Market Power in Mixed Hydro-Thermal Electric Systems

This paper shows that, unlike what has been found in other papers, a hydro reservoir is an effective tool to exercise market power. Its appealing as a tool is enhanced by the fact that there is no need to constrain total hydro production - a practice too easy to detect -; it suffices to distort the intertemporal allocation of hydro production over time. A hydro-producer may increase his profits by exploiting differences in price elasticity of demand across periods, allocating too little supply to less elastic periods and too much to more elastic periods. Differences in price elasticity across periods may result from the combination of a fluctuating market demand and capacity or transmission constraints that bind intermitently. This hydro scheduling decision is only available to hydro producers as thermal generators are not able to "store electric power" and decide when to sell it. It is also shown that total hydro production is not a sufficient indicator of market power being exercised as hydro producers may exercise market power even when all the water available in the\reservoir is used. The real indicator of market power being exercised is the hydro scheduling strategy usedUtilities; Market Power; Scheduling of Hydro-Reservoirs.

A note on systems with ordinary and impulsive controls

We investigate an everywhere defined notion of solution for control systems whose dynamics depend nonlinearly on the control $u$ and state $x,$ and are affine in the time derivative $\dot u.$ For this reason, the input $u,$ which is allowed to be Lebesgue integrable, is called impulsive, while a second, bounded measurable control $v$ is denominated ordinary. The proposed notion of solution is derived from a topological (non-metric) characterization of a former concept of solution which was given in the case when the drift is $v$-independent. Existence, uniqueness and representation of the solution are studied, and a close analysis of effects of (possibly infinitely many) discontinuities on a null set is performed as well.Comment: Article published in IMA J. Math. Control Infor

A Higher-order Maximum Principle for Impulsive Optimal Control Problems

We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to $u$. This lack of coercivity gives the problem an {\it impulsive} character, meaning that minimizing sequences of trajectories happen to converge towards discontinuous paths. As is known, a distributional approach does not make sense in such a nonlinear setting, where, instead, a suitable embedding in the graph-space is needed. We provide higher order necessary optimality conditions for properly defined impulsive minima, in the form of equalities and inequalities involving iterated Lie brackets of the dynamical vector fields. These conditions are derived under very weak regularity assumptions and without any constant rank conditions

Necessary conditions involving Lie brackets for impulsive optimal control problems

We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are unbounded and the absence of coercivity assumptions makes big speeds quite likely, minimizing sequences happen to converge toward "impulsive", namely discontinuous, trajectories. As is known, a distributional approach does not make sense in such a nonlinear setting, where instead a suitable embedding in the graph space is needed. We will illustrate how the chance of using impulse perturbations makes it possible to derive a Higher Order Maximum Principle which includes both the usual needle variations (in space-time) and conditions involving iterated Lie brackets. An example, where a third order necessary condition rules out the optimality of a given extremal, concludes the paper.Comment: Conference pape

Diagnosing and Mitigating Market Power in Chile's Electricity Industry

This paper examines generators' incentives to exercise market power and the strategies they would follow if all electricity supplies were traded in an hourly-unregulated spot market. The industry is modelled as a Cournot duopoly with a competitive fringe; particular care is given to the hydro scheduling decision. Quantitative simulations of generators� strategic behaviour indicate that the largest (Endesa) would have the incentive and power to act unilaterally. It would schedule its hydro resources to take advantage of differences in price electricity: too little supply in high demand periods and too much in low demand periods. Two market power mitigation measures are analysed: requiring Endesa to divest some of its generating capacity, and fixed price forward contracts for dominant generators. Conditions for the development of a voluntary contract market are analysed, as it is not practical to rel