setup In order to validate the theoretical analysis, several experiments are conducted to a dry-type three phase distribution transformer in the Laboratory for Electrical Machines, Transformers and Apparatuses (LEMTA). The characteristics of the equipment used are given as follows:

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• Three phase distribution transformer (Fig. 1a). Sn=4.5kVA, U1n=440V, Un2=380V, I1n=5.9A, I2n=6.84A, fn=50Hz, Dy5, R1=3.83Ω, R2=0.8Ω. • Omni-quant instrument for power quality measurement (Fig. 1b): for measuring parameters relevant to power quality. The instrument measures phase and line voltages and currents, active, reactive and apparent power, total voltage and current harmonic distortion, power factor, harmonic spectrum up to 50th harmonic etc. The computer connection is enabled through RS485 interface and Damon software. Other characteristics are given in Table 1. Table 1. Omni-quant instrument characteristics [7]. Current measurement Power

Voltage measurement (max 500V ~ phase voltage) ~ 0,2 VA

Input impedance

2 МΩ/phase

Rated current at Х/5 А (Х/1 А)

5 A (1 A)

Power

~ 0,1 VA

Current limit

6A

Phase voltage range

50 – 500 V ~

Overloading (1ѕ)

60 A

Line voltage range

90 – 870 V ~

Rated frequency

15 – 180 Hz

• Transformer load: variable resistors (Rmax=31.4Ω), single phase induction motor (Pn=370W, Un=220V, In=4.4A, cosϕn=0.68), compact fluorescent lights (CFL, Pn=5W). 4. Experimental setup The experiments conducted in this study consist of four steps and two different transformer loads: • No load and short circuit test: in order to evaluate transformer losses under non-linear conditions, the values of transformer rated losses are required. For this purpose, routine tests are conducted according to the IEC Standards [8]. The rated losses at no load condition are PNL=120W, and the losses at short circuit are PLL-R=465W;

a)

b) Fig. 1. (a) Transformer tested; (b) Omni-quant instrument for power quality measurements.

• Linear active symmetrical load: in each phase of the transformer’s secondary side a variable resistor is connected and power quality measurements are done only on the secondary side; • Nonlinear active-inductive asymmetrical load: in each phase a different load is connected, i.e. two CFL in parallel in phase A, single phase induction motor in phase B, and two variable resistors in series connected in phase C. Measurements are done on the secondary and on the primary side of the transformer. The equivalent electrical scheme for load-transformer experiments is shown in Fig. 2a and the experiment setup is presented in Fig. 2b.

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5. Results analysis 5.1. Case A: Linear load Each transformer phase is equally loaded with a variable resistor at its maximum resistance Rmax=31.4Ω (In Fig. 2a switch K2 is closed and K3 opened). Measurements of power quality parameters on the secondary side are shown in Table 2. The harmonic distribution of phase currents and its waveforms are shown in Fig. 2b. It is notable that: • Uf and If have almost equal values in each phase, meaning that transformer load is symmetrical and balanced, • Total voltage harmonic distortion THD(Uf) ≤ 5%, according to IEEE 519-2014 Standard [9], • Total current harmonic distortion THD(If) ≤ 3%, according to IEEE standard [9], • Power factor value is slightly smaller than 1, as expected, • The amount of reactive power usage is due to the relatively small inductance in the connections and in the variable resistors, • Even harmonics in the current spectrum have insignificant magnitudes compared to the odd ones, meaning the even harmonics can be omitted in calculations, • The most notable are 5th and 7th current harmonics, • The current waveforms have insignificant deviations from ideal sine wave.

a)

b) Fig. 2. (a) Electrical scheme for the experimental setup; (b) Experimental setup in LEMTA

a)

b) Fig. 3. Case A: (a) Harmonic spectrum of secondary phase current; (b) Waveforms of secondary phase current

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Table 2. Measurement results with linear active symmetrical load. Phase

L1

L2

L3

Unit

Uf

181.67

181.46

181.66

V

If

5.1807

5.2241

5.3226

A

THD Uf

4.7385

4.4721

4.6153

V

THD Uf

2.6083

2.4645

2.5406

%

THD If

0.1332

0.1227

0.1319

A

THD If

2.5707

2.3481

2.4789

%

Pf

939.97

946.76

965.58

W

Qf

47.164

47.736

50.323

VAr

Sf

941.16

947.96

966.89

VA

PFf

0.99874

0.99873

0.99864

PFtotal

0.99871

Ul (L12-L23-L31)

