Optimal Energy Reduction Schedules for Ice Storage Air-Conditioning Systems
Abstract
:1. Introduction
2. Problem Formulation
2.1. The Cooling Load Capacity of Chillers
- : the cooling load of chillers (kJ/hr);
- : the flow rate of chilled water (liter/hr);
- : the density of chilled water (1 kg/L);
- : the specific heat of water at average temperature (4.186kJ/kg-°C).
- is the temperature difference of chilled water (°C), which is defined as Equation (2):
- : the return temperature of chilled water (°C);
- : the supply temperature of chilled water (°C).
2.2. The Cooling Load Capacity of the Ice Storage Tank
- : the temperature difference of ice storage brine (°C);
- : the specific heat of ice storage brine at average temperature (3.6 kJ/kg-°C);
- : the return temperature of ice storage brine (°C);
- : the supply temperature of ice storage brine (°C);
- : the flow rate of ice storage brine (L/h);
- : cooling load capacity of the ice storage tank (kJ/h).
2.3. Power Consumption of Cooling Towers and Pumps
2.4. Power Consumption of Chillers and Ice Storage Tanks
2.5. Objective Function and Constraints
- : the power consumption of the i-th chiller at time t;
- : the power consumption of the i-th cooling tower at time t;
- : the power consumption of pump at time t;
- : the i-th unit on/off at time t, 1 is on and 0 is off;
- : power consumption of the ice storage at time t (kW);
- : the scheduling time;
- : the total number of chillers;
- : the total number of ice storage tanks.
3. The Proposed Methodology
3.1. Input Layer
3.2. Hidden Layer
3.3. Output Layer
- 1)
- Calculate Euclidean distance ║xji ﹣cjk║;
- 2)
- Calculate hidden layer output Hjk by Equation (15);
- 3)
- Calculate output layer output by Equation (17);
- 4)
- Calculate the error between simulation output yj and its expected value Tj by error function. In this paper, the fitness function is set to an error function which is defined as Equation (18):
3.4. Ant Colony Optimization (ACO) Process
3.5. Implementation of ARBFN
4. Case Study
Unit | a | b | c | d |
---|---|---|---|---|
65.7772 | 0.1961 | 1.3707E-08 | 1.249E-09 | |
128.7969 | 0.0449 | 1.139E-04 | −2.628E-08 | |
68.2033 | 0.1418 | 4.13921E-05 | −7.599E-09 | |
107.7250 | 0.1181 | 1.87115E-05 | −1.467E-09 | |
623.2087 | −0.4555 | 0.000228205 | −2.660E-08 | |
101.5365 | 0.0851 | 6.87455E-05 | −1.141E-08 | |
Charging Process Pice | 2204.5246 | −24.3534 | 9.252E-02 | −1.022E-04 |
Discharging Process Pice | −21.7173 | 0.2206 | 5.533E-05 | −1.591E-08 |
Chiller NO1 | Max. | Min. | Chiller NO2 | Max. | Min. |
