We consider a generalised comprehensive Look-ahead Security-constrained Optimal Power Flow (LASCOPF) formulation under the N−1 contingency criterion over multiple dispatch intervals. We observe that the number of decision variables varies quadratically with the number of intervals. To improve scalability, we propose a reduced LASCOPF formulation for which the number of decision variables varies only linearly. We extend these formulations to the N−k contingency criterion. For reduced LASCOPF we observe that the number of decision variables varies with the number of k-permutations of contingencies. To improve scalability, we propose a formulation that is further reduced to vary only with the number of k-combinations. Also, we show that our formulations can be extended simply to model recovery from the corresponding outages. Furthermore, we present LASCOPF under the N−1 contingency criterion using DC and AC power flow under generator contingencies. We prove that, barring borderline cases, solving the reduced formulation is equivalent to solving the comprehensive formulation. We extend these results to the N−k contingency criterion. Finally, we present numerical results on the IEEE 14 bus, IEEE 30 bus and IEEE 300 bus test cases, and the 1354 bus part of the European power system using AC power flow to demonstrate the computational advantage of the reduced formulations under the N−1 and N−2 contingency criteria.

The electricity industry has been one of the first to face technological changes motivated by sustainability concerns. Whilst efficiency aspects of market design have tended to focus upon market power concerns, the new policy challenges emphasise sustainability. We argue that market designs need to develop remedies for market conduct integrated with regard to environmental externalities. Accordingly, we develop an incentive-based market clearing mechanism using a power network representation with a distinctive feature of incomplete information regarding generation costs. The shortcomings of price caps to mitigate market power, in this context, are overcome with the proposed mechanism.

Power systems constitute a large-scale critical infrastructure and therefore, it is crucial that their operation be robust to deviations from normal functioning of its independent components. Furthermore, due to their large size, any inefficiencies in electricity market design can be very costly and therefore, must be optimised.

The first part of the thesis explores how generators must be optimally dispatched while maintaining robustness of the power system, which we model as the look ahead security constrained optimal power flow (LASCOPF) problem. LASCOPF optimises the generation dispatch given any objective, typically, a generation cost minimisation, over a planning horizon of multiple dispatch intervals, subject to physical constraints on the power system such as generator ramping constraints. In addition, we consider the $N-1$ contingency criterion, which is modelled as a set of security constraints that ensure that the system can transition to a feasible operating point if an outage in any one of its components were to occur. We observe that the problem size is quadratic in the number of intervals in the planning horizon and therefore, propose a reduced LASCOPF formulation for which the dependence is linear. We extend these results to the $N-k$ contingency criterion, which requires security against multiple simultaneous contingencies and observe that the problem size depends upon the number of permutations of contingencies. To overcome this, we propose a further reduced problem for which the dependence is on the number of permutations of contingencies. We model LASCOPF specifically using DC power flow under both generator and transmission line contingencies, and AC power flow under generator contingencies. For these, we prove that, barring borderline cases, the reduced formulations are equivalent to the corresponding comprehensive formulations. Numerical results on benchmark and real systems show that the reduced formulations have a significant computational advantage over the corresponding comprehensive ones.

The second part of the thesis explores how to use incentive mechanisms in electricity market design to overcome inefficiencies. The first problem we consider is that power generation causes environmental pollution with an associated damage cost, which we model as a negative externality. By definition, negative externalities are not included in the competitive market clearing used in electricity markets and, as we show, cannot be incorporated into the price. Since producers control generation sources, we propose a Pigouvian tax on them as an incentive to incorporate their pollution damage in their costs. The second problem we consider is producers' strategic behaviour where producers can declare higher costs to increase the prices and therefore, their profits. However, we show that even if producers are forced to declare costs truthfully, they may decrease their generation capacity to achieve the same effect. To overcome strategic behaviour of both these kinds, we propose to subsidise producers with their marginal contributions to the consumer surplus as an incentive. Our tax and subsidy mechanism is derived by aligning producers' profit maximisation with the social welfare maximisation resulting in an optimal generation dispatch.

The problems solved in this thesis contribute towards improving the efficiency of electricity markets by minimising generation costs and externalities such as environmental pollution while keeping the power system robust to outages in individual components.

Kraftsystem utgör en storskalig kritisk infrastruktur och därför är det avgörande att deras drift är robust mot avvikelser från normal funktion hos dess oberoende komponenter. Dessutom, på grund av deras stora storlek, kan eventuella ineffektiviteter i utformningen av elmarknaden bli mycket kostsamma och måste därför optimeras.