314.06

314.87

V

314.66

5.2. Case B.1 Nonlinear load secondary side measurements On transformer’s secondary side nonlinear active-inductive load is connected, consisting of variable resistor, CFL and inductive motor (In Fig. 2 switch K2 is opened and K3 closed), and measurements are done on the secondary side. Relevant parameter values are given in Table 3. The current harmonic distribution and its waveforms are shown in Fig. 4. Table 3. Measurement results on the secondary and on the primary side with nonlinear active-inductive asymmetrical load

Phase

Secondary side measurement data L1

L2

L3

Unit

Primary side measurement data L1

L2

L3

Unit

Uf

187.24

184.7

167.21

V

215.76

216.79

216.18

V

If

0.009610

2.2846

2.4367

A

1.812

1.8524

1.7982

A

THD Uf

4.7308

4.6881

2.4862

V

5.1213

5.3530

5.2409

V

THD Uf

2.5266

2.5382

1.4869

%

2.3736

2.4692

2.4243

%

THD If

0.0116

0.0488

0.0482

A

0.1258

0.1947

0.1596

A

THD If

120.66

2.1363

1.979

%

6.9445

10.509

8.8758

%

Pf

9.896

46.287

406.78

W

230.22

227.88

216.53

W

Qf

15.029

419.43

23.142

VAr

315.97

330.67

322.86

VAr

Sf

17.994

421.97

407.44

VA

390.94

401.59

388.75

VA

PFf

0.54996

0.10969

0.99839

0.58889

0.56745

0.557

PFtotal Ul (L12-L23-L31)

0.54633 322.26

292.56

317.39

0.57111 V

374.85

373.6

375.39

V

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Fig. 4. Case B.1 (a) Harmonic spectrum of secondary phase current; (b) Waveforms of secondary phase current.

From Table 3 and Fig. 4 the following conclusions can be made: • Through phase A flows the smallest current: although it has THD IAf >> 3%, in absolute values it is relatively small (THD(IAf) < 0.02A) and does not necessarily mean threat to the power system. However, this requires further attention. • Phase voltage harmonic distortions are higher than in case A, yet still remain in the allowable limits, • Induction motor in phase B requires the highest reactive power, due to its magnetic core and principle of operation. It has the lowest power factor (PFB < 0.11) which leads to significant decrease in the system PF, • Phase C draws the highest active power and the highest current, since variable resistors are connected. This causes the largest voltage drop. • In phase A the 3rd harmonic amplitude is almost 9 times bigger than the fundamental, and other even harmonics have a significant influence on RMS values, • In phase B the 5th current harmonic is the most significant, while in phase C it is the 3rd. However, in each phase harmonics higher than 9th are negligible. • Phase B and C current waveforms are notably close to the pure sine wave, although phase A shows significant distortion. 5.3. Case B.2 Nonlinear load primary side measurements Transformer load remains the same as in Case B.1, but measurements of power quality parameters are done on the primary side. The results are shown in Table 3, while current THD spectrum and waveforms of primary phase currents are shown in Fig. 5. The analysis of these measurement data show that: • Total current harmonic distortion in each phase exceeds the limit of 3% according to standards. However, these distortions are less then 0.2A, meaning the current might not cause problems in the power system, but will definitely affect the transformer. • Phase voltages are almost equal in each phase, and also the line voltages are equal, which was not the case on the secondary side.

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• Reactive power is notably larger than active power in each phase, which indicates low power factor because of the large inductance. • System power factor is PF ≈ 0.57, due to the load characteristics. • 3rd and 5th current harmonics have the greatest impact on the current RMS values, and harmonics higher than the 5th can be neglected again. • Current waveforms are substantially distorted in phase B and C, and closest to pure sine wave in phase A.

Fig. 5. Case B.2 (a) Harmonic spectrum of primary phase current; (b) Waveforms of primary phase current.

