Evaluating and Derating of Three-Phase Distribution

2014 IEEE 8th International Power Engineering and Optimization Conference (PEOCO2014), Langkawi, The Jewel of Kedah, Malaysia. 24-25 March 2014

Evaluating and Derating of Three-Phase Distribution Transformer under Unbalanced Voltage and Unbalance Load Using Finite Element Method 1

Atabak Njafi , 2 İres İskender, 3 Naci Genc

1,2

Gazi University, Electrical and Electronics Engineering department, Ankara , turkey

3

Yuzuncu Yil , Engineering and architecture faculty, Electrical and Electronics Engineering Dpt, Van ,Turkey 1

[email protected] , 2 [email protected], [email protected]

Abstract: Power transformers illustrate the majority of capital investment in transmission and distribution centers. Additionally, interruptions of power transformer have a significant economic Effects on the Performance of an electrical network. For this reason , the safe and reliable Performance relate directly to the Security and stability of power system. This paper studies the growth of power losses and Derating of Distribution transformer, working under unbalance voltage and unbalanced load conditions. In this paper, computerbased simulation utilizing the two and three dimensional finite element methods (3-D and 2_D FEM) are exploited as a tool for visualizing magnetic fields of distribution transformers. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. The performance of the transformer when the load and supply are balanced compared to the case in which voltage or load is unbalanced indicates that the unbalanced load only causes the copper loss to increase, while the unbalanced voltage not only increases copper loss but also adds to the core loss. The indices of voltage unbalance factor (VUF) are used in this paper to evaluate the unbalance propagation. This process enables the software to simulate and analyze different electromagnetic parameters such as magnetic flux lines, flux density, losses, and etc, under different input sources with high accuracy.

the networks. Mostly, for calculate the percentage of asymmetry of three-phase voltages is used the ratio of their negative to positive sequence component. This ratio is introduced as the voltage unbalance factor (VUF). Assuming that the magnitudes of three-phase voltage phasors being Gaussian coincidental variables and no phase angle diversions (i.e., 120 out of phase with together), Pierrat and Morrison [5] developed a probability model of the VUF And demonstrated that if the unbalance were generally propagate by asymmetry in system impedances, the VUF would have a Gaussian distribution, and showed that if system impedances were symmetric voltage phasors the VUF would have a Rayleigh distribution, as it can be different in amplitude and/or phase angle. Unbalanced load Distribution over three phases can cause a voltage unbalance that is further difficult to reduce. An unbalance power component was characterized in the total apparent power in conditions of the symmetric ingredient [6]. The proportion of negative series component on the positive series component was used for calculate the

Keywords: distribution transformer, derating, time stepping finite element (TSFEM), unbalanced voltage, unbalanced load

unbalance percentage in [7]. Derating of the transformers is the elementary and useful method for the secure operation of transformers under non-sinusoidal and unbalance operating situation. Derating is the intentional reduction in load capacity of

I.

Introduction

Nowadays , a significant concern for power quality specialists is Voltage and load asymmetry due to its problem on the load and the source. Study the diffusion of asymmetry through the electric power system and the methods to minimize it, is essential because of the negative effects of the voltages and load asymmetry on

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a transformer under non-sinusoidal and unbalance operation [8]. In this paper, for modeling the transformer under unbalance voltage and load, the time-stepping finiteelement method (TSFEM) is used .TSFEM, provides an effective method of analysis and simulation of distribution transformer under this condition. Afterwards, Based on the data obtained from the FEM, a

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2014 IEEE 8th International Power Engineering and Optimization Conference (PEOCO2014), Langkawi, The Jewel of Kedah, Malaysia. 24-25 March 2014

%VUF=

distribution transformer under different unbalanced condition has been derated . Subsequently, the transformer under the unbalanced supply voltage has been Studied and the impacts of the unbalanced supply voltage on load current represented.

3 C. Approximated definition:

The approximated quantification of voltage unbalance factor is given by: VUF

β

(a)

1

3

6β

1

3

6β

v v

v v

100%

v v

4

Where Vab , Vbc and Vca are the rms values of the three-phase basic frequency line-to-line voltage phasors. One of the most accurate quantification method is IEC, due to it uses the relation of negative and positive sequence voltage. QUANTITY Primary voltage Secondary voltage Rated power No.of primary winding turns No.of secondary winding turns Primary winding resistance Secondary winding resistance Width of window Height of window Height of LV winding Height of HV winding

(b) Fig. 1.mesh operation of studied transformer a) 3-D b) 2-D II. Determine the amount of Voltage Unbalance

Several definitions are available For amount of unbalanced voltage

Determine the

A. IEEE Definition: The recent IEEE std.1159 gives both the IEEE 112 and 936 definitions and the proportion of negative and positive- series voltage (the “true value”). The IEEE quantification of voltage unbalance is given by:

VUF

max V , V , V

min V , V , V V

Unit KV KV KVA ……… ……… ohm ohm mm mm mm mm

Table (1): Electrical parameters of studied transformer

III.Unbalanced Current : unbalanced current caused by unbalance voltage and load that leads to an unanticipated performance of transformer. Therefore, Relationship between the unbalanced voltage and current are studied here.

