Model predictive control of compressed air systems

Abstract

The present invention relates to a computer-implemented method for controlling a finite set of components flexibly connected to a common compressed air distribution system, wherein the method comprises the following steps, namely - A step of receiving prediction data for the above-mentioned compressed air distribution system; - A step of receiving characteristic data for each component of the above set of components; - A step of determining one or more sets of continuously differentiable functions, wherein each set of functions represents a unique order of operation of a component in the set of components; - A step of selecting an optimal set of functions from one or more sets of continuously differentiable functions, wherein a unique sequence of operations represented by the optimal set of functions satisfies the prediction data; - A step of deriving configuration data for the set of components from the optimal set of functions; - A step of configuring each component of the set of components based on the above configuration data It includes repeating it over and over.

Description

Technology Field

[0001] The present invention relates to the field of compressors, and more specifically to model predictive control of a compressor room. Background Technology

[0002] It is known that a compressor is used to compress air or gas in one or more compression stages. At this time, the compressed air or gas is supplied to one or more consumers. The distribution of such air or gas is provided through a compressed air system or a compressed gas system.

[0003] For example, in industrial plants or hospitals, because the number of consumers is massive and can be spatially distributed over a significant area, a central hub is usually installed to supply compressed air or gas from a central hub.

[0004] The central hub typically includes one or more compressor rooms, and one or more compressors are installed in each compressor room. Furthermore, auxiliary devices such as valves, filters, dryers, vessels, sensors, control components, and / or other devices for managing and / or controlling the compressor rooms are likewise installed. Next, pipes or ducts begin from one or more compressor rooms to supply to consumers. As the final part of this chain, the compressed air or gas is utilized by consumers for various applications.

[0005] Furthermore, between the compressor and the consumer, there may be another set of devices, such as safety valves, distribution valves, control sensors, or other devices, to control and protect the distribution of compressed air or gas.

[0006] The setup described above will be further referred to as a compressed air or gas system. Accordingly, the compressed air or gas system may include a single compressor supplying a single consumer, but generally, it will be considered to be more complex and include multiple components, thereby constituting a complex system of various elements interacting with one another.

[0007] To utilize a compressed air or gas system, different parts of the system need to be controlled. It is already known that compressors are controlled individually by independent local controllers, thereby setting the different controllers to predefined pressure values ​​and sequentially switching the compressors on or off depending on the consumption of compressed air.

[0008] It is also known that a method of controlling a compressed air or gas system by means of a plurality of communication controllers for controlling a component that is part of the compressed air or gas system is applied, according to which the component is controlled such that none of the controllers determine the operating state of any component controlled by another controller. WO2008 / 009073 discloses such a method.

[0009] WO2008 / 009072 discloses another method for controlling a compressed air unit composed of several compressed air or gas networks having at least one common controllable component, according to which at least one common component is controlled by at least one controller based on measurement data of at least one of the compressed air or gas networks.

[0010] However, the disadvantage of these control methods is that they operate based solely on the current state of the compressed air or gas system, which means they cannot account for arbitrary types of predictions. This results in suboptimal control and higher energy costs.

[0011] The present invention aims to overcome the aforementioned disadvantages and other disadvantages. To this end, a first aspect of the present invention relates to a computer-implemented method for controlling a finite set of components flexibly connected to a common compressed air distribution system, wherein the method comprises repeating the following steps.

[0012] - A step of receiving forecast data representing predicted future pressure and / or airflow demand for a compressed air distribution system, wherein the forecast data spans a forecast period.

[0013] - A step of receiving characteristic data for each component of a set of components, wherein the characteristic data includes at least air flow data, air pressure data, and energy consumption data.

[0014] - A step of determining one or more sets of continuously differentiable functions, wherein each set of functions describes the pressure and / or airflow of a compressed air distribution system, and each set of functions represents a unique order of operation of a component in a set of components, and said unique order of operation satisfies predicted future pressure and / or airflow data for at least the initial part of a prediction period.

