# Electric power system

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### Objective:

Electric power system is a process deals with generation, transmission & distribution of electrical power which incorporates of electrical devices such as electric motors, generators and transformers. A distribution network is created using a commercially available software package for the system design and understanding of load flow analysis, balanced & unbalanced short circuit analysis, distributed generation reactive power compensation and Power & voltage control which are discussed in detail.

### 1. Load Flow Analysis:

The aim of load flow analysis is to obtain complete voltage angle and magnitude of each bus in a power system for a particular load. Based on the obtained data the active and reactive power flow can be analytically determined on each branch including the generator reactive power output as well. During the load flow, active and reactive power gradually drops down from the supply end to the consumer. The drop in reactive power is more than as compared to drop in active power because of the short circuit level of the circuit. The major constraints that affect the power flow analysis are resistance and reactance components. In electrical transmission system, X/R ratio is high which implies the line resistance can be ignored which leads to the effect of line resistance is very small compared to line reactance. Therefore it clearly state that the vast drop in reactive power is due to the line reactance of the network.

### 2. Set-up of VAR compensator:

The main purpose of VAR compensator is to generate or absorb reactive power. An under- excited machine absorbs the reactive power whereas over-excited machine generates the reactive power. In this instant, a synchronous motor is setup which nearly absorbs half of the reactive power. In long transmission lines, the inductive reactance is very high results the low power to be transmitted in the system. To minify this voltage drop, capacitors are connected in series with the line conductors where they reduce the inductive reactance to increase the power transmission capability.

### 3. Unbalanced short-circuit analysis:

To study the fault on Bus-4 of the network, synchronous motor is replaced by restoring with the original network leads to faults like: Single phase to Earth fault and

Phase to Phase fault.

### 4. Distributed Generation:

Distributed generation is also called as Dispersed or Embedded generation. In general distributed generators are connected to the medium or low voltage grid and typically smaller than 30MW.The main advantage of distribution generation is to reduce the losses in transmission line.

However the Potential problems occurred due to DG are: voltage rise, voltage unbalance (for 1-ph DG), reverse power flow, increase in fault levels and malfunction of protection equipment. The installation of a wind turbine employing an induction motor at busbar5 is incorporated in this network to study the potential problems. During the load flow study, the induction generator supplies power to the busbar5.To compare with the load flow of original network, the response of the network remains the same in both cases due to the induction generator connected to the busbar5 which is very less when compared to other loads of the network when the load is supplied on the busbar5.

### 5. Derivation for Active and Reactive Power Flow:

The following circuit represents the part of a network by its Thevenin equivalent circuit.

Thevenin circuit includes voltage source and series impedance.

Consider a circuit shown in fig1 of a line supplying a load, where the line is represented by series impedance (R+jX).

Let the apparent power at the receiving end be:

S = P + j QÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ______Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (1)

And V1 be the reference phasor, i.e. V1 = V1__|0____0__Â Â Â Â Â Â Â Â Â

S= V1I*****= P + j QÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ______Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (2)

Hence,

I = P-jQV1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â _____Â Â Â Â Â Â Â Â Â Â Â Â Â (3)Â Â Â Â Â Â Â

Therefore, V2Â Â Â =Â Â Â Â V1+(R+jx) P-jQv1Â Â Â Â Â Â Â Â Â Â Â Â Â Â _____Â Â Â Â Â Â Â Â Â Â Â Â Â Â (4)

=Â Â V1 + RP+XQV1 + jXP-RQV1Â Â Â _____Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (5)

The line voltage drop is,

Î”VÂ Â = V2 - V1 =Â Â RP+XQV1 + jXP-RQV1Â Â Â Â Â Â Â Â Â Â _____Â Â Â Â Â Â Â Â Â (6)

Generally, XP- RQ is very small as compared to RP + XQ.

This results in that magnitude of the voltage drop across the line is greatly determined and hence approximately given by:

Î”V =Â Â RP+XQV1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â _____Â Â Â Â Â Â Â Â (7)

While the angular shift is largely determined by:

Î´V = XP-RQV1Â Â Â Â Â Â Â Â Â Â Â ____Â Â (8)

This perhaps shown on the phasor diagram of the circuit and the line voltage drop may be derived as follows.

From the phasor diagram;

V22Â Â =Â Â (V1 + Î”V)2Â +Â Â Î´V2Â Â Â Â Â Â Â Â Â ____Â Â Â Â Â Â Â (9)

= (V1 +R I cosÏ†+ X I sin Ï†) 2 + (X I cosÏ†âˆ’ R I sin Ï†) 2____Â Â (10)

Since P = V1 I cos Ï† and Q = V1 I sin Ï†Â Â Â Â

Therefore, V22 =Â VV1 + RPV1+XQV12Â + XPV1-RQV12Â Â Â

Normally, Î´V << V1 + Î”V

Therefore, V22 â‰ˆ V1 + RPV1+XQV12Â Â Â Â Â Â

Hence magnitude of the line voltage drop is approximately given by:

V2 - V1 = Î”V = RP+XQV1

And the angular shift determined by:

Î´V = XP-RQV1Â Â Â Â Â Â Â Â Â Â Â

Which are the same as equations (7) and (8)

In distribution circuits, the effect of the line resistance (R) is often significant so the effect of the line resistance is very small and may be ignored i.e. R= 0. Thus;

Î”V â‰ˆXQV1

And,

Î´V â‰ˆ Â XPV1

Equations (15) and (16) show that Î”V âˆ Q and Î´V âˆ P.

