Controller, compressor device with such controller and method for controlling a compressor device
By employing mathematical models and control algorithms in the compressor equipment to optimize liquid flow and compressor speed, the problem of mismatch between heat demand and heat recovery system is solved, achieving the effects of reducing total operating costs and improving heat recovery efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ATLAS COPCO AIRPOWER NV
- Filing Date
- 2025-04-24
- Publication Date
- 2026-05-29
AI Technical Summary
Existing compressor equipment in heat recovery systems fails to effectively consider changes in the temperature demand of the heat pipeline network, resulting in a mismatch between heat demand and the operating costs and energy consumption of users or customers.
By employing mathematical models and control algorithms, combined with compressor units and heat recovery systems, and through model predictive control or artificial intelligence, liquid flow and compressor speed are optimized to achieve precise control of the temperature and compressed gas pressure range of the heat pipeline network, thereby reducing total operating costs.
By optimizing control, the total operating cost was reduced to the minimum, the use of the heat production unit was saved, the total system operating cost was reduced by 10%, and the heat recovery efficiency was improved.
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Figure CN122106870A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a compressor device having a heat recovery system, comprising: a compressor unit that supplies compressed gas to a pressure network; and a heat recovery system that recovers heat from the compressor unit and provides the recovered heat to a heat application or a heat network, the heat network optionally including a heat production unit.
[0002] A heat network is, for example, a heating system or a domestic hot water system, that is, any system that uses heat to heat spaces, fluids, etc., and can be interpreted broadly. A heat production unit is, for example, a gas boiler or a heat pump. A pressure network is a network for consumers of compressed gas, and should also be interpreted broadly. A heat recovery system is a system with pumps, valves, and one or more heat exchangers that uses liquid to extract heat from a compressor unit and supply it to the heat network.
[0003] More specifically, the present invention aims to provide a method for controlling such compressor equipment to reduce the overall operating costs of the compressor equipment and the heat network that receives heat from the heat recovery system of the compressor equipment. Background Technology
[0004] As is well known, compressors generate heat when compressing gases.
[0005] It is also known that there are compressor devices that include a heat recovery system that recovers at least a portion of the heat generated during compression.
[0006] The compressor equipment is equipped with a cooling circuit containing a coolant (such as water), or the compressor equipment is equipped with an oil circuit containing oil.
[0007] The liquid (oil or water) is used to cool the compressor unit of the compressor equipment, and then the liquid is cooled to a lower temperature and returned to the compressor unit.
[0008] To cool liquids, a heat recovery system can be used, which recovers heat and provides it to other systems where the heat can be used in a usable manner, rather than simply dissipating it.
[0009] Traditionally, in known compressor equipment, the compressor unit is controlled to provide the required flow of compressed gas at the desired pressure, thereby ensuring that the compressor's electrical power consumption is as low as possible.
[0010] On the other hand, the heat recovery system will be controlled to ensure that the liquid in the cooling circuit is cooled to a fixed temperature before it returns, or the temperature of the liquid in the cooling circuit will be adjusted so that the temperature of the liquid leaving the compressor unit is within a specific range.
[0011] However, this does not take into account the heat demand of the heating network.
[0012] In fact, the temperature requirements and heat demands of users or customers in a heat pipe network usually change over time.
[0013] If the actual temperature of the liquid discharged from the heat recovery system is too low, i.e. lower than the user's or customer's needs, then the heat is useless to the user or customer.
[0014] If the actual temperature of the heat recovery system is too high, heat recovery will be reduced. If less heat is removed during compression, this will naturally lead to lower gas compression efficiency and higher specific energy requirements.
[0015] If heat demand is high and the heat recovery system is unable to provide the necessary heat at the correct temperature, the operating costs of the user's or customer's heat network will be higher because a heat production unit will have to be used to provide the required heat. Summary of the Invention
[0016] Therefore, the object of the present invention is to provide a solution to one or more of the above-mentioned disadvantages, as well as other disadvantages.
[0017] Therefore, the present invention provides a method for controlling a compressor device having a heat recovery system, the compressor device comprising: a compressor unit that supplies compressed gas to a pressure network; and a heat recovery system that recovers heat from the compressor unit and provides the recovered heat to a heat network, characterized in that the method comprises the following steps:
[0018] - Provide mathematical models for compressor units and heat recovery systems;
[0019] - Provides electricity costs, as well as optional gas costs and / or heating costs for the heat pipe network;
[0020] - Provides the desired pressure range for compressed gas and the desired temperature range for the heat pipe network;
[0021] - Provides control algorithms for controlling the speed of the compressor unit and the flow rate of liquid in the heat recovery system;
[0022] This method enables the control algorithm to use mathematical methods to determine the control sequence of liquid flow rate and compressor speed in the heat recovery system, thereby enabling the delivery of the desired temperature range of the heat network and the desired pressure range of the compressed gas, taking into account electricity costs and heating costs of the heat network, and minimizing total operating costs.
[0023] By using the provided mathematical model, the flow rate of the liquid in the heat recovery system, as well as the appropriate control of the machine status and speed of the compressor unit, will be determined. The machine status may be, for example, stopped or idling.
[0024] These mathematical models can be physics-based models or data-based models.
[0025] Total operating costs are determined by total energy costs, which include the electricity costs for driving the compressor unit and the thermal savings achieved by using heat recovery systems through heat recovery systems (instead of using heat production units), as well as the increased maintenance costs due to operation at higher temperatures.
[0026] "Thermal savings" refers to the savings in gas or electricity due to the elimination of thermal production units.
[0027] The advantage is that this combined control of the compressor unit and the heat recovery system can minimize total operating costs, not just the energy cost of the compressor.
[0028] This will result in a reduction in the overall operating costs for users or customers, with additional savings of up to 10% compared to known methods or when only the compressed air network or heating network is optimized (without considering the correlation between the two networks).
[0029] Surprisingly, compared to known methods, the method according to the invention can result in higher energy consumption of the compressor unit, thereby improving heat recovery, providing more heat to the heat network, eliminating the use of the heat production unit, and thus reducing the total operating cost of the system.
[0030] The control algorithm preferably uses model predictive control or artificial intelligence-based control algorithms.
[0031] This will allow for minimizing total power consumption and altering control inputs based on mathematical models (also known as digital twins) of different components of the compressor equipment and related systems.
[0032] According to a preferred embodiment, the step of providing the electricity price and, optionally, the gas price and / or the heating cost of the heat network is performed by the user of the compressor equipment or the user system.
[0033] Real-time energy pricing should be interpreted as including not only the energy cost itself, but also taxes, distribution, and / or transportation costs. Furthermore, real-time energy pricing includes not only standard real-time prices, but also variable prices and dynamic prices related to different markets: day-ahead, intraday, imbalance, ancillary service incentives, competency-based compensation mechanisms, etc.
[0034] For example, such a user system could be a user program or similar program that is coupled to a control algorithm to provide such input.
[0035] Of course, this can be done without the user's intervention, but this method ensures that the system receives the latest and most relevant information.
[0036] The heating cost of the aforementioned heat pipe network is typically temperature-dependent. This can be covered by a mathematical model that includes heat production units.
[0037] According to a preferred feature of the invention, the water flow rate of the heat recovery system is controlled by controlling one or more valves and / or pumps in the heat recovery system, and / or the speed of the compressor unit is controlled by controlling the driver of the compressor unit.
[0038] Specifically, the control algorithm will control the water flow rate of the heat recovery system between the minimum and maximum flow rates, and / or control the machine state and speed of the compressor unit to keep it at zero speed or between the minimum and maximum speeds.
[0039] The present invention also relates to a controller configured with a control algorithm to execute the method according to the present invention.
[0040] The present invention also relates to a compressor device having a heat recovery system, comprising: at least one compressor unit that supplies compressed gas to a pressure network; and a heat recovery system that recovers heat from the compressor unit and supplies the recovered heat to a heat network, the heat network optionally including a heat production unit characterized in that it is equipped with a controller according to the present invention.
[0041] Clearly, the advantages of this controller and compressor equipment are the same as those of the method described above according to the present invention. Attached Figure Description
[0042] To better illustrate the features of the invention, and without any limitation, an embodiment of a method for controlling a compressor device with a heat recovery system according to the invention, a controller provided with a control algorithm to perform the method, and a preferred embodiment of the compressor device provided with such a controller will be described below with reference to the accompanying drawings, wherein:
[0043] Figure 1 A compressor device according to the present invention is shown schematically;
[0044] Figure 2 The method according to the present invention is illustrated schematically. Detailed Implementation
[0045] Figure 1The compressor equipment 1 shown mainly includes a compressor unit 2 and a heat recovery system 3.
