Bus 1 is called a voltage controlled bus because it is apparent that the reactive power generation at bus 1 is being used to control the voltage magnitude. This type of bus is also referred to as a p-v bus because of the specified quantities. Typically, all generator buses are treated as voltage controlled buses Bus Classifications There are four quantities of interest associated with each bus: al power, 2. reactive power, Q 3. itude. v At every bus of the system two of these four quantities will be specified and the remaining two will be unknowns. Each of the system buses may be classified in accordance with the two quantities specified. The following classifications are typical Slack bus--The slack bus for the system is a single bus for which the voltage magnitude and angle are specified. The real and reactive power are unknowns. The bus selected as the slack bus must have a source of both real and reactive power, because the injected power at this bus must"swing"to take up the "slack "in the solution the best choice for the slack bus(since, in most power systems, many buses have eal and reactive power sources)requires experience with the particular system under study. The behavior of the solution is often influenced by the bus chosen. ( In the earlier discussion, the last bus was selected as the slack bus for convenience. Load bus(P-Q bus)-A load bus is defined as any bus of the system for which the real and reactive power specified Load buses may contain generators with specified real and reactive power outputs; however, wer as a Voltage controlled bus(P-V bus)Any bus for which the voltage magnitude and the injected real power are specified is classified as a voltage controlled (or P-v) bus. The injected reactive power is a variable(with pecified upper and lower bounds) in the power flow analysis. (A P-v bus must have a variable source of reactive power such as a generator or a capacitor bank Generalized Power Flow Development The more general(n bus)case is developed by extending the results of the simple four-bus example. Consider the case of an n-bus system and the corresponding n+l node positive sequence network. Assume that the buses are numbered such that the slack bus is numbered last. Direct extension of the earlier equations(writing the node voltage equations and making the same substitutions as in the four-bus case) yields the basic power flow The Basic Power Flow Equations(PFE s=B-jQk=VΣYV fork=1,2,3,,n-1 P-jQ=V2Y V (63.13) e 2000 by CRC Press LLC© 2000 by CRC Press LLC Bus 1 is called a voltage controlled bus because it is apparent that the reactive power generation at bus 1 is being used to control the voltage magnitude. This type of bus is also referred to as a P-V bus because of the specified quantities. Typically, all generator buses are treated as voltage controlled buses. Bus Classifications There are four quantities of interest associated with each bus: 1. real power, P 2. reactive power, Q 3. voltage magnitude, V 4. voltage angle, δ At every bus of the system two of these four quantities will be specified and the remaining two will be unknowns. Each of the system buses may be classified in accordance with the two quantities specified. The following classifications are typical: • Slack bus—The slack bus for the system is a single bus for which the voltage magnitude and angle are specified. The real and reactive power are unknowns. The bus selected as the slack bus must have a source of both real and reactive power, because the injected power at this bus must “swing” to take up the “slack” in the solution. The best choice for the slack bus (since, in most power systems, many buses have real and reactive power sources) requires experience with the particular system under study. The behavior of the solution is often influenced by the bus chosen. (In the earlier discussion, the last bus was selected as the slack bus for convenience.) • Load bus (P-Q bus)—A load bus is defined as any bus of the system for which the real and reactive power are specified. Load buses may contain generators with specified real and reactive power outputs; however, it is often convenient to designate any bus with specified injected complex power as a load bus. • Voltage controlled bus (P-V bus)—Any bus for which the voltage magnitude and the injected real power are specified is classified as a voltage controlled (or P-V) bus. The injected reactive power is a variable (with specified upper and lower bounds) in the power flow analysis. (A P-V bus must have a variable source of reactive power such as a generator or a capacitor bank.) Generalized Power Flow Development The more general (n bus) case is developed by extending the results of the simple four-bus example. Consider the case of an n-bus system and the corresponding n+1 node positive sequence network. Assume that the buses are numbered such that the slack bus is numbered last. Direct extension of the earlier equations (writing the node voltage equations and making the same substitutions as in the four-bus case) yields the basic power flow equations in the general form. The Basic Power Flow Equations (PFE) (63.12) and (63.13) S P jQ V Y V for k = 1, 2, 3, , n – 1 k * k kk * ki i n i =1 =− = ∑ … P jQ V Y V n nn * ni i n i =1 − = ∑