[0015] - A step of selecting an optimal set of functions from one or more sets of continuously differentiable functions, wherein the unique operating sequence represented by said optimal set of functions satisfies predicted future pressure and / or airflow data for at least a second part of the prediction period.

[0016] - A step of deriving configuration data from an optimal set of functions for a set of components.

[0017] - A step of configuring each component of the component set based on the above configuration data.

[0018] In the first step of the above method, forecast data is received. In the context of the present disclosure, "forecast data" should be interpreted as an estimate of future values ​​of one or more process variables. In the case of a compressed air distribution system, the forecast data includes at least one of an estimated future pressure demand and / or an estimated future air flow demand. The forecast data spans at least a forecast period that may have a duration of seconds, minutes, hours, days, or a longer period. The duration of the forecast period may change each time another iteration is performed from one iteration of the above method. Preferably, the forecast data includes time series data in which estimates of future variables are provided for one or more distinct moments during the forecast period. The forecast data may include an estimated value and / or an estimate confidence interval and / or an estimate boundary for one or more process variables. The forecast data may be generated based on a model of the compressed air distribution system, past process variable data and / or current process variable data, or other input data such as production plans, maintenance plans, calendar data, holiday data, or weather forecast data.

[0019] In the second step of the above method, characteristic data is received. In the context of the present disclosure, “characteristic data” should be interpreted as data characterizing the technical or functional features of one or more parts of a compressed air system. The characteristic data may be in the form of a mathematical model, a lookup table, measurement data, a specification sheet, or any other form of data that can be interpreted by a skilled person or by an appropriate algorithm. The characteristic data includes at least data for each component of a set of components. The characteristic data for each component includes at least air flow data, air pressure data, and energy consumption data. In the specific case of a compressor, it is useful to embed the compressor’s operating envelope in the characteristic data. This operating envelope represents the acceptable operating area of ​​the compressor in the air pressure-air flow plane and imparts energy efficiency to the compressor for each operating point within this operating envelope.

[0020] In the third step of the above method, one or more sets of continuously differentiable functions are determined. These sets of continuously differentiable functions include one or more continuously differentiable functions, and each set represents a unique sequence of operation of components belonging to a set of components. Each set includes at least one continuously differentiable function describing the pressure and / or airflow within a compressed air system and the energy consumption of the components. The unique sequence of operation of the components in each set is selected such that the pressure and / or airflow within the compressed air system satisfies the predicted data for the pressure and / or airflow demand during at least an early part of the prediction period. Preferably, said early part is a time longer than the sum of the period required to complete one iteration of the above method and the period required to bring at least one compressor of the set of components from a stopped state to a steady-state loaded condition. Possible choices for the continuously differentiable functions and the sequence of operation of the components are disclosed in the remainder of this disclosure in connection with embodiments of the present invention.

[0021] In the fourth step of the above method, an optimal set is selected from one or more sets of continuously differentiable functions. This selection process is performed such that a unique order of operation of components associated with the selected subset causes pressure and / or airflow within a compressed air system that satisfies predicted data for pressure and / or airflow demand during at least a second part of the prediction period, said second part being longer than the initial part of the prediction period. Preferably, a unique order of operation of components associated with the selected optimal set causes pressure and / or airflow within a compressed air system that satisfies predicted data for pressure and / or airflow demand during the entire prediction period. Preferably, a unique order of operation of components associated with the selected optimal set causes energy consumption of the compressed air system that is lower than the energy consumption associated with any other order of operation that satisfies the predicted demand for pressure and / or airflow. Those skilled in the art will understand that other optimization criteria may be used. In the remainder of this disclosure, possible methods for selecting an optimal set in relation to embodiments of the present invention are disclosed.

[0022] In the fifth step of the above method, configuration data is derived from a selected optimal set. In the context of the present disclosure, “configuration data” should be interpreted as data determining command inputs to be applied to one or more parts of a compressed air system to assign a unique operating sequence selected for a set of components. The configuration data includes at least data for each component of the set of components. Examples of the configuration data include the time at which a specific compressor must be started, stopped, loaded, or unloaded, the speed at which a specific compressor must be operated, the valve position or the time at which the valve position must be changed, or the flow rate of a cooling circuit.

[0023] In the sixth step of the above method, each component of the set is configured according to the configuration data.

[0024] The advantage of the above method is that it enables real-time simultaneous control of a set of components by taking into account not only the current state of the components and the compressed air distribution system but also the predicted future demand of the compressed air distribution system.

[0025] Although the above method is applicable to all components of a compressed air distribution system, for the remainder of this disclosure, only the compressor will be used as an exemplary embodiment of the component. Since the compressor is, in general, the most important, complex, and difficult to control among the components of a compressed air distribution system, those skilled in the art will understand that the compressor is the most useful embodiment for illustrating the possibility of the above method without any loss of generality.

[0026] A person skilled in the art will understand that during normal operation, the compressor may be located in one of three operating zones or states, and these states are as follows.

[0027] - Stop state. During the stop state, moving parts of the compressor that transmit energy to the medium to be compressed, such as the impeller, scroll, or piston, are not in operation. Typically, during the stop state, the motor driving the compressor's moving parts is also stopped, or power transmission between the motor and the compressor's moving parts is interrupted by a clutch.

[0028] - Unloaded state. During the unloaded state, the compressor is driven by a motor, and the compressor's moving parts operate to displace fluid, but this fluid is discharged at a pressure equal to the fluid's suction pressure. In a compressed air system, this can be achieved, for example, by including a bypass valve after the compressor's exhaust that allows the compressor to discharge into ambient air. Alternatively, the compressor's inlet can be regulated, and in this case, the negligible airflow generated by the compressor can be discharged directly into the compressed air distribution system. Typically, the unloaded state is an intermediate stage between the compressor's stopped state and the loaded state. In some applications, particularly those featuring large compressors, the time required for the compressor to move from the stopped state to normal operating speed can be significantly longer than the dynamic characteristics of the compressed air system's demand fluctuations. In such situations, the compressor may be kept in the unloaded state whenever it is not required.

[0029] - Loaded state. During the loaded state, the compressor is driven by a motor, and the moving parts of the compressor are operated to displace fluid, which is discharged into the compressed air system against the back pressure of the system. For the purposes of this disclosure, the compressor is considered to be in a loaded state when operating within the compressor's normal operating envelope, and is considered not to be in a loaded state when one or more of the compressor's surge limit, choke limit, power limit, or speed limit are exceeded.

[0030] When a compressor deviates from normal operation, it may also be placed in a shutdown, surge, choke, overspeed, or even other state, and these additional states will not be discussed in more detail. However, those skilled in the art will understand from the remainder of this disclosure that the method according to the present invention can also address these states. Preferably, the method will attempt to actively prevent these states. Furthermore, those skilled in the art will understand that other components of a compressed air distribution system, such as valves, for example, may also be expressed by their state.

[0031] In an embodiment of the method according to the present invention, each component of a set of components is represented by a state machine also referred to as a finite-state machine or finite-state automation, which is a mathematical modeling technique for describing distinct state systems. For the purposes of the present method, the state machine model of a component preferably includes at least different states, information about how the states are interconnected, and time-dependent constraints associated with these states.

[0032] The unique order of operation of a finite set of components is associated with each set of continuously differentiable functions. Therefore, the selection of the optimal set results in selecting the optimal order of operation of the components of said set.

[0033] In an embodiment of the method according to the present invention, determining one or more sets of continuously differentiable functions comprises generating state space data representing a possible order of operation of a set of components. Since the state space is limited in dimension by the number of components in the set and the number of possible states per component, the state space representing the possible order of operation is limited in dimension insofar as the number of permissible transitions per component is limited over a given time horizon. The representation of components by a state machine thus allows transforming an infinite space of possible order of operation into a finite space that can be explored in a thorough manner.