Den första delen av avhandlingen undersöker hur generatorer måste skickas optimalt samtidigt som robustheten hos kraftsystemet som vi modellerar som LASCOPF-problemet (\emph{look ahead security constrained optimal power flow} på engelska). LASCOPF optimerar generationsutskick givet varje mål, typiskt en minimering av produktionskostnaden, över en planeringshorisont med flera sändningsintervall som är föremål för fysiska begränsningar på kraftsystemet så som generatorrampningsbegränsningar. Dessutom överväger vi $N-1$-kontingenskriteriet som är modellerat som en uppsättning säkerhetsbegränsningar som säkerställer att systemet kan övergå till en genomförbar driftpunkt om ett avbrott i någon av dess komponenter skulle inträffa. Vi observerar att problemstorleken är kvadratisk i antalet intervall i planeringshorisonten och föreslår därför en reducerad LASCOPF-formulering där beroendet är linjärt. Vi utökar dessa resultat till $N-k$-kontingenskriteriet som kräver säkerhet mot flera samtidiga oförutsedda händelser och observerar att problemets storlek beror på antalet permutationer av oförutsedda händelser. För att övervinna detta föreslår vi ett ytterligare minskat problem där beroendet är av antalet permutationer av oförutsedda händelser. Vi modellerar LASCOPF specifikt med användning av DC-strömflöde under oförutsedda händelser i både generatorer och transmissionsledningar, och AC-strömflöde under oförutsedda händelser i generatorer. För dessa bevisar vi att, med undantag för gränsfall, de reducerade formuleringarna är likvärdiga med motsvarande omfattande formuleringar. Numeriska resultat på benchmark och verkliga system visar att de reducerade formuleringarna har en betydande beräkningsmässig fördel jämfört med motsvarande omfattande.

Den andra delen av avhandlingen utforskar hur man kan använda incitamentmekanismer i elmarknadsdesign för att övervinna ineffektivitet. Det första problemet vi tar upp är att elproduktion orsakar miljöföroreningar med tillhörande skadekostnader som vi modellerar som en negativ externitet. Per definition ingår inte negativa externa effekter i den konkurrensutsatta marknadsclearing som används på elmarknader och kan, som vi visar, inte inkorporerad i priset. Eftersom producenter kontrollerar produktionskällor, föreslår vi en Pigouvian skatt på dem som ett incitament att inkorporera deras föroreningsskador i deras kostnad. Det andra problemet vi överväger är producenternas strategiska beteende där producenter kan deklarera högre kostnader för att öka priserna och därmed deras vinster. Men vi visar att även om producenterna tvingas deklarera kostnader sanningsenligt, kan de minska sin produktionskapacite för att uppnå samma effekt. För att övervinna strategiskt beteende av båda dessa slag, föreslår vi att subventionera producenter med deras marginella bidrag konsumentöverskottet som ett incitament. Vår skatte- och subventionsmekanism härleds genom att anpassa producenters vinstmaximering med den sociala välfärdsmaximeringen, vilket resulterar i en optimal generationsutskick.

De problem som lösts i denna avhandling bidrar till att förbättra effektiviteten på elmarknaderna genom att minimera produktionskostnader och externaliteter som miljöföroreningar samtidigt som kraftsystemet hålls robust mot avbrott i enskilda komponenter.

We consider the look-ahead security-constrained optimal power flow (LASCOPF) problem under transmission line and generator contingencies. We first formulate LASCOPF under the N - 1 contingency criterion (LASCOPF(1)) using the dc power flow model. We observe that the number of decision variables in the comprehensive formulation increases quadratically with the number of look-ahead intervals, T, making the problem infeasible to solve for large T. To overcome this, we propose the reduced LASCOPF problem (LASCOPF-r(1)) in which the number of decision variables increases only linearly with T. Thereafter, we prove that, barring borderline cases, if LASCOPF(1) is feasible then the optimal solutions of LASCOPF(1) and LASCOPF-r(1) are equivalent. We then extend our results to the N - k contingency criterion (LASCOPF-ru(k)) for any collection of k contingencies, and we prove that the ordering of the contingencies does not affect the optimal solution. We then illustrate LASCOPF(1) on a simple 2-bus 2-generator system. We show the numerical benefits of the proposed LASCOPF-r(1) formulation on the IEEE 118-bus, the IEEE 300-bus, and the 2383-bus Polish systems.