A tool for generation of stochastic occupant-based internal loads using a functional data analysis approach to re-define ‘activity’

Figures & data

Figure 1. Schematic illustration of base methodology.

Table 1. Building and metering information.

Building	Date of construction	Gross floor area (m^2)	Primary use	Small power meters	Lighting meters
1	2001	10,241	IT Laboratory, Research Office	15	14
2	2016	2947	Research Office	5	5
3	2009	4506	Laboratory Research Office	9	3
4	1970	13,107	Museum, Laboratory, Research Office	35	32

Figure 2. Plug Loads: first 4 Principal Components for phase, X. The impact of adding each PC to the mean function is shown using a + ve (solid red) or -ve (dotted red) score.

Figure 3. Plug Loads: first 4 Principal Components for amplitude, Y. The impact of adding each PC to the mean function is shown using a + ve (solid red) or -ve (dotted red) score.

Figure 4. Scores for first phase and amplitude PCs, with normalized electricity consumption for each zone.

Figure 5. Plug Loads: sample data generated from scores sampled from probability distribution used in conjunction with PCs.

Figure 6. Lights: sample data generated from scores sampled from probability distribution used in conjunction with PCs.

Figure 7. Scores for the first phase and amplitude components for lighting, Zone 2.1. The highlighted area shows sampled scores that fall outside the score space defined by the data.

Figure 8. Dendrogram for plug loads and normalized monitored data. The dendrogram shows the hierarchical relationship between zones with zones linked together according to similarity. On the right hand side the normalized monitored data have been plotted by cluster grouped in 12, 7 and 4 clusters.

Figure 9. Comparison of demand reconstructed from scores and generated from clusters. The monitored data are shown as black dotted lines with the mean and 90% CL highlighted in red. The model output 90% CL is shown coloured according to the variability selected (Figure 8).

Figure 10. Wasserstein distance for KPIs.

Figure 11. Dendrogram for lighting and normalized monitored data. The dendrogram shows the hierarchical relationship between zones with zones linked together according to similarity. On the right hand side the normalized monitored data have been plotted by cluster grouped in 10, 5 and 3 clusters.

Figure 12. Sample weekly data, variability from 1 (top) to 4 (bottom). Sample data are calculated for 2019 and start on a Tuesday. Black dotted lines show the individual weekly demand profiles and the mean and 90% CL are highlighted in red.

Table 2. Test zone information: base load and load range from the test data compared against the mean values for zones with similar activity in the training dataset and the NCM activity database values (Building Research Establishment (2016)). Also given is the assumed variability used for generation of sample data.

			Monitored		Mean activity		NCM
		Variabi	Base	Load	Base	Load	Base	Load
Zone	Activity	lity	Load	Range	Load	Range	Load	Range
1.1	Office	2	3.5	3.3	2.8	3.6	0.6	11.3
2.4	Office	2	4.2	3.7	2.8	3.6	0.6	11.3
4.5	Office	1	2.3	4.9	2.8	3.6	0.6	11.3
3.5	Office	2	3.5	3.6	2.8	3.6	0.6	11.3
1.7	Classroom	3	1.8	1.0	1.3	1.7	0.1	4.5
4.8	Circulation	2	2.5	3.5	1.4	2.3	0.1	1.7
3.2	Laboratory	3	3.7	3.6	17.6	8.7	0.1	8.2
4.23	Laboratory	4	10.4	1.6	17.6	8.7	0.1	8.2
4.17	Lecture Theatre	2	1.5	4.3	2.5	1.9	0.1	1.7
4.24	Food Preparation	2	9.1	81.7	15.6	60.0	0.1	32.0

Figure 13. Model outputs for 10 test zones calculated using known base load and load range and assumed variability as given in Table 2. The monitored data are shown as black dotted lines with the mean and 90% CL highlighted in red. The model output 90% CL is shown coloured according to the variability selected (Figure 8).

Figure 14. Plug load model outputs for 10 test zones calculated using known base load and load range and assumed variability as given in Table 2, comparison of KPIs.

Table 3. Plug load model outputs for 10 test zones calculated using known base load and load range and assumed variability as given in Table 2, numerical comparison of KPIs.

	Hourly base load		Peak hourly demand		Peak time		Daily total
	(Wh/m^2)		(Wh/m^2)		(Hour)		(Wh/m^2)
Zone	Median	IQR	Median	IQR	Median	IQR	Median	IQR
1.1 Data	3.5	0.8	6.8	1.9	15	2	108	27
1.1 Model	3.4	0.9	6.6	2.3	14	3	113	35
2.4 Data	4.2	0.7	7.9	1.8	15	2	132	24
2.4 Model	4.0	1.0	7.6	2.6	14	3	133	35
4.5 Data	2.3	0.3	7.2	1.6	13	3	95	13
4.5 Model	2.1	1.3	6.6	2.4	13	2	98	39
3.5 Data	3.5	0.9	7.1	2.1	14	3	117	32
3.5 Model	3.3	1.1	7.0	2.7	14	3	116	35
1.7 Data	1.8	1.2	2.8	1.1	14	4	51	30
1.7 Model	1.7	0.6	2.8	0.9	14	7	53	14
4.8 Data	2.5	0.3	6.0	1.1	14	2	89	10
4.8 Model	2.3	0.9	5.8	2.2	14	4	90	31
3.2 Data	3.7	1.2	7.3	6.9	13	4	116	58
3.2 Model	3.6	2.9	7.7	3.5	11	12	128	76
4.23 Data	10.4	2.3	12.0	2.9	15	6	276	60
4.23 Model	10.2	1.2	12.0	1.7	11	12	265	41
4.17 Data	1.5	1.2	5.8	4.4	12	5	66	35
4.17 Model	1.4	1.1	5.4	2.7	14	3	71	35
4.24 Data	9.1	0.0	90.8	27.2	10	4	872	309
4.24 Model	16.3	19.4	92.9	62.9	14	5	1157	863

