class: center, middle # EE-361 # VOLTAGE REGULATION ## Ozan Keysan [keysan.me](http://keysan.me) Office: C-113
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Tel: 210 7586 --- # Voltage Regulation -- ### A transformer's ability to keep its output voltage constant. -- # Ideal transformer: ## \\(V\_{out}\\) at No Load = \\(V\_{out}\\) at Full Load -- # Practical transformer: ### \\(V\_{out}\\) under load is generally smaller than \\(V\_{out}\\) at No Load --- # Voltage Regulation ## $$\frac{V\_{2(No\;Load)}-V\_{2(Full\;Load)}}{V\_{2(Full\;Load)}}$$ -- ## 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: \\(V_{reg}>0\\) -- - ## Resistive: \\(V_{reg}>0 \\) -- - ## Capacitive: \\(V_{reg} = ?\\) --- # Voltage Regulation  --- # Voltage Regulation ### [Burdur GES](https://goo.gl/maps/JF91W3KiWgH2) -- ## [Effects to Electric Grid](https://en.wikipedia.org/wiki/Voltage_regulation)
--- # 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. --- # Transformer Efficiency # $$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$$ -- ## $$\mathrm{Efficiency (\eta) = \frac{Pout}{Pout+\mathrm{Losses}}}$$ --- # Transformer Efficiency # $$\mathrm{Efficiency (\eta) = \frac{Pout}{Pin}}$$ ## $$\mathrm{Efficiency (\eta) = \frac{Pin - Losses}{Pin}}$$ --- # Transformer Efficiency - ## Constant Losses: Core Losses (Eddy, Hysteresis) ### $$\frac{V_1^2}{Rcore}$$ -- - ## Variable Losses: Copper Losses ### $$I_1^2 (R_1 + R_2')$$ --- # Best Power Transformer - ## Efficiency as high as possible - ## Voltage Regulation as low as possible --- # Temperature Effect
### How does the resistance change with time? --- # Temperature Effect ## Temperature Coefficient ## $$R(T) = R(T_0)(1 + \alpha\Delta T)$$ -- # Resistivity of copper increases by 30 % from 20 C to 100 C. ## For copper $$\alpha = 0.393 \%$$ per degree C --- # Losses and Cooling
--- # Losses and Cooling: Small Transformers
--- # Losses and Cooling: Large Transformers
--- # Losses and Cooling: Large Transformers
--- # Losses and Cooling: Large Transformers
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### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/) ---
### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/) ---
### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/) ---
### [Who’ll Freeze First? A Puzzle About Size and Staying Warm](http://noticing.co/on-size-and-warmth/) ###[Size and Metobolism](http://noticing.co/on-size-and-metabolism/) --- ## (Heat \\(\propto\\) Mass, Heat Dissipation \\(\propto\\) Surface Area)
### [Square-Cube Law by Prof. Walter Lewin](http://www.youtube.com/watch?v=qoM17ikreio) ### [Square-cube law, small is mighty](https://www.youtube.com/watch?v=qzq710aOHjE) --- ## (Heat \\(\propto\\) Mass, Heat Dissipation \\(\propto\\) Surface Area)
[Small is mighty](https://www.youtube.com/watch?v=qoM17ikreio) --- # What about in humans? --
--- # What about in humans?
--- # What about in humans?
### [Bermann's rule](https://en.wikipedia.org/wiki/Bergmann%27s_rule), [How insects breathe?](http://noticing.co/how-insects-breathe/) --- --- # 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). --- #Question: ## What is the point that the transformer has maximum efficiency? -- - ## Full Load? -- - ## Half Load ? -- - ## No Load ? --- # Efficiency Graph  --- # A transformer has maximum efficiency when: -- # Copper Losses = Core Losses # But, Why? --- ## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)