---|---|---|---|---|---|
PLR(%) | 100 | 50 | PLR(%) | 100 | 50 |
5 | 2.5 | 5 | 2.5 | ||
5 | 3 | 5 | 3 | ||
Chiller NO3 | Max. | Min. | Chiller NO4 | Max. | Min. |
PLR(%) | 100 | 50 | PLR(%) | 100 | 50 |
5 | 2.5 | 5 | 2.5 | ||
5 | 2 | 5 | 3.5 | ||
Chiller NO5 | Max. | Min. | Chiller NO6 | Max. | Min. |
PLR(%) | 100 | 50 | PLR(%) | 100 | 50 |
5 | 2.5 | 5 | 2.5 | ||
5 | 3.5 | 5 | 2 | ||
Charge Process | Max. | Min. | Discharge Process | Max. | Min. |
3.9 | 1.9 | 11 | 5.6 | ||
4.2 | 2.6 | Control Valve(LPM) | 5109.1 | 3627 |
4.1. Results at Different TOU Intervals
Hour | Chiller | ICE (%) | Power (kW) | Cost (NT$) | |||||
---|---|---|---|---|---|---|---|---|---|
NO1 | NO2 | NO3 | NO4 | NO5 | NO6 | ||||
22 | 1 | 1 | 1 | 0 | 1 | 1 | 7.10 | 3152.97 | 4620.07 |
23 | 1 | 1 | 0 | 1 | 1 | 1 | 14.64 | 3144.25 | 4593.52 |
24 | 0 | 0 | 1 | 1 | 1 | 1 | 22.78 | 3037.77 | 4409.24 |
1 | 0 | 1 | 1 | 1 | 1 | 1 | 31.42 | 3013.29 | 4353.75 |
2 | 1 | 1 | 1 | 0 | 1 | 1 | 40.64 | 3087.55 | 4452.04 |
3 | 1 | 1 | 1 | 1 | 1 | 0 | 49.18 | 3062.86 | 4424.93 |
4 | 0 | 1 | 1 | 1 | 1 | 0 | 58.17 | 2760.67 | 3948.25 |
5 | 0 | 1 | 0 | 1 | 1 | 1 | 65.85 | 2667.75 | 3836.68 |
6 | 0 | 1 | 1 | 0 | 1 | 1 | 73.39 | 2583.26 | 3716.21 |
7 | 0 | 0 | 1 | 1 | 1 | 0 | 65.87 | 1758.33 | 5292.58 |
8 | 0 | 0 | 1 | 1 | 1 | 1 | 60.12 | 2532.70 | 7623.44 |
9 | 0 | 0 | 0 | 1 | 1 | 1 | 51.25 | 2203.22 | 6631.69 |
10 | 0 | 0 | 1 | 1 | 1 | 1 | 44.73 | 2507.66 | 11510.18 |
11 | 1 | 1 | 1 | 0 | 1 | 1 | 37.33 | 2625.41 | 12050.61 |
12 | 1 | 0 | 1 | 1 | 1 | 0 | 27.98 | 2379.28 | 7161.63 |
13 | 0 | 1 | 1 | 1 | 1 | 1 | 20.87 | 2702.69 | 12405.37 |
14 | 1 | 0 | 1 | 1 | 1 | 0 | 11.50 | 2445.28 | 11223.84 |
15 | 1 | 0 | 1 | 1 | 1 | 1 | 1.94 | 2589.96 | 11887.91 |
16 | 1 | 0 | 1 | 1 | 1 | 1 | 0.00 | 2792.89 | 12819.35 |
17 | 1 | 0 | 1 | 1 | 1 | 1 | 0.00 | 3143.81 | 14430.08 |
18 | 0 | 1 | 1 | 1 | 1 | 1 | 0.00 | 3163.51 | 9522.18 |
19 | 0 | 1 | 1 | 1 | 1 | 1 | 0.00 | 3027.51 | 9112.82 |
20 | 1 | 1 | 1 | 1 | 0 | 1 | 0.00 | 2878.31 | 8663.70 |
21 | 0 | 0 | 1 | 1 | 1 | 1 | 0.00 | 2655.52 | 7993.12 |
Total | 65916.46 | 186683.17 |
Hour | Chiller | ICE (%) | Power (kW) | Cost (NT$) | |||||
---|---|---|---|---|---|---|---|---|---|
NO1 | NO2 | NO3 | NO4 | NO5 | NO6 | ||||
22 | 0 | 1 | 0 | 1 | 1 | 1 | 7.69 | 1885.10 | 2466.67 |
23 | 1 | 1 | 1 | 1 | 0 | 1 | 16.96 | 2139.77 | 2810.98 |
24 | 0 | 1 | 1 | 1 | 1 | 1 | 25.43 | 2098.53 | 2766.18 |
1 | 0 | 1 | 0 | 1 | 1 | 1 | 34.68 | 2103.68 | 2758.08 |
2 | 1 | 0 | 0 | 1 | 0 | 1 | 43.67 | 2042.69 | 2674.30 |
3 | 1 | 0 | 1 | 1 | 0 | 1 | 52.65 | 2057.44 | 2699.09 |