[0034] When considering the representation of a component by a state machine, the operation sequence of the component includes at least information regarding (i) the initial state of the component, (ii) the state transitions that the component will undergo, and (iii) the order in which the component will undergo said state transitions. The operation sequence of the component does not necessarily include the time of a specific moment when the component will undergo a specific state transition. In this regard, the operation sequence of a finite set of components controlled by the method of the present invention includes a set of operation sequences of individual components of the set, which includes exactly one operation sequence for all components of the set. In contrast, the configuration data derived by the method includes the operation sequence of the set of components and additionally includes at least the time of the moment when a state transition occurs during the prediction period.

[0035] In an embodiment of the method according to the present invention, state space data representing a possible order of operation of a set of components is generated based on an acceptable state transition from a previous state of one or more components of the set of components to a subsequent state of one or more components of the set. Since the acceptable state transition depends on the current state of the components, the number of acceptable state transitions is always limited. Accordingly, the representation of the order of operation based on the order of state transitions allows for a further reduction in the dimension of the state space in which the set of functions is determined, thereby reducing the computational cost of the method.

[0036] In an embodiment of the method according to the present invention, the state space data is pruned based on at least one boundary condition or the value of an objective function. This pruning allows for a further reduction in the dimension of the state space in which the set of functions is determined, thereby reducing the computational cost of the method.

[0037] In an embodiment of the method according to the present invention, a set of continuously differentiable functions according to the method may be described as (f(x,y),g(x,y)), wherein , is. In this equation, X and are each and It is a polyhedral subset and a bounded polyhedral subset of, and the above objective function and the above constraint function It is assumed to be convex and twice consecutively differentiable. Vector x may include continuous variables of the compressed air system, such as, for example, pressure, airflow, temperature, relative humidity, the rotational speed of one or more compressors from a compressor set, or the time at which one or more compressors of a compressor set transition to a different state. Vector y includes state variables of each component from a set of components.

[0038] Those skilled in the art will recognize that, in the context of minimizing the energy consumption of a compressed air system, the objective function f includes a measure of the system's energy consumption, such as the system's instantaneous energy consumption or total energy consumption over a forecast period. The objective function f may include additional terms representing direct or indirect measures of the system's energy consumption or energy efficiency. The objective function f may include other terms. Likewise, those skilled in the art will recognize that the constraint function g may include equations modeling the components of the system, or equations describing process variables such as, for example, pressure, air flow, air temperature, and relative humidity.

[0039] The step of selecting an optimal set of continuously differentiable functions comprises the problem of minimizing f(x,y), which depends on the boundary condition lb ≤ g(x,y) ≤ ub, wherein the lower boundary (lb) and the upper boundary (ub) may include predicted future pressure and / or airflow demand and may also include additional boundary conditions imposed by the system or consumers connected to the system. For example, the boundary conditions may include the maximum temperature and / or maximum relative humidity of the compressed air or the maximum rotational speed of one or more compressors. This problem is a mixed integer non-linear problem.

[0040] In this embodiment, the step of selecting an optimal set of continuously differentiable functions includes, at the time, searching for a local minimum of at least the objective function f(x,y).

[0041] In an embodiment of the method according to the present invention, the local minimum of the objective function is searched using a branch and bound algorithm. The advantage of using a branch and bound algorithm is that it enables systematic search and organization of the state space.

[0042] In an embodiment of the method according to the present invention, the time at which a component of a set of components undergoes a specific state transition of the operation sequence is determined to achieve a local minimum of the objective function f(x,y). The method has two degrees of freedom to achieve optimal control. The first degree of freedom relates to the selection of the operation sequence of the components of the set. For this degree of freedom, the available state space is explored, for example, using a branching and combining algorithm or any other suitable approach. The second degree of freedom relates to the selection of the time at which the state transition of the operation sequence occurs. To determine the time at this moment, it is necessary to solve a mixed-integer nonlinear problem of minimizing f(x,y) dependent on the constraint lb≤g(x,y)≤ub.

