*4.2. Analysis of Optimization Results*

The subject of this case analysis was 240 slabs actually processed by a certain steel plant. The rolling operation started from 03:00. The genetic algorithm was used to solve the rolling batch-processing model under two conditions: considering the TOU electricity pricing, and not considering the TOU electricity pricing. Figure 11 presents the iteration curves under the two conditions. As it could be observed from Figure 11a, when TOU electricity pricing was not taken into consideration, the penalty value remained basically unchanged after 10 iterations. The initial penalty value was 23,537, and the value became 22,029 after optimization, amounting to an improvement of 6.4%. As presented in Figure 11b, when the TOU electricity pricing is taken into consideration, the penalty value remained basically unchanged after nine iterations. The initial penalty value was 27,880, while the value became 26,238 after optimization, amounting to an improvement of 5.9%. This indicated that a feasible solution with a low penalty value could be obtained through model optimization.

**Figure 11.** (**a**) TOU electricity pricing not considered (**b**) TOU electricity pricing considered Convergence curve resulted from genetic algorithm iterations.

Table 5 presents the penalty values of three hot-rolling batch processing plans prepared with different methods. It could be observed that the two rolling plans formulated through the hot-rolling batch-processing model under two electricity pricing conditions (TOU plan, non-TOU plan) had apparently lower penalty values, compared to the rolling plan formulated by the man–machine interaction method (MMI plan), even though all three rolling plans had the same number of rolling units. This indicated that better slab arrangement (width, thickness, and hardness) could be achieved after the model-based optimization, which would further lead to a smoother hot-rolling operation. The optimization model, in which the TOU electricity pricing was considered, had higher penalty value compared to the optimization model without the TOU electricity-pricing consideration. This occurred because the penalty incurred by the electricity cost had been added to the objective function. The introduction of the electricity cost penalty created the condition for simultaneous quality and power consumption optimization for the hot-rolling process.


**Table 5.** Penalty values of three hot-rolling batch-processing plans.

Figure 12 presets the electricity costs during rolling. The different colors represented different rolling units. The MMI plan induced an electricity cost of 11,230 yuan, the non-TOU plan induced 10,770 yuan and the TOU plan induced 10,230 yuan. In other words, the TOU plan induced 8.9% less electricity cost than the MMI plan and 5.0% less electricity cost than the non-TOU plan. Because the model considering the TOU electricity pricing is good for reducing peaks and filling valleys, the cost of electricity consumption is effectively reduced.

Figure 13 presents the power consumption data during the period from 04:00 to 10:00. The electricity price was 0.31 yuan/kWh in the period of 04:00–06:00, 0.53 yuan/kWh in the period of 06:00–8:00 and 0.76 yuan/ kWh in the period of 08:00–10:00. It could be observed that when the electricity price was 0.31 yuan/kWh, the MMI plan, non-TOU plan, and the TOU plan consumed 4293 kWh, 5134 kWh and 4808 kWh of electricity, respectively. When the electricity price was 0.76 yuan/kWh, the TOU plan consumed 4132 kWh, while the MMI plan consumed 5574 kWh. The former was 25.9% lower than the latter. This demonstrated the benefit of model-based optimization. After the model-based optimization, the high-load rolling units were arranged in the trough-price and flat-price periods, while the low-load rolling units were arranged in the peak-price period.

**Figure 12.** Electricity costs of three rolling plans.

**Figure 13.** Electricity consumptions at different time periods.

Figure 14 presents the electricity costs of three kinds of rolling plans at different time periods. It could be observed that when the electricity price was low (0.31 yuan/kWh), the MMI plan, TOU plan, and non-TOU plan induced electricity costs of 1331 yuan, 1592 yuan and 1490 yuan, respectively. When the electricity price was medium (0.53 yuan/kWh), the electricity costs induced by the three rolling plans were very close. When the electricity price was high (0.76 yuan/kWh), the MMI plan, non-TOU, and TOU plans induced costs of 4236 yuan, 3984 yuan and 3140 yuan, respectively. In other words, the TOU plan induced a 21.2% lower electricity cost than the non-TOU plan, and 25.9% lower than the MMI plan. Therefore, the TOU plan could effectively reduce the electricity cost and contribute to the power grid fluctuation reduction of electricity consumption.

**Figure 14.** Electricity costs at different TOU electricity pricing periods.
