A Selective Scheduling Problem with Sequence-dependent Setup Times: A Risk-averse Approach

This paper addresses a scheduling problem with parallel identical machines and sequence-dependent setup times in which the setup and the processing times are random parameters. The model aims at minimizing the total completion time while the total revenue gained by the processed jobs satisfies the manufacturer’s threshold. To handle the uncertainty of random parameters, we adopt a risk-averse distributionally robust approach developed based on the Conditional Value-at-Risk measure hedging against the worst-case performance. The proposed model is tested via extensive experimental results performed on a set of benchmark instances. We also show the efficiency of the deterministic counterpart of our model, in comparison with the state-of-the-art model proposed for a similar problem in a deterministic context

Overcommitment in Cloud Services -- Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance

A Mixed-Integer SDP Solution Approach to Distributionally Robust Unit Commitment with Second Order Moment Constraints

A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of stochastic parameters can be inferred from historical data, and then employed to model the set of probability distributions. The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP) with finite constraints. The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation. Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility checking problem, which is an intractable biconvex optimization. Experimental results on a IEEE 6-bus system are presented, showing that without any tunings of parameters, the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general, and our method also enjoys higher reliability of dispatch operation

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization

Secure and cost-effective operation of low carbon power systems under multiple uncertainties

Power system decarbonisation is driving the rapid deployment of renewable energy sources (RES) like wind and solar at the transmission and distribution level. Their differences from the synchronous thermal plants they are displacing make secure and efficient grid operation challenging. Frequency stability is of particular concern due to the current lack of provision of frequency ancillary services like inertia or response from RES generators. Furthermore, the weather dependency of RES generation coupled with the proliferation of distributed energy resources (DER) like small-scale solar or electric vehicles permeates future low-carbon systems with uncertainty under which legacy scheduling methods are inadequate. Overly cautious approaches to this uncertainty can lead to inefficient and expensive systems, whilst naive methods jeopardise system security. This thesis significantly advances the frequency-constrained scheduling literature by developing frameworks that explicitly account for multiple new uncertainties. This is in addition to RES forecast uncertainty which is the exclusive focus of most previous works. The frameworks take the form of convex constraints that are useful in many market and scheduling problems. The constraints equip system operators with tools to explicitly guarantee their preferred level of system security whilst unlocking substantial value from emerging and abundant DERs. A major contribution is to address the exclusion of DERs from the provision of ancillary services due to their intrinsic uncertainty from aggregation. This is done by incorporating the uncertainty into the system frequency dynamics, from which deterministic convex constraints are derived. In addition to managing uncertainty to facilitate emerging DERs to provide legacy frequency services, a novel frequency containment service is designed. The framework allows a small amount of load shedding to assist with frequency containment during high RES low inertia periods. The expected cost of this service is probabilistic as it is proportional to the probability of a contingency occurring. The framework optimally balances the potentially higher expected costs of an outage against the operational cost benefits of lower ancillary service requirements day-to-day. The developed frameworks are applied extensively to several case studies. These validate their security and demonstrate their significant economic and emission-saving benefits.Open Acces

Frequency response from aggregated V2G chargers with uncertain EV connections

Fast frequency response (FR) is highly effective at securing frequency dynamics after a generator outage in low inertia systems. Electric vehicles (EVs) equipped with vehicle to grid (V2G) chargers could offer an abundant source of FR in future. However, the uncertainty associated with V2G aggregation, driven by the uncertain number of connected EVs at the time of an outage, has not been fully understood and prevents its participation in the existing service provision framework. To tackle this limitation, this paper, for the first time, incorporates such uncertainty into system frequency dynamics, from which probabilistic nadir and steady state frequency requirements are enforced via a derived moment-based distributionally-robust chance constraint. Field data from over 25,000 chargers is analysed to provide realistic parameters and connection forecasts to examine the value of FR from V2G chargers in annual operation of the GB 2030 system. The case study demonstrates that uncertainty of EV connections can be effectively managed through the proposed scheduling framework, which results in annual savings of Misplaced &6,300 or 37.4 tCO2 per charger. The sensitivity of this value to renewable capacity and FR delays is explored, with V2G capacity shown to be a third as valuable as the same grid battery capacity

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors