The standard power ﬂow or loadﬂow problem involves solving for the set of voltages and ﬂows in a network corresponding to a speciﬁed pattern of load and generation. Matpower includes solvers for both AC and DC power ﬂow problems, both of which involve solving a set of equations of the form

| (4.1) |

constructed by expressing a subset of the nodal power balance equations as functions of unknown voltage quantities.

All of Matpower’s solvers exploit the sparsity of the problem and, except for Gauss-Seidel, scale well to very large systems. Currently, none of them include any automatic updating of transformer taps or other techniques to attempt to satisfy typical optimal power ﬂow constraints, such as generator, voltage or branch ﬂow limits.

4.1 AC Power Flow

4.1.1 Cartesian vs. Polar Coordinates for Voltage

4.1.2 Current vs. Power for Nodal Balance Equations

4.2 DC Power Flow

4.3 Distribution Power Flow

4.3.1 Radial Power Flow

4.3.2 Current Summation Method

4.3.3 Power Summation Method

4.3.4 Admittance Summation Method

4.3.5 Handling PV Buses

4.4 runpf

4.5 Linear Shift Factors

4.1.1 Cartesian vs. Polar Coordinates for Voltage

4.1.2 Current vs. Power for Nodal Balance Equations

4.2 DC Power Flow

4.3 Distribution Power Flow

4.3.1 Radial Power Flow

4.3.2 Current Summation Method

4.3.3 Power Summation Method

4.3.4 Admittance Summation Method

4.3.5 Handling PV Buses

4.4 runpf

4.5 Linear Shift Factors