1	Chapter 24 Three-Phase Systems
2	Three-Phase Voltage Generation Three-phase generators Three sets of windings and produce three ac voltages Windings are placed 120° apart Voltages are three identical sinusoidal voltages 120° apart
3	Three-Phase Voltage Generation Set of voltages such as these are balanced If you know one of the voltages The other two are easily determined
4	Four-Wire Systems Three loads have common return wire called neutral If load is balanced Current in the neutral is zero Current is small Wire can be smaller or removed Current may not be zero, but it is very small
5	Four-Wire Systems Outgoing lines are called line or phase conductors
6	Three-Phase Relationships Line voltages Voltages between lines either at the generator (E_AB) or at the load (V_AB)
7	Three-Phase Relationships Phase voltages Voltages across phases For a Y load, phases are from line to neutral For D load, the phases are from line to line
8	Three-Phase Relationships Line currents Currents in line conductors Phase currents Currents through phases For a Y load two currents are the same
9	Voltages in a Wye Circuit For a balanced Y system Magnitude of line-to-line voltage is times the magnitude of phase voltage Each line-to-line voltage Leads corresponding phase voltage by 30° Line-to-line voltages form a balanced set
10	Voltages for a Wye Circuit Nominal voltages 120/208-V 277/480-V 347/600-V systems
11	Voltages for a Wye Circuit Given any voltage at a point in a balanced, three-phase Y system Determine remaining five voltages using the formulas
12	Currents for a Wye Circuit Line currents Same as phase currents I_a = V_an/Z_an Line currents form a balanced set If you know one current Determine the other five currents by inspection
13	Currents for a Delta Load In a balanced delta The magnitude of the line current is times the magnitude of the phase current
14	Currents for a Delta Load Each line current lags its corresponding phase current by 30° For any current in a balanced, three-phase delta load Determine remaining currents by inspection
15	Power in a Balanced System To find total power in a balanced system Determine power in one phase Multiply by three Use ac power formulas previously developed
16	Power in a Balanced System Since magnitudes are the same for all three phases, simplified notation may be used
17	Active Power to a Balanced Wye Load P_f = V_fI_fcos q_f P_T = 3P_f = 3V_fI_fcos q_f P_T = V_LI_Lcos q_f P_f = I_f²R_f P_T = 3I_f²R_f
18	Reactive Power to a Balanced Wye Load Q_f = V_fI_fsin q_f Q_T = V_LI_Lsin q_f Q_f = I_f²X_f Units are VARs
19	Apparent Power to a Balanced Wye Load S_f = V_fI_f S_T = V_LI_L S_f = I_f²Z_f
20	Apparent Power to a Balanced Wye Load Units are VAs Power factor is F_p = cos q_f = P_T/S_T = P_f/S_f
21	Power to a Balanced Delta Load Power formulas for D load are identical to those for Y load In all these formulas Angle q_f is phase angle of the load impedance
22	Power to a Balanced Delta Load You can also use single-phase equivalent in power calculations Power will be power for just one phase
23	Measuring Power in Three-Phase Circuits Measuring power to a 4-wire Y load requires three wattmeters (one meter per phase) Loads may be balanced or unbalanced Total power is sum of individual powers
24	Measuring Power in Three-Phase Circuits If load could be guaranteed to be balanced Only one meter would be required Its value multiplied by 3
25	Measuring Power in Three-Phase Circuits For a three-wire system Only two meters are needed Loads may be Y or D Loads may be balanced or unbalanced Total power is algebraic sum of meter readings
26	Measuring Power in Three-Phase Circuits Power factor for a balanced load Obtain from wattmeter readings using a watts ratio curve
27	Measuring Power in Three-Phase Circuits From this, q can be determined Power factor can then be determined from cos q
28	Unbalanced Loads Use Ohm’s law For unbalanced four-wire Y systems without line impedance Three-wire and four-wire systems with line and neutral impedance Require use of mesh analysis
29	Unbalanced Loads One of the problems with unbalanced loads Different voltages are obtained across each phase of the load and between neutral points
30	Unbalanced Loads Unbalanced four-wire D systems without line impedance are easily handled Source voltage is applied directly to load Three-wire and four-wire systems with line and neutral impedance Require use of mesh analysis
31	Power System Loads Single-phase power Residential and business customers Single-phase and three-phase systems Industrial customers Therefore, there is a need to connect both single-phase and three-phase loads to three-phase systems
32	Power System Loads Utility tries to connect one third of its single-phase loads to each phase Three-phase loads are generally balanced
33	Power System Loads Real loads Seldom expressed in terms of resistance, capacitance, and inductance Rather, real loads are described in terms of power, power factors, etc.