%PVUR

max voltage deviation from the avg phase voltage avg phase voltage

Value 34.5 0.4 100 7469 50 313.26 0.0108 180 360 310 254

1

CUF

2

I I

V Z V Z

Z Z

V

Z

×V =Z ×VUF

(5)

Here Z1 and Z2 are the impedances of positive and negative components of the transformer.

B. True quantification (IEC): Fortescue ingredients or symmetrical ingredients apply To determine an unbalance in voltage or current of a three-phase system. The three-phase system is decomposed into a direct or positive- series, inverse or negative- series and zeroseries system. The IEC definition, is given:

IV. Distribution Transformer Analysis by time method

domain finite element

The FEM is a scalar procedure for solving partial differential and integral equations. This technique will either resolve the differential equation and make the problem steady-state or approximate the equations into

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2014 IEEE 8th International Power Engineering and Optimization Conference (PEOCO2014), Langkawi, The Jewel of Kedah, Malaysia. 24-25 March 2014

a system of common differential equations and afterwards apply the scalar integrating method that provide by the standard methods such as Euler’s, RungeKutta methods ,etc. The basic idea behind the FEM is to divide the region to be studied into minor sub-regions named finite elements. A 3-phase, Dy11, 100 kVA, 34.5kV/400V distribution transformer is studied in this paper. Fig. 1, demonstrated The Two-dimensional and Three dimensional modeling of the distribution transformer under mesh operation and Table ( 1) briefly illustrate the characteristics of the proposed transformer. İn the Three-dimensional modeling, all the meshes shapes is tetrahedral . FEM with utilize magnetic parameters and geometrical dimensions of the transformer Applied to compute the magnetic- field distribution inside the transformer. The time step that has been chosen about 0.2 ms, for all simulations of this paper. In magnetic field evaluation, the magnetic vector potential (A), include a series of information of magnetic field intensity (H), and magnetic flux density (B). Reference [4] displays the temporary and spatial variations of A.

A

µσ

A

µJ

0

There is dependence between The magnetic flux density and magnetic vector potential. Other words, the magnetic flux density is dependent to the Percentage change in the magnetic vector potential. when the

(a)

(6) (b)

In this equation, µ is the magnetic permeability, σ is the electrical conductivity, and J0 is the applied current density A

jwA

Fig 2: Distribution of magnetic field in transformer core in 2d model: (a) balanced voltage(b) unbalanced Voltage

unbalance voltage happens, its leads to the rise in flux density. In a transformer with unbalanced supply voltage, distribution of flux density is asymmetric, for this reason, core loss and copper loss increase. Distributions of Magnetic flux lines inside the core with balanced and unbalanced voltages at same time are shown in Fig. 4(a) & 4(b), respectively.

(7)

By using the complicated form of the magnetic field in the three dimensional model in Cartesian coordinate (x, y ,z), hence: A

A

µ

µ

J

A µ

0

(8)

curl of the B , used to calculate vector potential A: B=

jwσA

A

The magnetic (9)

The fundamental equation of the electric circuits is given by; VS=RS i+LS

(10) Fig3: magnetic field Distribution in transformer core in 3D model under

Fig. 2 & 3 displayed the flux density distributions in a transformer with balanced and unbalanced voltages.

unbalanced Voltage (case 2

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2014 IEEE 8th International Power Engineering and Optimization Conference (PEOCO2014), Langkawi, The Jewel of Kedah, Malaysia. 24-25 March 2014

Fig. 5 shows the primary maximum induced voltage for the given transformer at balance and unbalance voltage (case 2). Fig. 7 shows the primary current of the distribution transformer, those changes with time for balance and unbalance voltage situation, respectively. It can be observed in this Fig. (7) that Inrush current after, about 300 ms reduced to the normal value.

