ADVANCED POWER SYSTEM (Technical Elective 3)

Course Description:

This course introduce the basic theories and applications of power systems, basic structure of power systems, recent trends and innovations in power system, complex power,per unit quantities, network modeling and calculations, load flow studies, short circuit calculations and use of computer for simulation.

Course Objective:

At the end of the course, the students shall be able to:

1. Understand a broad range of topics in the power systems.
2. Learn the basic theories and applications in the power system.
3. Learn some numerical methods used in power system.
4. Solve problems about power system.
5. Emphasize the important role of computer in power system computations and advancement.

PER-UNIT SYSTEM

In power systems many transformers at various (different) voltage levels are involved. Per Unit System is a normalization procedure which provides a mathematical basis for analyzing power networks with relative ease and convenience. In addition, when various quantities are expressed in per unit ( pu ) or per cent values, they usually convey a message. For example, if a bus voltage is 0.98 pu, it means that this value is 98 % of the nominal or base value which could be at any level in the network. It also immediately conveys a message that the value is an acceptable one. On the contrary, if the voltage value is 1. 08, then it immediately conveys that the value is higher than the acceptable level of 1.05 pu. Similar conclusions can be drawn for other quantities such as current, power and impedance. The idea here is to express various variables as a fraction of their corresponding base (fixed) variables.

Quantity in per unit (p.u.) Actual Quantity

Base Value of Quantity (1)

There are several advantages offered by using per unit systems. These are listed below.

SINGLE-PHASE SYSTEMS

The basic idea is to select two electrical variables such as power and voltage as

independent base values. Then the base values for other two variables, namely, current and impedance follow by Ohm’s Law. We will illustrate this procedure for single-phase systems:

Let base value for power = S_1B (single-phase)

base value for voltage = V_B (line-neutral)

= V_B (ln)

Then I_B¹ (line) = I_B (l) = (2)

and Z_B(y) = (3)

The Z_B is on a per phase basis.

We will consider an example to illustrate the use of per unit system.

V Z = R + jX

One should realize that V, I, and Z are actual complex values. The base values used for normalization are, however, real values. Therefore by equation (1) the respective per unit values are also complex.

Now,

V_p.u. = (4)

I_p.u. = (5)

Z_p.u. = (6)

= R_p.u. + jX_pu (6a)

and S_pu = (7)

or = (8)

= (9)

= P_pu + j Q_pu (10)

Numerical Example

Let_. V = 118 0⁰ volts

Z = 5 30⁰ ohms

Then I = 23.6 -30⁰ amperes

& S = V I* = (118 0⁰)(23.6 +30⁰) va

= 2,784.8 30⁰ va

For this example, it is appropriate to choose:

S_lB = 3,000 va

V_lB = 120-volts

Then I_lB = = 25 amperes

& Z_lB = = 4.8 ohms

Three-Phase Systems

Three-phase systems may be normalized by picking appropriate three-phase bases. We will illustrate the various base choices for both Y and D systems on a comparative basis:

Wye (Y)	Delta (D )
Choose (1) S3B = 3SlB	(1) S3B = 3SlB
(2) VB (ll) = VB(ln)	(2) VB(ll)
IB (l) =	IB (l) =
Since S3B = VB(ll)IB(l)	IB(ph) =
ZB(Y) =	ZB(D ) =
ZB(Y) =	ZB(D ) =

Base Equations for D Systems

Choose S_3B as the three-phase apparent power base (rating if available) and V_B(ll) as the line-to line base. Here again if the system nominal line-to-line is available or known, choose this value as the base.

I_B (l) = or I₁(pu) =

I_B(ph) = Þ I_ph(pu) =

Z_B(D ) = Þ ZD (pu) =

Base Equations for Y Systems

Choose S_3B as the three phase power base and V_B(ll) as the line-to-line voltage base.

Then I_B(l) = =

where V_B(ln) =

and Z_B(Y) = =

This can also be shown =

Change of Base

It is often necessary to convert the base values of several pieces of equipment connected together to form a power system (or interconnected power system). Usually the name plate ratings of these individual devices are different and hence their respective individual base values will be also different. In order to refer all per unit values to a common system base, it is necessary to change all device p.u. values to the common p.u. values. An example later will illustrate this procedure. However, the key equation development is as follows:

=

or = =

ß ß

l-l values three-phase values

Advantages of Per-Unit System (P.U.)

1. Per-unit representation results in a more meaningful and correlated data. It gives relative magnitude information.

2. There will be less chance of missing up between single - and three-phase powers or between line and phase voltages.

3. The p.u. system is very useful in simulating machine systems on analog, digital, and hybrid computers for steady-state and dynamic analysis.

4. Manufacturers usually specify the impedance of a piece of apparatus in p.u. (or per cent) on the base of the name plate rating of power () and voltage (). Hence, it can be used directly if the bases chosen are the same as the name plate rating.

5. The p.u. value of the various apparatus lie in a narrow range, though the actual values vary widely.

6. The p.u. equivalent impedance (Z_sc) of any transformer is the same referred to either primary or secondary side. For complicated systems involving many transformers or different turns ratio, this advantage is a significant one in that a possible cause of serious mistakes is removed.

7. Though the type of transformer in 3-phase system, determine the ratio of voltage bases, the p.u. impedance is the same irrespective of the type of 3-phase transformer. (Yç D , D ç Y, D ç D , or Yç Y)

8. Per-unit method allows the same basic arithmetic operation resulting in per-phase end values, without having to worry about the factor ‘100’ which occurs in per cent system.

Experience will, definitely, show the usefulness of the p.u. system.