Sections: Voltage Regulation | Efficiency | Temp. Rise

Voltage Regulation

I_pR = I_pR_p + I_sR_s(T_p/T_s)
But, I_s = I_p x I_p(T_p/T_s)

Thus, R = R_p + R_s(T_p/T_s)²

Also, E_p = (I₁R + E₁cosq) / cosf
Where:
cosq = power factor of the external load
cosf = power factor of the primary side.
tanf = (I₁X + E₁sinq) / (I₁R + E₁cosq)

%Reg = [%R_eq + 100(cosq - cosf] / cosf + (%IXcosq - %IRsinq)² / 200
The last term is usually negligible.

At unity power factor: %Reg = %IR + (%IX)²/200.

---

Sections: Voltage Regulation | Efficiency | Temp. Rise

Efficiency

If W = E_sI_scosq, and w = total losses (iron plus copper losses)
Efficiency, h = 1 - w / (W + w)
Thus:
Total Losses, w = W(1 - h) / h

If h₁ is the efficiency at unity power factor:
The efficiency at cosq is:
h_cosq = cosq / [cosq + (1 - h)/h]

If W = full-load output in watts
a = efficiency at full-load
x = full-load copper loss, watts
y = full-load core loss, watts
w = total loss at full-load
then: w = x + y = w x (1 - a) / a

If b = efficiency when output is n time the full-load
nW = output, watts
n²x = copper loss, watts
w_n = total loss when load is W
then: w_n = n²x + y = w x (1 - b) / b
w - w_n = x - n²x
Full load copper loss, x = (w - w_n) / (1 - n²)

The All-day efficiency is calculated for a period of 24-hour operation-idle cycle with respect to the power output and the losses.

---

Sections: Voltage Regulation | Efficiency | Temp. Rise

Temperature Rise

Permissible temperature rise in oil is usually 50²C.

Cooling coefficients for transformer tanks with smooth surface:

Cooling Coefficient	Temp. Rise
0.0041	30²C
0.005	40²C
0.0057	50²C

Where c = W/tS

S is the total area of the vertical sides plus 1/2 the area of the lid. If oil is in contact with the lid, the whole area of the lid is taken into consideration.

If the surface is corrugated, with l as the surface width of the sides per pitch and l as the pitch of the corrugations, the effective surface would be: l_e = l + (l - l) x [2l / (l + l)]

For Design Notes, click here.

---

Home | EMD | Sites | ABdA | Help | E-mail