Systems Flashcards
What are the formulas for the current of: 1 - purely resistive load 2 - purely inductive load 3 - purely capacitive load Draw the phasor diagrams for each one
1) I = V/R
Voltage and Current in line (to the right)
2) I = V/(jX)
Voltage leading current (V pointing right, I pointing
down)
3) I = V/(-jX)
Current leading voltage (V pointing right, I pointing
up
What is the general equation for instantaneous voltage?
v(t) = √2 * V * cos(wt + 𝛿)
What is the general equation for instantaneous power?
P(t) = V * I * [1 + cos(2(wt + 𝛿))]
What are the equations for average power of:
1 - purely resistive load
2 - purely inductive load
3 - purely capacitive load
1) P(av) = I² R
2) P(av) = ∫(PL(t) dt)/ T = 0 (between T and 0)
3) P(av) = ∫(PC(t) dt)/ T = 0
What are the equations for instantaneous power over an inductive or capacitive load?
P(t) = V * I * sin(2(wt + 𝛿))
How do you calculate the power factor and from the PF how can you tell if the load is inductive or capacitive?
PF = cos (𝛿 - β)
If 𝛿 ≥ β the load is inductive
If β ≥ 𝛿 then load is capacitive
How can you calculate complex power S?
S = V I* (complex conjugate of the current) S = P + jQ
How do you calculate apparent power S?
S = √(P² + Q²)
Draw a balanced 3 Phase Y - Connection
E(cn), E(bn) and E(an) meeting at a neutral point and going to inductors Z(y) which also have a neutral point
What are the relationships between balanced line to neutral voltages
E(an) leads E(bn) by 120
E(bn) leads E(cn) by 120
What are the line-to-neutal voltages equations?
E(an) = E ∠ 0 E(bn) = E ∠ -120 E(cn) = E ∠ 120
What are the line-to-line voltages equations?
E(ab) = √3 E(an) ∠ 30 E(bc) = √3 E(bn) ∠ 30 E(ca) = √3 E(cn) ∠ 30
How do you calculate line current?
I(a) = E(an)/Z(y)
How do you calculate the load current for a Δ circuit?
I(A) = √3E(AB)∠ -30/Z(Δ)
How do you calculate the load current for a Y circuit?
I(A) = E(AB)∠ -30/(√3 * Z(y))
How do you convert from Δ to Y?
Z(y) = Z(Δ)/3
How do you calculate the real power in a three phase load/generator?
P(3Ф) = √3 * V(LL) * I(L) * cos (𝛿 - β)
What are the 4 advantages of balances three phase vs single phase?
1) reduce capital costs
2) reduce operating costs
3) better voltage regulation
4) total instantaneous power delivered by 3 phase is constant
How do you calculate the per-unit quantities?
p.u. = Actual value/base value in the same unit
What are the 4 advantages to using the p.u.?
1) systems and losses and voltage may vary widely - for system with the same p.u. losses and voltage drops are in the same order
2) the use of √3 in three phase calculations is reduced
3) the solution of networks containing several transformers is facilitated
4) easier for digital computation
What are the 5 per unit values for a single-phase circuit?
1) active power, P(p.u) = P/S(base)
2) reactive power, Q(p.u) = Q/S(base)
3) voltage, V(p.u) = V(LN)/V(bas, LN)
4) Current, I(p.u) = I/I(base)
5) Impedance, Z(p.u) = Z/Z(base)
What are the 4 base unit values for a three-phase circuit?
1) power base, S(base) = S(base)/3
2) voltage, V(base) = V(base, LL)/√3
3) Current , I(base) = S(base)/√3V(base,LL)
4) Impedance, Z(base) = V²(base, LN)/S(base)
What are the 5 per unit values for a three-phase circuit?
1) active power, P(p.u) = P/S(base) = same as 1
2) reactive power, Q(p.u) = Q/S(base)=same as 1
3) voltage, V(p.u) = V(LN)/V(bas, LN)=same as 1
4) Current, I(p.u) = I/I(base)
5) Impedance, Z(p.u) = Z/Z(base)
Why is the calculation of per unit values with changing of bases required?
- Power system consists of generators, transformers, transmission lines and loads
- parameters such as voltages are sometimes given with respect to their own bases rather than the whole system
- need to therefore chose a common base for whole system
