Balanced three-phase circuits

In a balanced three-phase circuit, the total power is three times the power in each phase, or... 

The theory of operation of such a protection scheme is based on the prineiple that in a balanced cireuit the phasor sum of currents in the three healthy phases is zero, as illustrated in Figure 21.7, and the current through the grounded neutral is zero. In the event of a ground fault, i.e. when one of the phases becomes grounded, this balance is upset and the out-of-balance current flows through the grounded neutral. A healthy three-phase circuit, how ever. 

A standard design of motor is used. An external auto-transformer is connected between the main circuit breaker, or contactor, and the motor during the starting and run-up period. Figure 5.8 shows the connections that are commonly used in a balanced three-phase arrangement. The voltage ratio of the auto-transformer needs to be carefully selected. If it is too high then the full benefit is not achieved. If too low then insufficient torque will be created. The most effective ratio is usually found... 

The three-phase windings of an a.c. generator may be star connected or delta connected as shown in Fig. 2.54. The important relationship between phase and line currents and voltages is also shown. The square root of 3 (Vs) is simply a constant for three-phase circuits, and has a value of 1.732. The delta connection is used for electrical power transmission because only three conductors are required. Delta connection is also used to connect the windings of most three-phase motors because the phase windings are perfectly balanced and, therefore, do not require a neutral connection. 

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 ... 

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... 

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. 

This reaction is currently unavoidable and appears to be favored at hot and dry operating conditions of the fuel cell. The peroxide decomposition forms reactive radials such as hydroxyl, OH, and peroxyl, OOH, that cause oxidative degradation of both the fuel cell membrane and catalyst support [67]. Both electrodes currently use Pt or Pt alloys to catalyze both the HOR and ORR reactions. The catalyst particles are typically supported on a high surface area, heat-treated carbon to both increase the effectiveness of the catalyst and to provide a path for the electrons to pass through to the external circuit via the gas diffusion media (which is typically also made of carbon) and the current collecting bipolar plates. In addition, the catalyst particles are coated in ionomer to facilitate proton transport however, the electrode structure must also be porous to facilitate reactant gas transport. A schematic of a typical PEM MEA is shown in Fig. 17.1. A boundary condition exists at the catalyst particle where protons from the ionomer, electrons from the electrically conducting Pt and carbon, and reactant gases meet. This is usually referred to as the three-phase boundary. The transport of reactants, electrons, and protons must be carefully balanced in terms of the properties, volume, and distribution of each media in order to optimize operation of the fuel cell. 

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. 

Since the three-phase sheath conductors are short-circuited and grounded in every major section as illustrated in Figure 3.6, the sheath voltages of three phases are equal at each earthing joint. Assuming sheath currents are balanced among three conductors, the sheath currents do not flow into the earth at each earthing joint ... 

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. 

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