Power demand risk models on milling machines

The measurement of power demand risks in manufacturing power systems will benefit manufacturers and the wider society. If the risks can be characterized using manufacturing parameters, manufacturers can better control risks originating in those parameters, select less power-risky production plans, and reduce utility costs and resource consumption. The measurement of risk can also help manufacturers and power suppliers to protect their power systems from unexpected disturbances. Existing measures of risk, however, do not consider time duration, and thus cannot accurately quantify the risks in manufacturing power systems; the risks of a period of high power demand must be evaluated with the duration of the surge. Therefore, new methods of measuring power demand risks are proposed, adapting measures drawn from the field of finance. With a focus on milling operations, processing power is shown to be a function of processing amount (A) and processing time (T), and a power demand distribution is directly derived as a joint distribution of A and T. A bivariate random variable model with copulas is applied to examine the correlation in the joint distribution. Then, based on evaluation of a probability distribution of power demand from A and T, new risk measures are introduced. Illustrative examples are provided to show how the proposed measures can quantify the power demand risks from milling machines, based on manufacturing parameters. Certain manufacturing parameters are found to affect overall power demand risks, including i) raw material type, ii) variability in processing time, and iii) correlation between A and T. In the examples, these three factors increase power demand risks by up to 108%, 67%, and 1% respectively.