Figure 15. Lighting: sample weekly data calculated with a mean base load of 3 Wh/m² and a mean load range of 8 Wh/m², variability from 1 (top) to 5 (bottom). The data are calculated for 2019 and start on a Tuesday. Black dotted lines show the individual weekly demand profiles and the mean and 90% CL are highlighted in red.

Table 4. Test zone information: base load and load range from the test data compared against the mean values for zones with similar activity in the training data set and the NCM activity database values. (Building Research Establishment 2016).

			Monitored		Mean activity		NCM
		Variabi	Base	Load	Base	Load	Base	Load
Zone	Activity	lity	Load	Range	Load	Range	Load	Range
1.1	Office	2	1.2	9.5	0.9	8.8	0.0	6.7
2.4	Office	1	0.3	4.0	0.9	8.8	0.0	6.7
3.11	Office	3	2.7	6.1	0.9	8.8	0.0	6.7
4.5	Office	3	1.1	12.4	0.9	8.8	0.0	6.7
1.7	Classroom	4	1.7	4.7	0.7	7.9	0.0	5.0
4.8	Circulation	4	0.7	6.3	1.0	7.1	0.0	1.7
4.17	Lecture Theatre	4	0.3	11.1	0.8	5.6	0.0	5.0
4.38	Laboratory	3	0.4	4.1	1.3	4.3	0.0	13.3
4.39	Kitchen	5	0.4	9.7	–	–	0.0	8.3

Figure 16. Lighting: model outputs for 9 test zones calculated using known mean base load and load range and assumed variability as given in Table 4. The monitored data are shown as black dotted lines with the mean and 90% CL highlighted in red. The model output 90% CL is shown coloured according to the variability selected (Figure 11).

Figure 17. Lighting: comparison of KPIs for model outputs for 9 test zones calculated using known mean base load and load range and assumed variability as given in Table 4.

Table 5. Lighting: numerical comparison of KPIs for model outputs for 9 test zones calculated using known mean base load and load range and assumed variability as given in Table 4.

	Hourly base load		Peak hourly demand		Peak time		Daily total
	(Wh/m^2)		(Wh/m^2)		(Hour)		(Wh/m^2)
Zone	Median	IQR	Median	IQR	Median	IQR	Median	IQR
1.1 Data	1.2	0.0	10.7	1.9	17	2	119	17
1.1 Model	1.4	3.3	10.2	3.3	16	2	117	39
2.4 Data	0.3	0.0	4.3	0.4	15	4	57	8.2
2.4 Model	0.6	1.3	4.0	1.3	14	4	55	20
3.11 Data	2.7	0.7	8.8	1.3	14	3	134	18
3.11 Model	2.7	3.5	7.9	3.5	13	5	128	55
4.5 Data	1.1	0.3	13.5	1.6	15	6	190	20
4.5 Model	2.5	7.4	13.8	7.4	13	5	200	131
1.7 Data	1.7	0.1	6.4	3.3	18	4	74	29
1.7 Model	1.6	2.8	5.2	2.8	13	5	73	39
4.8 Data	0.7	1.0	7.0	1.0	17	6	109	13
4.8 Model	1.1	3.9	6.0	3.9	13	5	74	52
4.17 Data	0.3	0.1	11.4	5.7	13	7	74	82
4.17 Model	0.9	4.3	11.2	4.3	16	3	121	45
4.38 Data	0.4	0.4	4.5	3.0	13	4	45	30
4.38 Model	0.9	2.4	4.2	2.4	13	4	63	32
4.39 Data	0.4	1.7	10.1	3.7	19	7	133	59
4.39 Model	4.6	5.8	12.5	5.8	13	8	213	119

Figure 18. Lighting: Zone 1.7 with X1 and X3 scores shifted by −2. The monitored data are shown as black dotted lines with the mean and 90% CL highlighted in red. The model output 90% CL is shown in blue.

Figure 19. Lighting: Zone 4.8 with X1 and X3 scores shifted, limits imposed. The monitored data are shown as black dotted lines with the mean and 90%CL highlighted in red. The model output 90% CL is shown in blue.

Figure 20. Retrofit model results for lighting Zone 1.7. In the left plot the monitored data are shown in black with the mean and 90% CL highlighted in red; the mean and 90% CL of the simulation results are shown in blue. The box plots show the KPI comparison.

Figure A1. Procedure for generation of sample plug loads; the procedure for lighting is the same except there are 5 clusters instead of 4.

Figure A2. Procedure for generation of stochastic sample loads from existing data.

Building Research Establishment. 2016. National Calculation Methodology (NCM) Modelling Guide (for buildings other than dwellings in England). Technical Report.

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