I have a very theoretical doubt. I'm trying to fully understand the load flow analysis and its application. So I have a network with about 300 nodes (AC transmission network). Inside every node I have load and generation. Also the nodes are connected each other by different voltage lines (110kV, 220kV and 380kV). So, my task is to create the admittance matrix of the system. Therefore, I have to assume certain conditions. The nodes are regions of a certain country, so inside them they are cities and substation and whatever necessary. Im only considering the lines that come in and out from the nodes. So, my doubts are:

1.- How do I deal with nodes connected by more than one line? specially when these lines have different lengths and max I capacities.

2.- How do I establish generation and load nodes (base on the load flow analysis theory http://en.wikipedia.org/wiki/Power_flow_study) Should I divide the nodes? (Considering that the equations for these kind of nodes vary in relation to the known variables).

3.- The transformers are inside the nodes (as I said my idea is to consider only the lines coming out and in from the nodes) Is this correct? can I neglect the transformers and consider only the lines?

4.- The only way for having the whole network entirely connected is considering all the voltages lines as one. Explanation: a region is connected with other by a 380kV line and then this one connects with other by a 110kV line and so on. Is this correct?

It is hard to understand on the fly the load flow analysis as I have to jump into a complex problem with a short notice.


2 Answers 2


Load flow analysis usually deals with systems with nodes which are connected by more than one line. An admittance matrix describes the connections between the nodes. You can see more about the admittance matrix here: http://en.wikipedia.org/wiki/Nodal_admittance_matrix

The different line lengths are taken into account in the admittance matrix. The longer the line, the higher the impedance, and the lower the admittance. If there are no controllable components in the system, you cannot take current limits into account, since the currents cannot be steered.

You do not need to divide the nodes between generation and load nodes. For each node you need to know either the active power and voltage (PV node) or the active and reactive power (PQ node). You can sum the impact of the generator and the load. Often, if the node has a generator, then it is a PV node.

The reactance of transformers is very high compared to the reactance of the lines themselves, and thus cannot be ignored. A transformer can be represented by an impedance, which can be added to the impedance of the line to which it is connected.

I'm not sure what you mean in your last question, but if you are asking if the system needs to be simplified so that it is represented as a chain of nodes, then the answer is no. The admittance matrix describes the relationship between the nodes, and can accommodate systems more complex than a chain.

If your system has 300 nodes, then your system is fairly large. For systems larger than a few nodes, calculating an admittance matrix by hand is laborious. I would recommend using power flow software to perform your load flow. A fairly comprehensive list of software for power systems analysis can be found here: http://www.openelectrical.org/wiki/index.php?title=Power_Systems_Analysis_Software

  • \$\begingroup\$ Ok, got it. Just one more detail. So I have these areas with lines of different voltages coming in and out. Then how would you add the transformers? I'm assuming a given characteristic for the lines (electronics.stackexchange.com/questions/35915/…) still without answer, hint ;) Can I assume a given transformer type for the voltage combinations? what do you think about doing something like this? cheers! \$\endgroup\$
    – zom-pro
    Commented Aug 8, 2012 at 8:13
  • \$\begingroup\$ Adding impedances is just like adding resistances, except for AC systems. If I were creating an arbitrary network, then a reactance of 0.1 p.u. would not be unreasonable. However, you seem to be recreating the German grid. Without data and/or help from the TSO, I don't think you'll get very far. For example, if you don't have the length of the lines, it will be impossible to calculate their impedance. \$\endgroup\$
    – Katt
    Commented Aug 8, 2012 at 19:49
  • \$\begingroup\$ Oh sorry I didn't express my self correctly. Actually I have a detailed (real) map of all the lines 110kV, 220kV, 380kV. Even I have the sub-stations. However, in order to simplify it a little bit I took some areas and assume the resistance inside the area as zero. So know I need to figure it out how to simulate the transformers inside the areas (if necessary) or just take into consideration the lines between the areas and consider the load and generation only. (By the way, OSM offers the info about the lines download.geofabrik.de in the xml under the "power" tag) \$\endgroup\$
    – zom-pro
    Commented Aug 9, 2012 at 7:49

Just for completing the topic. The strategy I'm finally using is:

I have 3 voltages 110kV, 220kV and 380 kV. In each region I will divide the node in these 3 voltages and I will connect these new 3 nodes with a transformer. Then all the lines of a given voltage will be connected with their correspondent node. If there are more than 1 line between the same two nodes, I will aggregate them if they have the same voltage. Otherwise, I'll calculate them as separate lines.

This approach seems to be working quite well.


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