# 3 Phase Transformer Calculation Formulas

The short-circuit current available (I). The following conditions are to be fulfilled before paralleling two three phase Transformers:-. A three phase transformer or 3φ transformer can be constructed either by connecting together 3 single-phase transformers, thereby forming a so-called three phase transformer bank or by using one pre-assembled and balanced three phase transformer which consists of three windings mounted onto one laminated core. 44 will not present there. A 3-phase transformer has three different voltages, and the currents differ in phase-time. The required transformer would be a 750VA or. So 200/5 = 40. So if we calculate 15000/ (1. For an example let's use Load voltage = 480 volts, Load current, = 80 Amps and Line voltage = 208 volts. 99% ) Voltage Drop 13. Calculator With Utility and XR ratios Cover Sheet Detailed_Calculations Main_Sheet Simple_Calculations Xfmr_Tables Nominal amperes at nameplate kVA, all transformer types kVA Volts Amps = kVA X Maximum amps for Oil/Silicon filled 65 deg, fan rating Nominal X 1. 97% ) Primary Config: Transformer Size: 15 kVA 30 kVA 45 kVA 75 kVA 112. The new formula for 3-phase is W=(E*1. Presuming a three phase, four wire supply at 220/380 volts, then a total load of 60KW is clearly 20KW per phase if perfectly balanced. Three Phase Fault In a three phase fault, all three phases (L1, L2 and L3) are shorted together. Highest rated motor is one with highest FLC. The relationship between units in a per-unit system depends on whether the system is single-phase or three-phase. So 3600=(208*1. Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors. 732 x 11000V x 5. Yes, that looks correct. A Unified Three-Phase Transformer Model for Distribution Load Flow Calculations. 732xVp Transformer Primary. 39 x the FLA = 20,903A. The current difference is mainly caused by different three-phase load. 30 3-phase core type transformer (Distribution): 0. Three Phase Transformer Full-Load Current (Amps) = kVA × 1000 / (1. Note the neutral formula. These calculations are for single phase transformer design. WBHP = 31/2 U I PF μ / 746 (3) WBHP = brake horse power (hp) μ = device efficiency. 35%, while the third has a percent impedance of 4. Transformer Current Ratings: A transformer's A. 3 phase motor current calculation formula is P/ (√3xVxPfxEff) or P/ (1. This is because 3-phase systems have built in efficiencies for high power transmission systems. For other single phase systems select the line-to-neutral voltage. Connect the circuit as shown in the circuit diagram 2. This simple introductory exercise is aimed at giving students an opportunity to familiarise themselves with the theory and calculation procedures and to. What is the formula for Heat Units (HU) for single phase? What are the correction factors used for 3 phase 6 pulse & 3 phase 12 pulse? What % increase is the intensity of the beam? HU = mA x Sec x kV. The following calculators compute real power in a three-phase system based on Kvar and KVA or voltage, current, and power factor. php on line 143 Deprecated: Function create_function() is deprecated in. The first option is to use the three-phase equation: Line values - three-phase formula: Coil values - three-phase formula: The second option is to determine the load on the individual transformers and add these together. Three-phase has three lines of AC power, with each line 120 degrees out of phase with the other two. Refer to operational specifications to find the power factor. The advantage of the bank concept is the relatively low cost of providing a spare fourth unit as a strategic reserve. What is Power Factor Power Factor is the cosine of the phase angle between current and voltage. The polarity must be same. 4 Equations for the various currents p. Transformer Calculations Quiz. Transformer Formulas. 25 this equals 720VA and most transformers are sized by a factor of 25VA or 50VA. Transformer impedance is usually expressed as a percent. Pick a 3 VA base for the entire system, 2. We will use some of the tools and calculators to accomplish this. 89 and PF is 0. The SPICE model below is for a four winding transformer having a 10 turn push-pull primary winding and two 1 turn secondary windings. This calculator provides the missing variable in the three transformer characteristics. When this is true, the delta phase current will be exactly in phase with the delta phase voltage, and the active power output in watts (P) will be equal to the apparent power volt-amp rating (S). So, what is actually changing in an ideal transformer is the ratio of volts to amps. Due to temperature rise, the rating of the transformer is generally measured in kilo-volt-ampere(kVA) instead of Kilowatts(kW). 3-Phase Fault Current Calculation - basis • Per-Phase Analysis with Injection & Thevenin. 3-Phase AC Calculations Revisited. 45kVA Three Phase Transformer, Input Voltage: 480VAC Delta. Go to “How to size a transformer” on page 1. Zig-zag windings are used to suppress third harmonics or to provide a neutral connection as an earthing transformer, and to obtain a phase angle shift. the transformer, which means adequate protection should be provided for quicker isolation of the transformer under such conditions. This is typically single-phase or three-phase. We hope to provide you with the best online voltage drop calculator, as well as all relevant information regarding voltage drop formulas, equations, and calculations, and more!. 4- or 6-wire connection If 6-wire connection is used, the total length of the wire, naturally, will be two times the distance between the CT and the relay. These calculations are for single phase transformer design. 25A = 100,025 VA = 100kVA. The Secure code is a 3 or 4 digit code printed on your credit card. So 200/5 = 40. Be sure to ask your students to describe how they arrived at the answers to this question. Secondary Config:. 732 gets added into the equations accordingly. The treat-ment throughout the Handbook is practical with very little emphasis on theory. repaired a 200 kva three phase distribution transformer his stander iron losses is 495 & copper losses is 3410 but the measured iron losses is 692 what formula is to know de-rated in kva ? pl answer with expal. For example, to find the Voltage in a circuit: If the circuit has a current of 2 amperes, and a resistance of 1 ohm, (< these are the two "knowns"), then according to Ohms Law and the formulas above, voltage equals current multiplied by resistance:. Transformer size can be manually derived from load voltage, load current amps and line voltage. This calculation applicable for both the primary and secondary. (K= 1,000) The full value in VA, 75,000 divided by 1. Percentage impedance will be same on single phase basis or three phase basis as ohmic. 3 %,100-400 MVA -0. The Handbook of Electric Power Calculationsprovides detailed step-by-step calculation procedures commonly encountered in electrical engineering. S: As for 3 phase transformers, this derivation is different so the factor 4. Verify all calculations with a professional engineer. The percentage impedance should be same. This is how the transformer power factor calculation and correction is done to increase efficiency. Anyway, when 'looking' from one of the sides of the transformer, the simple formula is: P=U*I*1. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. By removing the impact of varying voltages. It can be seen from equation (12. (Three Phase) Transformer Size for Four Wire Delta Secondary. The 400 Hz is reserved for high-powered applications such as aerospace and some special-purpose computer power supplies and hand-held machine tools. repaired a 200 kva three phase distribution transformer his stander iron losses is 495 & copper losses is 3410 but the measured iron losses is 692 what formula is to know de-rated in kva ? pl answer with expal. Please help how do I calculate Current (Amps) in a 3 phase circuit with 6. 73 1000 (2) To determine Amperes when KVA and volts are known: Amps = 3 Phase KVA x 1000 Volts x 1. 2KVA transformer. Microprocessor-based digital relays use internal calculations instead of CT connections to compensate for winding connections. Three-phase systems Three-phase electricity consists of three ac voltages of identical frequency and similar amplitude. 50 rms: The square root of the average value of the square of the voltage or current taken throughout one period. These Calculation Worksheets can then be exported to a CAD program or other document file using the Windows Clipboard. That gives us 416. I is A in one phase. P total = 126. Calculation of winding resistance and leakage reactance: The input power which is measured in the short circuit test is unlikely to be the same as V I calculated from measurements. So both calculations are overstated. SCA secondary = 3 Phase Short Circuit Amps at the secondary bus. Multiple motors started at the same time may be summed and treated as one motor. of a single 3-phase transformer. 73); Three phase formulas do not use (2) * For three-wire, two phase circuits, the current in the common conductor is 1. High voltage windings, are connected in the star configuration. Convert Ptotal from KVA into Kilowatts using the formula: P (KW) = P (KVA) x power factor. 3 phase kVA to amps calculation formula Calculation with line to line voltage The phase current I in amps (with balanced loads) is equal to 1000 times the apparent power S in kilovolt-amps, divided by the square root of 3 times the line to line RMS voltage V L-L in volts: I (A) = 1000 × S (kVA) / (√ 3 × V L-L(V)). The total equivalent circuit of the transformer is obtained by adding in the primary impedance as shown in – Fig-3. Unbalanced current of transformer refers to current difference of three-phase transformer windings. Loading considerations when paralleling transformers It can be seen by using equations (1) and (2) below, that if the percent impedances in each transformer are the same, as shown in Figure 1, that there will be equal current division and load sharing on each transformer. 3-Applicable procedures for calculating power transformer voltage regulation, 4-Special Cases In Transformers Sizing Calculations: Secondary Unit Substations Power And Distribution Transformers Sizing Calculations – Part Five. 2 Application E xamples. 73 1000 (2) To determine Amperes when kVA and volts are known: Amps = 3-Phase kVA x 1000. Load voltage, or secondary voltage, is the voltage needed to operate the load. Pac= 3 Vp Ip cos phi, where vp is the rms phase voltage and Ip is the rms phase current and cos phi is the power factor. Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors. In the SPICE model, each section. Phase A starts at 0 at 0 degree phase angle, rises to 1 at 90 degrees, back to 0 at 180, to -1 at 270 degrees, and back to 1 at 360 degrees. For a three phase system multiply by three to get the total power. 732xVxPfxEff) Both are same. The second letter (y or d) indicates a low-voltage wye or delta winding connection. 89 and PF is 0. You can enter equipment data and parameters via user friendly interface. 7% higher, and the 2500kVA pad would price 7. Using the calculation yields a 66 KVA transformer. 3 Phase I SCA = KVA Base √3 KVLL total PUZ KVA Base = 10,000 Single Phase Two separate calculations must be done for single phase systems. In this interactive object, learners follow steps to find phase voltages in a partial three-phase power distribution circuit. The winding direction of the central unit b is made opposite to that of units a and c. 7 A) and throw that at the balanced three-phase formula and see if you get something that is in the ball park of when you do the per-leg unbalanced computation. (I personally designed and used it). High voltage windings, are connected in the star configuration. Formula to calculate power, current and voltage in three-phase wiring (balanced load, equal loads on each of three phases) : P=√3*U*I*cosφ I=P/(√3*U*cosφ) U=P/(√3*I*cosφ) P = power in watt (W) U = voltage in Volt (V) I = current in ampere (A) cos φ = cosinus phi (without unit). 5 kVA 150 kVA 225 kVA 300 kVA 500 kVA. E phase (load) = 7. pptx 12 Example 9-1: A 100 kVA, 7200 -480 V 60 Hz single phase transformer has the following parameters all given in ohms: R LS = 0. It should be noted that the calculation of X 3 concerns only separated circuit without mutual inductance. Calculate the sizing, kVA, windings, and turns ratio for a 3 phase & single phase transformer. Three-phase systems Three-phase electricity consists of three ac voltages of identical frequency and similar amplitude. 3 phase kVA to amps calculation formula Calculation with line to line voltage. Buy the complete 9 DVD series with workbook at codeelectricprep. The software will do all the thermal calculations involved in the design and will generate a summary of all results. Phase A starts at 0 at 0 degree phase angle, rises to 1 at 90 degrees, back to 0 at 180, to -1 at 270 degrees, and back to 1 at 360 degrees. It has two types, single phase and three phase transformer. These legs will not be 120 degrees apart, as they would be in a true three phase, however, they will be close enough that 3 phase motors and transformers will be happy. The bank is actually a Wye-Delta. 6 Amps per phase 16. If i have three single phase transformers of different capacities, say two 50 kVa transformers and one 75 kVA, connceted in a star-star configuration, and i also have the line and phase voltages and currents on the secondary side of the bank taken by a clip-amp meter or some other device, how do i determine the total load the bank is supplying?. 866 (30° ) lagging. However, in many cases a common return. What is the transformer law? What formula is used to determine the voltage & current?. Determine if a single-phase transformer is overloaded. Basically a wye source to a delta load, and in the past 24 months, we have shorted the motor windings on six different occasions. Design Formulas: Here we take the reference of winding data on enameled copper wire table and dimensions of transformer stampings table to select input and output windings SWG and core of the transformer for given specifications. The maximum flux in the core. Calculate electrical power transformer kva, current amps, and voltage. Power Transformers II Y. Multiple motors started at the same time may be summed and treated as one motor. If the circuits in parallel are close together the value of X 3 will be higher. The treat-ment throughout the Handbook is practical with very little emphasis on theory. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. Then, also select if the service is three phase or single phase. step up transformer sizing going from 208v 3 phase to 480v 3 phase, i have found a 30KVA delta wye step up transformer ide like to use. Transformer loss calculations are based on voltage and current, not Watt-hours or Var-hours. This data can be easily obtained from the transformer nameplate. Transformer size can be manually derived from load voltage, load current amps and line voltage. Its requires each three-phase winding to be split in half. 85 and 1, see Resources), the current and the voltage. 732 = KVA = KW = HPX746 1000 PF 1000XEfficiencyxPF 2 L. 3 phase motor current calculation formula is P/ (√3xVxPfxEff) or P/ (1. But the current in each phase winding is given as: 1/√ 3 × I L of the line current, where I L is the line current. Using the calculation yields a 66 KVA transformer. Line and Phase currents are related to each other as: I_line=square_root(3)*I_phase Which means that whatever supply current we have, we need a wire cross-section for 1/ square_root(3) times line current only. Connect the circuit as shown in the circuit diagram 2. Figure 1 shows a typical low-voltage dry-type transformer and Figure 2 shows a sample transformer nameplate. The efficiency of a three-phase power transformer is affected by power losses. This is how the transformer power factor calculation and correction is done to increase efficiency. Let us suppose for the moment that the impedance at the primary terminals is a series combination of resistance R % and reactance X %. Formula to calculate power, current and voltage in three-phase wiring (balanced load, equal loads on each of three phases) : P=√3*U*I*cosφ I=P/(√3*U*cosφ) U=P/(√3*I*cosφ) P = power in watt (W) U = voltage in Volt (V) I = current in ampere (A) cos φ = cosinus phi (without unit). 3 phase kVA to amps calculation formula. The general consensus, for a 2%Z transformer is + or -. Converter: The converter formula of a three-phase transformer is the same as that of a single-phase transformer, that is, I 1 /I 2 = U 2 / U 1 =1/ K U = K I. Use the formulas below as a guide, shown for common D. () 2 3 s p Pg T ω = Pg is power in the air gap of the machine. 6 Amps per phase 16. Small transformers, under 10 kVA, may be designed using handbook data and pencil-and-paper calculations, but larger or mass-produced units are often designed with extensive computer aided modeling. 1 Rabins’ Method Applied to Calculate the Leakage Reactance between Two Windings That Occupy Different Radial Positions253 9. Calculation of winding resistance and leakage reactance: The input power which is measured in the short circuit test is unlikely to be the same as V I calculated from measurements. 732)*I 3600 = 360*I. There are two main sources of losses: Winding and core losses which contribute to the total losses of the electrical system . The high voltage guy told my supervisor it is only rated at 360 amps,which is the rating for a 3 phase 150 kVa transformer, but wouldn't are system be rated at 450 kVa? Am I doing the above calculations wrong, or is the high voltage maintenance guy giving us incorrect information?. MOTOR FORMULAS AND CALCULATIONS: The formulas and calculations which appear below should be used for estimating purposes only. Eddy current Loss. To find the fault current at any point in the network, a sum is made of the impedances in the network between the source of supply (including the source impedance) and the point at which the fault is occurs. The line voltage ratios of the two transformers must be equal. Mathematical calculation for KVA and MVA for transformer. 3 Phase I SCA = KVA Base √3 KVLL total PUZ KVA Base = 10,000 Single Phase Two separate calculations must be done for single phase systems. Measurements are taken by applying a known low voltage across one winding and measuring the induced-voltage on the corresponding winding. Once selected at a point in the network, the three-phase voltage base must vary according to the line-to-line transformer turns ratios. It is also the percentage of the normal terminal voltage required to circulate full-load current under short circuit conditions. 3-Phase Fault Current Calculation - basis • Per-Phase Analysis with Injection & Thevenin. running a vfd lathe 7. Calculate the short-circuit current at the secondary of the transformer. Where: V is the voltage (volts) and I is the current (amps). Please help how do I calculate Current (Amps) in a 3 phase circuit with 6. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. Full Load current calculation 3 Phase Motor: In most of the Three-phase systems, electricity consumption happens through star and delta connection. 89) So 15000 / 497. Calculations Transformer Turns Ratio - Volts and Current Transformer Turns Ratio - Volts and Turns Direct Current for Current, Horsepower, Voltage, or Efficiency Tables Transformer Impedance Factors Full-load current for single-phase transformer voltage Full-load current for three-phase transformer line-to-line voltage Definitions Tap Changer. Short-Circuit Current Calculations Three-Phase Short Circuits M 2 1 3 System A Available Utility Infinite Assumption 1500 KVA Transformer 480V, 3Ø, 3. I phase (load) = 5. The simple formula to calculate the rating of three phase Transformers is:. The grounding transformer is usually of the wye delta or zig-zag connections(2), (4), but in this paper we shall concentrate on the zig-zag connection, with the neutrals connected to earth. Transformer Calculations Quiz. The information needed in the Transformer Impedance Subview, requires several steps and calculations. Determination of the impedance of each component 1- Network upstream of the MV/LV transformer The 3-phase short-circuit fault level P SC, in kA or in MVA. The simple formula to calculate the rating of three phase Transformers is: KVA = (√3. 035 Ω respectively. 75% impedance will have a calculated available short circuit secondary current of 31,374 amps. Leverage Watlow's growing toolkit of calculators, equations, reference data and more to help design your thermal system. Motor branch circuit protection devices can protect the motor from short circuit and ground fault but cannot protect from overload. Take 600 times 1. Practice problems complete the activity. MOTOR FORMULAS AND CALCULATIONS: The formulas and calculations which appear below should be used for estimating purposes only. 8 lagging pf. 00800 R HS = 1. utility line design calculations The following calculations are included in the website, requires minimal training and take seconds to perform. The short-circuit kVA can be calculated from the short-circuit current using the following equation. Calculate the short-circuit current at the secondary of the transformer. dieselserviceandsupply. Further, the standard. In this figure, the power supply, and the transformer are assumed ideal. 