Tabiquería de placa de yeso laminado con estructura metálica

End

Breaker

the synchronous source voltages and remains fixed as they are fixe

IGURE 3. (a! One-line diagram of a two-machine power system. Phasor diagram to inertial rotating phasors which cannot change their rotational sp _{howing initial conditions. Phasor diagram immediately after tripping circuit breakers a} instantly, Since and are momentarily fixed in magnitude and

displaced by a (momentarily) fixed angle, the sum of the voltage dro across the system remains the same. However, because the

reduced from the initial value ch between input power (from turbine) and output

As shown in phasor diagram Figure all the bus voltages V,, a nit to accelerate during which time the angle will are instantly shifted in phase relative to each other and the sour

voltages and The magnitudes of the bus voltages increase mome When a disturbance is large enough to cause the unit to change speed tarily during the transient period. If both source voltage phasors were (such as a major line trip in this example) even if momentarily, the

ehavior is followed and

period would be complete and phasor diagram (Figure wou ch are discussed in subsequent sections.

represent the final equilibrium state. ample, however, the voltage phasor will rotate so

Let us assume the receiving-end system is so large in MVA cap to increase angle and subsequently settle at a larger angle consistent that is essentially fixed in magnitude and rotates continuously at a th the initial active power delivered by the sending-end generator. The

synchronous speed (377 in a 60-Hz system). The phas agnitudes of voltages V,, and will be changed back toward their however, is associated with a generating unit of finite MVA rating. itial values by the unit's voltage regulator action. Adjustment of we assume the power delivered to the sending end generator by its t witchable passive reactive compensation

bine is constant, the sending end turbine generator unit will tend can provide additionai "control" to restore the accelerate. That occurs because the reduction in current from to es in the system to their nominal or desired magnitudes.

136 Reactive Power Compensation and Dynamic Performance

3.2.2. The First-Swing Period and Transient Stability

In the line switching example discussed in Figure 3, the post disturbance power input to the sending-end generator (from its prime mover) was assumed to remain constant at the prefault level, while the power output of the generator decreased. This caused the generator to accelerate. If a short-circuit fault had preceded the line outage and caused the breakers to operate under relay control, the unit's acceleration would be greater than that caused by merely opening the breakers without the fault. The transmission angle is still a direct measure of the mechanical phase angle between the rotors of the sending-end and receiving-end synchro- nous machines. The postfault acceleration of the sending-end generator results in a much greater increase in 6 and an associated transient redistri- bution of angular momentum, which must be limited; otherwise, syn- chronism will be lost. In systems the corrective action necessary to prevent this loss of "transient stability" must be taken within a fraction of a second.

These dynamic variations are summarized in Figure 4 for the fault dis- cussed above. Figure 3 b represents the initial conditions for this exam- ple. Figure 4 a shows the phasor diagram for the time t = when 6 = Figure 4 b maps the transition of electrical power P versus the

angle 6 on the transient power-angle diagram. Finally, Figure shows the machine's load angle the electrical power and the midsystem bus voltage for the entire scenario, including the fault period and the first-swing period.

The need for dynamic reactive compensation is evident in the V, trace in Figure and the phasor diagram in Figure 4 a . As the power P in- creases, the voltage drops to a minimum value at time Reactive compensation at bus could minimize the otherwise large voltage varia- tions during this period. The nature of this improvement is illustrated in Figure 5a. The compensator can be a synchronous condenser or a static compensator, and the performance of different compensators is described more fully in Sections 3.4 and 3.5. The voltage support provided at inter- mediate points tends to reduce the transmission angle variations, as indi- cated in Figure 5b. In some cases it can maintain transient stability in a system that would otherwise become unstable.

The electromechanical behavior of synchronous machines during the first-swing period differs from that described under the transient period. During the first-swing period the internal voltage may increase as a result of rapidly increasing field current forced by the exciter. From Equation 38, Chapter 2, this tends to increase the power transfer capa- bility of the generator and transmission system at any given This results in a reduction of first-swing angular excursion during the post- disturbance synchronizing power swings.

3.2. Four Characteristic Time Periods

t,

FIGURE 4. Phasor diagram for system of Figure at maximum transmission angle; Power-versus-angle curves: ---- before disturbance; = after line section is disconnected; A initial operating point; B = final operating point. Transient response of system of Figure

3.2.3. The Oscillatory

The third characteristic time period following a disturbance is defined in Figure 2 as the oscillatory period, that is, the period between the first swing in synchronizing power (and machine rotor angle) and the time at which a quasi-steady state is reached. Depending on the characteristics of the power system, the oscillations will damp out (if they damp at all) in anywhere from 2 to 20 Sometimes, so-called negative damping influences can prevail, causing the postdisturbance oscillation to grow until one or more generators loses synchronism. This form of instability is sometimes called "dynamic instability." Net negative damping in post- disturbance oscillations is most likely to be found in systems in which high power levels are transmitted over long (electrical) distances. To maintain transient stability of the generators in these systems,

Reactive Power and Dynamic Performance

Fault

Rotor Angle,

F I G U R E 5. Effect of dynamtc reactive on voltage and power angle swings. ( a ) Voltage at intermediate substation. angle: uncompensated;

- with large dynamic compensator at bus

response, high-gain excitation systems are employed. Working through the generators' relatively large field time constants, these can themselves have a tendency toward oscillatory instability, and supplementary stabiliz- ing circuits are often used in conjunction with their exciter control sys- tems. These stabilizers sense the oscillation in rotor speed, deviations in bus frequency, or power, and modulate the voltage regulator reference signal in the excitation controller so as to damp out the oscillation. voltage dc transmission links can also be utilized to damp out the oscilla- tory synchronizing power swings in the adjoining ac system. ,Special damping controls act on the dc power flow in response to ac bus fre- quency deviations, thereby causing a damping influence on ac power swings. We shall also see later in this chapter that by modulating the reactive power flows in the system, compensators can exert a significant positive damping influence.

The steady-state reached at the end of the oscillatory period does not persist without change for very long. Even if no more major disturbances occur, the system load continually changes at a varying rate. A typical load cycle spanning a 24-hour period for a large interconnected power sys- tem is shown in Figure 6. Although the rates of change appear to be slow relative to those seen during and after a fault, the morning load rise

3.2. Four Characteristic Time Periods