[0046] Although there may be only one compressor unit 2, there may also be more than one compressor unit 2. This can be, for example, in the case of a multi-stage compressor or a compressor room equipped with multiple compressors.
[0047] Compressor unit 2 supplies compressed gas to pressure pipeline network 4.
[0048] In this case, but not necessary for the present invention, the compressor unit 2 is also provided with a pressure vessel 5.
[0049] Pressure network 4 is, for example, a network that includes compressed gas consumers (such as pneumatic tools and devices).
[0050] In addition, the compressor unit 2 is also provided with a drive 6, which can be any type of suitable drive 6, such as an electric motor or similar device, which will regulate the speed of the compressor unit 2.
[0051] In this case, but not necessarily, the compressor unit 2 is an oil-free compressor unit 2, and is equipped with a water cooling system 3', wherein the water cooling system 3' includes a heat recovery system 3.
[0052] Preferably, the water cooling system 3' is at least connected to the heat recovery system 3, but typically the two systems 3', 3 can be combined or at least partially integrated.
[0053] Of course, compressor unit 2 can also be an oil-injected compressor unit, whereby oil is injected for cooling, sealing, and lubrication. In this case, the oil cooling system includes a heat recovery system 3.
[0054] This means that for the heat recovery system 3, the working fluid can be water, oil, or any other cooling fluid used for the cooling system 3'.
[0055] The heat recovery system 3 recovers heat from the compressor unit 2 and provides the recovered heat to the heat network 7, which includes the heat production unit 8.
[0056] The heat recovery system 3 is a network of pipes and valves, which includes a pump 9 that pumps fluid through the heat recovery system 3, and the heat network may also optionally include a heat exchanger 10.
[0057] exist Figure 1 In the example, the heat recovery system 3 includes a heat exchanger 10 and a so-called backup cooler 11, as well as a first pump 9, which provides additional cooling for the water or liquid when the heat exchanger 10 is unable to adequately cool it, and the first pump is used to circulate the water or liquid.
[0058] A bypass 12 with a three-way valve 13 is disposed above the standby cooler 11. However, the invention is not limited thereto.
[0059] Clearly, the heat recovery system 3 can be implemented in many different ways, and additional pumps 9, valves, and pipes can be present.
[0060] According to the invention, the compressor device 1 further includes a controller 14 according to the invention, which is equipped with a control algorithm to execute the method according to the invention, as will be explained later. The controller 14 is connected to the aforementioned drive 6, the first pump 9, and the three-way valve 13.
[0061] The heat network 7 is a network that provides heated or heated water to users, such as a central heating system or a similar system, which includes heat production units 8 (such as gas boilers) and multiple heaters 15 (such as radiators or process heat exchangers).
[0062] exist Figure 1 In the example, the heat network 7 is coupled to the heat recovery system 3 because the working fluid of the heat network 7 flows through the heat exchanger 10 of the heat recovery system 3.
[0063] exist Figure 1 In the example, the heat storage tank 16 is located between the heat recovery system 3 and the heat pipeline 7, but this is not mandatory in the present invention.
[0064] exist Figure 1 In the example, the heat storage tank 16 is part of the heat network 7, and an additional second pump 17 is provided to allow liquid to flow from the heat network 7 through the heat storage tank 16 to the heat recovery system 3, and vice versa. A third pump may be provided between the heat storage tank 16 and the heat network 7.
[0065] The controller 10 is connected to the second pump 17 and the third pump of the thermal storage tank 16.
[0066] It should be noted that the heat network 7 may also include heat pumps or any other production technology to supplement or replace the gas boiler 8.
[0067] In addition, Figure 1 In the example, the compressor unit 2 is provided with a vent valve 18 at the outlet of the pressure vessel to vent the compressed gas.
[0068] According to the method of the present invention, the compressor device 1 is controlled as follows and as... Figure 2 As shown.
[0069] In the first step 19, two prediction algorithms may optionally be provided. The first prediction algorithm 20a is used for the heat and / or temperature demand of the heat network 7, and the second prediction algorithm 20b is used for the compressed gas flow demand of the pressure network 4.
