Reliable and efficient control of bus frequencies is crucial to the operation of any power grid. Classically, frequency control is implemented on the generation side via primary and secondary control schemes, with issues of optimality addressed at a much slower timescale via the optimal power flow (OPF) problem. In recent years, power systems have undergone significant changes, such as the liberalisation of the electricity markets, the introduction of new generation technologies, and the increased penetration of renewable energy sources. This expansion ofpower systems along with the stochastic nature of renewable energy inevitably lead to a need for faster, more efficient, and more reliable frequency control mechanisms. Furthermore, in a smart grid paradigm, frequency control schemes can be highly distributed due to the participation of the demand-side. Such approaches, incorporating control on both generators and loads, have the potential to reduce operational costs, improve system security, and increase the overall economic efficiency of the network's operation. In this chapter, we will discuss various approaches to distributed frequency control, paying particular attention to the incorporation of demand-side management and to the economic optimality ofthe schemes. We begin by describing the key concepts that will be considered.

Chapter Contents:

• 9.1 Introduction
• 9.1.1 Frequency control in the power grid
• 9.1.2 Optimality in frequency control
• 9.1.3 Demand-side management
• 9.2 Swing equation dynamics
• 9.3 Primary frequency control
• 9.3.1 Historical development
• 9.3.2 Passivity conditions for stability analysis
• 9.3.3 Economic optimality and fairness in primary control
• 9.3.4 Supply passivity framework for demand-side integration
• 9.4 Secondary frequency control
• 9.4.1 Historical development
• 9.4.2 Economic optimality and fairness in secondary control
• 9.4.3 Stability guarantees via a dissipativity framework
• 9.5 Future challenges
• Bibliography

Inspec keywords: load flow; frequency control; power generation control; renewable energy sources; distributed control; demand side management; power markets; smart power grids; power generation economics; stochastic processes

Other keywords: secondary control schemes; power grid; primary control schemes; operational costs; economic efficiency; generation technologies; smart grid paradigm; electricity markets; renewable energy sources; optimal power flow; bus frequencies; demand-side management; power systems; distributed frequency control; system security; OPF problem; network operation; generation side

Subjects: Other topics in statistics; Power system management, operation and economics; Frequency control; Control of electric power systems; Other topics in statistics; Energy resources