XY Plot 3

49.34

Maxwell2DDesign1 Curve Inf o

37.50 25.00

ANSOFT

max

InducedVoltage(Winding_1) Setup1 : Transient

48.4775

InducedVoltage(Winding_3) Setup1 : Transient

48.5317

InducedVoltage(Winding_5) Setup1 : Transient

48.4789

Y1 [kV]

12.50 0.00

-12.50 -25.00 -37.50 -49.67

325.12

340.00

360.00

380.00 Time [ms]

400.00

420.00

436.88

(a)

V. The impact of Unbalanced Voltage and Load on transformer losses: XY Plot 3

58.56

Commonly, Transformer losses are categorized into no load or core losses and load losses as shown in Fig .6

Max well2DDesign1 Curv e Inf o

40.00

ANSOFT

max

InducedVoltage(Winding_1) Setup1 : Transient

52.1675

InducedVoltage(Winding_3) Setup1 : Transient

53.4858

InducedVoltage(Winding_5) Setup1 : Transient

49.6878

Y1 [kV]

20.00

0.00

-20.00

-40.00

-57.12 388.33

400.00

412.50

Tim e [m s ]

425.00

437.50

450.00

453.81

(b) Fig5: primary winding induced voltage under a)balance b)unbalance voltage (case2)

This can be written in equation form:

PT= PNL+PLL (a)

(11)

PCore are the core losses or no load losses Because of the voltage excitation. PLL, categorize into Pdc losses or windings losses and stray losses that Because of the electromagnetic fields in the windings, magnetic shields, core clamps, enclosure or tank walls, etc . Pdc Can be calculated by multiplying the dc resistance of the winding with the square of the load current. The stray losses additionally divided into winding eddy losses and structural part stray losses. Winding eddy losses divided in to eddy current losses and Rotating current losses. Other stray losses Because of the losses in the clamps, tank or enclosure walls, etc. This can be shown as:

(b) Fig4: Magnetic flux lines Inside the the core: (a) balanced voltage(b) unbalanced voltage

Supply voltage

Phase (a-b-c)

P core (w)

P cu (w)

AC loss(w)

Total loss (w)

IEEE definition VUF%

Balance case Unbalanc e case 1 Unbalanc e case 2 Unbalanc e case 3

%0-%0-%0

271

1575

50

1896

--------

0.015-0.045- 0.03

288.13

1725

52,87

2066

0.015

0.07-0.09-0.025

307,49

1947

55.51

2310

0.032

0.12-0.10-0.08

332,55

1962

56.45

2351

0.037

Table (2): losses increases under unbalance voltage

163

Fig 6: Transformer loss classification

2014 IEEE 8th International Power Engineering and Optimization Conference (PEOCO2014), Langkawi, The Jewel of Kedah, Malaysia. 24-25 March 2014

LOAD Balance case Unbalance case 1 Unbalance case 2 Unbalance case 3

Phase (a-b-c) 0-0-0 0,015- 0,045- 0,03 0,07- 0,09 - 0,025 0,12 - 0,10 - 0,08

the unbalanced voltage Causes increase in the both copper loss and core loss, while unbalanced load only causes increase in the copper losses. In Reference [3], have also shown that unbalanced voltage increases the copper loss further than an unbalanced load .

Copper loss 1575 1707 1791 1869

Table (3): Copper loss increases under unbalance load VI. Derating of Transformers under Unbalanced condition:

The transformer (Figs. 1) under unbalance condition is used to compute the derating required for unbalance operating conditions. According to the reference [3], for derating the transformer under this condition, the following steps are involved: In the stage 1: by simulating the transformer under balance and sinusoidal load and supply voltage calculate losses with the nominal resistive load

Unbalance Unbalance Unbalance Unbalance voltage voltage case 1 voltage case 2 voltage case 3 Imax (pu) 0.931 0.92 0.90 Equivalent 93.1 92 90 KVA Table (4): Results of applying derating under unbalance voltage

XY Plot 8

Maxwell2DDesign1

15.00 10.00

Y1 [A ]

5.00

ANSOFT

Curve Info

max

Current(Winding_1) Setup1 : Transient

0.9639

Current(Winding_3) Setup1 : Transient

0.9860

Current(Winding_5) Setup1 : Transient

0.9595

Ploss= pwindings+pcore I

0.00

=

IW

R

R

(14)

-5.00 -10.00

stage 2: Enter an unbalanced state (unbalance load or unbalance voltage ) , in this step, basic load current and output voltage for keep the rated fundamental output KVA :

-15.00 18.63

100.00

200.00

Time [ms]

300.00

400.00

500.00

(a) XY Plot 8

18.41

Maxwell2DDesign1 Curve Inf o

15.00

10.00

IS

ANSOFT

max

Current(Winding_1) Setup1 : Transient

1.0344

Current(Winding_3) Setup1 : Transient

1.0915

Current(Winding_5) Setup1 : Transient

0.9815

(15)

Stage 3: in this step, under unbalance voltage or unbalance load, Compute total power losses to specify the additional losses:

5.00 Y1 [A]

VS = 1 PU

0.00

-5.00

-10.00

-15.00

20.32

100.00

200.00

Tim e [ms ]

300.00

400.00

∆LOSSES%

498.97

P

P

100

P

(b)

16

Fig 7: primary winding current of the distribution transformer for a) rated sinusoidal excitation b) case 2 unbalance voltage of HV winding

PLL= PDC+PEC+POSL

Stage 4: reduce the load amount by Use Maxwell optimization feature in order to, the total loss be equal to the nominal loss:

(12)

To account The total stray losses PSL , we can subtracting Pdc from the load losses PSL=PEC+POSL=PLL-PDC

P

IS

I

P

,

(17)

The result is the new current magnitude (Iderated, expressed in per-unit) that the transformer can deliver without exceeding rated losses.