[0043] In an embodiment of the method according to the present invention, the characteristic data further includes minimum starting energy data for at least one component of a set of components and / or a minimum activity period and / or average maintenance time after the starting data.

[0044] In an embodiment of the method according to the present invention, repeating includes repeating the steps of the method at separate fixed time intervals.

[0045] In an embodiment of the method according to the present invention, the prediction period varies over time. The prediction period may vary, for example, when the dynamic characteristics of demand within a compressed air distribution system change. When dynamic demand fluctuations are low, the prediction data may be extended over a longer time horizon, and vice versa.

[0046] In an embodiment of the method according to the present invention, the initial portion of the prediction period is determined based on at least the maximum processing capacity of the data processing means performing the method.

[0047] delete

[0048] A third aspect of the present invention relates to a computer program comprising instructions that cause the computer to perform a method according to the first aspect of the present invention when the program is executed by the computer.

[0049] A fourth aspect of the present invention relates to a compressed air system or a compressed gas system configured to be controlled according to the method of the first aspect of the present invention. Brief explanation of the drawing

[0050] FIG. 1 schematically illustrates a compressed air system controlled according to the present invention. FIGS. 2A and FIGS. 2B schematically illustrate the state machine representation of a compressor. FIGS. 3a and 3b schematically illustrate a time switch employed in an embodiment of the method to indicate a state transition. FIGS. 4a and FIGS. 4b present flowcharts of an embodiment of the method according to the present invention. FIGS. 5a to 5h present the results of executing an embodiment of the method according to the present invention. Specific details for implementing the invention

[0051] The present disclosure will be described in terms of specific embodiments that are not to be interpreted as limiting, as examples of the invention. It will be understood that the present disclosure is not limited by what is specifically illustrated and / or described, and that alternative or modified embodiments may be developed in light of the overall teaching of the present disclosure. The drawings described are merely schematic and are not intended to be limiting.

[0052] Throughout this description, the terms “one embodiment” or “one embodiment” mean that a specific feature, structure, or characteristic described in connection with an embodiment is included in one or more embodiments of this disclosure. Accordingly, whenever the phrases “in one embodiment” or “in one embodiment” appear in various places throughout this specification, they do not necessarily refer to the same embodiment, but may refer to the same embodiment. Furthermore, as will be apparent to those skilled in the art from this disclosure, specific features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0053] FIG. 1 illustrates a compressed air or gas system (100) comprising three compressors (101, 101', and 101'') configured to provide compressed air or compressed gas to a client network (105). The compressed air or gas system (100) further comprises a container or tank (103) for storing the compressed air or compressed gas and a valve (104) connected to the client network (105). One or more consumers exist in the client network (105). Additionally, it should be understood that the compressed air or gas system (100) may further comprise other devices such as a dryer, a filter, a regulator, and / or a lubricator; however, for the purposes of this document, the invention will be illustrated with reference to FIG. 1 as a setup of the compressed air or gas system (100). In FIG. 1, solid lines represent fluid connections, while dotted lines represent data connections.

[0054] The compressors (101, 101', 101'') can each be locally controlled by their respective controllers (102, 102', 102''). Furthermore, to efficiently control the compressed air or gas system (100), the controllers (102, 102', 102'') will be controlled in a coordinated manner. In other words, the controllers (102, 102', 102'') are prevented from individually controlling their respective compressors (101, 101', 101''). Conversely, the controllers (102, 102', 102'') are directed by the master controller (106) so that the overall performance and efficiency of the compressed air or gas system (100) are increased.

[0055] The master controller (106) may be located near the controllers (102, 102', 102''), but may also be located at a remote location relative to the compressed air or gas system (100). Alternatively, one of the controllers (102, 102', 102'') may be configured to operate as a master controller to control all compressors (100, 100', 100'').

