Summary To control the risk of intraday operation incurred by wind power, this paper proposes a distributionally robust dynamic economic dispatch model with conditional value at risk (DRDED‐CVaR) recourse function, where the CVaR recourse function is used to measure the risk of load shedding and wind spillage. In contrast to traditional stochastic optimization and robust optimization, the DRDED‐CVaR model describes the uncertain wind power output considering all possible probability distribution functions (PDF) with mean and covariance information derived from historical data, and it optimizes the expected operation cost under the worst possible distribution. We derive an equivalent semidefinite programming (SDP) for the DRDED‐CVaR model and use the delayed constraint generation (DCG) algorithm and the alternate convex search (ACS) algorithm to solve this model. The proposed DRDED‐CVaR is compared with the existing dynamic economic dispatch (DED) model on the IEEE 30‐bus system. The simulation results demonstrate that the DRDED‐CVaR model can effectively control the risk of load shedding and wind curtailment according to the risk preference of the operators.

It is often claimed that coal-fired units are highly inflexible to accommodate variable renewable energy. However, a recently published report illustrates that making existing coal-fired units more flexible is both technically and economically feasible. Auxiliary firing is an effective and promising measure for coal-fired units to reduce their minimum loads and thus augment their flexibility. To implement the economic valuation of low-load operation with auxiliary firing (LLOAF) of coal-fired units, we improve the traditional fuel cost model to express the operating costs of LLOAF and present the economic criterion and economic index to assess the economics of LLOAF for a single coal-fired unit. Moreover, we investigate the economic value of LLOAF in the power system operation via day-ahead unit commitment problem and analyze the impacts on the scheduling results from unit commitment policies and from extra auxiliary fuel costs. Numerical simulations show that with the reduction of the extra auxiliary fuel costs LLOAF of coal-fired units can remarkably decrease the total operating costs of the power system. Some further conclusions are finally drawn.

In the plastic injection molding process, interaction between design and analysis is very intensive. However, current computer-aided systems (CAD and CAE) are realized as isolated modules. Thus, designers need to transform data models between CAD and CAE systems. Defects of many data errors and duplicated work are inevitable. This paper presents a CAD/CAE integrated system, building on top of existing CAD and CAE systems. The framework of the system is designed. A parametric integration model is established to achieve bidirectional association between the two systems. Details of key technologies in pre- and post- processing are discussed, such as mesh generation, feature recognition, and automatic evaluation of analysis results. A practical engineering case is studied to illustrate that the system can effectively avoid mesh repair and remodeling in pre-processing, reduce the dependency on experience in analysis result evaluation, and greatly improve the efficiency of iterative design-analysis-optimization process.

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

Abstract:The existing optimization approaches regarding network-constrained unit commitment with large wind power integration face great difficulties in reconciling the two crucial but contradictory objectives: computational efficiency and the economy of the solutions. This paper proposes a new network-constrained unit commitment approach, which aims to better achieve these two objectives, by introducing newly proposed reserve models and simplified network constraints. This approach constructs the reserve models based on a sufficiently large number of stochastic wind power scenarios to fully and accurately capture the stochastic characteristics of wind power. These reserve models are directly incorporated into the traditional unit commitment formulation to simultaneously optimize the on/off decision variables and system reserve levels, therefore, this approach can comprehensively evaluate the costs and benefits of the scheduled reserves and thus produce very economical schedule. Meanwhile, these reserve models bring in very little computational burden because they simply consist of a small number of continuous variables and linear constraints. Besides, this approach can evaluate the impact of network congestion on the schedule by just introducing a small number of network constraints that are closely related to network congestion, i.e., the simplified network constraints, and thus concurrently ensures its high computational efficiency. Numerical results show that the proposed approach can produce more economical schedule than stochastic approach and deterministic approach but has similar computational efficiency as the deterministic approach.