The Effect of Tap Changing Transformer on Load Flow

The effect Of Tap Changing Transformer on Load Flow

Najimaldin M. Abbas#1, Parween Raheem K. AL-Dawodi*2

#1College of Engineering , Kirkuk University

Kirkuk, Iraq

* Technical Institute / Haweja

Kikuk, Iraq

Abstract--It is necessary to run networks of electrical power system based on economic criteria as well as other criteria such as improving voltage and reduce power losses as possible. Load tap changer transformer (LTC) is one of the tools that used to control voltage and reactive power in electrical power system to face sudden changes in voltage caused by natural load fluctuations . The aim of this work is to establish an on load tap changer model for determining optimum voltage profile and minimum total losses in the power system, Newton-Raphson algorithm is used for solving power flow problem and the effect of tap changer has been analyzed.The results and simulation obtained are presented using MATLAB programming. The results show the ability of LTC to improve voltage profile and reduction of total power losses when added singly or doubly in the system, and the result showed that the magnitude of voltage is increased with tap ratio increasing and vice versa, and reactive power losses is reduced then start to increase with increasing in tap ratio for LTC, while the active power losses not effected by changing tap ratio. Also the results show the efficiency of LTC in improving line loadability by redistribute power flow in lines and reduce loadability in overloading line and redirect the power flow to less loading line.

KEY WORDS-- tap changing transformer, load flow analysis, power system, voltage control .

Introduction:

Load flow analysis is the determination of current, voltage, active power and reactive power at various points in a power system operating under normal steady state conditions .[1]

In daily operation of electric power system , a stable power supply is becoming very important. The purpose of optimizing power system transformer tap setting is to minimize power system losses and at the same time maintaining an acceptable voltage profile . minimization of losses is important because it can be lead to a more economic operation of power system. If more losses can be minimized ,the power can be consumed efficiently. A more powerful tool is required to meet the demand.[2]

In this paper , tap changer transformer techniques applied to assist the power system operation. This is used to reduce the line losses while the voltage profile of the power system improved.

System model for load flow Studies:

The variables and parameters associated with bus i and a neighbouring bus k are represented in the usual notation as follows:[3]

Vi=Viexp(j δi)=Vicosδi-jsinδi ….(1)

Where:

Vi : voltage of bus i

δi phase angle of the bus voltage .

Yij=Yijexp(j θij)=Yij(cosθij+jsinθij) ….(2)

Where:

Yij : off diaognal terms of Ybus matrix (mutual admittance)

θij phase angle of the admittance for element connected between the busses i and j in the Ybus

Complex power :

Si=Pi+jQi=ViIi* ….(3)

Where :

Si complex power

Pi real power of bus i

Qi reactive power of bus i

Using the indices G and L for generation and load,

Pi=PGi-PLi=RE[ViIi*] ….(4)

Qi=QGi-QLi=Im[ViIi*] ….(5)

Where :

PGi& QGi Generated real and reactive power in bus i PLi& QLi Demand real and reactive power in bus i

Ii current of bus i

The bus current is given by:

Ii=j=1nYij.Vj ….(6)

Hence , from the equation (3) and (6), for an n-bus system :

Ii=Pi-jQiVi*=Yii.Vi+j=1j≠in Yij.Vj …..(7)

And from equation (7)

Vi=1Yii[Pi-jQiVi*-j=1j≠inYij.Vj] ….(8)

Further ;

Pi+jQi=Vij=1j≠inYij .Vj ….(9)

In the polar form :

Pi+jQi=j=1nVi.Vj.Yijexp(j(δi-δj-θij)) ….(10)

So that

Pi=j=1nVi.Vj.Yijcos(δi-δj-θij) ….(11)

and

Qi=j=1nVi.Vj.Yijsin(δi-δj-θij) ... (12) where :

δ phase angle of the bus voltage .

i=1,2,…..n

i≠slack bus

The power flow equation (11) and (12) are nonlinear and it is required to solve 2(n-1) such equations involving Vi, δi, and Qi at each bus i for the load flow solution . Finally, the powers at the slack bus may be computed from which the losses and all other line flows can be ascertained.

Line flow and losses: [1][4]

After iterative solution of bus voltage , the next step is the the computation of line flow and line losses . the line current Iij from bus i to bus j is computed as :

Iij= yij Vi-Vj+yi0Vi …..(13)

The complex power Sij from bus i to bus j and Sji from bus j to bus i are :

Sij=ViIij* ..…(14)

Sij=ViIij*=ViVi*- Vj*. yij*+Vi2. yi0* ……(15)

Sji=ViIji*=VjVj*- Vi*. yji*+Vj2. yj0* ……(16)

The power loss in line i-j is the algebraic sum of the power flows determined from (15) and (16) i.e.