3 Voltage Drop is Line to Neutral Calculations and not Line to Line. That is why we need to build a transformer model to calculate the inrush current. At Churchill Falls Terminal Station 2, of the Lower Churchill Project, a bank of three single-phase 3x280 MVA 735 kV power transformers was selected because of the required capacity. It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power. Incident-energy calculations—IEEE 1584. Pick a 3 VA base for the entire system, 2. Power Supply Electric Transformer 3 Phase Isolation Transformer , Find Complete Details about Power Supply Electric Transformer 3 Phase Isolation Transformer,Transformer,Power Transformer,Isolation Transformer from Transformers Supplier or Manufacturer-Foshan Ouli Electronic Co. So 3 HP , 115 volts Single phase with 34 A FLC is highest rated motor. The input power (P) to the system is the same, irrespective of the connection. This transformer calculator helps you to quickly and easily calculate the primary and secondary full-load currents of the transformer. I got the reactive ohms by multiplying the impedance base ohms by the %X. 6 Amps per phase 16. Load voltage, or secondary voltage, is the voltage needed to operate the load. To calculate kVA, you need to enter the known values of voltage and the current into the respective fields. Calculations Transformer Turns Ratio - Current and Turns Transformer Turns Ratio - Volts and Turns Direct Current for Current, Horsepower, Voltage, or Efficiency Tables Transformer Impedance Factors Full-load current for single-phase transformer voltage Full-load current for three-phase transformer line-to-line voltage Definitions. A 3 phase transformer has three magnetic circuits that are interlaced to give a uniform distribution of the dielectric flux between the high and low volts windings. 2 Needs of transformer short-circuit current calculation Today more than ever before, the electricity grid is developing so quickly — the power plant capacity, the substation capacity and electricity loads, as well as load density,. Step 3 – Check / Calculate Voltage Drop: Check for voltage drop with the cable size chosen. 5 Amp fuse Rounding to next available = 25 Amp * *Note: 50 Amps max. The single-phase, 4,160-to-120/240-volt transformer is rated 100 kVA and has a 1. The most important three-phase power equations relate power (P, in watts) to current (I, in amps), and depend on the voltage (V). Core losses are roughly constant from no-load to full-load when feeding linear loads. Calculation between phase angle φ° in degrees (deg), the time delay Δ t and the frequency f is: Phase angle (deg) (Time shift) Time difference Frequency λ = c / f and c = 343 m/s at 20°C. its not 380V for your information, the given voltage is 400V i know what you are trying to say but sorry to say it is 400V. A three phase auto transformer is special type in which common winding is being shared by the high voltage and low voltage. For Alaska, Hawaii, Canada and others, please call 865-680-4959 for a shipping quote. Wye Transformer Calculations. This is for the per unit method. Amperage of 3 Ph Generators Amperage (120/208 3-Ph, 80% PF) KW x 1000 E x PF x 1. Calculator can be used for step down transformer as well as step up transformer sizing applications. Full Load current calculation 3 Phase Motor: In most of the Three-phase systems, electricity consumption happens through star and delta connection. The filtering requirement is reduced as compared to. 41,= Vdc/ 1. Centre on the power transmission and transformation industry, our group company has 5 major brands covering insulation materials, electronic copper clad sheet, enameled wire, transformer, power transmission and distribution industry etc. 3 Phase Energy Meter Connection Diagram Explanation A three phase kWh meter have 8 terminals where we can enter the serves line supply which come form a utility pole or substation / step down transformer. 3 in place of figure 3. X/R ratio varies from 10 ( DT) to 125 (Large Transformers) based on rating. Thus a step down transformer has a larger number of turns in its primary winding than in its secondary coil. Efficiency from the transformer equivalent circuit parameters:. In other words, the percentage impedance of a. Open delta transformer Calculations. 035 Ω respectively. The Three-Phase Voltage System. High voltage, three phase, oil-cooled transformer Practical transformer design requires knowledge of electrical principles, materials, and economics. 3 phase converter efficiency 3 phase diesel inverter generator 3 phase grid inverter 3 phase inverter air conditioner 3 phase inverter air conditioning 3 phase inverter application note 3 phase inverter bridge 3 phase inverter ebay 3 phase inverter explained 3 phase inverter generator a three-phase multilevel inverter for high-power induction motors diy three phase converter how a three phase. 5 kVA / (√3 * 220) = 82. A 3-phase transformer has its primary connected in D and its secondary in Y. That is why we need to build a transformer model to calculate the inrush current. The maximum prospective fault current on a 3-phase circuit will depend on a number of factors. If you have balanced three-phase power, where all three phase voltages are equal in magnitude and 120° apart in phase, then: $$V_{L-L} = \sqrt{3} \times V_{L-N}$$ To see why, consider the phasor diagram: Applying some basic trig:. It can be seen from equation (12. E phase (load) = 7. Calculate Voltage Regulation of Transformer Example: A 100 kVA transformer has 400 turns on the primary and 80 turns on the secondary. Line to Line voltage x 1. The transformer steps down to 208Y/120 volts to a lighting panel with a continuous load of 30 amperes on each phase. Three Phase Transformer Full-Load Current (Amps) = kVA × 1000 / (1. However, in a three-phase wye system, even if only two of the three phases and the neutral run a single-phase load, you must use the neutral formula. In these connection the 4 points for incoming Line 1, L2 , L3 and neutral and other 4 are for out going 3 phase 4 wire supply to load. 3 phase motor current calculation formula is P/(√3xVxPfxEff) or P/(1. So, for a 100 KVA 240v single phase transformer the full load ampacity is 416. Connect Secondary windings in series & parallel. Refer this online tutorial to learn how to calculate kilovolt-ampere(kVA) in a three phase transformer. 