Author: Anshuman Singh Jhala

Reading Time: 16 minutes

Can you imagine a day without electricity?  In this modernized world, we are heavily dependent on machines which directly or indirectly rely on electric power either your mobile, laptop, cooling, lighting equipment, automobiles(electric), trains, metros, medical equipment etc. The system involving the process from the generation of electric power to transmission to distribution is termed as power system. The power system is the largest and most complex man-made physical system.

The power system is a system that deals with the generation, transmission, distribution and the consumption of electricity. Power generating stations are not always close to the load centres especially in case of hydro, nuclear, and tidal generating stations. Here comes the role of electric power transmission. The electric power is transmitted over HVDC/HVAC lines which is then received by substations of various load centres where distribution sector comes into play.

Also, all power plants can’t work throughout the year with same capacity due to many factors (like weather factors, fault, maintenance etc.), so they need power back up during that time from other generating stations. Due to all these factors, for an uninterrupted power supply, the power grids of different parts need to be interconnected.

The fault occurred at any of these units may result in severe damage to the system. The most common faults are short circuit and rare one is the open circuit fault. The fault may occur due to a number of factors that may be natural, physical, mechanical or chemical etc. The main factors for the fault are natural including winds, lightning strike, floods and many others which are not in our control so under such condition it becomes very important to have fast, effective and efficient protective devices.

The effects of faults can be very drastic, under severe condition it may result into blackouts, failure of the power grid. One can understand it by the effect of power cut off in hospitals, transportation, mining sites, industries, and other institutions solely dependent on electric power. If you are a regular reader of CEV blogs then probably you would have striken with one of the amazing blogs over the blackouts in India and Ukraine by Rahul Kumar.

The faults are mostly short circuit faults in both DC or AC transmission lines, 60-80% of which occurs due to natural factors like strong winds, cyclones, lightening etc. In India, most of the electric transmission occurs on high voltage 3 phase AC lines though we are moving towards HVDC lines for long distance transmission due to several advantages over ac transmission

• low power loss (R_dc < R_ac due to skin effect),
• asynchronous mode of transmission (enables us to connect the power grids operating at different frequencies due to no frequency restriction unlike AC),
• smaller towers and less copper requirements (2 wires are required while HVAC requires 3 wires),
• easy power flow control (no capacitive or reactive drop) etc.,

The conclusion is that HVDC transmission is more economical as compared to HVAC but for small and medium distance transmission HVAC transmission systems are more economical because HVDC involves convertor at sending end and invertor at receiving end which increases the setup cost to manifolds. HVDC transmission is also possible just because of the invention of AC.

HVDC is a complement of AC, not a competitor.

Now, let us come back to the discussion over fault. It is clear that the protection from fault is of immense importance. As soon as the fault occurs it becomes very important to detect, locate and isolate the faulty system to protect the rest of the system. The very first step for the protection against fault is to locate and detect the type of fault. Previously we were having electrically and mechanically controlled devices which are slow and less efficient. Now we are having power electronic devices to sense the faults very fast (senses faults in milliseconds). Here comes the role of relays. A relay in simple language is a device which senses a disturbance in the power system based on the measurement of current, voltage phasors or various other criteria and sends signal to take suitable action. There are number of relays available but most widely used is distance relay whose functioning can be explained as follows-

Distance Relay- Distance relay observes the power system based on the calculation of apparent impedance using the synchronised voltage and current phasors measurements at the bus where relay is provided. They are fast, accurate, directional, can provide backup protection. Primarily they were used only for transmission line protection but now they are also used for generator backup, transformer protection etc.

There is a total of 10 short circuit faults which can be categorised as follows-

• Symmetrical fault- It includes the 3 phase to ground fault and are called symmetrical because I and v remain balanced even after fault. They account for 8-10% of the total faults in power system
• Asymmetrical faults- It includes – line to ground fault (A-G, B-G, C-G : 75-80%), line to line(A-B, B-C, C-A : 5-7%), line to line to ground (A-B-G, B-C-G, C-A-G: 10-12%) and are called asymmetrical as I and v are no longer balanced after fault.

