Data series · Chapter 10

Scenario 2 — Heating with PT1 behaviour

Step to 150 kW heating power, time constant 12 s. Reaches 63.3 % at t = τ and 95.1 % at 3τ; mean deviation from the analytical solution 0.040 %.

Scenario: 2 Heating
Expectation (criterion): heating rate 0.0814 K/s; PT1 63.2 % at τ, 95.0 % at 3τ
Measurement: 63.3 % at τ, 95.1 % at 3τ; mean deviation 0.040 % of maximum power
Result: passed
Rows: 6,000
Time range: 0.05–300.00 s
Time step: Δt = 0.05 s
Columns: 9

Download CSV To the chapter: Chapter 10 — Five test scenarios

Chart
Columns
Statistics
Values
Source and citation

Time series

Each quantity has its own axis and unit in its own panel; all share the time axis. The sensor bits appear as step lines. Clicking the legend shows or hides a quantity.

Time series of the measurement

Building the chart …

Quantities (click to show or hide)

Controls: ← → move cursor (with ⇧ ten times) · Pos1 Ende to the edge · + − zoom · Bild↑ Bild↓ pan · 0 full series · Esc remove cursor. Drag a region with the mouse to zoom in. Values at the cursor belong to the nearest plotted data point; when zoomed far out the chart shows the minimum and maximum per pixel bucket so that single peaks stay visible. Exact values: zoom in or use the tables.

The interactive chart needs JavaScript. Instead, a sample of the series (twelve evenly spaced rows); all values are in the table further below and in the CSV.

Sample of the series
No.	Zeit (s)	Füllstand (l)	Temperatur (°C)	Druck (bar)	Heizleistung (W)	B1 Füllstand max
1	0.05	450.05	16.131	0.0072	625.0	1
546	27.3	450.05	17.48	0.0	134653.6	1
1,092	54.6	450.05	19.612	0.0	148429.9	1
1,637	81.85	450.05	21.82	0.0	149838.7	1
2,182	109.1	450.05	24.036	0.0	149983.4	1
2,728	136.4	450.05	26.257	0.0	149998.3	1
3,273	163.65	450.05	28.474	0.0	149999.8	1
3,819	190.95	450.05	30.695	0.0	150000.0	1
4,364	218.2	450.05	32.913	0.0	150000.0	1
4,909	245.45	450.05	35.13	0.0	150000.0	1
5,455	272.75	450.05	37.351	0.0	150000.0	1
6,000	300.0	450.05	39.568	0.0	150000.0	1

Column description

Name and unit come from the header row of the CSV file; the meaning follows the heated-tank model (chapter 8) and the recording (chapter 10).

Columns of the series — Scenario 2 — Heating with PT1 behaviour

No.	Column (CSV header)	Unit	Type	Meaning
1	Zeit (s)	s	Time axis	Time stamp of the row (model time); one row per calculation step of Δt = 0.05 s.
2	Füllstand (l)	l	Process variable	Water level in the tank (tank volume 0.5 m³ = 500 l).
3	Temperatur (°C)	°C	Process variable	Water temperature, calculated from energy and water mass.
4	Druck (bar)	bar	Process variable	Pressure in the head space (steam and air, partial pressures added).
5	Heizleistung (W)	W	Process variable	Currently effective heating power (PT1 lag, τ = 12 s, up to 150 kW).
6	B1 Füllstand max	—	Sensor bit (0/1)	Upper level sensor: 1 from 450 l, otherwise 0.
7	B2 Füllstand min	—	Sensor bit (0/1)	Lower level sensor: 1 at 50 l or less, otherwise 0.
8	B3 Temperatur ≥95 °C	—	Sensor bit (0/1)	Temperature sensor: 1 from 95 °C, otherwise 0.
9	B4 Druck ≥2,8 bar	—	Sensor bit (0/1)	Pressure sensor: 1 from 2.8 bar, otherwise 0.

Statistics of the series

All figures are computed from the rows of the CSV file (over the whole series, without smoothing) and describe this single run only. They make no statement about a real tank.

