class: center, middle # EE-361 # Per-Unit System ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113
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Tel: 210 7586 --- #Per-Unit Calculations -- ##Per Unit Value = \\(\mathrm{\frac{Actual\;Value}{Base\;Value}}\\) -- ## Parameters you need: ##\\(S\_{base} \; \mathrm{and} \; V\_{base}\\) ### which are the rated power(VA) and the rated voltage --- #Per-Unit Calculations ##\\(S\_{pu}=\frac{S}{S\_{base}}\\) -- ## \\(S\_{pu} = 0.5 \quad\\): Half-load -- ## \\(S\_{pu} = 1.0 \quad \\): Full-load -- ## \\(S\_{pu} = 1.1 \quad \\): 10% overload --- #Per-Unit Calculations ## We know \\(S\_{base} \; \mathrm{and} \; V\_{base}\\). Therefore: -- # \\(I\_{base}=\frac{S\_{base}}{V\_{base}}\\) -- ## \\(Z\_{base}=\frac{V\_{base}}{I\_{base}}=\frac{V\_{base}^2}{S\_{base}} \\) --- #Per-Unit Calculations ##\\(S\_{pu}=\frac{S}{S\_{base}}\\) ##\\(V\_{pu}=\frac{V}{V\_{base}}\\) ##\\(I\_{pu}=\frac{I}{I\_{base}}\\) ##\\(Z\_{pu}=\frac{Z}{Z\_{base}}\\) --- # Why do we use Per-phase? -- ![](http://www.geni.org/globalenergy/library/national_energy_grid/turkey/graphics/teias_map.gif) --- # Why do we use Per-phase? ## Turkey Grid Control Room (Gölbaşı)
--- # Why do we use Per-phase? ## USA Grid Control Room
--- # Why do we use Per-phase? ![](http://static.squarespace.com/static/538d65b3e4b0d6fa15b1d9a9/538fdb52e4b03adbe1ea921b/538fdb73e4b07567a85c09fd/1401936756809/W005.JPG) --- ![](http://2.bp.blogspot.com/-6N7qH53Vhu8/UwxlPh8J5qI/AAAAAAAAAHY/DGsNnJiMk54/s1600/6.png) --- ![](http://www.tucsontransformer.com/img/cooper-rte-substation-transformer-44-1041-np.jpg) --- # Why do we use Per-Units? -- - ## Almost always used in power systems -- - ## Easier to spot any anomalies -- - ## p.u values are constant on each side of the transformer -- - ## System reduces just a series of impedances --- # Example ## Consider a 660:220 V, 7260 VA single-phase transformer. If, ### \\(Z\_{eq}= 0.36 + j 2.4~ \Omega\\) referred to primary. Calculate: - ### Equivalent impedance in p.u on the primary side -- - ### Equivalent impedance in p.u and actual value on the secondary side -- - ### Power in p.u if a \\(20~\Omega\\) load is connected to secondary (assume secondary terminal voltage is 220 V). --- # Procedure for Single Phase -- - ## Pick \\(V\_{base}\\) and \\(S\_{base}\\) -- - ## Use **Phase Voltages** (line-to-neutral) -- - ## Calculate \\(Z\_{base}\\) and \\(I\_{base}\\) -- - ## Convert actual values to pu. --- # Procedure for Three Phase -- - ## Pick \\(S\_{base}\\) for entire system (3-phase power) -- - ## Use **Line-to-Line Voltage** for \\(V\_{base}\\) -- - ## Calculate \\(Z\_{base}\\) -- - ## Calculate \\(I\_{base}\\) -- - ## Convert actual values to pu. --- #3-Phase Per-Unit Calculations ##\\(S\_{base}=\sqrt 3 V\_{base(l-l)} I\_{base}\\) -- ##\\(I\_{base}=\frac{S\_{base}}{\sqrt 3 V\_{base(l-l)}}\\) -- ##\\(Z\_{base}=\frac{V\_{base(l-l)}^2}{S\_{base}}=\frac{V\_{base(l-l)}}{\sqrt 3 I\_{base}}\\) --- ## Comparison of 3-Ph & 1-Ph Base Values ### Power ### \\((P\_{base}, Q\_{base}, S\_{base})\_{3-phase} = 3 VA\_{(base/1-phase)}\\) -- ### Voltage ### \\(V\_{base(line-to-line)} = \sqrt{3} V\_{base-1phase}\\) -- ### Current ### \\(I\_{base(per-phase-\Delta)} =\dfrac{I\_{base(per-phase-\Delta)}}{\sqrt{3}}\\) --- # Extra Reading Materials ## [Per-Unit System](http://my.ece.msstate.edu/faculty/donohoe/ece3614per_unit_system.pdf) ## [Why we need per unit system in power system?](https://www.quora.com/Why-we-need-per-unit-system-in-power-system) ## [Per Unit System](http://circuitglobe.com/what-is-a-per-unit-system.html) ## [Matlab-Per Unit](https://www.mathworks.com/help/physmod/sps/powersys/ref/per-unit-and-international-systems-of-units.html) --- ## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)