Stability analysis and synthesis of hybrid closed-loops of modern power systems
The electricity sector changed a lot the last two decades. The evolutions of the general regulatory and organisation framework imposed changes at the technical level. For example, price signals are involved in several regulations. This leads to commutations from one control law to another or to the change of the number and nature of the actuators in function of the time evolution of energy and/or transfer capacity market. The secondary frequency control is an example of a control of which actuators may change in time. Indeed, for the classical pro-rata (or parallel) activation of the secondary reserve, the system operator objective is to activate the required secondary control reserve in a fast enough deployment time, by activating in parallel all units that have accepted bids in the secondary frequency control reserve market. In the new merit order approach (constructed by units’ bids for the deployment of secondary control reserves) to activate the secondary controls the providers are activated sequentially. This transforms the secondary control loop from a continuous to a hybrid one. Analytical investigation of the stability is a more difficult task in this case. Also, the impact of this change to the lower level controls (the faster ones like primary frequency and voltage controls) have to be clarified. Two approaches have to be developped : first, stability has to be investigated when using the actual controllers. Stability margins are to be deduced. Next, new optimal controls have to be proposed in order to maximize the aforementioned margins.
The secondary frequency regulation mentioned above is just an example of the modification of a standard and well-known controller in power systems into a class of so-called atypical regulations for which basic properties (like stability) should be carefully analysed in the actual context of power systems.
Keywords : stability analysis, hybrid systems, secondary frequency/voltage control.
Besides basic knowledges in power systems, a candidate for this intership must be acquainted with stability theory (in the sense of Lyapunov), optimal control (Pontryagin Maximum Principle for non linear systems) and preferably hybrid (or switched) systems