## 2 Materials and Methods
### The Proposed Algorithm  
The software solution to the problem of the occurrence of large power peaks in the electrical grid caused by unsynchronised switching on of a large number of heaters requires the development of an algorithm that will enable their activation to be scheduled in such a way as not to disturb the temperature control process in the creep test machine furnaces. It was assumed that the implementation of delays sufficiently short in relation to the dynamics of the furnaces would not significantly affect the temperature stabilisation on them. Two temperature deviations from the set point are defined in the laboratory, which triggers alarm states. A temperature rise of 0.5 \({}^{\circ}\)C above the set point generates a warning in the system, while a temperature rise of 1.0 \({}^{\circ}\)C or more above the set point interrupts the ongoing creep test. Considering that temperature disturbances not suppressed by the control system are typically 0.2 \({}^{\circ}\)C, it was assumed that heater switch-on delays, resulting from the operation of the power peaks minimisation algorithm, should not causetemperature changes greater than 0.3 \({}^{\circ}\)C. In order to determine the maximum delays that can be inserted into the temperature control system of the furnace, an experiment was carried out in which the furnace model of a single-sample creep test machine was excited with a rectangular signal with constant filling while increasing its period. As a result, it was determined experimentally that for a period equal to 35 s, the temperature did not exceed the assumed deviations. The result of the experiment is shown in Figure 3. The value obtained was corrected by the average time between heater activations, with a minimum permissible temperature setpoint of 400 \({}^{\circ}\)C, in order to determine the permissible heater activation delays. On this basis, it was determined that the controller signal could be delayed up to 20 s while maintaining the assumed temperature deviations from the set point. Taking into account that the dominant time constant for single-sample machines is about 7200 s and for multi-sample machines it is about sixteen times higher, and that of the two determined permissible delay times, the shorter one should be chosen for further discussion, the experiment was not conducted for multi-sample machines. The developed algorithm for limiting power peaks occurring in the electrical grid uses a similar mechanism to a hardware solution based on a capacitor bank as a filter and energy storage at the same time [42]. Each temperature control system was extended with a software buffer placed between the controller output and the actuator. During the time the controller output is on, the buffer content is increased by one in the following sampling periods. During the time the heater is activated, the buffer content is decreased by one in the following sampling periods. The master algorithm decides when to turn on the heater. If the average buffer fill remains constant over the experimentally determined period, it can be expected that no exceedances of the permissible temperature deviations from the setpoint will occur. The task of the master algorithm is to determine the number of heaters to be switched on and then to select them. If the total power of the activated heaters is close to the average value determined in a certain time window, it should be expected that peaks will occur at most at the power level of a single heater. This effect is caused by quantised power values generated in the system as a result of relay control.