SLij =Sij+Sji ……(17)

Newton Raphson Power flow : [5]

The solution strategy for Newoton- Raphson method is :

1- Assign initial voltage magnitudes and zero voltage angles to all bus-bars except the slack bus-bar.

2- Using available bus-bars voltages, calculate values for∆P and ∆Q for all bus-bars from eqs:

∆Pi=Pi sch-j=1nVi.Vj.Yijcos(δi-δj-θij) ….(18)

∆Qi=Qi sch-j=1nVi.Vj.Yiksinδi-δj-θij ….(19)

3- Check whether the values of ∆P and ∆Q are smaller than the prefined convergence tolerance ε

4- If convergence has been achieved, output all bus-bar and line flow conditions and terminate the procedure.

5- If convergence has not been achieved, then use Table (1) equations to derive the elements of the Jacobian matrix.

Table (1) Content of Jacobian Sub matrices in polar coordinates

Diagonal element / Off- diagonal element
J1 / ∂Pi∂δi / ∂Pi∂δj
J2 / Vi∂Pi∂Vi / Vj∂Pi∂Vj
J3 / ∂Qi∂δi / ∂Qi∂δj
J4 / Vi∂Qi∂Vi / Vj∂Qi∂Vj

6- Solve Eqs. (15) for all ∆δ and ∆VV

∆P∆Q=J1 J2 J2 J2∆δ∆VV ….(20)

7- Update values of δ and V in preparation for repeating the procedure, thus

δinew=δiold+∆δi ….(21)

Vinew=Viold+∆Vi ….(22)

Vinew=Viold1+∆ViVi ….(23)

Tap changing transformer :

The tap changing transformer can be used to control the voltage fluctuations at load busses[6]. It can also be used to control active and reactive power flow in a power system. The section below develops the bus admittance equation to include such transformers in power flow studies[4].The admittance Y is shown on the side of the ideal transformer nearest node (j), which is the tap changing side. The designation is important in using the equation which is to be derived. If we are considering a transformer with off-nominal turn ratio, t may be real or imaginary[7].

Fig(1) shows a detailed representation of a model for LTC with a turn ratio of 1/t where t represent tap setting [6].

Current Ii and Ij entering the two buses, and the voltage are Vi and Vj referred to reference node.

Complex power at both the primary and secondary are given by[6]:

Si= ViIi* …..(24)

Sj= tViIj* …..(25)

Since we assuming that we have an ideal transformer with no losses, the power Siinto the transformer from bus i must equal to the power - si out of the ideal transformer on the bus j side, and so from equation (1) and (2) we obtain [7] :

Ii= -t*Ij ……(26)

The current Ij can be expressed by :

Ij=Vj-tViY=-tYVi+YVj ….. (27)

Where t Tap Changing transformer turn ratio.

Any appreciable drop in voltage on the primary of a transformer due to the change of the load may make it desirable to change the tap setting on transformers provided with adjustable tap in order to maintain proper voltage at the load [7].

Fig(1): circuit having the node admittance of equations(6) when t is real. [3]

The voltage magnitude adjustment can investigate at a bus by means of the automatic tap – changing feature in the power flow program .

Description of the system used in the study

Fig(2) illustrate a five bus-bar system where bus number one is slack bus, bus number two is a PV bus and bus numbers three, four and five are load busses(8) .

Fig(2) the system used in the study[8]

Result and discussions :

A MATLAB program is used to find the Ybus of the system in figure(2), A software is written to find the Ybus of the system and consequently to find the voltage of the busses, system power flow and total losses. This work is applied on IEEE-5 bus test system as shown in fig(2). First the load flow analysis during steady state is carried out by a general load flow program method using Newton- Raphson method, Results of voltage, real power and reactive power for each bus is shown in table(2) and the power flow for each branch , losses of the branches and the total losses of the whole system is shown in table (3) without using tap changers.

Table (2): voltage, real and reactive power of the busses in figure(6).

