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Security Constrained Distributed Transaction Model for Multiple Prosumers
Massive access of renewable energy has prompted demand-side distributed resources to participate in regulation and improve flexibility of power systems. With large-scale access of massive, decentralized, and diverse distributed resources, demand-side market members have transformed from traditional “consumers” to “prosumers”. To explore the distributed transaction model of prosumers, in this paper, a multi-prosumer distributed transaction model is proposed, and the Conditional Value-at-Risk (CVaR) theory is applied to quantify potential risks caused by the stochastic characteristics inherited from renewable energy. First, a prosumer model under constraints of the distribution network including photovoltaic units, fuel cells, energy storage system, central air conditioning and flexible loads is established, and a multi-prosumer distributed transaction strategy is proposed to achieve power sharing among multiple prosumers. Second, a prosumer transaction model based on CVaR is constructed to measure risks inherited from the uncertainty of PV output within the prosumer and ensure safety of system operation in extreme PV output scenarios. Then, the alternating direction multiplier method (ADMM) is utilized to solve the constructed model efficiently. Finally, distributed transaction costs of prosumers are distributed fairly based on the generalized Nash equilibrium to maximize social benefits. Simulation results show the multi-prosumer distributed transaction mechanism established under the proposed generalized Nash equilibrium method can encourage power sharing among prosumers, increasing their own income and social benefits. Also, the CVaR can assist decision making of prosumers in weighting the risks and benefits, improving system resilience through energy management of prosumers.
On the role of Battery Energy Storage Systems in the day-ahead Contingency-Constrained Unit Commitment problem under renewable penetration
The integration of variable Renewable Energy Sources (vRES) to alleviate greenhouse gas emissions has introduced significant challenges for power systems operations. These challenges include high levels of uncertainty due to the intermittence associated with vRES and therefore impose the need to devise a reliable and cost-effective day-ahead unit commitment and power and reserves scheduling for real-time operations. Also, this increasing penetration of vRES requires higher ramping capabilities from units originally designed for other purposes (e.g., base-load generation), which might be exacerbated during contingency states. Hence, in this work, we propose a methodology to address the day-ahead Contingency-Constrained Unit Commitment (CCUC) problem that leverages the participation of Battery Energy Storage Systems (BESSs) to address load-following and post-contingency management, therefore alleviating the ramping burden on conventional thermal generators. To do so, we formulate a three-level optimization problem that represents the decision-making process of obtaining the least-cost commitment, generation and reserves scheduling, while restricting the Conditional Value-at-Risk (CVaR) of the system imbalance at real-time operations to user-defined tolerance levels. In addition, we devise a computationally efficient solution approach for the proposed problem based on the Column-and Constraint Generation (CCG) algorithmic framework. Two numerical experiments are conducted to empirically illustrate the benefits of the proposed methodology. Key results indicate a reduction in real-time ramping needs and a better usage of the system resources, with a reduction in the overall system commitment levels and reserve scheduling costs when compared to a benchmark case in which storage is not available.
SU-G-BRC-02: A Novel Multi-Criteria Optimization Approach to Generate Deliverable Intensity-Modulated Radiation Therapy (IMRT) Treatment Plans
Purpose: To present a novel multi-criteria optimization (MCO) solution approach that generates treatment plans with deliverable apertures using column generation. Methods: We demonstrate our method with 10 locally advanced head-and-neck cancer cases retrospectively. In our MCO formulation, we defined an objective function for each structure in the treatment volume. This resulted in 9 objective functions, including 3 distinct objectives for primary target volume, high-risk and low-risk target volumes, 5 objectives for each of the organs-at-risk (OARs) (two parotid glands, spinal cord, brain stem and oral cavity), and one for the non-target non-OAR normal tissue. Conditional value-at-risk (CVaR) constraints were utilized to ensure at least certain fraction of the target volumes receiving the prescription doses. To directly generate deliverable plans, column generation algorithm was embedded within our MCO approach for aperture shape generation. Final dose distributions for all plans were generated using a Monte Carlo kernel-superposition dose calculation. We compared the MCO plans with the clinical plans, which were created by clinicians. Results: At least 95% target coverage was achieved by both MCO plans and clinical plans. However, the average conformity indices of clinical plans and the MCO plans were 1.95 and 1.35, respectively (31% reduction, p<0.01). Compared to the conventional clinical plan, the proposed MCO method achieved average reductions in left parotid mean dose of 5% (p=0.06), right parotid mean dose of 18% (p<0.01), oral cavity mean dose of 21% (p=0.03), spinal cord maximum dose of 20% (p<0.01), brain stem maximum dose of 61% (p<0.01), and normal tissue maximum dose of 5% (p<0.01), respectively. Conclusion: We demonstrated that the proposed MCO method was able to obtain deliverable IMRT treatment plans while achieving significant improvements in dosimetric plan quality.
Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization
We propose a data-driven method to solve a stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The objective is to determine power schedules for controllable devices in a power network to balance operational cost and conditional value-at-risk (CVaR) of device and network constraint violations. These decisions include scheduled power output adjustments and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming the uncertainties across the networks follow prescribed probability distributions, we assume the distributions are only observable through a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real data-generating distribution, we formulate a distributionally robust optimization OPF problem to search for power schedules and reserve policies that are robust to sampling errors inherent in the dataset. A multi-stage closed-loop control strategy based on model predictive control (MPC) is also discussed. A simpIe numerical example illustrates inherent tradeoffs between operational cost and risk of constraint violation, and we show how our proposed method offers a data-driven framework to balance these objectives.
Binary Quantum Control Optimization with Uncertain Hamiltonians
Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. In conclusion, we demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model.