[0056] Through the master controller (106), the operation, switching, and idle costs of the compressed air or gas system (100) are handled, thereby reducing wear on the components of various devices while simultaneously optimizing their energy consumption. To this end, the master controller (106) utilizes an embodiment of the method according to the present invention. The master controller (106) receives characteristic data (110) representing the technical or functional characteristics of one or more parts of the compressed air system. Such characteristic data may be obtained from a database, model, measurement, or any other suitable means affecting one or more parts of the compressed air system (100). Furthermore, the master controller (106) also receives prediction data (120) representing at least future expected airflow and / or pressure demand of the client network. Again, such prediction data may be obtained from a database, model, measurement, or any other suitable means affecting one or more parts of the compressed air system (100) or the client network (105). Based on characteristic data (110), prediction data (120) and the method of the present invention, the master controller (106) transmits configuration data (130) to the controller (102, 102', 102'') to adjust the control of the compressor (101, 101', 101'').

[0057] FIGS. 2A and 2B schematically illustrate the state machine representations (200, 200'') of a compressor. The state machine (200) of FIG. 2A includes three possible states: a loaded state (201), an unloaded state (202), and a stopped state (203). Each state has at least two parameters, namely, the minimum time that the compressor must spend in a specific state for the loaded state, the unloaded state, and the stopped state, respectively ( , , (indicated by ) and, for each of the load, unload, and stop states, the minimum time that the compressor must remain in a different state before returning to a specific state ( , , Includes (indicated by ). The above stop state includes an additional parameter (indicating the maximum time the compressor can consume in the stop state) ...includes ). Those skilled in the art will understand that, in certain embodiments, the load state and the unload state may also be limited to a maximum holding time, or that these states may include additional parameters. Additionally, those skilled in the art will understand that certain parameter values ​​may vary from compressor to compressor and, among other things, depend on the type of compressor or operating conditions.

[0058] FIG. 2a also illustrates state transitions to adjacent states, namely, a transition (204) from an unloaded state (202) to a loaded state (201), a transition (205) from a loaded state (201) to an unloaded state (202), a transition (206) from an unloaded state (202) to a stopped state (203), and a transition (207) from a stopped state (203) to an unloaded state (202). Each transition includes at least a parameter indicating the time required to complete the transition, said parameter for each transition (204, 205, 206 and 207). , , , It is expressed as such. The above time required to complete the transition may vary between different state transitions. Additionally, those skilled in the art will understand that specific parameter values ​​may vary from compressor to compressor and, above all, depend on the type of compressor or operating conditions.

[0059] The state machine (200'') of FIG. 2b includes only two possible states, namely a loaded state (201) and a stopped state (203). As a result, the state machine (200'') of FIG. 2b includes only two possible state transitions, namely a transition from the loaded state to the stopped state (208) and a transition from the stopped state to the loaded state (209). Additionally, the state machine (200) may include transitions (208) and (209), but these transitions are not shown in FIG. 2a to avoid complicating the drawing.

[0060] Compared to the state machine representation (200) of FIG. 2a, the state machine (200'') of FIG. 2b has lower computational complexity due to a reduction in the number of states and transitions. The representation of a compressor by the state machine (200'') may be advantageous when there is insufficient available computational power to determine the optimal operating sequence of the compressor in real time using the state machine representation (200). Such situations may arise, for example, when it is necessary to control multiple compressors simultaneously or when the airflow demand of the compressed air system changes strongly and unpredictably. The reduction in the number of degrees of freedom of the state machine (200'') comes at the cost of allowing less precise control of the compressor. Additionally, for some compressors, an immediate transition from a stationary state to a loaded state may not be possible.

[0061] An embodiment of the method of the present invention may employ either of two state machines to represent a compressor in a compressor set. Additionally, the method may employ both representations, such that some compressors in the set are represented by a state machine containing three states, while other compressors in the set are represented by a state machine containing only two states. Furthermore, during the execution of the method, the method may dynamically transition between two state machine representations to represent one or more compressors, thereby dynamically changing the balance between the execution speed and control accuracy of the method.