[0070] The first prediction algorithm 20a can, for example, determine future demand for heating or heated sanitary water based on historical data and / or production and / or building occupancy plans.
[0071] These historical data can also include historical and current weather data.
[0072] The second prediction algorithm 20b can, for example, determine future compressed gas flow rate requirements, and (optionally) compressed gas pressure or pressure range requirements, based on historical data and information about the tools present in the pressure network 4.
[0073] According to the present invention, in the second step 21, a mathematical model 22 is provided for the compressor unit 2, the heat recovery system 3 and the heat production unit 8.
[0074] Such mathematical models 22, also known as “digital twins,” will be used to calculate or simulate the effects of changing the operating parameters of the aforementioned compressor unit 2 and / or heat recovery system 3, and / or to calculate or simulate the heating cost of the heat production unit 8 if it will meet the future heat and / or temperature requirements of the heat network 7.
[0075] In this second step 21, mathematical models 22 may also be provided for the heat pipe network 7 and the pressure pipe network 4 themselves, but this is not required by the present invention. Of course, these mathematical models 22 may also be simplified mathematical methods 22, depending on the complexity of the heat pipe network 7 and the pressure pipe network 4, for example.
[0076] exist Figure 1 In the case of compressor equipment 1, the second step 21 may optionally include the step of providing a mathematical model 22 of the heat storage tank 16, and may optionally also include the step of providing a mathematical model 22 of the standby cooler 11.
[0077] Of course, if either or both are not present, this step will not be provided.
[0078] In the third step 23 of the method according to the invention, the electricity cost 24 and optional gas cost and / or heating cost 24 of the heat network 7 are provided.
[0079] This step can be performed by the user of compressor device 1, for example by inputting the aforementioned cost 24 into the aforementioned controller.
[0080] Alternatively, a user system may exist capable of handling this step and inputting the real-time energy price 24 and the heating cost 24 of the heat pipe network 7. Such a user system could be an application or other type of software that provides this information.
[0081] In the fourth step 25 of the method according to the invention, a desired pressure range 26 for the pressure network 4 and a desired temperature range 27 for the heat network 7 are provided.
[0082] This information or data can be entered by the user again, or it can be determined by the two prediction algorithms 20a and 20b mentioned above.
[0083] The desired pressure range 26 is related to the pressure required by the compressed gas users of the pressure network 4, while the desired temperature range 27 of the heat network 7 is related to the heating temperature or the temperature of the heating water that the heat network 7 must provide.
[0084] These values can be fixed over time, but they can also change over time.
[0085] In the fifth step of the method according to the invention, a control algorithm 28 is set to control the speed of the compressor unit 2 and the flow rate of the liquid in the heat recovery system 3.
[0086] In this case (not essential for the present invention), control algorithm 28 is based on model predictive control, which is a method for a control system (in this case, compressor device 1) to simultaneously satisfy a set of constraints or limitations. The advantage of model predictive control is that it allows for the consideration of future predictions by optimizing the control of the system for future forecasts while the current control system is in operation, and for further optimization of the system after a specific control sequence has been achieved. In this way, model predictive control can consider future predictions and anticipate them.
[0087] However, control algorithm 28 can also be based on artificial intelligence or reinforcement learning.
[0088] exist Figure 1 In the current embodiment of the compressor device 1 shown, the speed of the compressor unit 2 is controlled by controlling the driver 6 of the compressor unit.
[0089] In addition, Figure 1 In the current embodiment of the compressor device 1, the water flow rate of the heat recovery system 3 is controlled by controlling the first pump 9 and / or the second pump 17 and / or an optional third pump and / or the three-way valve 13.
[0090] It should be noted that although terms such as "first step" and "second step" are used in the discussion of the above methods, this is not necessarily to indicate the order of the steps, but rather to facilitate the distinction between different steps. Those skilled in the art should understand that the third step 23 described above can be performed first, or simultaneously with the first step 19. Furthermore, those skilled in the art should understand that the third step 23 may require periodic completion and / or periodic updates, while the first step 19 may not require such updates.
