Hello,

I wonder multiphase systems, especially 6 and four phase systems. Do you know about this systems? Why can we need to use this systems say in transmission systems motors, bridges etc...

 

Electrics... see

http://control.com/thread/1026242304

Phil Corso

 

Electrics... further to my earlier advisory the original N-phase thread is:

http://control.com/thread/964724872

Regarding your question about 4,6, 12-phase, systems; they substantially reduce ripple-voltages in DC-rectification power supplies!

Phil

 

yes , multiphase systems are very much possible but the problem is the higher cost. we need a minimum of two phases for production of a rotating magnetic field , this is one of the reasons why the earliest generation was done in two phases. But three phase provides us with the optimum compromise between the power transfer capability and the the cost of generation and transmission of electricity. i will give you a brief mathematical derivation of why we use three phase and not more than three phases.

let us assume a single phase system with the induced and current I .
power output = E*I
assuming unity pf

for a two phase system , let us suppose that the induced voltage is still E and current I
per phase voltage in a two phase system = 1/root(2) * E (with two conductors in series and 90 deg electrically apart.
so power output = 2*1/root(2) * E *I
= root(2) *E*I
= 1.414 EI

for a three phase system , let the induced voltage still be E and the current I
per phase voltage in a three phase system = 1/2 * E (with three conductors in series and 120 deg electrically apart.
so power output = 3/2 * E *I = 1.5 EI

thus for a n phase system let the induced voltage still be E and the current I
per phase voltage in a n phase system = piE/2n
so power output = n * piE/2n * I = 1.57 EI

thus from the above it can be seen that when we move from single phase to two phase the power delivered increases by 42% then in three phase by 50% and in a n phase or higher phases maximum by 57 %

thus 3 phase provides the optimum compromise between the power delivered and the economics of laying n no of wires.

note * - well the last derivation i had given assumes a very large no of phases. the problem can be visualized as trying to fit n no of phases in a semicircle with dia as E. so for a large no of phases emf per conductor can be taken as
length of the semicircle / no of phases
(pi *E/2)/ n
pi E/ 2n

the general formula is
power output = K* (E/ ( sigma n-0 to K-1 cos ( mod((pi-pi/k)/2-n*pi/K)) ) * I

well if you solve the equation i have given above you will get the same answer. with a slight error.

hope that clears why we use three phase system and not more than three phases for generation.

 

Dear Phil, I guess the losses are better as the phase number increases. So single phase is worse than 3 phase in terms of losses. Also I plead you show me with a pic maybe how 6 phase is used with rectifier?

 

It would be hard to draw, but I suggest you look at an automotive alternator print for a 3 phase example, and it extends to N phase with 2 more diodes for each added phase. One to the positive output and one to the negative, in other words, two 3 phase rectifiers would work for 6 phase with the + and - in parallel.

Regards
cww

 

Electrics...

a) No! The losses do not decrease as the number of phases increase! It can be shown that for the conditions given in Control.com Thread # 1026242304, regardless of the number of phases, the 3-phase case results in the smallest loss! Yes, even for the 1-ph vs 3-ph case! Also, for the 2-ph case twice as many wires as the 1-ph case are used. And, even though each is has ½ the cross section of 1-ph case, the 2-ph case has the same loss as the 1-ph case!

b) For a picture of 6-phase rectification circuit, contact me off-forum.

c) I forgot to mention, that increased number of phases requires less capacitance to smooth the ripple!

Process Value...
I found it difficult to follow your equation development. What was your goal?

Control.com Thread # 974724872 compared 3-ph vs 1-phase, as well as the 3 vs 4-phase. The constant pi is not used to calculate power transmitted, but the angle “theta” is! And, theta is the phase-displacement angel, not the load-angle.

Regards, Phil Corso (cepsicon [at] aol [dot] com)

 

excuse me dear phil, I figured you had said one phase at least is better than 3 phase, So u are right, but I am confused:

Yes cost increases far off optimization but I guess the losses must decrease,at least my logic says so, so one should ask what is the magic of three-phase??? "İt cant be both cost -effective and efficient in view of losses "seems to me...

 

Electrics... I sense that you didn’t read the 2000 and 2007 related threads or you didn’t understand the mathematics related to the loss ratios.

Therefore, let me know what additional detail you want!

