Elastic properties of classical bulk materials can hardly be changed or adjusted in operando, while such tunable elasticity is highly desired for robots and smart machinery. Although possible in reconfigurable metamaterials, continuous tunability in existing designs is plagued by issues such as structural instability, weak robustness, plastic failure and slow response. Here we report a metamaterial design paradigm using gears with encoded stiffness gradients as the constituent elements and organizing gear clusters for versatile functionalities. The design enables continuously tunable elastic properties while preserving stability and robust manoeuvrability, even under a heavy load. Such gear-based metamaterials enable excellent properties such as continuous modulation of Young’s modulus by two orders of magnitude, shape morphing between ultrasoft and solid states, and fast response. This allows for metamaterial customization and brings fully programmable materials and adaptive robots within reach.

To address the uncertain renewable energy in the day-ahead op-timal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to characterize the uncertainties over the multiple stages by a scenario tree. Most importantly, to deal with the “Curse of Dimensionality” of sto-chastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a lin-ear piecewise function. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.

Mechanical metamaterials with high recoverable elastic energy density, which we refer to as high-enthalpy elastic metamaterials, can offer many enhanced properties, including efficient mechanical energy storage^1,2, load-bearing capability, impact resistance and motion agility. These qualities make them ideal for lightweight, miniaturized and multi-functional structures^3,4,5,6,7,8. However, achieving high enthalpy is challenging, as it requires combining conflicting properties: high stiffness, high strength and large recoverable strain^9,10,11. Here, to address this challenge, we construct high-enthalpy elastic metamaterials from freely rotatable chiral metacells. Compared with existing non-chiral lattices, the non-optimized chiral metamaterials simultaneously maintain high stiffness, sustain larger recoverable strain, offer a wider buckling plateau, improve the buckling strength by 5–10 times, enhance enthalpy by 2–160 times and increase energy per mass by 2–32 times. These improvements arise from torsional buckling deformation that is triggered by chirality and is absent in conventional metamaterials. This deformation mode stores considerable additional energy while having a minimal impact on peak stresses that define material failure. Our findings identify a mechanism and provide insight into the design of metamaterials and structures with high mechanical energy storage capacity, a fundamental and general problem of broad engineering interest.

With the growing development in demand response, load serving entities (LSEs) may participate in electricity market as strategic bidders by offering coupon-based demand response (C-DR) programs to customers. However, due to customers' versatile electricity consumption patterns under C-DR programs as well as the increasing penetration of wind power generation, obtaining the deterministic bidding decision becomes unprecedented complex for LSEs. To address this challenge, a new strategic bidding model for an LSE is proposed in which the primary objective is to maximize the LSE's profit by providing optimal C-DR considering high wind power penetration. The proposed strategic bidding is a bi-level optimization problem with the LSE's net revenue maximization as the upper level problem and the ISO's economic dispatch (ED) for generation cost minimization as the lower level problem. This bi-level model is converted to a stochastic mathematic program with equilibrium constraints (MPEC) by recasting the lower level problem as its Karush-Kuhn-Tucher (KKT) optimality conditions. Then, the stochastic MPEC is transformed to a mixed-integer linear programming (MILP) problem, which is solvable using available optimization software, based on strong duality theory. In addition, the effectiveness of the proposed method has been verified with simulation studies of two sample systems.

The development of intelligent demand-side management with automatic control enables a large amount of residential demands to provide efficient demand-side ancillary services for load serving entities. In this paper, we introduce the concept of a comfort indicator, present an advanced reward system, and finally propose a framework for aggregating residential demands enrolled in incentive-based demand response (DR) programs. The proposed framework not only allocates load serving entities' demand reduction requests among residential appliances quickly and efficiently without affecting residents' comfort levels but also rewards residential consumers based on their actual participation. Also, since the framework is designed with the practical considerations of simplicity and efficiency, it can be utilized as a quick implementation for existing pilot development works. The effectiveness and merit of this framework are demonstrated and discussed in the comparison studies with conventional incentive-based DR.