MATLAB coding to find out post fault Current and Voltages

In a power system, faults occur because of insulation failure, or because of a damaged insulator, or a broken conductor. Various other reasons such as improper operating habits may also lead to a fault; for example, loading a distribution transformer beyond its normal rated capacity. 

Nearly one half of the faults occur on power lines which are widely branched, have greater length, operate under variable weather conditions and are more exposed to atmospheric disturbances. Faults give rise to abnormal operating conditions. 

When a fault occurs at any point in the power system large currents, large forces and or abnormal voltages are developed. The excessive current because of the fault is determined by the internal e.m.f.s of the machines in the network, their impedances, and the impedance in the network between the machines and the fault.

Faults currents, also called short circuit currents, are many times greater than the normal currents. Large voltage stresses the insulation of the various equipments which are way beyond their breakdown value causing the failure. Sometimes faults lower the system voltage below the permissible voltage limit causing unwanted and teasing interruption of various equipments and components. Faults can also cause a three-phase system to become unbalance.

To obtain proper setting of the protective relays and the interrupting capacities of circuit breakers, the values of these fault currents and voltages should be known with great accuracy. Short circuit studies and calculations provide currents and voltages on a power system during fault conditions. 
 

For Unsymmetrical faults

The majority of faults that occur in a power system are unsymmetrical faults involving only one or two phases. The most common type of unsymmetrical fault is a short circuit between a phase and the earth. In case of unsymmetrical faults, voltages and currents in the network become unbalanced and each phase is to be treated individually for computational purpose.

The magnitude of fault currents in the three lines is different having unequal phase displacements. The calculation procedure called as “method of symmetrical components” is used to find the currents and voltages in this type of fault.      

In this blog we are going to find out how to write the MATLAB code so that the post fault currents and voltages, in case of occurrence of an unsymmetrical fault, can be determined. 

Lets us assume that a 25 MVA alternator is working without load. A single line to ground fault occurs at one of the terminals of the alternator. The alternator has positive sequence impedance (Z1) of 0.25 p.u., negative sequence impedance (Z2) of 0.35 p.u. and zero sequence impedance (Z0) of 0.1 p.u. Now we have to find the fault current and line to line voltages.

Let the Line to neutral voltage at the fault point before the fault, ‘Ea’ be 1+ 0i p.u. 

The MATLAB coding is as follows:

>> Ea= 1+0i;

>> Z1= 0.25i; Z2= 0.35i; Z0= 0.1i;

% Assuming that fault occurs at phase ‘a’, the positive sequence component of current in the ‘a’ phase (for a single line to ground fault without impedance),

>> Ia1= (Ea/ (Z1+Z2+Z0));

% Also, for a single line to ground fault, Ia1=Ia2=Ia0

>> Ia2= Ia1;

>> Ia0 =Ia1;

% Also, Fault current in phase ‘a’, Ia = Ia1+ Ia2 + Ia0

>> Ia = Ia1+ Ia2+ Ia0;

% From the positive sequence network

>> Va1= Ea-(Ia1*Z1);

% From the negative sequence network

>> Va2 = -Ia2*Z2;

% From the zero sequence network

>> Va0= -Ia0*Z0;

% For operator ‘a’ i.e. an operator which causes a rotation of 120 degrees in the anti-clockwise direction.

>> a=pol2 rect(1,((pi/180)*120));

% If Va1, Vb1 and Vc1 are the positive sequence component of the unbalanced voltages,

>> Vb1=a^2*Va1;

% If Va2, Vb2 and Vc2 are the negative sequence component of the unbalanced voltages,

>> Vb2=a*Va2;

% If Va0, Vb0 and Vc0 are the negative sequence component of the unbalanced voltages,

>> Vb0=Va0;

>> Vc0= Va0;

>> Vc1=a*Va1;

>> Vc2=a^2*Va2;

>> Vb= Vb1+Vb2+Vb0;

>> Vc= Vc1+Vc2+Vc0;

>> Va=0;

>> Vab= Va-Vb;

>> Vab_mag=abs(Vab);

 Similarly we can find out the values of line voltages Vbc and Vca. The values of fault current and post fault voltages are in p.u. values, we can convert them into actual values by assuming proper base values. 

Plug setting and Time setting in Induction type Relay

Electromagneticinduction relays, one of the most widely used relays for protective relaying purposes, operate on the principle of electromagnetic induction and therefore can be used only on AC circuits. 

Setting in Induction type Relay:

"In induction disc relay there is a facility for selecting the plug setting and the time setting such that the same relay can be used for a wide range of current, and time characteristics." 

The minimum torque required for the movement of the disc is fixed for a particular design, i.e. the ampere-turns required for the disc movement are fixed. 

