Balancing three phase loads

Substituting Equation (3) into Equation (1) we have, for any balanced three-phase load. 

In any star-connected system currents flow along the lines (/O, through the load and return by the neutral conductor connected to the star point. In a balanced three-phase system all currents have the same value and when they are added up by phasor addition, we find the resultant current is zero. Therefore, no current flows in the neutral and the star point is at zero volts. The star point of the distribution transformer is earthed because earth is also at zero potential. 

A balanced star-connected three-phase load of lon per phase is supplied from a 400 V, 50 Hz mains supply at unity power factor. Calculate (a) the phase voltage, (b) the line current and (c) the total power consumed. 

State the reasons for balancing single-phase loads across a three-phase supply. 

When three-phase loads are balanced, for example, in motor circuits, one wattmeter may be connected into any phase, as shown in Fig. 4.18. This wattmeter will indicate the power in that phase and, since the load is balanced, the total power in the three-phase circuit will be given by ... 

This equation is true for any three-phase load, balanced or unbalanced, star or delta connection, provided there is no fourth wire in the system. 

When this balance is disturbed, due to either an unbalance in the loads or due to a ground fault, a residual or zero phase sequence voltage in the neutral circuit will appear. When one of the phases in the secondary of a three-phase transformer is open circuited and a three-phase supply is applied to its primary windings, there will appear... 

When a three-phase four-wire system feeds non-linear or single-phase loads this balance is upset and the unbalanced current flows through the neutral. The same relationship can be expressed as... 

Below we describe improvised bus systems to limit the reactance and hence the voltage drop and obtain an inductively balanced system to achieve a balanced voltage and equal load sharing by the three phases at the far end. The systems are... 

However, there may not be an appreciable improvement in the proximity effect between each section, unless the transpositions are increased infinitely, as in the case of a stranded three-phase cable which has continuously twisted conductors and represents an ideal transposition. In addition, there is no change in the skin effect. This arrangement therefore has the purpose primarily of achieving an inductively balanced system and hence a balanced sharing of load and equal phase voltages at the far end. 

The air velocity through a heater battery should be to the manufacturer s rated output within its range of safe temperatures. In large units the electrical load is balanced across the three phases of the electrical supply. 

Power measurements can be made in three-phase, four-wire circuits by a three-element wattmeter (Figure 3.55). Such a design is seldom utilized because the two-element wattmeter movement can be modified to permit measurement on three-phase, four-wire systems by reconnecting one of the fixed coils for each element. Meters of this type are known as 21/2-element wattmeters. They will correctly indicate power for three-phase, four-wire loads as long as the line-to-neutral voltages are balanced for all three phases. 

Three-phase, Three-wire,— Three single-phase circuits, the return currents neutralizing. Balanced when the phases are equally loaded. 

It is therefore necessary to provide a sensitive method for detecting earth fault currents. The most common method is to provide a core balance current transformer at the circuit breaker or contactor. This current transformer has a current or turns ratio, which is independent of the ratios used by the transformers connected in the three-phase conductors. This is because a particular level of current is to be detected rather than a fraction or multiple of the stator load current. The switchgear manufactnrer will normally recommend the ratio of the core balance transformer and the matching relay. The relay will be either instantaneous 50 N or an inverse time 51 N type depending upon whether the motor is controlled by a circuit breaker or a contactor. 

Linear algebra provides a notation for concisely representing linear algebraic equations and it provides a set of operations by whidi those equations can be solved. Linear equations arise in many common situations, such as taking inventories by material balances. As a particular example, consider a closed system initially loaded with N total moles of three liquid components 1, 2, and 3. That initial mixture had mole fractions z, Z2, and Z3. When equilibrium is attained, the system is found to have divided into three phases a, P, and y. The mole fractions for phase a are ze,, those in phase p are x,, and those in phase y are 1/ . These mole fractions are related to the original overall mole fractions z,- by material balances ... 

When single-phase loads are supplied from a three-phase supply, the load should be balanced across the phases. That is, the load should be equally distributed across the three phases so that each phase carries approximately the same current. This prevents any one phase from being overloaded. 

This is the most commonly used method for measuring power in a three-phase, three-wire system since it can be used for both balanced and unbalanced loads connected in either star or delta. The current coils are connected to any two of the lines, and the voltage coils are connected to the other line, the one without a current coil connection, as shown in Fig. 4.19. Then,... 

All these measures are applicable to monitor the development of the properties of the rock during loading and deformation. The development of the dilatancy can be divided very roughly into three phases. Phase I characterizes a decrease of the volume attributed to elastic compression of the rock salt, a decrease of permeability and an increase of seismic velocity. The volume becomes nearly constant at the end of Phase I. It can be assumed that elastic compression processes and dilatancy processes balance at this point. Dilatant microcracking generates only weak AE activity. 

In three-phase systems the individual phase voltages (230 V) are equally displaced timewise (phase displacement of 120°) and because of this the voltage across phases is higher. Three-phase supplies can be used to supply both singlephase equipment (with the loads balanced as equally as possible between the three phases) or three-phase equipment such as to large motors. 

The basic control circuit consists of a full-voltage starter and a balanced, adjustable three-phase resistor, wye-connected in the rotor circuit. Speed can be established for a given load by adjusting rotor resistance once set, speed will vary with load conditions. 

The event of a three phase open circuit at the feedthrough, cable or inside the alternator windings would result in the loss of load on the alternator. Since the Brayton TCA shaft speed is based on the torque balance between the alternator, turbine and compressor, the loss of load would lead to an acceleration of the rotor shaft until some mechanical failure occurred, or a new stable operating speed was reached. For a single phase open circuit on the alternator a similar acceleration to the point of stability or mechanical destruction would occur, but the rate of acceleration would be much slower. 

In a G/F the three CTs will also measure the unbalanced load current, if any, in addition to G/F current. For an appropri.ite setting of the relay, therefore, it will be essential that the likely system unbalanced current be measured and the relay set in excess of this to detect a G/F, For systems feeding single-phase or unbalanced loads, prone to carrying high and widely fluctuating unbalanced neutral currents, it may be difficult to determine ihe likely amount of unbalance and provide a suitable setting for the G/F relay. In such cases use of four CTs or core-balanced CTs (if it is a four w ire system) would be more appropriate. 

---