(13)

Because of the increase of flux density in the transformer core under unbalanced voltage, causes a large increase in core loss and copper loss. Table 2 demonstrates the considerably increase of the core

Stage 5: The new apparent power (derated) can be calculate as:

KVAderated=KVArated×Iderated

and copper losses under unbalance voltage and Can be observed that winding eddy current losses have a slight increase. Table 3 represents the increase quantity of the copper loss due to unbalanced load. If we compare the Tables (2 ) & (3) With each other , It can be seen that,

(20)

In Table 4, the results of applying derating have been shown for three cases, when the percentage of voltage unbalance increases. Table 4 demonstrate that by

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2014 IEEE 8th International Power Engineering and Optimization Conference (PEOCO2014), Langkawi, The Jewel of Kedah, Malaysia. 24-25 March 2014

Increasing the percentage of voltage unbalance degree , the core and copper losses increase for this reason derating factors increase.

Atabak Najafi:

VII. CONCLUSION:

In this paper, a 3-phase, Dy11, 100 kVA, 34.5kV/400V distribution transformer under unbalanced voltage and load by using the time domain finite element method was simulated. In order to visualizing magnetic fields distribution in a distribution transformer, the three and two dimensional finite element method (3-D & 2_D FEM) is utilized . It can be seen in Fig. 2 that, when an unbalanced voltage Happens in transformer, its lead to the increase in flux density. For this reason, in a transformer under this condition the core loss and copper losses increase. If we compare the effect of unbalance voltage and unbalance load with each other in a transformer, it can be seen in the Tables (2) & (3) that, the unbalanced voltage Causes increase in the both copper loss and core loss, while unbalanced load only causes increase in the copper loss.

received his M.Sc. degree in Electrical and Electronic Engineering in 2009, from the University of Tahran , Iran . he is currently pursuing the P.h.D degree in electrical engineering at the University of GAZI , Ankara, turkey . His main interests are power electronics, Power Quality in Power Systems, digital signal processing and Electrical Machines

Ires iskender:

received his M.Sc. and Ph.D. degrees in Electrical and Electronic Engineering in 1990, 1996, and , respectively, from Middle east Technical university, turkey. He is currently an Professor in the Department of Electrical and Electronic Engineering, GAZI University, Ankara, Turkey. His research interests include power electronic, renewable energy,fuzzy control,electrical machine, power quality

Reference: [1] Asheesh K” Some Observations on definitions of Voltage Unbalance” Power Symposium, 39th North American , 2007. [2] Jouanne,A. V., & B. Banerjee. “Assessment unbalance.” IEEE Trans. Power Delivery 16:782–790, 2001.

of

Naci Genc

voltage

[3] M. A. S. Masoum and P. S. Moses “Impact of balanced and unbalanced direct current bias on harmonic distortion generated by asymmetric three phase three-leg transformers,” IET Electro. Power Appl., vol. 4, no. 7, pp. 507–515, Aug. 2010. [4] Makbul Anwari, Ayong Hiendro “New Unbalance Factor for Estimating Performance of a Three-Phase Induction Motor With Underand Overvoltage Unbalance” IEEE Transactions on Energy Conversion, Vol. 25, No. 3, pp. 619-625, Sept. 2010. received his M.Sc. and Ph.D. degrees in Electrical and Electronic Engineering in 2002, 2010 , respectively, from Yuzuncu Yil University , Van, turkey and Gazi University, Ankara , turkey. He is currently an associate Professor and the Discipline Leader for Electrical Power Engineering in the Department of Electrical and Electronic Engineering Yuzuncu Yil University, Van , Turkey. His research interests include power electronics, electric machines, renewable energy, solar photovoltaic energy systems and control systems.

[5] L.Pierrat andR.E.Morrison, “Probabilistic modeling of voltage asymmetry” IEEE Trans. on Power Delivery, vol. 10, no. 3, pp. 1614– 1620, July 1995. [6] A. E. Emanuel “On the definition of power factor and apparent power in unbalanced poly-phase circuits with sinusoidal voltage and current” IEEE Trans. Power Delivery, vol. 8, pp. 841–847, July 1993. [7] G. T. Heydt andW. T. Jewell, “ Pitfalls of electric power quality indices” IEEE Trans. Power Delivery, vol. 13, pp. 570–578, Apr. 1998. [8] IEEE Recommended Practice for Establishing Transformer Capability When Supplying Non-sinusoidal Load Currents, ANSI/IEEE Std. C57. 110-1986, 1988.

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