The Power Flow Equations iastateedu功率流方程iastateedu.docVIP

Three Bus Power Flow Analysis 1.0 Introduction In discussions that you will have in the next few weeks, you will make reference to the power system diagram of Fig. 1, where G denotes generators and C denotes consumers. Fig. 1 You will use the notation qA, qB, and qC to denote MW delivery (generation) into buses A, B, C by the generators and xA, xB, and xC to denote MW consumption (demand, or load) from buses A, B, C by the consumers. Finally, you will write down the following equation: where the left-hand-side is the flow on the line from region A to region B. Our goal for this presentation is to clarify for you the source of this kind of equation and to enable you to write them down for more general networks configurations. First note that what is inside the parentheses of each term in the above equation is the power injection at nodes A and B, respectively. Let’s make the following assumptions: The impedance of each line is j1 pu. Node C has no active injection but rather is short circuited to ground. We may treat power just like we treat current. With these assumptions, one can apply current division to the network of Fig. 1 to obtain the flow on line A-B. Flow from A to C along line A-B: Path A-C Impedance (Node A Injection Path A-C Impedance+Path A-B-C Impedance Flow from B to C along line A-B: Path B-C Impedance (Node B Injection Path B-C Impedance+Path B-A-C Impedance To obtain the composite flow, we subtract Flow computed in (2) from flow computed in (1). Question: On what basis can we make our assumptions 2 and 3? Conventions and nomenclature We mention at the outset that there are conventions and nomenclature used in the previous page are generally unfamiliar to the power engineer. Convention: The one-line diagram is similar to that drawn in Fig. 1, but the conventional diagram uses lines for nodes, circles for generators, and arrows for loads. Fig. 2 is the one-line diagram that is equivalent to Fig. 1. Fig. 2 Nomencla