Symmetrical Components– To analyse the faults, sequence components are used as the faulted system may or may not be balanced, so it is better to convert the 3-phase system into the 3 sets of 3 balanced phasors –

1. zero sequence components (all phasors have equal magnitude and are in phase) :

          V_a0 =  V_b0 = V_c0

2. positive sequence components (all phasors have equal magnitude and are 120° displaced from each other in same sequence as the original phasor). If a = 1∠120° then,

         V_b1 = a² V_a1 ;           V_c1 = a V_a1 ;

3. negative sequence components (all phasors have equal magnitude and are 120° displaced from each other in the opposite sequence of the original phasor)

          V_b2 = aV_a1 ;           V_c2 = a² V_a1 ;

Such that:

Now the sequence component can be calculated as:-

  

Similar conversion can be done for the current phasors also.

Fault Analysis by impedance calculations-

Assumptions-

1. Fault impedance is zero, i.e., solid grounding of the fault.
2. Pre-fault currents are assumed to be zero as they are negligible in comparison to the high short circuit currents.
3. System is in balanced state before the occurrence of fault.

Consider a balanced 3 phase transmission line

1. 3 phase fault (Phase fault protection)–

Ia+Ib+Ic=0

If the fault has occurred at x percent of total distance from the start as shown in figure –

V^abc = x Z^abc I^abc [As V_n =0]

V⁰¹² = x diag(Z₀, Z₁, Z₂) I⁰¹²

Using I⁰¹² = T^-1 I^abc and Ia+Ib+Ic=0,

I₀=0, I₁= I_a and I₂ = 0

Or V₀ = V₂ =0 and V₁ = xZ₁I₁ = xZ₁I_a = V_a

Thus,

Now, x can be determined as the ratio of apprent impedance seen by the relay to the positive sequence impedance of the line and thus, the fault can be loacated using the line current and voltage measurement.

 

2. Line to Line fault (Phase fault protection)–

Consider a transmission line with B-C fault at x percent of the total length as shown below-

I_c + I_b = 0,  I_a =0 [Pre-fault current are zero]

ΔV_a =V_a = 0,

ΔV_b =V_b = x(Z_s-Z_m)I_b =xZ₁I_b ,

ΔV_c =V_c = -x(Z_s-Z_m)I_b = -xZ₁I_b = -V_b,

,

which is same as the above case, so these two faults can be located with the same set of equations.

 

3. Line to Ground fault (Ground fault protection)-

Consider a transmission line with A-G fault at x percent of the total length as shown below-

Using I_c =I_b =0 and I⁰¹² = T^-1 I^abc

I₀= I_a /3, I­₁=a *I_a /3 and I₂ = a²*I_a/3

ΔV_b = ΔV_c = xZ_mI_a

ΔV_a =V_a = xZ_sI_a

V_a = x(Z_s – Z_m + Z_m)I_a

V_a = x(Z₁+ Z_m)I_a

The above equation is used for locating the ground faults.

4. Line to Line to Ground fault (Ground fault protection)-

Consider a transmission line with B-C-G fault at x percent of the total length as shown below-

 

Ia=0, ΔV_b =V_b, ΔV_c =V_c

Using I_a =0 and I⁰¹² = T^-1 I^abc

I₀= (I_b + I_c)/3

So, the ground faults can be detected by the above equations.

 

Zone Setting –

This is how the distance realays work. But the assumption described above are not found in pracitcal scenerios and hence creates inacuracy in the meaurements. To avoid that, models needs to be modified accordingly.

Distance relays are used to provide both primary as well as the backup protection. Primary protection should be fast and accurate while the backup protection should work only if the primary protection fails. This is done by setting up the impedance zones for the relays. Generally, 3 zones are set-up, first being for the primary protection while the other two for the backup protection.

Zone 1 is set upto 80% of the primary line impedance. The complete primary line is not considered in the zone 1 because measurement instruments (CT,PT) are present near the buses which are prone to give errors in measurement of apparent impedance, thus making it difficult to locate the fault. In addition, the assumptions used in the equations for the relays are not valid in the practical cases.

Zone 2 covers the complete primary line impedance and 50% of shortest adjacent line impedance. This is done so as to overlapping of zone 2 of 2 different relays. For example, in example below if zone 2 of R₁ covers more than 80% of the BE then it will overlap with the zone 2 of DE which may create undesirable competetion between them to send the trip signal.

Zone 3 covers the complete primary line impedance and 120% of longest adjacent line impedance.

