Hi Md. Asaduzzaman Shoeb 

As first step, you must know that the nodal data is in various forms: (1). Load nodes: complex power Sn= Pn +jQn taken from or injected into the network. (2). Generator nodes: the injected power, Pn, and the magnitude of the nodal voltage |Vn | are specified.  or (3). Floating bus or slack bus: the nodal voltage magnitude | Vn | and phase angle δn are specified.

The floating bus is always needed because it is not possible to specify the total power in and out of the system without knowing the system losses, which depend on the nodal voltages. Solution of the load flow problem uses an iterative technique, known as the Gauss-Seidel method, in which Load flow studies involve solution of the equations: S_n = V_n . I_n and I_n = sum(Y_(n,k) . V_k) for each node n= 1…N.

The Gauss-Seidel method can use the impedance matrix (ZBUS) or the admittance matrix (YBUS) for the calculation of power flow of an electrical network. The YBUS matrix is usually constructed, starting with the slack bus, with the exclusion of shunts connections (static capacitances, loads, etc.) with the ground as well as the other nodes. In fact, these shunts to ground connections are considered sources of current. That being said, the process starts by selecting the set of voltage nodes (slack bus and PV nodes). The node currents can be calculated by: I_k ={[ (P_k - jQ_k)/V*_k ]-[y_kV_k]}

To determine the voltage values in each node, it is sufficient to use the representation in matrix form.

For more information contact me privately.

Good Luck,

Omar

Thank you for the answer. 

I was asking about the situation of a droop controlled islanded microgrid, where it is not convenient to consider any source as a slack generator.  

How about using distributed slack bus? Have you thought about it?

I think I am doing sort of like that. 

How would you use the distributed slack bus?

The concept of distributed slack bus (which is already known) is that you want to have all sources to react to changes in the system instead of just one (as it is customary in rather big systems). So, one way to implement this is using so-called participation factors of sources, which are themselves determined taking into account different factors into account such as load distribution in the system, generator capabilities, network topology, etc. You may find further information in the following works:

http://123.49.46.157/bitstream/handle/10361/4340/10271004.pdf?sequence=1

http://ieeexplore.ieee.org/document/1425579/

https://idea.library.drexel.edu/islandora/object/idea%3A1229

You will find many more sources that explain the concept and implementation of distributed slack bus.

I hope this helps.

Thanks for the help. I have learned a lot about distributed slack bus. I was trying in a similar way, distributing the losses between the generators.  

However, I am struggling with the validation process. I am validating with the PSCAD program. I got similar voltage magnitude, generator real power and frequency but reactive power and voltage angle does not match. I have checked with the numerical errors of Ybus matrix.   

Dear Shoeb,

Reporting the percent deviations would be helpful to comment on. But I would like to suggest you to distribute the reactive power losses (in a similar fashion as active ones) in case you have not done so. This may be one reason behind the mismatches. I am saying this because in the literature, you will find out that most people use the slack bus concept to distribute active power losses. I have not tested this, I have the feeling that the reactive power losses should be distributed as well. This means you should have participating factors dedicated for the reactive power losses (perhaps, the same as those used for active power losses). Another possible reason could be concerned with the distribution factors. This is down to whether or not these factors make sense from a practical point of view. As far as I know, assigning the factors is rather complex and based on assumptions. But I don't mean to undermine the use of distributed slack bus; it's far better and more practical than the use of a single slack bus. You may want to vary the factors and observe the changes.

Kind regards,

Desta

Dear Desta,

Thank you for the reply. 

I have distributed both the real and reactive losses based on the ratio of the generator capacity. 

Even, I have tried with a single load and single generator system, and still, I have the same error. The error in voltage magnitude, generator real power and frequency is within 0.3% but the reactive power error is above 10%, and voltage angles are not even close compared to PSCAD. 

Being a droop controlled system, the frequency is not assumed fixed, and the droop control governs generator voltage magnitude.    

Regards,

Shoeb

Dear;

for more information please check the following documents :

http://123.49.46.157/bitstream/handle/10361/4340/10271004.pdf?sequence=1

http://ieeexplore.ieee.org/document/1425579/

Regards