According to the mathematical procedure described in IEEE Std. C57.110 and explained in section 2 of this paper, a detailed analysis of the transformer losses can be done. From the data obtained at no load and short circuit tests, the rated losses are calculated as follows:

(

)

(

)

PR = I 2 Rrated = K ⋅ I 12− R R1 + I 22− R R2 = 1.5 ⋅ 5.9 2 ⋅ 3.83 + 6.84 2 ⋅ 0.8 = 256.13 W

(13)

From Eq. (4) – (6) the eddy current and other stray losses are distinguished from the measurement data: PTSL − R = PLL − R − PR = 465 − 256.13 = 208.87 W

(14)

PEC − R = 0.67 ⋅ PTSL − R = 139.95 W

(15)

POSL − R = PTSL − R − PEC − R = 208.87 − 139.95 = 68.92 W

(16)

In Table 4 are summarized the measurement results of harmonic components of the secondary currents in each phase, which are essential for calculating the harmonic factors and losses correction. As stated in section 5, the even harmonic components are much smaller than the odd ones, and therefore can be neglected in the calculation. Harmonics of number higher than h=9 are negligible as well. Table 4. Secondary phase current spectrum (case B) and basic data calculation for harmonic factors h

Phase A

Phase B

Phase C

Ih/I1

(Ih/I1)

(Ih/I1) ·h

1

1.000

1.000

1.000

3

8.594

73.852

5

6.370

40.579

7

3.902

15.224

745.991

72.213

0.0075

0.0001

0.0027

0.0002

0.0078

0.0002

0.0030

0.0003

9

1.475

2.177

176.314

12.624

0.0014

0.0000

0.0002

0.0000

0.0007

0.0000

0.0000

0.0000

132.83

2602.532

410.751

1.0004

1.0108

1.0015

1.0004

1.0064

1.0011

Total

2

Ih/I1

(Ih/I1)

(Ih/I1) ·h

1.000

1.000

1.000

1.000

664.668

177.852

0.0097

0.0001

1014.473

147.054

0.0167

0.0003

2

2

(Ih/I1) ·h 2

0.8

2

Ih/I1

(Ih/I1)

(Ih/I1)2·h2

(Ih/I1)2·h0.8

1.000

1.000

1.000

1.000

1.000

0.0008

0.0002

0.0173

0.0003

0.0027

0.0007

0.0070

0.0010

0.0051

0.0001

0.0007

0.0001

2

2

(Ih/I1) ·h 2

0.8

2

10

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The load losses at assumed sinusoidal conditions for transformer load as connected in Case B are calculated taking into account the average current value from all the phases. Using Eq. (7) and (8) and the basic data from Table 4 and Table 5, PEC and POSL are calculated. Harmonic factors which are used for correction of the additional losses at non-sinusoidal conditions are calculated using Eq. (9) and (10) (Table 5). The summarized losses are given in Table 6 and in Fig. 6. In total, transformer losses are increased for 74.01W, i.e. 46.6% in actual harmonic conditions compared to the case when sinusoidal conditions are assumed. Table 5. Harmonic factors at nonlinear load as in Case B.

Σ(Ih/IR)2h2 Σ(Ih/IR) h

Phase A

Phase B

Phase C

Average value

0.1127

0.1277

0.0021

0.0808

0.1117

0.1270

0.0003

0.0797

FHL

19.5924

1.0104

1.0060

7.2029

FHL-STR

3.0922

1.0011

1.0007

1.6980

2

0.8

(

)

(

)

P = I 2 R = K ⋅ I 12 R1 + I 22 R2 = 1.5 ⋅ 1.82 2 ⋅ 3.83 + 1.58 2 ⋅ 0.8 = 22.04 W

PEC = PEC − R

h = hmax

 h =1

POSL = POSL− R

 Ih   IR

h = hmax

 h =1

(17)

2

 2  h = 139.95 ⋅ 0.0808 = 11.312 W 

 Ih   IR

(18)

2

 0.8  h = 68.93 ⋅ 0.0797 = 5.492 W 

(19)

Table 6. Transformer losses at rated conditions and nonlinear conditions, with and without taking into account the harmonic factors Type of losses

Rated losses (W)

Load losses (W)

120

120

IR

256.13

Eddy current losses (PEC)

139.95

Other stray losses (POSL) Total

No load 2

Harmonic factor

Corrected losses (W)

/

120

22.04

/

22.04

11.31

7.2029

81.48

68.93

5.49

1.6980

9.33

585.01

158.84

/

232.85

Fig. 6. Transformer losses at rated and nonlinear conditions.

