NRLF - NEWTON-RAPHSON LOAD FLOW FORMULATION Dr Bruce Mork EE 5200 Fall 2009 At a given bus i in the system there can exist Fixed P and Q injection

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Sched Gen Sched Load P + jQ Li Li P + jQ Gi Gi P + jQ Ti Ti Bus N Bus 1 Bus 2 Bus i REF NETWORK AS DEFINED BY LINES, XFMRS, SHUNT CAPS, REACTORS Y BUS V i ~ + - I i ~ NEWTON-RAPHSON LOAD FLOW FORMULATION Dr. Bruce Mork EE 5200 - Fall 2009 At a given bus i in the system, there can exist : Fixed P and Q injection consisting of : < Scheduled generation that injects P G i into the bus. < A fixed load of P L i + jQ L i (an injection of - P L i - jQ L i ) P and Q flowing into bus from the network (all part of [Y BUS ]): < Transmission lines - short, medium, long; single-circuit, double-circuit where mutual coupling is neglected, or double-circuit with mutual coupling effects. < Transformers - 2-winding or 3-winding; fixed ratio, LTC, or Phase-Shifting. < Shunt reactors: Y = 1/(j ω L) = - jB REACT < Shunt capacitor banks: Y = j ω C = jB CAP < A voltage-dependent load represented as a shunt admittance: Y LOAD = G + jB. Important things to note : < The scheduled generation P G i is dictated by the system dispatch center via SCADA. The generator’s governor is given a “set point” and holds P G i constant within a close tolerance. Also, the generator’s exciter holds the bus voltage V i at a constant magnitude (its angle δ i is not directly controlled and is an unknown). < The fixed load P L i + jQ L i represents the aggregate load supplied to local consumers. In planning studies, this is usually a worst-case projection of what planners think the load will be 5 or 10 or more years into the future. < P T i and Q T i are the total P and Q flowing INTO the transmission grid defined by [Y BUS ]. This includes the effects of shunt capacitor banks and reactors.
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PP P P INTO BUS i Gi Li Ti =−−= 0 QQ Q Q INTO BUS i Li 0 When forming equations, it is extremely important to establish a reference direction for the flow of P, Q, and current. This is clearly labeled on the sketch on the preceding page. Recall that the current is the net current injected into the ~ I i network at bus i by the generator and load (this is the same injected current that occurs in the equation [Y BUS ][V] = [I] ). Bus voltages are measured with respect to the same reference that [Y BUS ] is referred to.
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This note was uploaded on 10/20/2010 for the course ECE 5200 taught by Professor Bonk during the Fall '10 term at Michigan Technological University.

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NRLF - NEWTON-RAPHSON LOAD FLOW FORMULATION Dr Bruce Mork EE 5200 Fall 2009 At a given bus i in the system there can exist Fixed P and Q injection

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