73); Two phase-four wire formulas do not use (1. Step One: Single Phase or Three Phase Application IF Three Phase: Three wire source: Must use Open Delta; Four-wire source: Use Open Delta if only need three wires for load. 7 A) and throw that at the balanced three-phase formula and see if you get something that is in the ball park of when you do the per-leg unbalanced computation. So the power in any phase, assuming, again, a balanced load is the line voltage times the line current divided by the square root of 3. Or P = √3 x V x I (secondary voltage x secondary current). It is also used to power large motors and other heavy loads. Transformer power capacity is rate kilo-volt amperes (kVA). I got the reactive ohms by multiplying the impedance base ohms by the %X. (1) shows the zig-zag transformer connection and the Delta Wye connection. The thyristors are fired at an interval of 60˚. This can be represented diagrammatically by both waveforms and a vector diagram (Figure 2). It is advantageous to use two or more Transformer units in parallel instead of using a single large unit. Calculate the sizing, kVA, windings, and turns ratio for a 3 phase & single phase transformer. Fault Calculations The different types of short-circuit fault which occur on a power system are: - single phase to earth, - double phase, - double phase to earth, - three phase, - three phase to earth. The current difference is mainly caused by different three-phase load. V x I) /1000. • Assume all initial bus voltages are 1∠0° – therefore all initial currents are 0 • Use the 3,3 element of Zbus for the Thevenin impedance. kW to volts calculator. its not 380V for your information, the given voltage is 400V i know what you are trying to say but sorry to say it is 400V. Or P = √3 x V x I (secondary voltage x secondary current). Multiply 120 volts times 5 amps this equals 600VA now lets multiply the 125 percent start factor. So now, if we calculate by using the formula of eq. =1804A 25’ - 500kcml Cu 3 Single Conductors 6 Per Phase Magnetic Conduit 2000A Switch KRP-C 2000SP Fuse 400A Switch LPS-RK-400SP Fuse 50’ - 500 kcmil Cu 3 Single. Time has elapsed. PF is the cosine of the angle by which line currents lead or lag the line-to-neutral voltage. This configuration belongs to the vector group of transformer Dyn1 where the LV lags the HV by 30°. Phase A starts at 0 at 0 degree phase angle, rises to 1 at 90 degrees, back to 0 at 180, to -1 at 270 degrees, and back to 1 at 360 degrees. Transformers are available in single phase or three phase construction. 5-250 kVA single phase 25-500 kVA three phase 12. 732 = KVA = KW = HPX746 1000 PF 1000XEfficiencyxPF 2 L. Enter two and calculate the third value quickly. The paper sets out to describe an accurate analytical method which can be used to find the inrush current in any 3-phase transformer in common use. Three-phase imbalance means that inconsistent amplitude of three-phase current (or voltage) in electrical power system and that amplitude difference surpasses the specified range. Three phase systems are used for two reasons: 1. ﬁle 00412 Answer 3 E phase = 277 V Notes 3 More important than obtaining the correct answer is for students to explain what they did to get that answer. 3-phase outputs require 3-phase inputs. 14 shows the schematic of three-phase controlled rectifier connected with highly inductive load. 3 Impedance per phase calculations Utility impedance: 2 line 4. How to Calculate 3-Phase Line-To-Ground Voltage. 1 kV Amps […]. This offers flexibility for maintenance as well as operation. Power factor (cosΦ). FORMULAS USED IN CALCULATOR: 1-Phase KVA = Volts x Amps / 1000 1-Phase Amps = KVA / Volts x 1000 3-Phase KVA = Volts x Amps x 1. These legs will not be 120 degrees apart, as they would be in a true three phase, however, they will be close enough that 3 phase motors and transformers will be happy. Nominal System Voltage Actual System Voltage (use for calculations) Single Phase 120/240 volts, 1 phase 115/230 volts =. SEQUENCE IMPEDANCE OF 3-PHASE ALTERNATOR BY FAULT. Allowable Voltage Drop. 5% higher, the single phase pad, 4. 29 A and 69 kV primary voltage. This thesis presents the physical background of the inrush current phenomenon and a useful model of a three-phase power transformer for calculating the inrush current. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. 41,= Vdc/ 1. Jul 25, 2018 - Image result for 3-phase Transformer calculations Stay safe and healthy. The thyristors are fired at an interval of 60˚. The software will do all the thermal calculations involved in the design and will generate a summary of all results. Series transformer: To provide the required boost or buck voltage and Control transformer: For sensing the output voltage and for power supply. There is more than one place to start in determining the solution here, and more than one way to calculate some of the figures. (3#1Al, 1#6Cu) 1 1/4" EMT. kVA rating = √3 x 11 x 5. Short-Circuit Current Calculations Three-Phase Short Circuits M 2 1 3 System A Available Utility Infinite Assumption 1500 KVA Transformer 480V, 3Ø, 3. The base values in a system are so selected that the per-unit voltages and currents in the system are approximately unity. 1 product rating - TESTED ACME T-2-79370-4S 75 KVA STEP UP TRANSFORMER 208V to 480V 277V 3-PHASE. Two of the transformers have percent impedances of 5. Businesses that require three-phase power need to add an extra component in the formula to arrive at the correct transformer size, i. Transformer configuration names like and derive from the way the windings are connected inside the transformer. ** To pay by check call for quote. – The Single-Phase Full-Bridge Diode Rectifier 2 For completeness of discussion, we can note that there exists an analogy between single-phase and 3-phase diode bridges. NOTE: the above calculations are an estimate only because other factors such as site conditions, motor efficiencies and iron losses are not taken into consideration. By combining delta/delta and delta/wye transformers, you can abate harmonic distortion in an electrical system. In a balanced Y-connected power system, calculate the phase voltage (E phase) if the line voltage (E line) is 480 volts. Configuration for Single Phase Transformer. It seems a hell of a long time since I sat at evening classes drawing vectors and I don't really get that involved in three phase. The required current varies with type of rectifier chosen and filter type. 4-3 Experience is a great help in minimizing and crudely quantifying thermal resistance. Can 60 Hz transformers be used at higher frequencies? ACME transformers can be used at frequencies above 60 Hz up through 400 Hz with no limitations provided nameplate voltages are not exceeded. 732 x 11000V x 5. Four possible connections for a 3-phase transformer bank are: 1) Y-Y 2) Y-Δ 3) Δ-Δ 4) Δ-Y. Sponsored Links. Zig-zag windings are used to suppress third harmonics or to provide a neutral connection as an earthing transformer, and to obtain a phase angle shift. The impedance, voltage regulation, efficiency, and other calculations for 3-phase transformers are done on a per-phase basis, using the techniques studied previously for single-phase transformers. 