A systematic energy-aware scheduling framework for manufacturing factories integrated with renewables

Figures & data

Figure 1. An example of the complex energy flows of a factory integrated with RESs.

A schematic of an energy system with supply, storage, and demand components, indicating electricity and thermal flows.

Figure 2. Classification of current research.

Comparison of off-line, on-line, and hybrid energy-aware scheduling in terms of problem formulation, strengths, weaknesses, and related literature.

Figure 3. Framework and example of ETHS.

A diagram of ETHS with a scheduling process flowchart and graphs showing objective function values over time for scheduling decisions.

Figure 4. System components and energy flow of the factory.

Diagram showing energy and material flow among photovoltaic (PV), energy storage system (ESS), grid, gas turbine (GaT) and a production line of 5 machines.

Table 1. States variables for the metal production factory.

States	Description
States in ND Components
$x_1\in {\mathcal{R}}^1$	Power of PV generation
States in PD Components
${\mathbf{x}}_2\in {\mathcal{R}}^{10}$	Machine status on or off for each machine
${\mathbf{x}}_3\in {\mathcal{R}}^{10}$	Operation status starts or not start on each machine
${\mathbf{x}}_4\in {\mathcal{R}}^{10}$	Number of operations finished on each machine
$x_5\in {\mathcal{R}}^1$	GaT generation power
States in FD Components
$x_6\in {\mathcal{R}}^1$	ESS charging power
$x_7\in {\mathcal{R}}^1$	ESS discharging power
$x_8\in {\mathcal{R}}^1$	ESS state of charge (SOC)
$x_9\in {\mathcal{R}}^1$	Grid electricity procurement power
$x_{10}\in {\mathcal{R}}^1$	Grid electricity feed-in power

Table 2. Parameters for the metal production factory.

Parameter	Description	Value
${\mathit{\theta }}_1\in {\mathcal{R}}^4$	Machine power for 5 machines (kW)	[25.8,0.66,0.65,1.69,35.8]
${\mathit{\theta }}_2\in {\mathcal{R}}^4$	Operation time for 5 operations (5 min)	[3,2,3,1,2]
${\theta }_3\in {\mathcal{R}}^1$	Gas price ($)	1.83
${\theta }_4\in {\mathcal{R}}^1$	ESS charging/discharging efficiency	0.9
${\theta }_5\in {\mathcal{R}}^1$	ESS fixed operational cost ($/5 min)	0.003
${\theta }_6\in {\mathcal{R}}^1$	ESS charging/discharging degradation cost ($/kWh)	0.0006
${\theta }_7\in {\mathcal{R}}^1$	ESS maximum capacity (kWh)	50
${\theta }_8\in {\mathcal{R}}^1$	ESS depth of discharge	80%
${\theta }_9\in {\mathcal{R}}^1$	ESS maximum charging/ discharging power (kW)	50
${\mathit{\theta }}_{10}\in {\mathcal{R}}^{288}$	Grid electricity procurement price ($/kWh)	0.330 from 9am to 9pm 0.187 from 9pm to 9am
${\theta }_{11}\in {\mathcal{R}}^1$	Grid electricity feed-in tariff ($/kWh)	0.052
${\theta }_{12}\in {\mathcal{R}}^1$	Production disturbance possibility parameter	0.1
${\theta }_{13}\in {\mathcal{R}}^1$	Production disturbance time parameter	2
${\theta }_{14}\in {\mathcal{R}}^1$	Number of production task	50

Figure 5. Production schedule disturbance.

A Gantt chart showing the production schedule of 5 machines which cannot finish on time due to disturbances.

Figure 6. PV generation disturbance.

Graph comparing predicted and observed PV generation over time.

Table 3. Result of standard ETHS.

Energy cost per product ($)	Finished products	Computational time (s)	Rescheduling frequency
1.77	50	117	8

Figure 7. Schedule comparison with traditional methods.

Four production schedules showing that ETHS and T4 are able to complete the production task while T1 and T5 can't.

Table 4. Performance comparison with traditional methods.

Scenario	Energy cost per product ($)	Finished products	Computational time (s)
Standard ETHS	1.77	50	117
T1	2.49	48.3	3
T4	2.16	50	330
T5	1.83	48.3	8

Table 5. Sensitivity Analysis of S2, S3 and S4.

Scenario	Energy cost per product ($)	Finished products	Computational time (s)
Standard ETHS	1.77	50	117
Remove S2	2.22	50	112
Remove S3	1.69	50	4152
Remove S4	1.83	48.3	8

Figure 8. Gap between predicted and observed objective function value.

Graphs showing that with S2 the gap between observed and predicted objective function value can be reduced significantly.

Table 6. Selection of different component categories.

Fully-dispatchable Components	Energy cost/ product	Finished products	Number of matching objective reference
Grid, ESS	1.77	50	284/288
Grid, ESS, GaT	1.75	50	288/288
Grid, ESS, GaT and powder coating machine	1.75	50	288/288

Figure 9. Reschedule time steps comparison between two performance evaluation functions.

Graphs showing that different weights in S3 can result in different rescheduling time steps.

Table 7. Threshold comparison.

Threhold	Finished products	Energy cost per product ($)	Computing time ($)	Reschedule frequency
$ϵ=25$	50	1.73	213	16
$ϵ=45$	50	1.77	117	8
$ϵ=65$	50	1.80	86	6

Data availability statement

The data that support the findings of this study are available from the corresponding author, [Li], upon reasonable requests.