Power distribution system configured as a radial network

A power distribution system including, in electrical connection, an electricity generation plant, an electricity transmission grid, and an electricity distribution grid having a plurality of power distribution lines, wherein the power distribution system is configured as a radial network comprising:

• a plurality of buses including a root bus having respective voltages;
• the plurality of distribution lines having respective currents and impedances,
• wherein the radial network interconnects the plurality of buses with the plurality of distribution lines beginning with the root bus in a tree-like manner, where the number of buses between a bus and the root bus defines a layer,
• wherein subsets of the plurality of distribution lines are of different lengths,
• wherein a voltage of a bus at one of the layers is different from a voltage of a bus at a different one of the layers,
• wherein at least one of the buses has a link to at least two of the distribution lines,
• wherein the bus voltages and distribution line currents are determined by a processing circuitry configured to:
• receive a Branch Matrix (BM) having a row for each distribution line and a column for each bus, wherein the BM contains values indicating buses and associated distribution lines,
• iteratively determine currents for the plurality of distribution lines and voltages across each of the buses until a difference between a bus voltage and a previous iterated bus voltage at each bus is below a predetermined tolerance and output final bus voltages and final distribution line currents, and
• assign the final voltages to each respective bus and the final currents to each respective distribution line,
• wherein
• the circuitry iteratively determines the currents by
• determining an initial current matrix (CM) using the BM by multiplying a node current with corresponding matrix elements in the BM, wherein the node current is a ratio of a complex power at a bus and a voltage of the bus, and
• determining the currents for the plurality of distribution lines in a zig zag manner over the matrix elements in the CM′ and records the determined currents in a final current matrix (CM),
• the circuitry iteratively determines the voltages by
• determining the voltage across each bus based on a voltage drop between buses, starting from buses upstream and moving to buses downstream in a direction of voltage flow.