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## THÈSE DE DOCTORAT DE L UNIVERSITÉ PARIS-SACLAY, préparée à Centrale-Supelec

Indeed, the use of fixed constraints on inertia, for example, will over-schedule primary regulation resources for cojrs time steps, and nothing guarantees that the security threshold will always be respected. Some examples include the increase of network capacity, the deployment of alternative protection schemes and the extension of reactive power sources.

A stochastic scenario is defined here as a representation of a deviation from the deterministic scenario. For instance, two proposed metrics are the V-RES instantaneous non-synchronous penetration SNSP level and the ratio of kinetic energy stored in conventional generators plus load and the dispatched power of the largest in-feed. Finally, conclusion are drawn in section Background The analysis of the impacts of V-RES on power systems planning and operation is quite a broad topic, and it has been widely addressed in the literature, especially for wind power [28, 51].

As a consequence, the aggregated deployment rate of the reserve may decrease before the xsservissement is reached.

Nonetheless, the DP is still used, but to solve sub-problems following decomposition approaches, such as LR. Finally, tertiary reserve is deployed to improve the economical performance of the dispatch, to manage congestions and to restore faster reserves. Then, the primary frequency control will automatically and locally increase the power output of the units designated to provide this ancillary service, until the power balance is regained and the system frequency is stabilised.

Then, it is necessary to determine the frequency trajectory as a function of the system initial state the demand and the UC decision variable for a fixed hand, of course, the time, following a large disturbance of power P step, this is f t,p step,u h,g h,df h.

Then, some frequency metrics, such as the nadir and the ROCOF are computed for every possible single outage by exhaustive simulation, using the implemented ROSFR model xpge in corus 2. In addition, the scheduled primary reserve and K factor are lower in the weekend example.

Formulation of classic models to study the primary frequency response 29 In addition, an operational limit is generally curs on the maximal primary reserve that can be allocated in a specific unit R pr,max jsince it must be deployed in some seconds. As aforementioned, the trivial representation of a scenario is an unique operational point, i. Future developments include the implementation of stabilisation algorithms, based on bundle methods for instance, to improve the convergence properties of the proposed FCUC formulation.

## LaTeX en SI

These results support the preliminary conclusion provided in section 2. It represents a possible realization of the underlying stochastic process. Moreover, according to the rigorous investigation on the nature of this non-linearity presented in this section, it is concluded that a linearisation method is not suitable for the purpose of this work.

Therefore, in order to asses the impact of V-RES from a certain operational view, it is easier to approach the topic in terms of a comparison. Model of the conventional power plant Figure 2.

### cours asservissement cpge pdf – PDF Files

In conclusion, the proposed MMR-ROSFR model includes a more accurate and flexible representation of the primary frequency response underlying processes, which have a significant impact on the frequency nadir, but it does not support a formal analytical study of the relation between the frequency nadir and the UC decision variables.

Hence, the installed capacity of RES, especially PV, have experienced an important growth in these regions, as presented in figure 1. Single bus model no network consideration is used, but DC power flow or quadratic formulation of AC constraints could be included. The goal is to ensure that the amount and quality of a scheduled resource, the primary reserve, is sufficient to ensure security when facing large disturbances in real-time operation.

A scenario is a set or sequence of operational points. Finally, section investigates the relation between some frequency metrics and the UC optimisation variables, while section discusses computational features. Day-ahead dispatches with dynamic primary reserve requirement model M 0 The week day dispatch is set as a reference and the cost of the different considered dispatches will be indicated in per unit pu.

It is shown that, although the enforcement of enhanced security constraints over certain parameters can produce secure schedules at some instants, the opposite effect may appear under different conditions.

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However, the provision of active power reserves and frequency regulation services could assedvissement more challenging to prescribe for non-dispatchable resources, although different alternatives have been proposed. Thus, the focus is placed on the last two time scales between the day-ahead and the real-time decision making processes.

Carmen Cardozo Optimisation of power system security with high share of variable renewables. Hence, some operational strategies are suggested, such as the definition of limits over coirs metrics.

The Benders method has been used before for handling non-linear constraints in the MILP formulation of the SCUC model [88], while strong hypothesis have been made on the primary frequency response for day-ahead scheduling purposes [85]. Ce sera l objet de la partie suivant.

Hence, some works propose the development of ad-hoc methods. This is the case of basic” voltage control in Europe and USA [13], while other services are now traded in dedicated markets, depending on the system. Voltage control is related to the local provision of reactive power [3], while frequency control is achieved by keeping the balance between the load and generation [4].

Thereafter, strong support policies for renewables were deployed in different countries, which have attracted significant investment on new technologies, first wind and then photovoltaic PV.

In this work, dynamic simulations were stopped after the frequency minimum is reached. Then, the actual Californian Independent System Operator CAISO practices were simulated to mimic different markets, with and without wind generation, in order to determine the load following requirements due to the additional wind.

Hence, models for g j t and D f t need to be built, which are given by the dynamic of the deployment of the active reserves and the load damping respectively. The acronym FCUC is specifically defined for this security problem, since the term security constrained UC SCUC is already used asservissemnt literature to designate the day-ahead scheduling problem with network constraint power flow and voltage limits [87], which are not considered here, but could be included in the proposed formulation.

In addition, they tend to be asynchronously connected to the grid by power electronics, which prevents them to naturally contribute to the system inertia asservissekent may deteriorate dynamic behaviour of the system. At least some statistics.

La taille du cercle indique le poids statistique de la classe.

This trend has been recently boosted by the transformation of the power system operational environment. Physicists often talk of the beauty of their picture of the world.