Bus No. / Bus voltage / Net Bus (p.u) / Net Bus (Mvar)
1 / 1.0600 / 1.2959 / -0.0742
2 / 1.0474 / 0.2000 / 0.2000
3 / 1.0242 / -0.4500 / -0.1500
4 / 1.0236 / -0.4000 / -0.0500
5 / 1.0179 / -0.6000 / -0.1000

Table (3): power flow , branch losses and the total losses of the busses

line / Line flow(p.u) / Losses(p.u)
from / to / MW / Mvar / MVA / MW / Mvar / MVA
1 / 2 / 0.7540 / - 0.2466 / 0.7933 / 0.0109 / 0.0346 / 0.0363
1 / 3 / 0.3802 / - 0.0205 / 0.3808 / 0.0103 / 0.0239 / 0.0260
2 / 3 / 0.2586 / 0.0472 / 0.2629 / 0.0038 / 0.0323 / 0.0325
2 / 4 / 0.2888 / 0.0387 / 0.2914 / 0.0047 / 0.0298 / 0.0302
2 / 5 / 0.5530 / 0.0769 / 0.5583 / 0.0112 / - 0.001 / 0.0112
3 / 4 / 0.1746 / - 0.0672 / 0.1871 / 0.0003 / 0.0204 / 0.0204
4 / 5 / 0.0585 / - 0.0283 / 0.0650 / 0.0003 / 0.0524 / 0.0524
Total
losses / 0.0415 / 0.1923

To find the effect of Tap Changer on the system we assume these cases:

Case study1: The first case study is to demonstrate the influence of the load tap changer to enhance the performance of the system when LTC is added on line 1-2 with a tap ratio 1.04. Results presented in Table (4) shows the active and reactive power flow and total active and reactive power losses, and Table(5) shows the voltage and the net bus MW and Mvar without increasing in load . When load on bus 2 is increased by 50% the results are as shown in Tables(6).

Table (4) power flow , branch losses and the total losses of the busses when a LTC is added on line 1-2 without increasing in load and Tap ratio equal to 1.04

line / Line flow(p.u) / Losses(p.u)
from / to / MW / Mvar / MVA / MW / Mvar / MVA
1 / 2 / 0.6838 / - 0.2813 / 0.7393 / 0.0094 / 0.0393 / 0.0404
1 / 3 / 0.3666 / - 0.0279 / 0.3676 / 0.0096 / 0.0262 / 0.0279
2 / 3 / 0.2645 / 0.0496 / 0.2691 / 0.0040 / 0.0320 / 0.0322
2 / 4 / 0.2936 / 0.0406 / 0.2964 / 0.0048 / 0.0296 / 0.0299
2 / 5 / 0.5554 / 0.0776 / 0.5608 / 0.0113 / - 0.0009 / 0.0113
3 / 4 / 0.1676 / - 0.0702 / 0.1817 / 0.0003 / 0.0206 / 0.0206
4 / 5 / 0.0561 / - 0.0294 / 0.0633 / 0.0002 / 0.0527 / 0.0527
Total
losses / 0.0396 / 0.1996 / 0.2034

Table (5): voltage, real and reactive power of the busses .

Bus No. / Bus voltage / Net Bus (p.u) / Net Bus (Mvar)
1 / 1.0600 / 1.2896 / -0.0816
2 / 1.0620 / 0.2000 / 0.2000
3 / 1.0356 / -0.4500 / -0.1500
4 / 1.0357 / -0.4000 / -0.0500
5 / 1.0321 / -0.6000 / -0.1000

Table (6) power flow , branch losses and the total losses of the busses when a tap changer of turn ratio 1.04 is interposed between bus 1 & 2 and the load on bus2 increased by 50%

The effect of using different taps (by changing the tap changer turn ratio) on the voltage of the busses and total active and reactive power losses is shown in Table(7)

Table(7) The effect of changing taps on bus voltage and total losses when bus 2 load (P,Q) increased by 50% .

tap / 1.02 / 1.04 / 1.06 / 1.08
V1 / 1.06 / 1.06 / 1.06 / 1.06
V2 / 1.0544 / 1.0589 / 1.0633 / 1.0678
V3 / 1.0297 / 1.0331 / 1.0366 / 1.0401
V4 / 1.0294 / 1.0331 / 1.0368 / 1.0406
V5 / 1.0247 / 1.0290 / 1.0334 / 1.0378
Total (P)Loses / 0.041l4 / 0.0415 / 0.0419 / 0.0424
Total (Q) Loses / 0.1906 / 0.1923 / 0.1933 / 0.1935

The effect of changing tap ratio on total losses when either(P or Q) is increased by 50% while the other is kept constant is given in Table(8)