Security constrained optimal power flow

The security constrained optimal power flow (SCOPF) is an optimal power flow that takes into account constraints arising from the operation of the power system under a set of postulated contingencies. It is therefore the codification of the security standards into a decision-making model. Under the traditional rules to security, the SCOPF determines the level of redundant infrastructure required to cope with a set of credible contingencies (e.g. N-2), whilst this is accomplished at the minimum cost [17].

In accordance with the deterministic security standards, conventional SCOPF models have been essential tools for system operators around the world for many years.

However, there are needs not only to reformulate the essential foundation of power system security but also to develop a generation of innovative operational tools. A number of issues make the new SCOPF much more challenging: the significantly larger size and complexity of the problem, the need to handle more discrete variables describing control actions and the variety of corrective control strategies in post-contingency states [17].

Initial research in this field included the use of corrective control within the conventional formulation of SCOPF. The classical SCOPF formulation becomes a two-stage decision making problem. In the first stage, the decisions (i.e. preventive controls) are applied on a fully known operating state, and have a direct effect on the operational cost function.

The second stage decisions correspond to corrective actions which are executed upon the occurrence of contingencies. These actions are typically modelled as “zero cost”

decisions considering that they have to be activated only rarely. The set of “second stages” is finite and is assumed known a priori (e.g. all single and double faults).

It is important to note that under this formulation the optimisation continue being purely deterministic, presenting the following drawbacks [17]:

 contingencies have no probability associated which disregards their individual likelihood of occurrence

 it optimises only the cost of pre-contingency state controls, disregarding the costs of post-contingency corrective actions, assuming thus that the likelihood of their use is small and that in the long run their cost will remain negligible

 it does not model the social and economic cost of blackouts that may result from the failure of corrective actions.

Because of the new complexities of power systems, static and equally weighted contingency lists of deterministic security standards are no longer appropriate to model uncertainty, and such lists should become dynamic to exploit all the information available at the moment of taking decisions. In other words, the set of post-contingency scenarios and the weight given to each of these scenarios should be optimised at the first-stage of the decision making process. In connection with this, some works [8] claim that this formulation does not completely cover the needs encountered in today’s operation and operational planning situations. According to Capitanescu et al. [17], in further developments a larger (in theory uncountable) contingency set should be considered to model the uncertainty between successive decision stages. It is also very likely that a two-stage reduction of the optimisation problem will no longer be sufficient. Instead, a multi-stage modelling framework could be required in which the couplings between decisions and uncertainties induced by adverse scenarios over longer time horizons could be modelled better. Several researches have introduced stochastic concepts into the SCOPF problem [3, 4, 40], which have resulted in novel operational methods based on multistage stochastic programming. The main innovation resides in the incorporation of the expected costs of corrective security in the objective function, thus defining a trade-off between preventive and corrective security characterised by:

 relying on probabilities of disturbance occurrence which often depend on the circumstances (e.g. adverse weather conditions or terrorist threat)

 a difficulty to estimate of the cost of corrective actions, especially in severe cases (e.g. cascading thermal overloads, voltage intability scenarios)

 the need of more than two stages to cover the whole spectrum of uncertainties At this point further research on the algorithmic side is needed, in particular to discretise the set of uncertain scenarios in order to build tractable approximations of the mother problem [17]. Moreno et al. [4, 6] propose a full probabilistic cost-benefit framework for the development of future efficient operating and design strategies and network security

standards considering corrective security. The authors optimally balance the costs of network constraints with various operational measures composed of preventive and corrective control actions, including expected unsupplied demand. The optimal network capacity released to network users in the operational timescales is determined depending on system parameters such as different weather conditions and wind penetration scenarios, and considering potential outages in the network. Figure 10 illustrates the ‘O+X’ problem that is composed of two cost terms. First, the problem includes the costs ‘O’ which are the operating costs from both the expected use of corrective control and the constraint costs (see section 2.1). Secondly, it considers the cost ‘X’ which denotes the risk in terms of expected unsupplied demand. Note that there are increasing (e.g. expected unsupplied demand, corrective control and losses) and decreasing costs (e.g. constraint costs) associated with further levels of network utilisation. Under a pure cost-benefit framework, the available capacity of the network in operational timescales should be increased up to the point that the cost associated with such levels of utilisation exceeds the benefits.

Figure 10: Balance to determine optimum transfer in a single transmission link [8]

Figure 11 illustrates the ‘T+O+X’ problem which considers optimal levels of network infrastructure investment in planning timescales. The extra cost term ‘T’ is attributable to the investment and maintenance in the network (e.g. wires, transformers, etc.). Note that further investments reduce the cost of constraints, the expected unsupplied demand, the expected use of corrective control and the losses, at the expense of increasing the investment costs and its maintenance associated. This problem states that network investments should continue up to the point that the cost associated with such

Figure 11: Balance to determine optimum transmission investment in a single transmission link [8]

The authors presented an initial investigation of the impacts from SPS malfunctions, yet their analysis was restricted to a crude model of SPS failures and its effects. Accordingly, it does not model the social and economic cost of blackouts (e.g. Value of Lost Load of

£30000/MWh) that may result from failures of corrective actions. However, this work anticipates important benefits from the use of system protection schemes, especially under scenarios of high wind penetration. Hug [43] continues to explore the trade-offs between generation cost and operational risks as opposed to formulating a traditional security constrained economic dispatch, but disregards SPS malfunction scenarios.

3.1.2 Risk assessment of power system operation considering