[0062] Finally, those skilled in the art will understand that the method of the present invention is not limited to representing a compressor with only two or three states, and that more states (each state representing a distinct operating regime of the compressor) may be added to the state machine. Furthermore, the foregoing description is equally valid for representations of a state machine with more than three states.

[0063] FIGS. 3a and 3b schematically illustrate two types of time switches that can be employed by an embodiment of the method to represent state transitions of one or more compressors as a function of time. Both of these two types of time switches depend on a ramp over time, which can be represented by a sigmoid function.

[0064]

[0065] Here, t represents time. The ramp (R) is the switching time (t s The value changes from 0 to 1 around ), and to perform this switch, time (t ramp ) is required. The ramp (R) is, therefore, ts Occurring in the surroundings and time (t ramp It can be used to represent a non-instantaneous state transition. The parameter c is a correction factor (c) that depends on the sigmoid function used. For example, in the case of a logistic function, this correction factor is 5. Embodiments of the above method may use various types of step functions to represent state transitions, such as a piecewise ramp. The requirements for the function representing the state transition are simply that (i) a first derivative of the function with respect to t exists, (ii) said first derivative is bounded, and (iii) t s Regardless of the value of, it is not always 0 for at least one distinct point in time on the time horizon.

[0066] FIG. 3a schematically illustrates a state machine representation (200) of a compressor comprising three states, namely, a loaded state, an unloaded state, and a stopped state, represented by reference numerals 201, 202, and 203, respectively. At the beginning of the time horizon, the compressor is in a loaded state (201), which is mathematically represented by a state (201) value of 1. By definition, because the different states of the state machine are mutually exclusive, the compressor cannot be in an unloaded state or a stopped state. This is mathematically imposed by requiring that the sum of the values ​​of all states of the machine be 1.

[0067] In FIG. 3a, an operation sequence including a state transition from a loaded state (201) to an unloaded state (202) is imposed on the compressor. Accordingly, a time switch (224) is introduced such that around a first transition time (220), the loaded state changes from a value of 1 to a value of 0, and the unloaded state changes from a value of 0 to a value of 1. Additionally, during the switching period, the sum of the values ​​of all states is maintained at 1. Prior to the initiation of the time switch (224), the state of the state machine (200) is known, and accordingly, the time from the initial time of the time switch (224) to the initiation is a period (222) of state certainty for the state machine (200). Since the state machine is placed in a known state adjacent to the time switch (224), a time switch having the same properties will be referred to as an "adjacent switch" for the remainder of this disclosure. Adjacent switches can be imposed only on state machines adjacent to the period of state certainty, that is, on state machines after the period in which the machine's state is known. It should also be noted that the concept of adjacent switches can be used in reverse order of time, and that adjacent switches can be imposed before the period of state certainty. This may be useful when the final state of the machine at the end of the aforementioned period, rather than the initial state of the machine, is known.

[0068] After the time switch (224) is completed, the machine (200) must be kept in an unloaded state (202) for at least a minimum time (210). Thus, the machine is placed in a period of state certainty (222) for at least a minimum time (210) after the start of the time switch (224). Once this period has elapsed, the machine (200) is placed in a period of state uncertainty (223), and during the period of state uncertainty, the state variables of the machine may have any value as long as the sum of the values ​​of these state variables is 1, and may optionally undergo other state transitions, such as a transition around the second switching time (221), although not necessarily required.

[0069] Mathematically, imposing an adjacent time switch on a state machine leads to the addition of the following set of equations for the constraint function g(x,y).

[0070]

[0071]

[0072]

[0073] Here, represents the set of all states of the machine (m), and represents the set of all machines, and represents the set of all instantaneous times, and n s is S m It is the size of, is the instant time (t i The state (s) of the machine (m) in ) k It is the value of ), and is the machine (m) in state (s j It is the time to transition to ). The unknowns in the above equation are the switching times that are added to the variable vector x and determined by the solution algorithm. For every adjacent switch applied to every machine, the above equation will be added to g(x,y).