[0091] According to the invention, the method (or more specifically, the control algorithm 28) causes the control algorithm 28 to use a mathematical model 22 and optionally based on prediction algorithms 20a, 20b (if available) to determine the control sequence 29 of the liquid flow rate and the speed of the compressor unit 2 in the heat recovery system 3, so that the required temperature range 26 and the required pressure range 27 of the compressed gas can be delivered to the energy recovery system 3.
[0092] The aforementioned control sequence 29 will include, for example, a set of control signals or similar signals sent to the drive 6 and / or the first pump 9 and / or the second pump 17 and / or the three-way valve 13, and will allow for the adjustment or control of the flow rate of the liquid in the heat recovery system 3 and the speed of the compressor unit 2.
[0093] When determining the control sequence 29, the control algorithm 28 will consider the predictions made by two prediction algorithms 20a and 20b for future heating demand or heating of domestic water and compressed gas flow rate demand.
[0094] Furthermore, according to the present invention, the control algorithm 28 will take into account the electricity cost 24 as well as the optional gas cost and / or the heating cost 24 of the heat network 7, in order to minimize the total operating cost.
[0095] For example, if the heating cost of the heat network 7 is relatively high compared to the electricity cost required to drive the compressor unit 2 due to reasons such as high gas prices, it is beneficial to generate more compressed gas so that the heat recovery system 3 can recover more heat for use in the heat network 7, so that the heat production unit 8 (gas boiler) does not need to provide the required heat demand.
[0096] Because the control algorithm 28 takes future demand into account, it will be able to proactively respond to predicted demand, and for example, if the demand for heat and / or temperature in the heat network 7 is expected to be high, a control sequence 29 will be determined that will allow the controller 14 to control the compressor device 1 to store heat in the storage tank 16 for use when the heat network 7 will experience such a high demand for heat and / or temperature.
[0097] When determining the appropriate control sequence 29, the control algorithm 28 will preferably (but not necessarily) control the flow rate of water in the heat recovery system 3 between the minimum flow rate and the maximum flow rate, and optionally, the control algorithm 28 will control the machine state and speed of the compressor unit 2 to be zero or between the minimum speed and the maximum speed.
[0098] exist Figure 1 In the example of compressor device 1, the method includes the step of blowing in compressed gas when the control algorithm 28 controls the speed of compressor device 2 such that the provided flow rate is greater than the current compressed gas flow rate requirement of pressure network 4.
[0099] If, for example, the heat recovery system 3 needs to recover a large amount of heat due to anticipated high heating demand or high costs in the heat pipe network 7, the compressor unit 2 will need to generate more heat, and the excess compressed gas will be discharged through the pressure relief valve 18. This pressure relief valve 18 is also controlled by the controller 14 (i.e., control algorithm 28), although it is not essential to the present invention.
[0100] A similar situation occurs when electricity prices are negative.
[0101] After control sequence 28 has been executed, certain parameters 30 in compressor equipment 1, such as pressure and temperature, can be measured.
[0102] Then, the measurement parameter 30 can be used to update the prediction results of the prediction algorithm 31, or to update one or more mathematical models 22 of the compressor unit 2, heat recovery system 3, pressure network 47, heat network 7 and / or heat production unit 8.
[0103] In this way, changes to compressor equipment 1 (e.g., due to wear, replacement, or maintenance) will be taken into account.
[0104] Although the control algorithm 28 only controls the flow rate of the liquid in the heat recovery system and the machine status and speed of the compressor unit as described above, it should be noted that the standby cooler 11 can also be controlled by the control algorithm 28 and other possible heat generators in the heat recovery system 3.
[0105] The aforementioned control sequence 29 will then additionally include, for example, a set of control signals or similar signals for the standby cooler 11.
[0106] The present invention is by no means limited to the forms described by way of example and the embodiments illustrated in the accompanying drawings. However, the method for controlling a compressor device with a heat recovery system, a controller provided with a control algorithm to perform the method, and a compressor device provided with such a controller, according to the present invention, can be implemented in various forms without departing from the scope of the invention.