6,000Rows (calculation steps)

300.00stime covered

0.05sTime step Δt

8recorded quantities

Statistics per process variable — Scenario 2 — Heating with PT1 behaviour

Quantity	Unit	Count	Minimum	Maximum	Mean	First value	Last value
Füllstand	l	6,000	450.05constant	450.05	450.050	450.05	450.05
Temperatur	°C	6,000	16.131t = 0.05 s	39.568t = 300.00 s	27.4043	16.131	39.568
Druck	bar	6,000	0.0000t = 0.30 s	0.0072t = 0.05 s	0.0000	0.0072	0.0000
Heizleistung	W	6,000	625.0t = 0.05 s	150,000.0t = 178.60 s	144,025.00	625.0	150,000.0

Below each extreme value is the time of the first row with that value. The mean is the simple mean over all rows (equal time steps).

Sensor bits: switching times — Scenario 2 — Heating with PT1 behaviour

Sensor bit	Rows with 1	Share	first 1 at	then 0 again at
B1 Füllstand max	6,000	100.000 %	0.05 sfirst row	—
B2 Füllstand min	0	0.000 %	—	—
B3 Temperatur ≥95 °C	0	0.000 %	—	—
B4 Druck ≥2,8 bar	0	0.000 %	—	—

1 means the sensor is active (threshold reached), 0 not active (chapter 8). “Changes” counts the rows in which the value differs from the previous row.

Values

All rows of the CSV file, unchanged, 100 rows per page. Search and sorting run on the server; you can jump to a row or a time. “No.” is a running row number and not part of the CSV.

3,001–3,100 of 6,000 rows Download CSV

Values — Scenario 2 — Heating with PT1 behaviour

No.	Zeit (s)	Füllstand (l)	Temperatur (°C)	Heizleistung (W)	B1 Füllstand max
3,001	150.05	450.05	27.368	149999.5	1
3,002	150.1	450.05	27.372	149999.5	1
3,003	150.15	450.05	27.376	149999.5	1
3,004	150.2	450.05	27.38	149999.5	1
3,005	150.25	450.05	27.384	149999.5	1
3,006	150.3	450.05	27.388	149999.5	1
3,007	150.35	450.05	27.392	149999.5	1
3,008	150.4	450.05	27.396	149999.5	1
3,009	150.45	450.05	27.4	149999.5	1
3,010	150.5	450.05	27.404	149999.5	1
3,011	150.55	450.05	27.408	149999.5	1
3,012	150.6	450.05	27.412	149999.5	1
3,013	150.65	450.05	27.416	149999.5	1
3,014	150.7	450.05	27.421	149999.5	1
3,015	150.75	450.05	27.425	149999.5	1
3,016	150.8	450.05	27.429	149999.5	1
3,017	150.85	450.05	27.433	149999.5	1
3,018	150.9	450.05	27.437	149999.5	1
3,019	150.95	450.05	27.441	149999.5	1
3,020	151.0	450.05	27.445	149999.5	1
3,021	151.05	450.05	27.449	149999.5	1
3,022	151.1	450.05	27.453	149999.5	1
3,023	151.15	450.05	27.457	149999.5	1
3,024	151.2	450.05	27.461	149999.5	1
3,025	151.25	450.05	27.465	149999.5	1
3,026	151.3	450.05	27.469	149999.5	1
3,027	151.35	450.05	27.473	149999.5	1
3,028	151.4	450.05	27.477	149999.5	1
3,029	151.45	450.05	27.482	149999.5	1
3,030	151.5	450.05	27.486	149999.5	1
3,031	151.55	450.05	27.49	149999.5	1
3,032	151.6	450.05	27.494	149999.5	1
3,033	151.65	450.05	27.498	149999.5	1
3,034	151.7	450.05	27.502	149999.5	1
3,035	151.75	450.05	27.506	149999.5	1
3,036	151.8	450.05	27.51	149999.5	1
3,037	151.85	450.05	27.514	149999.5	1
3,038	151.9	450.05	27.518	149999.5	1
3,039	151.95	450.05	27.522	149999.5	1
3,040	152.0	450.05	27.526	149999.5	1
3,041	152.05	450.05	27.53	149999.5	1
3,042	152.1	450.05	27.534	149999.5	1
3,043	152.15	450.05	27.538	149999.5	1
3,044	152.2	450.05	27.543	149999.5	1
3,045	152.25	450.05	27.547	149999.5	1
3,046	152.3	450.05	27.551	149999.6	1
3,047	152.35	450.05	27.555	149999.6	1
3,048	152.4	450.05	27.559	149999.6	1
3,049	152.45	450.05	27.563	149999.6	1
3,050	152.5	450.05	27.567	149999.6	1
3,051	152.55	450.05	27.571	149999.6	1
3,052	152.6	450.05	27.575	149999.6	1
3,053	152.65	450.05	27.579	149999.6	1
3,054	152.7	450.05	27.583	149999.6	1
3,055	152.75	450.05	27.587	149999.6	1
3,056	152.8	450.05	27.591	149999.6	1
3,057	152.85	450.05	27.595	149999.6	1
3,058	152.9	450.05	27.6	149999.6	1
3,059	152.95	450.05	27.604	149999.6	1
3,060	153.0	450.05	27.608	149999.6	1
3,061	153.05	450.05	27.612	149999.6	1
3,062	153.1	450.05	27.616	149999.6	1
3,063	153.15	450.05	27.62	149999.6	1
3,064	153.2	450.05	27.624	149999.6	1
3,065	153.25	450.05	27.628	149999.6	1
3,066	153.3	450.05	27.632	149999.6	1
3,067	153.35	450.05	27.636	149999.6	1
3,068	153.4	450.05	27.64	149999.6	1
3,069	153.45	450.05	27.644	149999.6	1
3,070	153.5	450.05	27.648	149999.6	1
3,071	153.55	450.05	27.652	149999.6	1
3,072	153.6	450.05	27.656	149999.6	1
3,073	153.65	450.05	27.661	149999.6	1
3,074	153.7	450.05	27.665	149999.6	1
3,075	153.75	450.05	27.669	149999.6	1
3,076	153.8	450.05	27.673	149999.6	1
3,077	153.85	450.05	27.677	149999.6	1
3,078	153.9	450.05	27.681	149999.6	1
3,079	153.95	450.05	27.685	149999.6	1
3,080	154.0	450.05	27.689	149999.6	1
3,081	154.05	450.05	27.693	149999.6	1
3,082	154.1	450.05	27.697	149999.6	1
3,083	154.15	450.05	27.701	149999.6	1
3,084	154.2	450.05	27.705	149999.6	1
3,085	154.25	450.05	27.709	149999.6	1
3,086	154.3	450.05	27.713	149999.6	1
3,087	154.35	450.05	27.717	149999.6	1
3,088	154.4	450.05	27.722	149999.6	1
3,089	154.45	450.05	27.726	149999.6	1
3,090	154.5	450.05	27.73	149999.6	1
3,091	154.55	450.05	27.734	149999.6	1
3,092	154.6	450.05	27.738	149999.6	1
3,093	154.65	450.05	27.742	149999.6	1
3,094	154.7	450.05	27.746	149999.6	1
3,095	154.75	450.05	27.75	149999.6	1
3,096	154.8	450.05	27.754	149999.6	1
3,097	154.85	450.05	27.758	149999.6	1
3,098	154.9	450.05	27.762	149999.6	1
3,099	154.95	450.05	27.766	149999.6	1
3,100	155.0	450.05	27.77	149999.6	1