1 shows the three-phase half-wave rectifier topology. The single-phase, 4,160-to-120/240-volt transformer is rated 100 kVA and has a 1. The maximum value of the magnetic flux density is 1. The reason I ask is that I have a delta connected 460 volt, 3 phase, 33 amp, 22 kw, 60 hz, motor that drives a compressor, and it is powered by a step up delta to wye transformer. Three-phase power systems have been used for the past century to provide electrical power throughout the world. The first set of calculations is to solve for Ro and Xo. By combining delta/delta and delta/wye transformers, you can abate harmonic distortion in an electrical system. The Phase-A leg is implemented using three Half-bridge IGBT with Loss Calculation blocks. The transformer of an industrial plant is 500,000VA three phase, with a voltage of 4160V in the secondary and an impedance of 5%, which will be the short level of this transformer. The after-the-fact calculations method requires the computer not only to have Delivered and Received Watt-hours and Var-hours, but to also have the per-phase voltages and the per-phase currents to accurately calculate the transformer losses. 3 kV Transformer amps. Required Tools. This is because 3-phase systems have built in efficiencies for high power transmission systems. In recent years, extending 3-phase power distribution all the way to server cabinets and racks has become extremely popular in new data center builds—for many good reasons. ii ABSTRACT This thesis is about calculating the short-circuit current on an overhead high voltage transmission line. 4Ω, 5Ω, 6Ω, Secondary Winding Resistance. 3-Phase or 1-Phase Transformer MVA rating Calculator Enter number only 22 Find 3 phase MVA rating of a power transformer Given 3 Phase Transformer with primary full load ampere (FLA) of 234. Full Load current calculation 3 Phase Motor: In most of the Three-phase systems, electricity consumption happens through star and delta connection. The first set of calculations is to solve for Ro and Xo. For a single-phase AC fixture welding gun or a robotic hip-mounted transformer welder, the equivalent three-phase current draw during welding is 270 amperes. Configuration for Single Phase Transformer. * For three-wire, two phase circuits, the current in the common conductor is 1. 4 kVA Example 2: Find the current drawn by 500 kVA transformer @ rated voltage 5 kV. The thyristor will conduct (ON state),. Formula to calculate power, current and voltage in three-phase wiring (unbalanced load, different loads on each of three phases) : Pt=P1+P2+P3 P1=V*I1*cosφ1 I1=P1/(V*cosφ1) Same thing for each phase… V=P1/(I*cosφ1) Pt = total power of the circuit in watt (W) P1, P2, P3 = power of phase 1, phase 2 and phase 3 in watt (W). Core losses are roughly constant from no-load to full-load when feeding linear loads. 73) % Z = Percent Impedance of Transformer SCAsecondary = Short Circuit Amps at Secondary Bus. Creating a 4 lines 3 phases net in a 3 lines 3 phases net using Zn transformer : 10 : Designing a single phase, 1kVA, 50/60Hz transformer with cooling channels : Designing a 3 phase,1MVA, 50Hz, "dry" distribution transformer 3x35kVA/3x400V. Short Circuit Current Calculations Three-Phase Short Circuits Basic Point-to-Point Calculation Procedure Step 1. Let us suppose for the moment that the impedance at the primary terminals is a series combination of resistance R % and reactance X %. Solution: Full load output = 20 x 1 = 20 kW Full load input = output/efficiency = (20/95. The EDR is the best way to calculate wire gauge through voltage and fault current electrical calculators. 35 (35%) & 3 phase 12 pulse 1. It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power. Now, by applying the three phase power equation, we can calculate the transformer low and high side Basecurrents, I H Base = MVA p 3V H xfmr (3) I L Base = MVA p 3V L xfmr; (4) where V H xfmr, and V L xfmr are the high and low side of the transformer voltage in KV and MVAis the power capacity of the transformer on the tap under the test. 15 (code factor). 3(B) Calculator Single Phase Motor Charts Three Phase Motor Charts Mobile Optimized Calculations. This panel schedule calculates either 1 or 3 phase, there is an "IF" function that calculates based on the phase type entry at the top of the spreadsheet (again 1 or 3). The reader is encouraged to review AN109, References 3, 4, and 5 as background for this Application Note. Three-phase line-to-neutral voltages actually exist in wye configurations; whereas, they are theoretical in delta configurations. Wired in parallel: Wye. ) from either the nameplate, the following formulas or Table 1: Multiplier = 100 *%Z transformer 3Ø Faults f = 1. It is the responsibility of the customer to specify the required motor Hp, Torque and accelerating time for his application. 85 according the above nameplate. 45kVA Three Phase Transformer, Input Voltage: 480VAC Delta. The voltages measured are the true phase-to-neutral voltages. 1 can be subdivided into different sections with different voltage levels determined by the transformer turns ratios. Three Phase Example: Using a 75 KVA Three Phase Transformer as a starting point. S: As for 3 phase transformers, this derivation is different so the factor 4. Following equation or formula is used for Transformer KVA calculator. Electric power calculator calculation general basic electrical formulas mathematical voltage electrical equation formula for power calculating energy work power watts calculator equation power law current charge resistance converter ohm's law and power law power formulae formulas understandimg general electrical pie chart two different equations to calculate power electricas ohms law audio. The transformer of an industrial plant is 500,000VA three phase, with a voltage of 4160V in the secondary and an impedance of 5%, which will be the short level of this transformer. Use this online transformer capacity calculator to find its volts, kVA and amps. This is the first example question for 3 Phase calculations. How to convert from kVA to Ampere in only 1 step: You must multiply the kVA by 1000 and divide the result between the voltage shown by the formula according to the system you have, monofasic, biphasic or three-phase. Inrush Current Calculator - Single and Three Phase About us Since 1994, Ametherm has provided the most reliable and effective inrush current limiting solutions available. 3 Voltage Drop is Line to Neutral Calculations and not Line to Line. Then, also select if the service is three phase or single phase. 8 lagging pf. • 10 Year Warranty - Guaranteed to last. Visit the post for more. Series transformer: To provide the required boost or buck voltage and Control transformer: For sensing the output voltage and for power supply. Parallel operation of three phase transformer is very common in three phase power generation, transmission and distribution. Voltage Drop 13. ) Leave a Reply Cancel reply. A much simpler answer to this question is that the current induced in the transformer secondary windings (assumed not an 'autotransformer') derive from an application of Lenz's law, which is to say, when the magnetic field in the common iron core of the transformer is forced to collapse by current being reversed and transitioning through zero in the primary windings, a current in the opposite. From table 430-150, they draw 40 amps, 14 amps, and 3 amps respectively. Zbase was found by dividing the phase-to-phase voltage squared by the three phase kVA of the transformer. There are many ways to get around three phase open delta, perhaps the best is a rotary phase converter. The 380/220 is indeed a 3-phase. 