Often it is desirable to adjust the pick-up current to any desired value. This adjustment is known as current setting and is normally achieved by the use of tapings on the relay operating coil (primary coil). Therefore, for different pick-up current settings, number of turns is changed effectively so as to keep the same ampere-turns. 

The value assigned to each tap are expressed in terms of percentage full-load rating of the Current Transformer (CT) with which the relay is associated and represents the value above which the relay disc starts to rotate and finally closes the trip circuit.

Plug Setting Multiplier (PSM):

Selection of the required current setting is done by means of a plug setting multiplier plug. While the plug is withdrawn for adjusting it to a different current setting during on-load condition, the maximum current tap is automatically connected and thus the risk of open circuiting the secondary of the CT is avoided.

The ratio of fault current in the relay coil to the pick-up current is known as plug setting multiplier (PSM). Hence,

PSM = (Fault current in relay coil / Pick-up current),

Since, Fault current in the relay coil = (Fault current / CT ratio)

Therefore,

PSM = (Fault current / (Pick-up current x CT ratio))  

Time Setting Multiplier (TSM):

The operating time of the relay depends upon the distance between the moving contact and the fixed contact of the relay. The distance between the contacts is adjusted by the movement of the disc backstop which is controlled by rotating a knurled moulded wheel at the base of a graduated time multiplier scale. This is known as time setting multiplier. 

The higher the time multiplier setting, the greater is the operating time. The time setting multiplier is marked from 0 to 1 in steps of 0.05. If the relay takes a certain time, say ‘S’ seconds with time multiplier setting as 1, then the same relay will take a time equal to 0.5 S seconds for a time multiplier setting of 0.5.                     

Let’s see how Protective Relays are classified

Protective relays and relaying systems detect abnormal conditions like faults in an electrical circuit and operate automatic switchgear to isolate faulty equipment from the system as quickly as possible. 

There are various types of protective relays used in a power system for protection. Normally the actuating quantity is an electrical quantity but sometimes the actuating quantity may be pressure or temperature also. Relays must have certain functional qualities such as reliability, selectivity, speed and sensitivity.

Classification of Relays:

One can classify electrical relays in a number of ways as given below:

1.       According to the function: Relays may be classified as main, auxiliary and signal relays according to their function in the protective scheme. 

Relays which respond to any change in the actuating quantity are called as main relays. The auxiliary or supplementary relays are those relays which are controlled by other relays to perform some auxiliary function. The auxiliary function may be the introduction of a time delay, increase in number of contacts, increase in making or breaking capacity.

Signal relay's function is to indicate the operation of some relay with the help of flag or target. Simultaneously, these relays may also actuate an alarm circuit.

2.       According to the nature of the actuating quantity: Relays may also be classified according to the nature of the actuating quantity i.e. as current, voltage, impedance, frequency relays etc.

Such relays are also differentiated as over relays and under relays. Relays which respond to the actuating quantity when they exceed a predetermined value are called “over-relays”, e.g. over-current relay. Relays which operate when the value of the actuating quantity drops below a predetermined value are called “under relays”, e.g. under-voltage relay, under-frequency relay etc.

3.       According to the connection of the sensing element: According to the connection of the sensing elements, relays may be classified as primary and secondary relays. Primary relays are those relays whose sensing elements are directly connected in the circuit or element they are supposed to protect. The sensing elements of secondary relays on the other hand are connected through a CT and/or PT. Relays normally used in the power system protection are the secondary relays because of the involvement of heavy currents and high voltages.

4.       According to the action upon the circuit breaker: Relays are divided as direct acting relays and indirect acting relays according to the method by which these relays act upon the circuit breaker. Direct acting relays are those relays whose control element act mechanically to operate a circuit breaker whereas in an indirect relay, the control element switches in an auxiliary power source to operate the circuit breaker.

5.       According to the principle of operation and construction: The protective relays used in an electrical system can be broadly classified as electro-magnetic relays and static relays. According to the principle of operation and construction, they may be further classified as electromagnetic attracted armature type, electromagnetic induction type, moving coil type etc.

6.       According to the time of operation: The relays can also be classified according to the timing characteristics i.e. as instantaneous relays, definite time-lag relays, inverse time-lag relay and inverse definite minimum time relays.

Instantaneous relays are those relays in which operation takes place after a negligible small interval of time after the incidence of the operating quantity. 
In definite time-lag relays the time of operation is quite independent of the magnitude of the actuating quantity. Similarly, in inverse time-lag relays, the time of operation is approximately inversely proportional to the magnitude of the quantity causing the operation of the relay. 
For inverse definite minimum time relays, the time of operation is inversely proportional to the smaller values of actuating quantities and tends to a definite minimum time as the value increases.