Source and citation

Data source: Own measurement series, recorded on the model function compute_step (step size Δt = 0.05 s) according to the test log of the bachelor thesis (2026); set-up and evaluation see Chapter 10 — Five test scenarios.

How to cite

Kotsch, A. H. (2026): Dataset „Scenario 2 — Heating with PT1 behaviour“ (6,000 rows, time 0.05–300.00 s). Supplement to the bachelor thesis „Digital twins for PLC-coupled laboratory systems“, Duale Hochschule Sachsen — Studienakademie Glauchau. https://thesis.kotsch.tech/daten/szenario-2-heizen (accessed 2026-09-30).

Limits of this data

Classification (chapter 10): The deviations are compatible with the discretisation error of the Euler method.
Limit: The expectation uses the same parameters (τ = 12 s, 150 kW); what is tested is the implementation of the equations, not their agreement with a real heating element.
The expected values come from hand calculation and the analytical solution with the parameters of the model; agreement shows the correct implementation, not the accuracy compared with a real tank. Each scenario covers a single run with fixed boundary conditions. (Chapter 10)
Without measurement data from a real tank, validation is limited to internal consistency. (Chapter 11)

More datasets

16 rows · 2 columns Key figures of the platform View → 3,000 rows · 9 columns Scenario 1 — Filling View → 25,809 rows · 9 columns Scenario 3 — Pressure build-up and venting View → 2,200 rows · 9 columns Scenario 4 — Draining View → 1,200 rows · 9 columns Scenario 5 — Edge case: empty tank View → 5 rows · 4 columns Five test scenarios — expectation versus measurement View →