Claims
1. A method for controlling a compressor device (1) having a heat recovery system (3), the compressor device comprising: A compressor unit (2) supplies compressed gas to a pressure network (4); and a heat recovery system (3), which recovers heat from the compressor unit (2) and provides the recovered heat to the heat network (7), characterized in that the method includes the following steps: - Provide mathematical models (22) for the compressor unit (2) and the heat recovery system (3); - Provides electricity costs (24), as well as optional gas costs and / or heating costs (24) of the heat network (7); - Provide the desired pressure range (26) of the compressed gas and the desired temperature range (27) of the heat network (7). - Provides a control algorithm (28) for controlling the speed of the compressor unit (2) and the flow rate of the liquid in the heat recovery system (3); The method thus enables the control algorithm (28) to use the mathematical model (22) to determine the control sequence (29) of the flow rate of the liquid in the heat recovery system (3) and the speed of the compressor unit (2), so as to deliver the desired temperature range (27) of the heat network (7) and the desired pressure range (26) of the compressed gas, thereby taking into account the electricity cost (24) and the optional gas cost and / or the heating cost (24) of the heat network (7), so as to minimize the total operating cost.
2. The method according to claim 1, characterized in that, The method further includes the following steps: - Provide a prediction algorithm (20a) for the heat and / or temperature demand of the heat network (7) and a prediction algorithm (20b) for the compressed gas flow demand of the pressure network (4). Thus, the method enables the control algorithm (28) to determine the control sequence (29) of the flow rate of the liquid in the heat recovery system (3) and the speed of the compressor unit (2) based on the prediction algorithm (20a, 20b).
3. The method according to claim 1, characterized in that, The step of providing a mathematical model (22) further includes the step of providing a mathematical model (22) or a simplified mathematical model (22) of the heat network (7) and the pressure network (4) of the compressor equipment (1).
4. The method according to claim 1, characterized in that, The heat pipeline network (7) includes a heat production unit (8), and the step of providing a mathematical model (22) further includes the step of providing a mathematical model (22) of the heat production unit (8).
5. The method according to claim 1, characterized in that, The heat storage tank (16) is located between the heat recovery system (3) and the heat network (7), and the step of providing a mathematical model (22) therethereby also includes the step of providing a mathematical model (22) of the heat storage tank (16), and / or the energy recovery system (3) is provided with a backup cooler (11), and the step of providing a mathematical model (22) therethereby also includes the step of providing a mathematical model (22) of the backup cooler (11).
6. The method according to claim 1, characterized in that, For the control algorithm (28), model predictive control or artificial intelligence-based control algorithm is used.
7. The method according to claim 1, characterized in that, The steps of providing the price of electricity and / or gas (24) and / or the cost of heating through the heat network (7) (24) are performed by the user of the compressor equipment (1) or the user system.
8. The method according to claim 1, characterized in that, The water flow rate of the heat recovery system (3) is controlled by controlling one or more valves (13) and / or pumps (9, 17) in the heat recovery system (3), and / or the speed of the compressor unit (2) is controlled by controlling the driver (6) of the compressor unit (2).
9. The method according to claim 1, characterized in that, The control algorithm (28) controls the water flow rate of the heat recovery system (3) between the minimum flow rate and the maximum flow rate, and / or the control algorithm (28) controls the machine state and speed of the compressor device (2) to be zero or between the minimum speed and the maximum speed.
10. The method according to claim 1, characterized in that, The method includes the step of discharging compressed gas when the control algorithm (28) controls the machine state or speed of the compressor unit (2) such that the provided flow rate is greater than the current compressed gas flow rate requirement of the pressure network (4).
11. The method according to claim 1, characterized in that, The compressor unit (2) is an oil-free compressor unit (2) or a compressor unit (2) with a water cooling system (3'), wherein the water cooling system (3') includes the heat recovery system (3).
12. A controller, characterized in that, The controller is equipped with a control algorithm (28) to perform the method according to claim 1.
13. A compressor device having a heat recovery system (3), the compressor device comprising: At least one compressor unit (2) supplies compressed gas to the pressure network (7); And a heat recovery system (3), which recovers heat from the compressor unit (2) and provides the recovered heat to the heat network (7), characterized in that the heat recovery system is equipped with a controller (14) according to claim 12.
14. The compressor device according to claim 13, characterized in that, The heat pipeline network (7) includes heat production units (8).
15. The compressor device according to claim 13, characterized in that, The at least one compressor unit (2) is an oil-free compressor unit (2) or a compressor unit (2) with a water-cooling system (3'), wherein the water-cooling system (3') includes the heat recovery system (3).