EE-361

VOLTAGE REGULATION & EFFICIENCY

Ozan Keysan

Office: C-113 • Tel: 210 7586

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Voltage Regulation2 / 32

Voltage RegulationA transformer's ability to keep its output voltage constant.2 / 32

Voltage RegulationA transformer's ability to keep its output voltage constant.Ideal transformer:Vout at No Load = Vout at Full Load2 / 32

Voltage RegulationA transformer's ability to keep its output voltage constant.Ideal transformer:Vout at No Load = Vout at Full LoadPractical transformer:Vout under load is generally smaller than Vout at No Load2 / 32

Voltage RegulationV2(NoLoad)−V2(FullLoad)V2(FullLoad)3 / 32

Voltage RegulationV2(NoLoad)−V2(FullLoad)V2(FullLoad)Smaller regulation is better.Regulation of an ideal transformer = 03 / 32

Voltage Regulation with Phasors

Drawing

Neglect the parallel branch (for now)

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Voltage Regulation

Drawing

Regulation can be calculated at any load.

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Voltage RegulationInductive: Vreg>0
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Voltage RegulationInductive: Vreg>0
Resistive: Vreg>0
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Voltage RegulationInductive: Vreg>0
Resistive: Vreg>0
Capacitive: Vreg=?
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Voltage Regulation

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Voltage Regulation

Burdur GES

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Voltage Regulation

Burdur GES

Effects to Electric Grid, Duck Curve

Drawing

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Example:For the same transformer(1000 VA) used in the previous problem, calculate the voltage regulation at:a) 0.8 pf lagging rated currentb) 1.0 pf rated currentc) 0.8 pf leading rated currentif the output voltage of the transformer is adjusted to be 115 V, under the given load condition.You can ignore the parallel branch.9 / 32

Transformer EfficiencyEfficiency(η)=PoutPin10 / 32

Transformer EfficiencyEfficiency(η)=PoutPinEfficiency(η)=PoutPout+Losses10 / 32

Transformer EfficiencyEfficiency(η)=PoutPinEfficiency(η)=Pin−LossesPin11 / 32

Transformer EfficiencyConstant Losses: Core Losses (Eddy, Hysteresis)
V21Rcore12 / 32

Transformer EfficiencyConstant Losses: Core Losses (Eddy, Hysteresis)
V21RcoreVariable Losses: Copper Losses
I21(R1+R′2)
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Best Power TransformerEfficiency as high as possible
Voltage Regulation close to zero
Minimum Cost
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Golden Rule of Engineering Projects

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You can only pick TWO from these three!

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Temperature Effect

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How does the resistance change with temperature?

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Temperature EffectTemperature CoefficientR(T)=R(T0)(1+αΔT)16 / 32

Temperature EffectTemperature CoefficientR(T)=R(T0)(1+αΔT)For copper α = 0.393 % per degree CResistivity of copper increases by 30 % from 20 C to 100 C.16 / 32

Losses and Cooling

Drawing

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Losses and Cooling: Small Transformers

Drawing

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Losses and Cooling: Large Transformers

Drawing

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Losses and Cooling: Large Transformers

Drawing

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Losses and Cooling: Large Transformers

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Drawing

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Who’ll Freeze First? A Puzzle About Size and Staying Warm

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Who’ll Freeze First? A Puzzle About Size and Staying Warm

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Who’ll Freeze First? A Puzzle About Size and Staying Warm

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Who’ll Freeze First? A Puzzle About Size and Staying Warm

Size and Metobolism

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(Heat $\propto$ Mass, Heat Dissipation $\propto$ Surface Area)

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Square-Cube Law by Prof. Walter Lewin

Square-cube law, small is mighty

Small is mighty

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Example:For the same transformer(1000 VA) used in the previous problems, calculate the efficiency at rated current and 0.8 pf lagging (assuming output voltage is 115 V).28 / 32

Question:What is the point that the transformer has maximum efficiency?29 / 32

Question:What is the point that the transformer has maximum efficiency?Full Load / Half Load / No Load ?
Unity pf, lagging pf, leading pf?
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Transformer Efficiency

A transformer has highest efficiency while delivering unity pf

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A transformer has maximum efficiency when:31 / 32

A transformer has maximum efficiency when:

Copper Losses = Core Losses

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You can download this presentation from: keysan.me/ee361

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EE-361

VOLTAGE REGULATION & EFFICIENCY

Ozan Keysan

Voltage Regulation

Voltage Regulation

A transformer's ability to keep its output voltage constant.

Voltage Regulation

A transformer's ability to keep its output voltage constant.

