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Overview of heat technology literature
If the goal is to compare technologies some characteristics might be omitted if they are the same for all technologies..
TODOS: build "kind of modelling categories" grouped by technology e.g. "constant efficiency, varying efficiency, ..." if literature review is finished!
| Source | Comments |
|---|---|
| 11 | Literature survey shows approaches of piecewise linear (PWL) formulations for different power plants |
| 4 | MILP compromise between accuracy and runtime. A constant fuel block occurs if the unit is turned on to minimum load and a linear part increases fuel consumption between min and max load: "Eine elegante Methode unterteilt den Brennstoffeinsatz in einen leistungsunabhängigen Grundumsatz und einen leistungsbezogenen Anteil /IFE 03 05/. Bei steigender Leistung schwindet der spezifische Einfluss des Grundumsatzes" |
| Source | Comments |
|---|---|
| 21 | "As transient operational conditions are critical for short operating periods, and technical considerations suggest for real-world operation to minimise the number of unit starts and stops, a constraint is furthermore introduced by which a unit (excluding boiler and thermal storages) is only allowed to operate at full capacity or not at all within each hour of operation. Under this constraint it is assumed that the use of steady-state operational parameters, such as constant conversion efficiencies, is reasonable." |
| 4 | Shows general formulation for different plant types |
| Source | Comments |
|---|---|
| 2 | General formulation and assumptions for extraction and back-pressure turbines |
| 4 | Shows general formulation for different plant types |
| Source | Comments |
|---|---|
| 1 | "Due to the dependency of the feed flow temperature on the ambient temperature and the implementation of a complete forecast for the ambient temperature, the temperature in the district heating network for every time interval is calculated during pre-processing for the entire planning period and thus is a parameter." |
| 2 | Foundation of 1 that has been published in Energy. Far more detailed but only available in German. "Die Zeitreihen der Strompreise bestehen aus historischen Daten des Day-Ahead-Spotmarkts der Leipziger Strombörse EEX, während die Wärmenachfrage aus dem skalierten synthetischen Lastgang des Berliner Fernwärmenetzes der Vattenfall Europe Wärme AG und der Wahl einer maximal auftretenden Wärmelast von 600 MW und einer Jahreswärmearbeit von 1.674 GWh zusammengesetzt wurde. Mit Hilfe von Durchschnittswerten der Außentemperatur und einer typischen Heizkurve, die ab einer Außentemperatur von unter 12 °C eine Vorlauftemperatur von 120 °C, bei einer Außentemperatur von über 12 °C eine Vorlauftemperatur von 80 °C vorsieht und dazwischen linear verläuft, wird die Vorlauftemperatur für jeden Zeitschritt berechnet. Hierbei ist darauf zu achten, dass die Wärmelast und die aus Heizkurve und Außentemperatur resultierende Vorlauftemperatur im Hinblick auf Gl. 7 aufeinander abgestimmt sind." |
| 3 | Not explained in detail but load directly related to the ambient temperature |
| 4 | Simple forecasting approach by including the ambient temperature and a "residual" social component |
| 9 | Classical thermal balance and load from simple forecasting approach |
| 8 | "Die im Fernwärmenetz erforderliche Vorlauftemperatur ist abhängig von der Umgebungstemperatur". Vorlauf und Rücklauftemperatur sind bekannt und somit kann durch das Delta zusammen mit c_p und dem Sollwärmebedarf der benötigte Massenstrom berechnet werden. |
| Source | Comments |
|---|---|
| 7 | "The district heating pipelines are modeled by mass balances for each node [...] and by diameter restrictions." |
| Source | Comments |
|---|---|
| 1 | 110 °C max. temperature with additional boilers if the feed flow temperature needs to be higher |
| 2 | To be evaluated! |
| 3 | Very simple and possibly not correct since the capacity is given through a heat storage volume V in MWh/h. It would normally refer to an amount of energy and this would imply that the heat exchangers can (un)fill the storage in one timestep. Is this realistic? |
| 9 | Classical storage balance including losses per time increment |
| 8 | Storage balance with mass flows and temperatures, filling level depending losses per time increment. Approach is based on the feed mass flow but could be transferred to an exergetic approach. |
| 7 | Modelling based on 8 |
| 18 | Simple "generic" storage equation as in 4 that is often used for electrical storages |
| 21 | "Sh is equal to the storage content in the previous time interval minus the storage loss Slh plus net production to the storage where the empty storage loss rate sleh is added to the differential storage loss rate sldh multiplied by the filled share of the storage. The differential storage loss rate is the full storage loss rate minus the empty storage loss rate." |
| 16 | Simple balance: "The heat content of the accumulator is restricted up by the capacity of the accumulator and down by a limit that is applied for safety reasons (23). Furthermore there is an upper limit of the heat that flows into and out of the accumulator (24)." |
| 23 | Simple balance as in 16 |
| Source | Comments |
|---|---|
| 3 | Simple approach Q_boiler=Q_fuel/eta_boiler with an operating range based on binary operational variables |
| 9 | Only load range without efficiency |
| 10 | Load range with linear fuel consumption |
| 7 | "The boiler is modeled by a constant thermal efficiency of 95%, coupling heat output and fuel consumption, and an upper load limit to be optimized." |
| 15 | Detailed modelling based on mass flows with non-linear piecewise approximated fuel consumption |
| 16 | Simple approach Q_boiler=Q_fuel/eta_boiler with an operating range based on binary operational variables |
| 23 | Simple approach as in 16 |
According to different people I have talked to, (electrical) heating rods can be represented like peak load boilers with a constant efficiency and an optional load range.
