Electr Eng DOI 10.1007/s00202-012-0247-5 ORIGINAL PAPER Voltage security constrained active and reactive power pricing considering reactive market power S. Hasanpour · R. Ghazi · M. H. Javidi Received: 23 December 2008 / Accepted: 16 February 2010 © Springer-Verlag 2012 Abstract Reactive power support and voltage stability are considered to be very essential for preserving system secu- rity. This paper proposes a new market-based approach for voltage security constrained active and reactive power pric- ing. The problem is modeled as a multi-objective OPF in which the social welfare and the distance to voltage collapse point are maximized at same time. An important feature of the proposed approach is using the reactive market power index, Herfindahl–Hirschman Index (HHI), to assign optimal weighting factors of the multi-objective function. In addi- tion, in this method not only the reactive power is consid- ered but typical price is also provided based on real costs. The results show that the proposed method allows market operators and participants to preserve the level of security and social welfare within acceptable range by controlling the weighting factors and monitoring the HHI with regard to reactive market power. Using the proposed method and con- sidering reactive power market, a suitable range of weighting factor can be determined ensuring the optimal bidding as well as satisfying the voltage security of the system. Keywords Electricity market · Multi objective optimal power flow · Reactive market power · HHI index · Voltage security S. Hasanpour (B ) Department of Electrical Engineering, Sadjad Institute of Higher Education, Mashhad, Iran e-mail: hasanpour_s@yahoo.com; s_hasanpour@sadjad.ac.ir R. Ghazi · M. H. Javidi Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran 1 Introduction Power industry has experienced restructuring during the past two decades. While this restructuring process has resulted in establishment of a competitive environment for energy trade, preserving the system security has remained as administrative role taken care by system operator. To support system secu- rity, services other than energy, specified as ancillary ser- vices, are required. Among these services, reactive power management is very essential to support power system secu- rity and preserve voltage stability. Reactive power has dom- inant effects on real energy transfer and it can support the secure operation of the system as an ancillary service. However, most researches have focused on active power mar- ket as the main good transacted in electricity markets. In stressed power systems, in which the transmission lines are heavily loaded, voltage stability margin becomes very small. As a result the system may become vulnerable to voltage collapse when the reactive power is not supported properly. Hence, maintaining the system security can be one of the main concerns for market operators and participants. On the other hand, to ensure the availability of ancillary ser- vices, the providers of such services should be paid prop- erly. Furthermore, reactive power can dominantly affect the energy market clearing price. The supply and demand of sys- tem should be balanced in real time by dispatching generation in the most economic way taking into account all physical constraints. Various investigations have been carried out to find the most economic solution for the problem. The spot pricing theory has been developed by Schweppe et al. [1] based on the principle of marginal cost in a perfectly competi- tive market in 1988. Strbac et al. [2] have proposed a new method for evaluating the optimal balance between preven- tive and corrective security actions. In [3, 4] Rosehart et al. 123