44 will not present there. Power factor in three-phase circuits. Note the neutral formula. Motor volts is 380 volts, Eff is 0. Small transformers, under 10 kVA, may be designed using handbook data and pencil-and-paper calculations, but larger or mass-produced units are often designed with extensive computer aided modeling. The phase current I in amps (with balanced loads) is equal to 1000 times the apparent power S in kilovolt-amps, divided by the square root of 3 times the line to line RMS voltage V L-L in volts:. This is the first example question for 3 Phase calculations. 28 4 Conclusion p. 3) Voltage drop ie regulation at full load in a transformer is IR cos fi+IX sin fi where IR is the copper loss expressed as a %of rated KW ( up to 3MVA 1. 5hp, bridgeport 2hp, 5hp bandsaw (will have a vfd soon) i may run the bandsaw at the same time as the other machines, but other than that its only me in the shop. Three Phase Transformer Example: Voltage = 11000 volt , current = 5. Rating of Single Phase Transformer: P = V x I. 25A = 100,025 VA = 100kVA. 1 kV2 In case of Three-phase 45 kVA Transformer3 45 kVA Transformer Complete Chart for different voltage levels 45 kVA Single Phase Transformer Amps when V = 1. Then, also select if the service is three phase or single phase. I am totally lost though! I think I understand the primary side, its basically just simple ohms law but if its three phase then 1. The impedance, voltage regulation, efficiency, and other calculations for 3-phase transformers are done on a per-phase basis, using the techniques studied previously for single-phase transformers. This is a short tutorial that explains you on how to calculate kVA rating of single phase transformer. The relationship between units in a per-unit system depends on whether the system is single-phase or three-phase. Load is a three phase induction motor, 25 horsepower @ 240 volts, 60 Hz and a heater load of 4 kilowatts @ 240 volts single phase. So 3600=(208*1. This results in an estimated incident energy exposure of only 0. The three phase system will have 3 line wires. Full Load Currents Rated Line Amps for KVA and Voltages of Single Phase Transformers (see below for 3 phase transformers) KVA 120V 240V 480V 600V 2400V 4160V Amps Amps Amps Amps Amps Amps 1. Single-phase has two lines of AC power. We deliver on that promise through innovative design. (28) For a three-phase transformer in which the window space is occupied by both windings of two phases, Q = 3 V ph I ph 10-3 = 3 4. Joules to volts calculator. These calculations were made in the complex area after the substitution the time behavior to phasor. 3 illustrates the calculation of fault current at the terminals of single-phase transformer served by a three-phase system. Transformer size can be manually derived from load voltage, load current amps and line voltage. 3-phase current calculation excel in Description Double Pipe Heat Exchanger Design DHex is a software tool that is made to demonstrate the chemical design calculations of Double pipe (hairpin) Heat Exchangers. Transformer configuration names like and derive from the way the windings are connected inside the transformer. User manuals, specification sheets, CAD drawings and more. So here is my thinking on PFC. Use the 3 phase and single phase transformer sizing calculator below to calculate primary and secondary full load current. Three-phase systems are prevalent in many power distribution systems. P total = 126. Calculate electrical power transformer kva, current amps, and voltage. Transformer short circuit fault current calculator. We require this code as a security measure to our customers. This piece of equipment will take a 240 volt split phase and add a third leg. Req’d All 2. The short-circuit current available (I). It has two types, single phase and three phase transformer. 15 %) IX is square root of IZ square-IR square. Deprecated: Function create_function() is deprecated in /www/wwwroot/dm. Verify all calculations with a professional engineer. The maximum prospective fault current on a 3-phase circuit will depend on a number of factors. Copper Loss Calculation. Then, also select if the service is three phase or single phase. Because of the relationships of the 3-phase voltages explained above, you have to do something to make the calculations correct. Abstract: The inrush current associated with energising power transformers can cause interference and damage to other system components. 73) Examples for Transformer Amps calculations 225 kVA, 3. In a three phase system there will be a total of 6 wires. Presented methodology is based on the power transformer nameplate data usage. Delta - Star 3-Phase Transformer Connection; Equations for Series and Parallel Connections; Basic DC Electrical Motor Construction; Magical Dancing Lights; Solar Energy Working; Types of Circuit Breaker; Patient Room Electrical Plan; Office Electrical Plan; Complete Electrical Formulas Sheet. As a quick sanity check, you can take the average of the three currents (which would be 68. Transformer Current Ratings: A transformer's A. Per unit systems is an important concept in power system analysis. Core losses consist of the hysteresis losses in the magnetic core of the transformer. That gives us 277. is voltage for a three-phase power, in volts. Mathematical calculation for KVA and MVA for transformer. than short-circuit kVA. What is the formula for Heat Units (HU) for single phase? What are the correction factors used for 3 phase 6 pulse & 3 phase 12 pulse? What % increase is the intensity of the beam? HU = mA x Sec x kV. 73 1000 (2) To determine Amperes when kVA and volts are known: Amps = 3-Phase kVA x 1000. Solution The system of Fig. Three Phase Circuits - 11. Voltage Drop Calculations Quiz-1; Motor Circuit Calculations -1; Motor Circuit Calculations -2; Motor Circuit Calculations-3; Branch Circuit calculations -1; Branch Circuit calculations -2; Dwelling Unit Calculations Quiz-1; Single Family Dwelling Practice Quiz-1; Flexible Cords and Fixture Wires quiz; Wiring methods (NEC 300) Junction and. for 50 Amp circuit breakers, 70 Amps max. The primary sidewill be connected in Y s (“wye”) configuration while the secondary sides and resistive loads will be connected in Δ (“delta”) configurationOne of the. Example 1: Find the apparent power in kVA drawn by a 200 V single phase generator having 2 Amps current passing through it. A three-wire three-phase circuit is usually more economical than an equivalent two-wire. 89) So 15000 / 497. So our motor power is 15KW with 15 x 1000 = 15000 Watts. 732 x 1000. So, for a 100 KVA 120/208v three phase transformer the full load. Transformer configuration names like and derive from the way the windings are connected inside the transformer. In other words, one transformer is producing reactive power and the other is consuming reactive power. 