Not literature found! It might be interesting to get some characteristics from the Stadtwerke Flensburg or other industry partners and have a look at it. This might add some value to publications if it differs from the simple approach described above.
| Source | Comments |
|---|---|
| 19 | Via COP as presented in 20: "The working domains of a model of a compression heat pump using different fluids and a model of a compression-absorption heat pump using water-ammonia mixtures are defined, plotted and discussed. These domains are defined by means of limiting values for their electrical coefficient of performance, volumetric heating capacity, and low and high pressure." |
| 22 | "Um den benötigten Strombedarf der Wärmepumpen vorhersagen zu können, muss die Leistungszahl bestimmt werden, mit der Strom in Wärme umgewandelt wird. Da die Leistungszahl abhängig von der variablen Wärmequellen- und Wärmesenkentemperatur ist, wird diese zunächst für jede Stunde des Jahres berechnet. Verschiedene Wärmequellen können im Modell durch Vorgabe des jeweiligen Temperaturverlaufs berücksichtigt werden. Zudem können die Wärmepumpen monovalent oder monoenergetisch, d.h. mit Heizungsunterstützung durch den selben Energieträger, betrieben werden." |
| 21 | Pre-calculated COP: "The fuel-to-energy conversion factors in Eq. (3) will use the HP unit’s COP." |
| 16 | Pre-calculated COP and min/max Q_out using binary variables |
| 24 | MILP representation with performance curves approximated using piecewise linear functions |
| 25 | Constant COP that is varied in calculation. Paper is not focused on optimization but on a general modelling approach for heat pumps in combination with CHP systems. "For the sake of simplicity, it is assumed that the EHP COP is independent of a Q , although in general it might change in dependence on the energy input according to off-design characteristics relevant to the specific machine [32]. However, this approximation does not affect the general validity of the models developed above, and more detailed studies could be run for specific cases." |
| 26 | Pre-calculated vs constant COP (to be discussed if this is formally correct). Result: "No significant impact was found when comparing fixed and varying operation characteristics of the HP." Approach: "We have further developed a more detailed description of heat pumps in the Balmorel model that capture the variation in COP over time. Equations (1) and (2) present the fuel consumption rate equations utilised in Balmorel. The addition to the standard Balmorel model, is that we use generation efficiencies, h , that depend on the network and ambient temperatures and thus vary over time, h g,t ." |
| Source | Comments |
|---|---|
| 13 | "There are situations where the convexity of a power plant cannot be assumed. If the marginal efficiency of the power plant is an increasing function of p or q, this results in a non-convex characteristic. It is also possible that the operating area in the (p, q) plane is non-convex. These situations are common with advanced production techniques, such as in backpressure plants with condensing and auxiliary cooling options, in gas turbines, and in combined gas and steam cycles." |
| 14 | Generic modelling approach with operational PQ-region for steam power plants (back-pressure and extraction) and combined cycle power plants based on a few plant characteristics. Comparison to dynamic modelling and discussion of shortcomings. Detailed explanation for different plant setups! |
| Source | Comments |
|---|---|
| 2 | Detailed and specific description. Only available in German. |
| 3 | Via fixed power a to heat ratio with fuel dependend operational costs P_t * C_fuel and costs at P_min if turned on |
| 4 | Via fixed power a to heat ratio with fuel dependend operational costs P_t * C_fuel and costs at P_min if turned on |
| 8 | Via fixed power a to heat ratio with costs linearly depending on the power and heat production |
| 14 | Generic modelling approach with operational PQ-region for steam power plants (back-pressure and extraction) and combined cycle power plants based on a few plant characteristics. Comparison to dynamic modelling and discussion of shortcomings. Detailed explanation for different plant setups! |