Phil

 

phil ,

i was deriving the formula for the power transfer capability with different phases with the same line voltage and current. as you will see in the derivation , i have used V and I same for all cases. This was to prove that the increase in phases with the same voltage and current does not offer any substantial power transfer capability. in the derivation you will see that , after the three phases where the power transfer capability increases by 50% compared to single phase , the "n" phase system for a very large n value the power transfer capability will only increase by 57%.

thus the difference between a three phase supply and a infinite "n" phase supply is only 7%. the above derivation can be visualized as trying to fit in "n" phases into a semicircle with the dia of the semicircle as the line voltage. for a infinitely large n phases this will look like a semicircle , and that is how the pi came in , the general formula for n phases is given in the post too.

and one more thing , in all power system studies , the power flow is calculated by the load angle only. for a standalone machine the active power delivered is given by the formula
P = EV/xd sin delta - V^2/Ra

where E is the internal generation voltage , V the terminal voltage , delta the load angle of the machine and Ra the internal resistance and Xd the impedance of the machine.

this can be generalized into the more commonly known form
P = E1 E2 / Xl sin delta
where E1 is the sending bus voltage , E2 the reviving end bus voltage Xl the impedance between the two connected buses and delta the load angle difference between the two buses. this forms the basis for determining the load flow in different buses. this is one of the basic formula used by all phasor domain and time domain simulation program mes.

 

ProcessV... I want to be sure I understand you so please answer the following question:

Assume that an 18-phase Generating Station is to transmit 1 MW at 0.8 PF lagging, to a Receiving Station, then by your formula, only 570kW reaches the Receiving Station, and 430kW is dissipated in the transmission line conductors?

Phil

 

or a three phase system, let the induced voltage still be E and the current I per phase voltage in a three phase system = 1/2 * E (with three conductors in series and 120 deg electrically apart.
so power output = 3/2 * E *I = 1.5 EI

Here this part is weird for me, why do we take the voltage E/2 ? it is said that voltage is E at the beginning and it is taken half of it later?

 

for example we use 12 phase supply, so what is the difference between 3 phase and 12 phase? İf it is the same E and I it means it will have 3 times bigger power delivery capacity and it will have also 3 times bigger losses and wire use, I cant see where is the disadvantage of using multiphase

 

I think this mathematics is a bit weird, why do u say voltage per phase is E/2? Also what is this series 3 phase voltages? 3 voltages having 120 deg difference sum up 0 volt. But you calculate two voltage 90 deg apart having a total E will be E/SQRT 2 each but this calculation is invalid for 3 phase Can you make it more clear pls?

 

Electrics... your 04-Nov-10 questions:

(05:36) Your constant for the 3-ph case, 1.5 is wrong. Also, where did you get 1/2 as the E multiplier?

(06:31) The development of the constant for the 3-ph case (and subsequently the 12-ph case) is illustated in Control.com Thread # 1026239915.

Phil Corso

 

dear phil:

"I think this mathematics is a bit weird, why do u say voltage per phase is E/2? Also what is this series 3 phase voltages? 3 voltages having 120 deg difference sum up 0 volt. But you calculate two voltage 90 deg apart having a total E will be E/SQRT 2 each but this calculation is invalid for 3 phase Can you make it more clear pls?"


this is what I wrote as the final post to the thread, so I am not the guy who wrote 1,5 times EI but the one who asks to our friend "process value" where did he get this formula and the one who couldn't understand it. Yes I got what you wrote already and I deeply thank you for your helps..

 

I feel the Cu losses will be definitely more in multiphase systems as the no. of transmission conductors increase proportionally.As for the core losses, the loss equations for polyphase systems have to be examined.

For starters, let there be a comparative between Cu and Iron losses between 3 phase systems and 12 phase systems.

It is evident that losses apart, transmitting electrical power long distances on a 12 phase system wud be economically unviable the no. of line conductors wud increase leading to logistical problems as well.

But still it wud interesting to have a comparative study of losses between the 2 systems on the open forum.

 

Shahvir... the comparative losses study you asked for was provided in the year 2000!

Control.com thread # 906472472 illustrates for the condition when transmitted power is equal and balanced, then, the 3-ph case results in a total copper weight just 75% that of both the single-phase and 4-ph cases!

Furthermore, the result is the same regardless of pf!

Regards, Phil