For example- Consider a 5bus system as shown below-

Zone1= 80% of Z_AB

Zone2= Z_AB +  50% of Z_BE

Zone3= Z_AB +  120% of Z_BD

Co-ordination time interval (CTI) –

When fault F₃ occurs the primary relay R₃ should get the first chance to trip the signal and if it fails then zone 2 of R₁ and finally the zone 3 of some relay should come into play. This is a crucial consideration as the objective of the power system is to supply the maximum possible power to the consumers. To ensure this, zone setting is done along with providing a time delay called CTI. Zone 2 is provided with 1CTI while the zone 3 is provided with 2 CTI as explained in the following timing diagram-

This is all about how distance relays works and how the fault can be detected but the principle of working also involve a number of situations that may lead to mal-tripping of line. Maltripping occurs when the apparent impedance seen by relay enter into the sensitive zone of the relay in a non-fault condition and the relay interpret it as fault issuing trip signal. The mal-tripping events are mainly associated with the zone-3 as it is extended over very wide area to provide backup protection. This situation may cause drastic impact on power system especially under overloading codition. Under stressed conditions, when any such maltrip occurs this resluts in increase in load over the other lines  as system will tend to draw power from the other path causing cascaded outage and blackout. The blackout occurred in 31 July, 2012 in India is initiated by distance relay zone-3 maltripping of Bina-Gwalior line.

Events causing maltripping are  briefed as follows:

1. Infeed and outfeed effect-

This effect is now almost nullified by the advancement in technology and modification in the operation of distance relay. Consider a 4bus 3 source system as shown below-

If the fault occurs ‘F’, apparent impedance seen by relay R₁ –

V_a = I_abZ₁ + I_{bc *}xZ₂

V_a = I_abZ₁ +(I_ab + I_ed) _*xZ₂

The above equation clearly indicates that Z­­_r is increased by-

due to infeed from generator 2. This may push the Z­­_r to move outside the sensitive zone of the relay and hence decrease the dependability of the relay.

If the Generator G2 is replaced by a load then the direction of I_ed will be reversed and thus Z­_r will decrease by-

Z_r =  Z₁ + xZ₂ –   *xZ₂

This pushes the impedance into the sensitive zone of the relay, and may detect fault even for the healthy system and hence decreases the security. This is highly undesirable as it may lead to casacaded outage and blackouts.

2. Load Encroachment –

Load encrochment or overloading is the major reason causing zone-3 maltripping. In the power system, energy is not stored so, the equivalence between the generation and consumption of power is must. The power consumption is not uniform throughout the day and it also varies depending on the weather conditions. In India, demand is at peak during day hours of summer due to heavy operation of coolers, ACs, fans and pumps for irrigation in the farms. In addition, many hydro power plants fails to supply power in summer due to deficiency of water. Under such cases, power system operate close to its stability limit and any contingency under such situation may result in maltripping, cascaded outage and the blackouts. One such example in front of us is the blackout of July, 2012 in India. India is energy efficient country but still the above mentioned condition may cause overloading and turn the system stressed. The depecndancy on electric power is increasing day by day over the world. Though the generation of power is increased at very appreciable rate yet the consumption rate is not perfectly matched. Consequently, in the near future, the probability of power system to work at its stability limit will increase and for ensuring the reliability and security of power system, preventing measures to avoid such cascaded outages must be introduced, some of which are discussed briefly later in this section:

Apparent impedance seen by the relay R is given by-

which means apparent impedance is directly proportional to the square of voltage magnitude and inversely proportional to the apparent power flow.

Under peak load conditions, power flow from the bus i towards bus j (P-jQ) will be very high and the increase in reactive power flow also decrease the voltage. The combined effect of these may cause the Z_r  to enter into sensitive zones of the relay causing maltriping which decreases the security of power system and may lead to voltage collapse, cascaded outage and blackouts.

To avoid the malfunctioning of the relays due to load encroachment, a number of methods are being described. Some of the methods proposed are:

1. For the loads power factor is high (R/X) while for the faults power factor is generally low due to high reactance of the line in comparision to the negligible resistance. Thus by blocking the high power factor region (shedded in the figure) of the zones we can prevent the malfunctioning of the relay due to load encroachment.
2. Relay Boundary Setting Adjustment- Malfunctioning of the relay can also be avoided by modifying the zones of relays based on the loading conditon and power system structure.
3. Voltage stability criteria can be chosen for identifying the fault and allowing the relay to function only under that condition else not.
4. System state indicator (SSI) can be used as a measure of power system condition and taking suitable action based on that.