4 | 1 | 1 | 0 | 1 | 1 | 1 | 59.48 | 1995.04 | 2652.43 |
5 | 1 | 1 | 0 | 1 | 0 | 1 | 68.17 | 2015.33 | 2650.33 |
6 | 1 | 0 | 1 | 1 | 1 | 0 | 75.66 | 1895.39 | 2499.20 |
7 | 1 | 0 | 0 | 0 | 0 | 1 | 68.49 | 958.99 | 2809.83 |
8 | 0 | 0 | 1 | 0 | 1 | 1 | 63.45 | 1543.89 | 4523.59 |
9 | 0 | 1 | 1 | 1 | 0 | 1 | 56.55 | 1551.37 | 4545.51 |
10 | 0 | 0 | 1 | 1 | 1 | 0 | 51.93 | 1679.36 | 4920.53 |
11 | 0 | 0 | 1 | 1 | 1 | 0 | 44.31 | 1432.15 | 4196.20 |
12 | 0 | 1 | 1 | 1 | 1 | 0 | 38.00 | 1717.87 | 5033.35 |
13 | 0 | 0 | 0 | 1 | 1 | 1 | 32.19 | 1645.15 | 4820.30 |
14 | 0 | 1 | 1 | 0 | 1 | 0 | 24.92 | 1541.14 | 4515.53 |
15 | 0 | 0 | 1 | 1 | 1 | 0 | 19.39 | 1496.22 | 4383.93 |
16 | 0 | 0 | 1 | 1 | 1 | 0 | 14.88 | 1416.48 | 4150.27 |
17 | 1 | 0 | 1 | 0 | 0 | 1 | 10.52 | 1363.52 | 3995.11 |
18 | 0 | 0 | 1 | 1 | 0 | 0 | 7.12 | 1236.36 | 3622.52 |
19 | 0 | 0 | 1 | 1 | 1 | 0 | 5.66 | 1273.19 | 3730.45 |
20 | 0 | 0 | 1 | 0 | 0 | 1 | 1.96 | 926.44 | 2714.47 |
21 | 0 | 0 | 0 | 1 | 1 | 0 | 0.00 | 944.50 | 2767.38 |
Total | 38959.58 | 84706.24 |
4.2. Energy Reduction Analysis
Actual | ARBFN | Difference | Reduction (%) | LSR | Difference * | Reduction (%) | ||
---|---|---|---|---|---|---|---|---|
Summer day | Power consumption (KW) | 68,481.8 | 67,562.4 | 1232 | 1.34 | 73,054.8 | 30,548 | 6.68 |
Total cost (NT$) | 194,726 | 192,310 | 2996 | 1.24 | 181,517 | 89,557 | 6.78 | |
Non-summer day | Power Consumption (KW) | 41,456.9 | 41,739.9 | 192 | 0.68 | 39,079.1 | 13,648 | 5.74 |
Total cost (NT$) | 91,457 | 92,249 | 689 | 0.87 | 98,605 | 51,823 | 7.25 |
4.3. Convergence Test
Algorithms | Summer Day | Non-Summer Day | ||
---|---|---|---|---|
Power consumption (KW) | Total Cost (NT$) | Power Consumption (KW) | Total Cost (NT$) | |
ARBFN | 65,916.46 | 186,683.17 | 38,959.58 | 84,706.24 |
GA-RBFN | 66,148.61 | 187,309.84 | 39,287.41 | 85,371.62 |
EP-RBFN | 66,431.83 | 188,131.15 | 39,514.37 | 85,984.38 |
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Lin, W.-M.; Tu, C.-S.; Tsai, M.-T.; Lo, C.-C. Optimal Energy Reduction Schedules for Ice Storage Air-Conditioning Systems. Energies 2015, 8, 10504-10521. https://doi.org/10.3390/en80910504
Lin W-M, Tu C-S, Tsai M-T, Lo C-C. Optimal Energy Reduction Schedules for Ice Storage Air-Conditioning Systems. Energies. 2015; 8(9):10504-10521. https://doi.org/10.3390/en80910504
Chicago/Turabian StyleLin, Whei-Min, Chia-Sheng Tu, Ming-Tang Tsai, and Chi-Chun Lo. 2015. "Optimal Energy Reduction Schedules for Ice Storage Air-Conditioning Systems" Energies 8, no. 9: 10504-10521. https://doi.org/10.3390/en80910504