[0:03]We have seen that a set of three unbalanced phasers may be represented by three separate sets of phasers known as positive sequence. Fazers, second negative sequence and third one is zero sequence phase. In which we have seen that, this one is having same phase sequence as that of the original unbalanced phaser. And balance in all respect. means all the three phasers are having same magnitude and phase displacement between any two phasers is 120 degree electrical. The same is for negative. right. zero sequence phasers are having same magnitudes. And same phase difference, but that difference is zero, not 120 degree electrical. So we can assume it as balance but with some Hiccups. So basically these phasers are having same phases. Phase difference between any two phasers is zero, it means same phasers. So these set of phasers are also known as co-phasal phasers. Co-phasal means, co-phasal phasers means phasers in same phase. Right. Phaser may be voltage current any phaser any phase. Right. So in case of current. We are having three unbalanced currents in the three phasers R, Y, B. So these three unbalanced phasers, a set of three unbalanced currents may be represented by three sets of. Balance currents, okay two balanced currents you can say two set of balanced currents and third one is zero sequence currents, that is co-phasal phasers. Right currents. So in place of phaser now we have assumed our phaser as current. So for a set of three un-bal unbalanced currents, we will have positive sequence current. Negative sequence currents and zero sequence currents. So an equipment. equipment any element of the power system may have different values of impedances for the flow of all these three sequence currents. The same equipments say transformer, may have different value of impedance for positive sequence current. And different for negative or zero. May be equal or may not be. We will see for different equipment the values of opposition to the flow of different sequence currents. Right. So therefore, each element of power system will have the corresponding impedances, three values of impedances. Same equipment of the power system will have three values of impedances, one corresponding to each sequence current. So one impedance will be known as positive.

[3:55]Sequence impedance, represented by Z one. Second one will be negative sequence impedance.

[4:26]Represented by Z two. And the third one will be zero sequence impedance.

[4:44]Represented by Z zero. So similar to three set of phasers, known as positive sequence currents, negative sequence currents, zero sequence currents. We will have three different values of impedances. Positive sequence impedance offered to the flow of positive sequence currents. What is negative sequence impedance? Impedance offered by the same equipment of the power system to the flow of negative sequence current. And zero sequence impedance Z zero is the impedance offered by the same equipment to the flow of zero sequence currents. If our system is balanced. If system is balanced then these two sequence currents will not exist, negative and zero. We know. In that case, each equipment of the power system will offer only positive sequence impedance. Is it clear to you? If our system is balanced. So when these two components are existing. When the system is unbalanced. So in that case case only if negative sequence current exists only then some opposition will be offered by any equipment and that opposition is known as Z two. Similarly for zero sequence currents, opposition offered by any equipment will be represented by Z zero of that equipment. So lots of equipments will be there, lots of elements of the power system will be there and each element will offer, may offer, we will see may offer. Because sometimes we will see whether the equipment is static or rotating. So for static generally these two will be same. So we will discuss later. So that's why we use may offer different impedances to the flow of various sequence currents. So if you are talking about balanced condition, in that case only positive sequence currents are there. Negative sequence currents and zero sequence currents will not exist for balanced condition. In that case, only Z one will be there offered by various equipments of the power system. Clear? Okay. Are you noting this? Just note down. So one point, what you noted for balanced condition, each equipment will offer only positive sequence impedance. Second point, for static equipments like transformers, transmission lines. So for static equipments, Z one will be equal to Z two.

[7:34]That is impedance offered by static equipments to the flow of positive sequence currents is same as that of the impedance offered to the negative sequence current. So you will write Z one will be equal to Z two. What you wrote here? For balance three phase condition.

[7:50]Only Z one will be there. What is Z one? Impedance offered to the flow of currents. And in balanced condition only positive sequence currents will be there. So the corresponding opposition will be known as Z one. There will be no Z two Z zero for balanced condition. Second. So what you wrote here? Z one is equal to Z two, that is positive sequence impedance will be equal to negative sequence impedance for all static elements of the power system such as transformers, transmission lines, no rotating parts here. Right? However, for rotating equipments like alternators, motors, Z one and Z two will generally be different. Just write down. Z one and Z two will be different in general. And for Z zero, write down. Z zero is usually different from Z one and Z two.

[8:58]Keep these three points in mind. So next write down. Sequence impedances. Sequence impedances of synchronous generator. So for synchronous generator, Z one will be equal to write down synchronous impedance.

[9:40]Synchronous impedance of the machine. So Z one is positive sequence impedance that will be equal to synchronous impedance of the machine. Z two is lesser than Z one, the value of negative sequence impedance is lesser than Z one. And Z zero will be variable. Item. Write here variable. As we have discussed this is rotating equipment. Is not it? Alternator is rotating. So for all rotating equipments, generally these two are different. Clear? So Z zero is variable item. May be taken as Z one if its value is not given.