And many other such techniques. But still we don’t have economical and completely effective method without any drawback.

The most practical and widely adopted methods are ‘c’ and ‘d’ which are based on the connection between voltage stability and load fluctuations.

Firstly, letus discuss about Volatage stability. It is ability of the power system to maintain steady voltage at all the buses, when subjected to a disturbance. Voltage instability may arise due to loss of load, tripping of transmission line, cascaded outages, loss of synchronism of the generator, mismatch between reactive power demand and supply, high inductive reactance of transmission line causing high voltage drop etc.

Based on the duration of distubance causing, instability it is classified into following categories-

Short- term or transient voltage instbility(1-10 sec)	Long- term voltage instability(1-60 minute)
i. Automatic corrective actions are taken as operator actions are difficult due to time constraints	Operator interventions are possible for larger time scale
ii. Mainly caused by rotor anle imbalance and loss of sysnchronism. It includes automatic voltage regulators, excitation systems, turbine and governor dynamics, induction motors, electronically operated loads and HVDC interconnections also fall in this category	Mainly caused due to large electrical distance between generator and load. The instability is caused due to high import of power from remote generating station to load, a sudden load build up, large distubance etc. Components operating in the long-term time frame are transformer tap changers, limiters, boilers etc.
iii. Steady state analysis (how stressed the system is, how close the system to point of instability) are useful	Suitable model of system needs to assumed and analysis needs to be done for the whole time frame of disturbance.

 

Now, for finding the relationship between the voltage stability and load encroachment, a 2-bus system analysed to see the effect of load (P-jQ) on the voltage stability.

The power transfers from bus 1 to 2 are given by-

Where E= E∠δ is the voltage at bus 1, V= V∠0 is the voltage at bus 2 and X is the reactance of the transmission line between the 2 buses.

The above equations are derived from power flow analysis.

Normalising the terms as v=V/E, p= PX/E² and q= QX/E²,

p = vsinδ  and q = vcosδ – v²

Eliminating δ from these two equations,

v⁴ +(2q-1) v² + (p² + q²) = 0

Now, based on the above equations power and voltage relationship can be discussed in the following way-

1. P-Q-V 3D curve:- For each (p, q) point, we are having 2 values of ‘v’, larger (stable) and smaller (unstable). The nose point where these two values are equal gives maximum power point and increase in power beyond this limit will result in voltage instability.

2. V-P Curve- The figure below depicts that maximum active power transfer limit increase and the rate of decay of voltage with ‘P’ decrease with increase in the power factor as shown below-

v₁ ,v₂ will exist only if v² is real i.e.,

If k is the power factor then, k = q / p;

and thus the nose point power or

So, the maximum limit of the active power at specific power factor exists above which the system may fail to maintain the voltage stability.

3. Q-Vcurve:- Voltage stability is closely related with available reactive power reserve (Reactive power margin). The points where dq / dv = 0 are termed as critical points or the nose points and they represent minimum reactive power compensation for a particular value of active power. On the left of nose points dq / dv < 0 i.e., VQ sensitivity is negative in this region showing the unstable region of operation for a particular value of active power. Whereas on the right of nose points dq / dv > 0 i.e., VQ sensitivity is positive in this region showing the stable region of operation for a particular value of active power

p = vsinδ  and q = vcosδ – v² , thus,

 

The distance between operating point and nose point is known as reactive power margin and it determines reactive power compensation required for avoiding the voltage collapse. It is clear from the figure below that reactive power compensation increases with an increase in normalised active power which increases the sensitivity of voltage with reactive power. Greater the load, greater will be the slope of q-v curve in the right side, and weaker will be the bus.

From this discussion, it is clear that voltage stability decreases with the load encroachment. Thus it is justified that both the distance relay maloperation and voltage stability are related to load encroachment in a similar way. Utilising this relationship, VQ sensitivity can be used as criteria to define the weakness of the bus and thus for the load shedding. This property can be used for providing an adaptive load shedding scheme to avoid the distance relay maloperation.