# Lossless nodal DC power flows

Currently, there are two different methods to represent lossless DC power flows. In the following the implementation of the nodal model is presented, based of node voltage angles.

## Key concepts

In the following, it is described how to set up a connection in order to represent a nodal lossless DC power flow network. Therefore, key object - and relationship classes as well as parameters are introduced.

**connection**: A connection represents the electricity line being modelled. A physical property of a connection is its connection_reactance, which is defined on the connection object. Furthermore, if the reactance is given in a p.u. different from the standard unit used (e.g. p.u. = 100MVA), the parameter connection_reactance_base can be used to perform this conversion.**node**: In a lossless DC power flow model, nodes correspond to buses. To use voltage angles for the representation of a lossless DC model, the has_voltage_angle needs to be`true`

for these nodes (which will trigger the generation of the node_voltage_angle variable). Limits on the voltage angle can be enforced through the max_voltage_angle and min_voltage_angle parameters. The reference node of the system should have a voltage angle equal to zero, assigned through the parameter fix_node_voltage_angle.**connection__to_node and connection__from_node**: These relationships need to be introduced between the connection and each node, in order to allow power flows (i.e. connection_flow). Furthermore, a capacity limit on the connection line can be introduced on these relationships through the parameter connection_capacity.**connection__node__node**: To ensure energy conservation across the power line, a fixed ratio between incoming and outgoing flows should be given. The fix_ratio_out_in_connection_flow parameter enforces a fixed ratio between outgoing flows (i.e. to_node) and incoming flows (i.e. from_node). This parameter should be defined for both flow direction.

The mathematical formulation of the lossless DC power flow model using voltage angles is fully described here.