FIGURE 63.2 Off nominal turns ratio transformer flows and losses in the network. 7. Check for constraint violations Formulation of the bus admittance matrix The first step in developing the mathematical model describing the power flow in the network is the formulation of the bus admittance matrix. the bus admittance matrix is an nxn matrix(where n is the number of buses in the system) constructed from the admittances of the equivalent circuit elements of the segments making up the power system. Most system segments are represented by a combination of shunt elements(connected between a bus and the reference node) and series elements(connected between two system buses). Formulation of the bus admittance matrix follows two simple rules: 1. The admittance of elements connected between node k and reference is added to the(k, k)entry of the 2. The admittance of elements connected between nodes j and k is added to the(])and(k, k)entries of the admittance matrix. The negative of the admittance is added to the (i, k)and (k, j) entries of the admittance matrix Off nominal transformers(transformers with transformation ratios different from the system voltage bases at the terminals) present some special difficulties. Figure 63. 2 shows a representation of an off nominal turns ratio transformer The admittance matrix mathematical model of an isolated off nominal transformer is Y -C"Y. Yelv where e is the equivalent series admittance (referred to node j c is the complex(off nominal)turns ratio , is the current injected at node j is the voltage at node j(with respect to reference) Off nominal transformers are added to the bus admittance matrix by adding the corresponding entry of the isolated off nominal transformer admittance matrix to the system bus admittance matrix. Example Formulation of the Power Flow Equations Considerable insight into the power flow problem and its properties and characteristics can be obtained by consideration of a simple example before proceeding to a general formulation of the problem. This simple case will also serve to establish some notation e 2000 by CRC Press LLC© 2000 by CRC Press LLC 6. Solve for the power flows and losses in the network. 7. Check for constraint violations. Formulation of the Bus Admittance Matrix The first step in developing the mathematical model describing the power flow in the network is the formulation of the bus admittance matrix. The bus admittance matrix is an n×n matrix (where n is the number of buses in the system) constructed from the admittances of the equivalent circuit elements of the segments making up the power system. Most system segments are represented by a combination of shunt elements (connected between a bus and the reference node) and series elements (connected between two system buses). Formulation of the bus admittance matrix follows two simple rules: 1. The admittance of elements connected between node k and reference is added to the (k, k) entry of the admittance matrix. 2. The admittance of elements connected between nodes j and k is added to the (j, j) and (k, k) entries of the admittance matrix. The negative of the admittance is added to the (j, k) and (k, j) entries of the admittance matrix. Off nominal transformers (transformers with transformation ratios different from the system voltage bases at the terminals) present some special difficulties. Figure 63.2 shows a representation of an off nominal turns ratio transformer. The admittance matrix mathematical model of an isolated off nominal transformer is: (63.1) where – Ye is the equivalent series admittance (referred to node j) – c is the complex (off nominal) turns ratio – Ij is the current injected at node j – Vj is the voltage at node j (with respect to reference) Off nominal transformers are added to the bus admittance matrix by adding the corresponding entry of the isolated off nominal transformer admittance matrix to the system bus admittance matrix. Example Formulation of the Power Flow Equations Considerable insight into the power flow problem and its properties and characteristics can be obtained by consideration of a simple example before proceeding to a general formulation of the problem. This simple case will also serve to establish some notation. FIGURE 63.2 Off nominal turns ratio transformer. I I Y cY -c*Y c Y V V j k e e e e j k       =  −             2 