Transmission Loss Allocation by Shapley Value Method

K. Janardhan, Dr. Y. N Vijay Kumar, G. V .


The introduction of deregulation and subsequent open access policy in electricity sector has brought competition in energy market. Allocation of transmission loss has become a contentious issue among the electricity producers and consumers. A closed from solution for transmission loss allocation does not exist due to the fact that transmission loss is a highly non-linear function of system states and it is a non-separable quantity. In absence of a closed form solution different utilities use different methods for transmission loss allocation. These schemes fall into the following categories: Prorate, proportional sharing, incremental transmission loss, and loss formula and circuit theory. Some approaches are based on DC power flow, while some use AC load flow for matching the calculation results and actual power flows. Some schemes are branch power-flow based, while some focus on the branch-current based allocation techniques. Different viewpoints and approaches may end up with different results and most of the existing allocation schemes face the problem due to a lack of economic foundations. Most of these techniques involve complex mathematical operations and time consuming computations. This paper proposes fair schemes for the transmission loss allocation under a pool-based electricity market. The power generations or loads associated with the market are modelled as individual current injections based on a real time solved AC power flow solution. Each load can be modelled as a current injection or equivalent constant impedance depending on whether it is required to be responsible for the system loss. Each current injection is then treated as an individual player of the transmission loss allocation game.

                The concept of Shapley value adopted from cooperative game theory is utilized to deal with the fairness of loss allocation. The basic models will be proposed in this thesis: one basic model allocates losses to the power supply side (each generation) only, and the other attributes  losses to both supply and demand sides (each generation and each load). The main difference is that the former treats the load demand as equivalent constant impedances based on a real-time solved AC power flow solution and accordingly the bus impedance matrix (Zbus) is then modified, while the later formulates the load demand as equivalent current injections. In this thesis the effectiveness of Shapley value method was tested by using test systems such as such Six bus.

Full Text:



Shih-Chieh Hsieh “Fair transmission loss allocation based on equivalent current injection and Shapley value” Power Engineering Society General Meeting, 2006.

Rezaul Haque, “Transmission loss allocation using artificial neural networks”, A Ph.D. thesis, Department of Electrical Engineering, University of Saskatchewan, march2006

A. J. Conejo, J. M. Arroyo, N. Alguacil, and A. L. Guijarro, “Transmission loss allocation: a comparison of different practical algorithms,” IEEE Trans. Power Syst., vol. 17, no. 3, pp. 571-576, Aug.2002.

Michal chmela, “Transmission loss allocation methods” A Ph.D. thesis, Department of Electrical Engineering, BRNO University of Technology, march2003

RM Saloman Danaraj, Shankarappa F Kodad and Tulsi Ram Das “Analytical solution to balanced quadratic cooperative game and its application to transmission loss allocation”

BAO Xin-zhong CUI Wei Allocation of Transmission losses in electricity System Based on Cooperative Game Theory,”

A. Gomez Exposito, J. M. Riquel me Santos, T. Gonzalez Garcia, and E.A. Ruiz Velasco, “Fair allocation of transmission power losses.



  • There are currently no refbacks.

© International Journals of Advanced Research in Computer Science and Software Engineering (IJARCSSE)| All Rights Reserved | Powered by Advance Academic Publisher.