Abstract
In recent years, the power system has undergone unprecedented changes that have led to the rise of an interactive modern electric system typically known as the smart grid. In this interactive power system, various participants such as generation owners, utility companies, and active customers can compete, cooperate, and exchange information on various levels. Thus, instead of being centrally operated as in traditional power systems, the restructured operation is expected to rely on distributed decisions taken autonomously by its various interacting constituents. Due to their heterogeneous nature, these constituents can possess different objectives which can be at times conflicting and at other times aligned. Consequently, such a distributed operation has introduced various technical challenges at different levels of the power system ranging from energy management to control and security. To meet these challenges, game theory provides a plethora of useful analytical tools for the modeling and analysis of complex distributed decision making in smart power systems. The goal of this chapter is to provide an overview of the application of game theory to various aspects of the power system including: i) strategic bidding in wholesale electric energy markets, ii) demand-side management mechanisms with special focus on demand response and energy management of electric vehicles, iii) energy exchange and coalition formation between microgrids, and iv) security of the power system as a cyber-physical system presenting a general cyber-physical security framework along with applications to the security of state estimation and automatic generation control. For each one of these applications, first an introduction to the key domain aspects and challenges is presented, followed by appropriate game-theoretic formulations as well as relevant solution concepts and main results.
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Notes
- 1.
This is the linearized lossless OPF formulation commonly known as the DCOPF. The more general nonlinear OPF formulation, known as the ACOPF, has more constraints such as limits on voltage magnitudes and reactive power generation and flow. Moreover, the ACOPF uses the AC power flow model rather than the linearized DC one. The ACOPF is a more complex problem to solve whose global solution can be very complex, and computationally challenging to compute, with the increase in the number of constraints involved. Hence, practitioners often tend to use the DCOPF formulation for market analyses. Here, the use of the terms AC and DC is just a notation that is commonly used in energy markets and does not, in any way, reflect that the used current in DCOPF or DC power flow is actually a direct current.
- 2.
In power system jargon, a bus is an electric node.
- 3.
p.u. corresponds to per-unit which is a relative measurement unit expressed with respect to a predefined base value (Glover et al. 2012).
- 4.
The π-model is a common model of transmission lines (Glover et al. 2012).
- 5.
- 6.
Various offer structures are considered in the literature and in practice, including block-wise, piece-wise linear, as well as polynomial structures. Here, a block-wise offer and bid structures are used; however, a similar strategic modeling can equally be carried out for any of the other structures.
- 7.
This LMP-based nodal electricity pricing is a commonly used pricing technique in competitive markets of North America. Here, we note that alternatives to the LMP pricing structure are implemented in a number of other markets and mainly follow a zonal-based pricing approach.
- 8.
The DA market is followed by a real-time (RT) market to account for changes between the DA projections and the RT actual operating conditions and market behavior. In this section, the focus is on dynamic strategic bidding in the DA market.
- 9.
For a discussion on general mean field games with heterogeneous players, see the chapter on “Mean Field Games” in this Handbook.
- 10.
Energy exchange with the main grid happens in two cases: (1) if the total demand in S cannot be fully met by the supply in S, leading some buyers to buy their unmet load from the distribution system, or (2) if the total supply exceeds the total demand in S; and hence, the excess supply is sold to the distribution system.
- 11.
Except for the reference bus whose phase angle is the reference angle and is hence assumed to be equal to 0 rad.
- 12.
This feasibility constraint in (38) insures the implementability and practicality of the derived defense solutions. To this end, a defender with more available defense resources may be more likely to thwart potential attacks. For a game-theoretic modeling of the effects of the level of resources, skills, and computational abilities that the defenders and adversaries have on their optimal defense and attack policies in a power system setting, see Sanjab and Saad (2016b).
- 13.
All the quantities in (51) are expressed in per unit based on the synchronous machine’s rated complex power.
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Acknowledgements
This work was supported by the US National Science Foundation under Grants ECCS-1549894 and CNS-1446621.
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Sanjab, A., Saad, W. (2017). Power System Analysis: Competitive Markets, Demand Management, and Security. In: Basar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-27335-8_28-1
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