**4. Results**

The method characterized in the previous section was used to conduct computational experiments. From the wide spectrum of possible energy consumption managemen<sup>t</sup> problems to be studied, the case of hard constraint power limiting was selected for the study. The analysis involved the level of the production cell. The purpose of the research was to verify the completeness and consistency of the proposed method. The possibility of building and including real production conditions in the simulation model in terms of power and electricity consumption was investigated. Based on the simulation experiments, different scenarios for responding to the situation of available power limitation were defined and investigated.

### *4.1. Defining the Subject of Energy Consumption Research*

The subject under study was the production cell of a selected enterprise in the mechanical industry. The production line produces two types of products (Product 1, Product 2), which are elements of the electric motor of production machines. The production cell consists of four machines and two belt feeders. Each production workstation is equipped with a buffer where materials, parts, and semi-finished products used for the production process are stored. An operator is assigned to each workstation, who operates the machine (loads/unloads semi-finished products) and controls the machine parameters during the process.

### *4.2. Identification of Enterprise Resources in Terms of Power and Electricity Consumption*

In the next step, all resources of the production line that consume power during the production process were identified (Table 4). The power consumption for buffers and belt feeders was constant at any time during the process, while for machines, it changed depending on the machine state.


**Table 4.** Resources of the production line.

### *4.3. Modeling Individual Detailed Resources of an Enterprise Due to Electricity Consumption*

In the next step, a simulation model of the investigated production process was developed. The simulation model consisted of resources whose power consumption during the process realization was variable. For the remaining resources, power consumption was constant in each of the assumed states. In the "Power Off" state, the power consumption was 0 kW, while in the "Processing" state, it was at the set level for the operation of the resource. For example, in the case of buffers in the process under study, the power consumption was at the level of 0 kW, because they are a place for depositing products. They do not require the use of special equipment in the form of cooling/heating/keeping the movement of products, which would consume energy. For each resource, there is a profile of power consumption, which in the case of machinery is more complicated. This required introducing rules of power consumption in each of the states of the machine as well as defining the possibility of switching between the states. Characteristics of the production process in the form of unit power consumption by the machine as well as the duration of individual operations (for two manufactured products) are presented in Table 5.


**Table 5.** Characteristics of the implemented production process.

The duration of operations was given for two states of the machine (Warm-Up, Processing) because the duration of the other two states (Power Off, Idle) was calculated as part of the procedure for selecting operations on machines implemented in the simulation model. The "Power Off" state occurs when the work in the examined production cell is switched off—outside the set calendar of working hours from 6:00 a.m. to 2:00 p.m. The "Idle" state occurs on machines when the machine is waiting for a technological operation to be performed. The waiting time varies for different machines and also depends on the adopted strategy for the implementation of the production schedule.

### *4.4. Building a Simulation Model of a Manufacturing System*

In a simulation model, the course of the investigated manufacturing process was mapped, taking into account the resources whose power consumption varies in time. To build the simulation model, data on the duration of individual operations and the volume of energy consumption for each state on specific machines were used (Table 5). Simulations were performed for a specific set of production orders scheduled during one working shift of 8 h. The simulation model developed in FlexSim 20.1.3 software is shown in Figure 2.

**Figure 2.** Simulation model of the production process.

Within the framework of the model, the logic of assigning tasks to be performed in the production process was developed. This logic is particularly important when there is a limitation of power consumption for a given production cell. The logic developed in the *ProcessFlow* tool of FlexSim program is presented in Figure 3.

**Figure 3.** Data processing logic in the simulation model.

The data processing logic of the model was built on three elements. The first is the production schedule; the second is a flow of operations when an order is started on a machine; and the third is an assignment of power to a specific machine. At each iteration of the process, the state of the used power is examined, and then the power that can be distributed in the production cell to the remaining machines is determined (based on the difference between the available power and the power already used in the system). The power must be distributed to those machines that have made a request, and the decision to allocate power to each machine is made based on the established priorities in the production flow (order of request, order of flow in the process, etc.).

### *4.5. Verification of Changes in Electricity Consumption with the Simulation Model*

The experiments analyzed the possible strategies for the company to deal with power curtailment in the assumed time interval. The analysis was performed at two levels. In the first, different variants of reducing peak power by 5, 10, 15, or 20 kW were analyzed.

In the second, different handling scenarios and their impact on the implementation of the production process were examined. Within each experiment, the following factors were investigated:

• Process schedule;


The first step of the analysis was to simulate the production process for the base state, without the occurrence of the constraint. The obtained results make it possible to identify the points where, in case of the occurrence of a power constraint, it will be necessary to make changes in the production schedule. The power consumption graph with the production schedule is shown in Figure 4.

**Figure 4.** Power consumption and production schedule for the base state.

In the base state, the total process execution time was 462.6 min (i.e., it was executed during one work shift). One worker was assigned to each machine, therefore, their availability was 480 min, taking into account a 20-min work break. The work break was assigned to each station at a different time of the production schedule, therefore, it did not affect the working restrictions of the machines. The productivity of the machines varied from 48.61% (M1, M4) to 95.28% (M3). At the same time, the presented machine load chart showed that machine M3 was the bottleneck of the process, according to the concept of theory of constraints. The production schedule showed that on three workstations (M1, M2, M3), the course of production in the absence of restrictions on power consumption took place without restrictions/interruptions. The only breaks/restrictions occurred at station M4, where they were caused by waiting for the machine to run off/flow of semi-finished products from machine M3. While waiting, the machine operates in "Idle" mode. The factors of the production process for the base state are shown in Table 6.

If a constraint occurs from 11:00 a.m. to 1:00 p.m., part of the production must be reduced due to exceeding the available power consumption volume. The company can solve this problem according to the four proposed action scenarios:

1. Execution of operations in a sequential manner, starting from the last link of the production process and switching on the remaining links;


**Table 6.** Production process factors for the base state.

