Large multi-axis propeller-measuring machines have two types of geometric error, position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs), which both have significant effects on the volumetric error of the measuring tool relative to the worktable. This paper focuses on modeling, identifying and compensating for the volumetric error of the measuring machine. A volumetric error model in the base coordinate system is established based on screw theory considering all the geometric errors. In order to fully identify all the geometric error parameters, a new method for systematic measurement and identification is proposed. All the PIGEs of adjacent axes and the six PDGEs of the linear axes are identified with a laser tracker using the proposed model. Finally, a volumetric error compensation strategy is presented and an inverse kinematic solution for compensation is proposed. The final measuring and compensation experiments have further verified the efficiency and effectiveness of the measuring and identification method, indicating that the method can be used in volumetric error compensation for large machine tools.

To address the issues of the low usage efficiency and illogical structure in rural regions, this study builds a rural integrated energy system (RIES) that incorporates the complementary use of biogas, wind, and light. For resolving the RIES optimum-low-carbon-economic-dispatch problem, a source–load-cooperative optimal-dispatch strategy is proposed. Firstly, a multi-energy integrated demand response (IDR) model based on time-of-use tariffs and time-varying biogas costs is established on the demand side. Secondly, power-to-gas devices are added on the supply side to optimize the system’s electricity–gas-coupling relationship and increase the wind power output space. Thirdly, an RIES-oriented carbon-trading model is constructed by considering the actual carbon emissions of gas loads and the stepped-carbon-trading mechanism. Finally, an optimal-dispatch model is built with the objective function of reducing the total energy cost, wind abandonment cost, IDR cost, and carbon emission cost, while the problem is transformed into a mixed-integer linear problem and solved using CPLEX 12.9. By setting up four scenarios for example analysis, the results show that on typical days in spring, summer, autumn, and winter, the total operating costs of the stepped-carbon-trading system (Scenario 1), taking into account the source-side power-to-gas (P2G) device and the load-side IDR, are reduced by 12.25%, 11.25%, 12.42%, and 11.56%, respectively, compared to the system without the introduction of the IDR (Scenario 3). In contrast to the system that lacks a P2G device at the source end (Scenario 2), the overall costs are decreased by 4.97%, 3.07%, 5.02%, and 5.36%, but the wind power consumption rates are increased by 11.63%, 7.93%, 11.54%, and 11.65%, respectively. Stepped emission trading (Scenario 1) reduces the total operating costs by 5.12%, 3.15%, 5.21%, and 6.84%, respectively, while reducing the biogas costs by 9.75%, 7.74%, 9.67%, and 9.57%, respectively, in comparison to traditional emission trading (Scenario 4). The example results demonstrate the economics, effectiveness, and reliability of a stepped-carbon-trading system with an integrated P2G load-side energy demand response.