Ideal transformer:

VoutV_{out} at No Load = VoutV_{out} at Full Load

Voltage Regulation

A transformer's ability to keep its output voltage constant.

Ideal transformer:

VoutV_{out} at No Load = VoutV_{out} at Full Load

Practical transformer:

VoutV_{out} under load is generally smaller than VoutV_{out} at No Load

Voltage Regulation

V2(NoLoad)−V2(FullLoad)V2(FullLoad)\frac{V_{2(No\;Load)}-V_{2(Full\;Load)}}{V_{2(Full\;Load)}}

Voltage Regulation

V2(NoLoad)−V2(FullLoad)V2(FullLoad)\frac{V_{2(No\;Load)}-V_{2(Full\;Load)}}{V_{2(Full\;Load)}}

Smaller regulation is better.

Regulation of an ideal transformer = 0

Voltage Regulation with Phasors

Neglect the parallel branch (for now)

Voltage Regulation

Regulation can be calculated at any load.

Voltage Regulation

Inductive: Vreg>0V_{reg}>0

Voltage Regulation

Inductive: Vreg>0V_{reg}>0

Resistive: Vreg>0V_{reg}>0

Voltage Regulation

Inductive: Vreg>0V_{reg}>0

Resistive: Vreg>0V_{reg}>0

Capacitive: Vreg=?V_{reg} = ?

Voltage Regulation

Voltage Regulation

Voltage Regulation

Effects to Electric Grid, Duck Curve

Example:

For the same transformer(1000 VA) used in the previous problem, calculate the voltage regulation at:

a) 0.8 pf lagging rated current

b) 1.0 pf rated current

c) 0.8 pf leading rated current

if the output voltage of the transformer is adjusted to be 115 V, under the given load condition.

You can ignore the parallel branch.

Transformer Efficiency

Efficiency(η)=PoutPin\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}

Transformer Efficiency

Efficiency(η)=PoutPin\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}

Efficiency(η)=PoutPout+Losses\mathrm{Efficiency (\eta) = \frac{Pout}{Pout+\mathrm{Losses}}}

Transformer Efficiency

Efficiency(η)=PoutPin\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}

Efficiency(η)=Pin−LossesPin\mathrm{Efficiency (\eta) = \frac{Pin - Losses}{Pin}}

Transformer Efficiency

Constant Losses: Core Losses (Eddy, Hysteresis)

V21Rcore\frac{V_1^2}{Rcore}

Transformer Efficiency

Constant Losses: Core Losses (Eddy, Hysteresis)

V21Rcore\frac{V_1^2}{Rcore}

Variable Losses: Copper Losses

I21(R1+R′2)I_1^2 (R_1 + R_2')

Best Power Transformer

Efficiency as high as possible

Voltage Regulation close to zero

Minimum Cost

Golden Rule of Engineering Projects

You can only pick TWO from these three!

Temperature Effect

How does the resistance change with temperature?

Temperature Effect

Temperature Coefficient

R(T)=R(T0)(1+αΔT)R(T) = R(T_0)(1 + \alpha\Delta T)

Temperature Effect

Temperature Coefficient

R(T)=R(T0)(1+αΔT)R(T) = R(T_0)(1 + \alpha\Delta T)

For copper α = 0.393 % per degree C

Resistivity of copper increases by 30 % from 20 C to 100 C.

Losses and Cooling

Losses and Cooling: Small Transformers

$V_{out}$ at No Load = $V_{out}$ at Full Load

$V_{out}$ at No Load = $V_{out}$ at Full Load

$V_{out}$ under load is generally smaller than $V_{out}$ at No Load

$\frac{V_{2(No\;Load)}-V_{2(Full\;Load)}}{V_{2(Full\;Load)}}$

$\frac{V_{2(No\;Load)}-V_{2(Full\;Load)}}{V_{2(Full\;Load)}}$

Inductive: $V_{reg}>0$

Inductive: $V_{reg}>0$

Resistive: $V_{reg}>0$

Inductive: $V_{reg}>0$

Resistive: $V_{reg}>0$

Capacitive: $V_{reg} = ?$

$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$

$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$

$\mathrm{Efficiency (\eta) = \frac{Pout}{Pout+\mathrm{Losses}}}$

$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$

$\mathrm{Efficiency (\eta) = \frac{Pin - Losses}{Pin}}$

$\frac{V_1^2}{Rcore}$

$\frac{V_1^2}{Rcore}$

$I_1^2 (R_1 + R_2')$

$R(T) = R(T_0)(1 + \alpha\Delta T)$

$R(T) = R(T_0)(1 + \alpha\Delta T)$

(Heat $\propto$ Mass, Heat Dissipation $\propto$ Surface Area)