Search for: All records

Micro-grids’ operations offer local reliability; in the event of faults or low voltage/frequency events on the utility side, micro-grids can disconnect from the main grid and operate autonomously while providing a continued supply of power to local customers. With the ever-increasing penetration of renewable generation, however, operations of micro-grids become increasingly complicated because of the associated fluctuations of voltages. As a result, transformer taps are adjusted frequently, thereby leading to fast degradation of expensive tap-changer transformers. In the islanding mode, the difficulties also come from the drop in voltage and frequency upon disconnecting from the main grid. To appropriately model the above, non-linear AC power flow constraints are necessary. Computationally, the discrete nature of tap-changer operations and the stochasticity caused by renewables add two layers of difficulty on top of a complicated AC-OPF problem. To resolve the above computational difficulties, the main principles of the recently developed “l1-proximal” Surrogate Lagrangian Relaxation are extended. Testing results based on the nine-bus system demonstrate the efficiency of the method to obtain the exact feasible solutions for micro-grid operations, thereby avoiding approximations inherent to existing methods; in particular, fast convergence of the method to feasible solutions is demonstrated. It is also demonstrated that through the optimization, the number of tap changes is drastically reduced, and the method is capable of efficiently handling networks with meshed topologies. 

Job shops are an important production environment for low-volume high-variety manufacturing. Its scheduling has recently been formulated as an Integer Linear Programming (ILP) problem to take advantages of popular Mixed-Integer Linear Programming (MILP) methods, e.g., branch-and-cut. When considering a large number of parts, MILP methods may combinatorial difficulties. To address this, a critical but much overlooked issue is formulation tightening. The idea is that if problem constraints can be transformed to directly delineate the problem convex hull in the data preprocessing stage, then a solution can be obtained by using linear programming methods without combinatorial difficulties. The tightening process, however, is fundamentally challenging because of the existence of integer variables. In this paper, an innovative and systematic approach is established for the first time to tighten the formulations of individual parts, each with multiple operations, in the data preprocessing stage. It is a major advancement of our previous work on problems with binary and continuous variables to integer variables. The idea is to first link integer variables to binary variables by innovatively combining constraints so that the integer variables are uniquely determined by the binary variables. With binary and continuous variables only, it is proved that the vertices of the convex hull can be obtained based on vertices of the linear problem after relaxing binary requirements. These vertices are then converted to tightened constraints for general use. This approach significantly improves our previous results on tightening individual operations. Numerical results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other ILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved. 

Nicotinamide riboside chloride (NRCl) is an effective form of vitamin B3. However, it cannot be used in ready-to-drink (RTD) beverages or high-water activity foods because of its intrinsic instability in water. To address this issue, we synthesized nicotinamide riboside trioleate chloride (NRTOCl) as a new hydrophobic nicotinamide riboside (NR) derivative. Contrary to NRCl, NRTOCl is soluble in an oil phase. The results of stability studies showed that NRTOCl was much more stable than NRCl both in water and in oil-in-water emulsions at 25 °C and 35 °C. Finally, we evaluated the bioavailability of NRTOCl by studying its digestibility in simulated intestinal fluid. The results demonstrated that NRTOCl was partially digestible and released NR in the presence of porcine pancreatin in a simulated intestinal fluid. This study showed that NRTOCl has the potential to be used as an NR derivative in ready-to-drink (RTD) beverages and other foods and supplement applications. 

Energy Storage Resources (ESRs) can help promote high penetrations of renewable generation and shift the peak load. However, the increasing number of ESRs and their features different from conventional generators bring computational challenges to operations of wholesale electricity markets. In order to improve the computational efficiency, this paper tightens the generic ESR formulation for unit commitment. To avoid the complexity caused by ESR operations in both discharge and charge directions, a novel “decoupled analysis” is conducted to analyze one direction at a time. For each direction, ESRs over two and three time periods are categorized into several types based on their parameters. For each type, our recent four‐step systematic formulation tightening approach is used to construct the corresponding tight formulation. In order to consider more periods without analyzing all the drastically increased number of types, a series of major types are selected based on how many periods an ESR is able to discharge (charge) consecutively at the upper power limit. A related generic form of tight constraints over multiple periods is established. Moreover, validity and facet‐defining proofs of our tight constraints have been provided. Numerical testing results illustrate the tightening process and demonstrate computational benefits of the tightened formulations.

 

Sub-hourly Unit Commitment (UC) problems have been suggested as a way to improve power system efficiency. Such problems, however, are much more difficult than hourly UC problems. This is not just because of the increased number of period to consider, but also because of much reduced unit ramping capabilities leading to more complicated convex hulls. As a result, state-of-the-art and practice methods such as branch-and-cut suffer from poor performance. In this paper, our recent Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) method, which overcame major difficulties of standard Lagrangian Relaxation, is enhanced by synergistically incorporating the concept of Ordinal Optimization (OO). By using OO, solving subproblems becomes much faster. Testing of Midcontinent ISO (MISO)’s problem with 15 minutes as the time interval over 36 hours involving about 1,100 units and 15000 virtuals demonstrates that the new method obtains near-optimal solutions efficiently and significantly outperforms branch-and-cut. 

With the emergence of the Internet of Things that allows communications and local computations and with the vision of Industry 4.0, a foreseeable transition is from centralized system planning and operation toward decentralization with interacting components and subsystems, e.g., self-optimizing factories. In this article, a new ``price-based'' decomposition and coordination methodology is developed to efficiently coordinate a system consisting of distributed subsystems such as machines and parts, which are described by mixed-integer linear programming (MILP) formulations, in an asynchronous way. The novel method is a dual approach, whereby the coordination is performed by updating Lagrangian multipliers based on economic principles of ``supply and demand.'' To ensure low communication requirements within the method, exchanges between the ``coordinator'' and subsystems are limited to ``prices'' (Lagrangian multipliers) broadcast by the coordinator and to subsystem solutions sent at the coordinator. Asynchronous coordination, however, may lead to convergence difficulties since the order in which subsystem solutions arrive at the coordinator is not predefined as a result of uncertainties in communication and solving times. Under realistic assumptions of finite communication and solve times, the convergence of our method is proven by innovatively extending the Lyapunov stability theory. Numerical testing of generalized assignment problems through simulation demonstrates that the method converges fast and provides near-optimal results, paving the way for self-optimizing factories in the future. Accompanying CPLEX codes and data are included.