The angle of transmission (Î´ - the angle between V2 and V1) is obtained from,

Î´ = sin-1Â Î´VV2

Where, Î´ V is given by equation (16).

Thus,Â Â Â Î´VV2=sin Î´

XPV2V1 =Â sin Î´

OrÂ Â Â P =Â V2V1X sin Î´

Equation (20) gives an estimate of the power transfer through a transmission line.

For accurate results, equation (5) or (11) is to be used.

For good approximation equation (13),(14) or (15),(16) can be used.

From equation (15);

V2 - V1 = Î”VÂ Â â‰ˆÂ XQV1

Q =Â V2V1-V12X

âˆ‚Qâˆ‚V1= V2-2V1X

âˆ‚Qâˆ‚V1 Represents the change in the reactive power required to produce a relative change in the voltage.

Equation (23) shows that the smaller the reactance associated with a node, the larger the value of âˆ‚Qâˆ‚V1 for a given voltage drop.

If the three phases of the line shown in Fig (2) are short circuited at the receiving end, the current flowing in the line is;

Isc = V2 XÂ Â Â Â Â Â (assuming R<<X)

Let SCL = V2Isc

Therefore, SCL = V22 X

Where SCL is defined as the short circuit level of the circuit.

With the system at no-load, V2 = V1

Hence, SCL = V12 X

Using equation (13), the relative voltage drop across the line of Figure (2) may be expressed as:

Î”VÂ Â V1 â‰ˆ RP+XQV12

= RP+XQV12 X XX

= XV12RXP+Q

â‰ˆÂ 1SCL RXP+Q

Since fault levels are normally known at all substations, equation (31) gives useful information regarding the p.u. voltage drop as a function of the SCL of the circuit.

When a reactive power (VAr) compensator is employed to control the voltage, equation (31) is modified to:

Î”VÂ Â V1=1SCL RXP+(Q-QC )

Where Qc is the reactive power supplied by the VAr compensator.

Equation (32) shows that by controlling the VAr compensator output (QC), it is possible to

limit or even eliminate the voltage drop due to variation not only in Q but also P.

If R = 0, equation (31) is simplified to:

Î”VÂ Â V1â‰ˆQSCL

Which gives a simple way of getting the approximate value for the voltage change due to any change of reactive power.

Alternatively, equation (33) may be rearranged as,

V2 - V1Â Â V1â‰ˆQSCL

Therefore, Q V2*SCLÂ V1 - SCL

Hence âˆ‚Qâˆ‚V1â‰ˆ -V2*SCLV12 - SCLV1

Equation (36) is the same as equation (23), assumingV2= V1 , and relates the voltage drop to the SCL of the circuit.

In general: P is controlled by the generators governor or phase- shift transformers.

Q is controlled by the generators field or VAR compensators.

6. Performance of VAr Compensation:

Ø Series VAr compensation:

In the replaced distributed network to reduce inductive reactance of long transmission lines, therefore capacitors are connected in series with the line conductors which results the increase in power transmission capability of the line and reduce the voltage drop.

Ø Shunt VAr Compensation:

Shunt capacitors are used to supply lagging VArs. Shunt capacitors are absorb leading VArs whereas reactors are used to absorbs lagging VArs. These capacitors and reactors are directly connected to the bus bars and connected through switches. The number of the elements connected to the system perhaps controlled in order to supply the required VAr demand to maintain a specified voltage value.

### 7. Methods of Voltage Control:

Voltage is controlled in two methods:

Ø Tap changing transformers

Ø Injection of Reactive power

Ø Tap changing Transformers:

This method is based on changing the turns of the transformer, so that the voltage in the secondary side is varied and voltage control is obtained. We have off-loaded tap changer and on-load tap changer, but most of the transformers have on-load tap changers. Off load tap changer requires the disconnection of the transformer when the tap setting is to be changed. Whereas, on-load tap changer the position is shown in the following figure; the voltage is at minimum and the current distributed equally in two halves of the coil L resulting: zero resultant and minimum impedance. When the voltage increases, S1 opens and the total current flows through the half of the reactor where S1 closes the selector switch A moves to the next contact resulting the circulating current flows through the L superimposed on the load current.

S2 opens and B moves to the next tappings; S2 then closes and operation is complete. In general the voltage change between taps is normally small about 1.25% of the nominal voltage, to avoid large voltage disturbances.

Ø Injection of reactive power:

- Shunt capacitors absorb leading VArs where as reactors are used to absorb the lagging VArs.
- Series capacitors are connected in series with the line conductors in order to reduce the voltage drop.
- Synchronous compensators are synchronous motors running with out mechanical loads. They can absorb or generate the reactive power depending on the level of their excitation. Over excited synchronous generator behave like capacitors and they generate VArs where as under excited absorb VArs and behave like reactors.

### Conclusion:

The study of this distribution network concludes distinctly the understanding and significance of load flow analysis, balanced & unbalanced short circuit analysis, distributed generation, reactive power compensation and power & voltage control by relating the theory and simulation procedures to computer aided techniques for system analysis and problem rectifying.