| 15 | Detailed modelling based on mass flows with non-linear piecewise approximated fuel consumption |
| 16 | Operational one segment PQ-region |
| 19 | Operational one segment PQ-region: "With this type of formulation, it is possible to include more than one unit type using in the same set of equations. In the case of a back-pressure CHP-plant, b can be fixed to 0. Similar, in the case of a separate electricity production plant, the electricity efficiency and total efficiency are equal, while b is fixed to 0." |
| Source | Comments |
|---|---|
| 1 | Operational one segment PQ-region |
| 2 | Operational one segment PQ-region. Only available in German. |
| 3 | Operational one segment PQ-region |
| 11 | Operational one segment PQ-region as in 1 and 2 and two segment PQ-region: "[...] it is mentioned that the irregular quadrilateral shape is suitable for modeling any cogeneration system, and the most appropriate for gas turbine systems. Also, it is indicated that the feasible two-segment model does not offer considerable advantages compared to the feasible simple one." Additional approach with PQ-region based on min/max power to heat ratio. |
| 12 | Operational PQ-region as in 1,2 and 11. |
| 14 | Generic modelling approach with operational PQ-region for steam power plants (back-pressure and extraction) and combined cycle power plants based on a few plant characteristics. Comparison to dynamic modelling and discussion of shortcomings. Detailed explanation for different plant setups! |
| 15 | Detailed modelling based on mass flows with non-linear piecewise approximated fuel consumption |
| 16 | Operational one segment PQ-region |
| 17 | Similar as back-pressure turbines via PQ-region |
| 19 | Operational one segment PQ-region: "With this type of formulation, it is possible to include more than one unit type using in the same set of equations. In the case of a back-pressure CHP-plant, b can be fixed to 0. Similar, in the case of a separate electricity production plant, the electricity efficiency and total efficiency are equal, while b is fixed to 0." |
| Source | Comments |
|---|---|
| 5 | Simple approach with a semi-continous power variable (P_el=P_min*y+P_part) and a similar formulation for the linear fuel consumption/costs (one segment linearisation) and a fixed heat-to-power ratio |
| 9 | Fixed heat-to-power ratio and load range |
| 7 | Fixed heat-to-power ratio and load range |
| 11 | Operational one segment PQ-region as in 1 and 2 and two segment PQ-region: "[...] it is mentioned that the irregular quadrilateral shape is suitable for modeling any cogeneration system, and the most appropriate for gas turbine systems. Also, it is indicated that the feasible two-segment model does not offer considerable advantages compared to the feasible simple one." Additional approach with PQ-region based on min/max power to heat ratio. |
| 12 | Operational one segment PQ-region as in 1,2 and 11. |
| 16 | Operational one segment PQ-region |
| Source | Comments |
|---|---|
| 3 | Via power a to heat ration with fuel dependend operational costs P_t * C_fuel and costs at P_min if turned on |
| 11 | Operational one segment PQ-region as in 1 and 2 and two segment PQ-region: "[...] it is mentioned that the irregular quadrilateral shape is suitable for modeling any cogeneration system, and the most appropriate for gas turbine systems. Also, it is indicated that the feasible two-segment model does not offer considerable advantages compared to the feasible simple one." Additional approach with PQ-region based on min/max power to heat ratio. |
| 12 | Operational one segment PQ-region as in 1,2 and 11. |
| 13 | "There are situations where the convexity of a power plant cannot be assumed. If the marginal efficiency of the power plant is an increasing function of p or q, this results in a non-convex characteristic. It is also possible that the operating area in the (p, q) plane is non-convex. These situations are common with advanced production techniques, such as in backpressure plants with condensing and auxiliary cooling options, in gas turbines, and in combined gas and steam cycles." |
| 16 | Similar as back-pressure turbines via PQ-region |
| 17 | Similar as back-pressure turbines via PQ-region |
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