[10:50]Write down if its value is not given. So while calculation, if value, value of Z zero is given, just use it. If not given, you may assume whatever the value of synchronous impedance of the machine is there. Right? So let us write sequence impedances of transformer. So transformer is a static device. Right?

[11:25]So for static device we have discussed that the two impedance is Z one and Z two will be equal. So write here Z one will be equal to Z two is equal to impedance of the transformer.

[11:48]So we have written Z one, Z two. What about Z zero? So Z zero will be equal to Z one if there is path for earth current.

[12:15]Only then I zero will flow. Earlier we have seen that the current through neutral is I N is nothing but three times of I zero. If path is there only then I zero will flow. If path is not there then I zero will be zero. It means corresponding impedance will be infinity. So if path is there then this Z zero will be equal to Z one. If not then it will be infinity.

[12:53]If path is not provided for the flow of zero sequence current. Clear? So if path is there then all the three impedances, three sequence impedances Z one, Z two and Z zero will be equal. If path is not there then these two will be equal as the device is static, but this Z zero will be infinity. That is open conductor. Right? Open circuit neutral and ground. Is not it? If path is not there then it will not flow. Write for transmission lines. Transmission lines. So transmission lines also static or rotating? Static. So if static then you may write Z one is equal to Z two.

[13:47]Is equal to impedance of the transmission line. What about Z zero? It is variable here.

[14:04]In case of transmission line, Z zero is variable item. May be taken as three times of Z one. That is positive sequence impedance if its value is not given.

[14:33]So if value is given, just use it. That will be variable different than these two. These two will be equal. So if value is not given then you can take three times of Z one. We will discuss it later. Again we have to use all these, all these values. So come to the sequence networks. You know what is network? What is sequence network?

[15:16]Sequence network is basically sequence network of any sequence current. Whether positive sequence current, negative sequence current or zero sequence current. So sequence network of any particular sequence current in a given power system is basically the path through which that particular sequence current flows in the system. In other words we can say that it, it is composed of all corresponding sequence impedances. If you are talking about positive sequence network, say, we will have three different networks corresponding to three different sequence currents. So for positive sequence current we will have positive sequence network. So what will be positive sequence network? It is composed of all impedances.

[16:15]Offered to the flow of positive sequence currents. That is all positive sequence impedances. This network is a path which is composed of all positive sequence impedances.

[16:30]And positive sequence impedances are the impedances offered to the flow of positive sequence currents. Right? So while drawing these networks, positive sequence network, certain points must be kept in mind. So what are those points? See our alternator earlier we have discussed it that all the sources will generate balanced voltages. Is not it? So alternator is also a source. Of generating voltages. So the design of alternator is such that it generates balanced EMF's. Clear? So once the condition is balanced. So there will not be any existence of negative sequence components and zero sequence components. For balanced condition only positive sequence components will exist. So if you are talking about generated EMF's. So your generators are always generating balanced EMF's. Right? You have fixed the speed of the turbine. You have controlled your excitation etc, etc. So the design is such that it generates balanced EMF's. Clear? So balanced EMF, it means only positive sequence EMF's will be there. So negative sequence EMF will not exist and zero sequence EMF will not exist. We will discuss how and why later. So for positive sequence network, the EMF's will be of positive sequence only. Impedances will be of positive sequence only. Currents will be of positive sequence only. Clear? For negative impedance network, sequence network, the impedances will be of negative sequence only. Currents will be of negative sequence only if exist. Right? EMF will be zero. Because there is no any existence of negative sequence EMF generated by the generators. Right? Similarly for zero sequence network, EMF will be zero. It will have only negative sequence currents and negative sequence impedances. And we will see if grounding reactances are there. Current limiting impedances are used between neutral of the generator and ground. Right? We will see one by one. So for positive sequence network, the steps will be for all generators available in the power system the induced EMF's. Generated EMF's will be in other words you can say that all generators will be replaced by generated EMF's in series with the associated impedance. Right? Write impedance if you are going to neglect resistance then that will be reactance. So write impedance. So what you will write? All generators will be represented by induced EMF's. In series with impedance. You will take neutral as reference. For static equipments like transformers, transmission lines etcetera etcetera. So for those cases, EMF's will be equal to zero. Right? So no EMF will be shown in negative and zero sequence networks for all static equipments of the power system. Second rule, write down. So write down the rule. First rule is for generated EMF's. Second rule. So first rule you noted down. Second rule is this. Third one is for motor loads. So the motor loads you will represent by an EMF in series with an impedance. But with certain modification as compared to generators. So if you are going to draw the sequence networks for various type of loads. So for static loads you will represent the loads by impedance only. There will be no EMF for static loads. Right? For static loads there will be no EMF's. But for rotating loads there will be EMF's. So for rotating loads EMF's will be there. So third rule is this. And fourth rule is this. So fifth rule is this. For transmission lines. We will ignore resistance. For transmission lines we will ignore shunt capacitances. Right? So this is for all the components of the power system. Okay. Thank you very much.