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11

The maximum low voltage winding eddy current loss density can be calculated according to Eq. (12) as follows: PEC − R (max) =

2.4 ⋅ PEC − R K

⋅ I 22− R

⋅ R2

=

2.4 ⋅139.95 1.5 ⋅ 6.84 2 ⋅ 0.8

= 5.982 pu

(20)

The maximum per-unit local loss density under rated conditions, PLL-R (pu) is then 6.983 pu. Therefore, the maximum permissible non-sinusoidal load current with the measured harmonic spectrum, from Eq. (11) is: I max =

6.982 = 0.398 pu 1 + 7.203 ⋅ 5.982

(21)

Transformer’s equivalent capability in continuous harmonic conditions is Imax=0.46.84=2.736A. When a transformer is subjected to a load current having significant harmonic content, the extra eddy-current loss in winding conductors will increase the hot-spot temperature above the normal operating value at sinusoidal conditions. In the end conductors, especially of the inner winding, the highest radial electromagnetic flux density passes through the conductor, causing eddy-current loss proportional to the square of the electromagnetic field strength (i.e. the load current that produces the field) and to the square of the frequency [5]. In order to reduce harmonic’s influence on transformers already in operation, the simplest, however not the cheapest solution, is to install filters on the secondary side of the transformer. It is recommended to use active filters which inject equal and opposite harmonics into the power system to cancel those generated by other equipment [10]. However, the problem is that current harmonic spectrum and amplitude generally do not remain constant due to the load changes. Therefore, it is also possible to electrically isolate the linear loads from the nonlinear ones by using an additional distribution transformer called separately derived system. If it is not possible to replace the existing transformer with a unit specially designed to withstand harmonic currents, the recommended practice is to reduce transformer capacity by derating, i.e. calculating the permissible continuous loading at non-sinusoidal conditions as it was shown in this paper. 6. Conclusion This study confirmed the theoretical assumptions about harmonic impact on distribution transformers and provides a better understanding of the problem. Two different types of load were analyzed: linear active and nonlinear active-inductive load. In the first case, no particular problems with power quality were noticed. The second case showed harmonic presence in transformer secondary currents, which was also reflected on the primary side. Current harmonic distortion caused additional power losses in the transformer, which were calculated according to the IEEE Std. 57.110-1998. For the transformer tested with a typical load, the losses increased by 74.01W. If this transformer operates continuously with the harmonic spectrum analyzed, its maximum load allowed is 2.74A in order for its life-expectancy to remain unchanged. References [1] O.C Ozerdem, A. Al-Barrawi, S. Biricik, Measurement and comparison analysis of harmonic losses in three phase transformers, International Journal on Technical and Physical Problem in Engineering, Vol.5 Issue 14, March 2013, pp. 114-118. [2] R.C. Dugan, M.F. McGranaghan, S. Santoso, H.W. Beaty, Electrical Power Systems Quality, third ed., McGraw Hill, 2012. [3] M.A.S. Masoum, E.F. Fuchs, Power Quality in Power Systems and Electrical Machines, Elsevier Academic Press, California, 2008. [4] N.R. Jayasinghe, J.R Lucas, K.B.I.M. Perera, Power System Harmonic Effect on Distribution Transformers and New Design Considerations for K Factor Trnasformers, IEEE Sri Lanka Annual Sessions, September 2013. [5] Transformers Committee of the IEEE Power Engineering Society, IEEE Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents, USA, 30 March 1999.

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[6] D.M. Said, K.M. Nor, Effects of Harmonics on Distribution Transformers, 2008 Australasian Universities Power Engineering Conference, University of New South Wales, Sydney, Australia 14-17.12.2008. [7] Omni-quant user’s manual, downloaded from http://www.haag-messgeraete.de/cms/front_content.php?idcat=98 [16.09.2016]. [8] IEC 60076-1:2011 Power Transformers – Part 1: General, 20.04.2011. [9] IEEE Recommended practice and Requirements for Harmonic Control in Electric Power Systems 519-2014, IEEE Power and Engineering Society, August 2014. [10] M.N. Rao, M. Mandal, Distribution Transformer – Impact of Harmonics, Estimation of Losses and Life Expectancy & Mitigation of Ill Effects, NTPC Electric Supply Company Ltd., available at http://www.academia.edu/6676494/Distribution_TransformerImpact_of_Harmonics-IEEE_Format-2, [09.07.2017]

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