55 X MHS = 7800 This transformer is operated in the step-down mode and delivers 75% of. 75 Amp Single phase transformer KVA = 109. Maximum power conditions for a transformer exist when the power factor is unity. 16 kV ÷ √3) = 31,921:1 Note: Both 230 kV and 4. the line to neutral (phase) voltage V LN = 400/√3 = 230 V three phase power is 36 kW, single phase power = 36/3 = 12 kW now simply follow the above single phase method. Wondering how to make a transformer? Designing your own transformer with professional standards is impossible without going through some complex calculations. The expressions below calculate the resistance and reactance in per-unit quanitities. The transformer short circuit current is calculated as follows: Ifault − actual = Sbase × 100 √3 × Vbase × Z% where Ifault − actual is in kA, Sbase is in kVA, Vbase is in V, and Z% is in percentage. Short Circuit Current Calculations Three-Phase Short Circuits Basic Point-to-Point Calculation Procedure Step 1. Or a pre-assembled three-phase transformer with three pairs of single-phase windings on a single laminated core can be used. Three-phase systems Three-phase electricity consists of three ac voltages of identical frequency and similar amplitude. Utility Line Design has over twenty-five planned calculations that will be added to the website at no added charge in the coming months. Now we turn our attention to the differences between delta and wye transformers and to wye transformer calculations. If the motors are all started together select “Staggered start = No". Industrial Cased Three Phase Transformers Our transformers in this range are suitably protected by a sheet metal case. Calculation of resistance Max wire length [PRO] Conduit fill [PRO] Motor from three-phase to single-phase Capacitor start motor single-phase [PRO] Calculation rpm motor [PRO] Motor efficiency [PRO] Maximum torque [PRO] Diagram three-phase motor (6 leads) Diagram three-phase motor (9 leads) [PRO] Diagram three-phase motor (12 leads) [PRO]. What is Transformer Frequency The three common frequencies available are 50Hz, 60Hz and 400Hz. 45kVA Three Phase Transformer, Input Voltage: 480VAC Delta. 30 3-phase core type transformer (Distribution): 0. Three phase power consists of 3 “hot” wires each having full line voltage with respect to the other two. (I personally designed and used it). Three-Phase Delta Transformer Calculations By James Bourassa. The maximum value of the magnetic flux density is 1. The short-circuit current available (I). With these two rules, a per-unit impedance remains unchanged when referred from one side of a transformer to the other. Three Phase Transformer Example: Voltage = 11000 volt , current = 5. Solution: The maximum kVA/hp for A class motor is 3. 5 kVA / (√3 * 220) = 82. There are many ways to get around three phase open delta, perhaps the best is a rotary phase converter. Now that you understand some transformer calculation basics and specifics on delta transformer calculations, you'll be able to size delta transformers correctly when the majority of the loads are line-to-line. (30) If a 1 T 1 = a 2 T 2 = a. looking to Calculate the % over-current for A PDU that would trigger an alarm. Agile Magnetics has established itself as an industry leader in quality assurance. Re: 3 phase voltage drop I had an epiphany last night. A single 3 phase transformer costs around 15 % less than a bank of three single phase transformers. Jul 25, 2018 - Image result for 3-phase Transformer calculations. 4 kVA Example 2: Find the current drawn by 500 kVA transformer @ rated voltage 5 kV. The 120 volt tap is at the center. The EDR is the best way to calculate wire gauge through voltage and fault current electrical calculators. Positive sequence impedance test circuit for three-phase 2-winding transformer The positive sequence impedance is measured from a standard short circuit test (see figure right). Assuming a three-phase short-circuit condition also simplifies calculations. Electrical and Electronic measuring equipment. Use example phase currents of five amps, eight amps and 10 amps. It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power. Single Phase Voltage Drop Formula Welcome to the Voltage Drop Formula website. At Churchill Falls Terminal Station 2, of the Lower Churchill Project, a bank of three single-phase 3x280 MVA 735 kV power transformers was selected because of the required capacity. Three Phase Example Question: Select a transformer to fulfill the following conditions. Example 1: Find the apparent power in kVA drawn by a 200 V single phase generator having 2 Amps current passing through it. The three phase system will have 3 line wires. S (kVA) = Kilovoltio-Amperes. 6 and choose the appropriate style of transformer for the application from the listing. kVA3phase = Transformer Three Phase kVA Sqrt (3) = Square Root of Three = (1. Design Phase (%) Load - facility, switchgear, MCC Load at each load center per NEC to determine bus,. Using the above example: Ptotal = 39KVA + 33. With the help of above formula we can calculate the losses in all the feeders in the system. Measurements are taken by applying a known low voltage across one winding and measuring the induced-voltage on the corresponding winding. In this paper, the voltage for each 3-phase power plan is 208 volts. Voltage Drop 13. , a voltage is 1. Vector group of Transformer Notation. Wye-Wye Transformer Connection 4. Three Phase Transformer Full-Load Current (Amps) = kVA × 1000 / (1. org Calculate & Find the Rating of Single Phase & Three Phase Transformers in kVA. We assume that any single transformer in a 3-phase transformer (bank) behaves exactly as a single-phase transformer. KVA To put it simply, VA (Volt Amps) is directly related to Watts. IEEE 1584 provides three equations for determining the incident energy at a specific working distance. The three phase power calculator calculates the active and reactive power current from the following parameters: Voltage (V): Enter the phase-to-phase ( VLL) voltage for a 3-phase AC supply in volts. 1%Z on the nameplate or about a 10% variance. Utility Line Design has over twenty-five planned calculations that will be added to the website at no added charge in the coming months. Joules to volts calculator. Wye transformer sizing example: What size transformer (480 to 208Y/120V, 3Ø phase) would you need for the following. Calculations Transformer Turns Ratio - Current and Turns Transformer Turns Ratio - Volts and Turns Direct Current for Current, Horsepower, Voltage, or Efficiency Tables Transformer Impedance Factors Full-load current for single-phase transformer voltage Full-load current for three-phase transformer line-to-line voltage Definitions. This piece of equipment will take a 240 volt split phase and add a third leg. There are advantages and disadvantages to each option. International Transaction of Electrical and Computer Engineers System , 2 (1), 34-38.
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