[0074] FIG. 3b schematically illustrates a state machine representation (200'') of a compressor including two states, namely a loaded state and a stopped state, indicated by reference numerals 201 and 203, respectively. At the beginning of the time horizon, the state of the compressor is unknown. At the switching time (220), a time switch (225) is introduced to transition the machine to the loaded state (201). Since the machine must be forced to remain in the loaded state for a minimum time (210), the state of the machine is known during this period. Thus, the introduction of the time switch (225) leads to a period of state certainty (222) in which the state of the machine (200'') is known and the values ​​of its state variables are fixed. The length of the period of state certainty (222) is equal to the minimum period during which the machine needs to remain in a specific state. However, after the expiration of the aforementioned minimum period or before the initiation of the time switch (225), the machine (200'') is placed in a period of state uncertainty (223). Since the introduction of the time switch (225) is independent of knowledge of the state of the machine (200'') and can therefore be made anywhere within the time horizon, a time switch having the same properties will be referred to as a "free-floating switch" in the remainder of this disclosure.

[0075] Mathematically, imposing a free-floating-time switch on a state machine leads to the addition of the following set of equations for the constraint function g(x,y).

[0076]

[0077]

[0078] As with adjacent switches, the unknowns in the above equation are the switching times to be determined by the solution algorithm, which are added to the variable vector x. As with adjacent switches, for all free-floating switches applied to all machines, the aforementioned equation will be added to g(x,y).

[0079] Embodiments of the above method may implement adjacent switches or free-floating switches, and both of these switches may be combined. Both types of switches may be further extended to include a tolerance around a ramp so that the state variable can achieve an integer value after the switch is completed. This is useful in cases where transitions between integer values ​​for the state variables are prevented by other constraints.

[0080] FIG. 4a illustrates a flowchart of an embodiment of the method according to the present invention. Prior to the iterative execution of the method, an initialization step (300) is performed. During this initialization step, a queue and a container are created. Both the queue and the container are empty at this point.

[0081] The first step of the above-mentioned iterative method is a data collection step (301). During this data collection step, both characteristic data for one or more compressors and predictive data for the compressed air system are collected.

[0082] In step 302, the queue is updated. In the first iteration of the method, this update relates to the generation of a first set of continuously differentiable equations (f(x,y), g(x,y)) dependent on the boundary condition lb ≤ g(x,y) ≤ ub, and the associated problem of minimizing f(x,y). This set of equations and the associated problem are added to the queue as an item. After the second iteration of the method and in subsequent iterations, the update step (302) may serve various purposes, as further described in the disclosure of the present embodiment.

[0083] Since the method of the present invention aims for real-time control of a set of one or more compressors, the method has only a finite amount of execution time. The size of this time may be constant or variable based on known characteristics of the system. For example, the method may calculate a maximum time for execution based on received prediction data in every iteration. A timer (303) tracks the time elapsed during the execution of the calculation part of the method, and if the calculation time exceeds a predetermined maximum time, the timer (303) stops the calculation and causes the method to proceed to the next iteration step.

[0084] During the execution of the above method, items corresponding to a set of successively differentiable equations representing the unique operating sequence of the compressors and the associated minimization problem of the compressors, respectively, may be added to or removed from the queue. In step 304, the method checks whether the queue still contains items. If the queue is empty, step 304 causes the method to proceed to the next iteration step before the maximum time for the iteration has elapsed.

[0085] In step 305, the method attempts to resolve one or more of the items in the queue using a branch and combine algorithm, which is illustrated in more detail in FIG. 4b. The branch and combine algorithm adds fully resolved items to a container, and furthermore, the branch and combine algorithm may add partially resolved items to the queue and / or remove items from the queue.

[0086] Once the above method stops the calculation loop, because the maximum time for one iteration has expired or the queue is empty, the method checks at step 306 whether the container contains a completely solved solution. If the container contains a completely solved solution, at step 308, the best solution (meaning the solution with the lowest cost for the objective function f(x,y)) is selected from the container.

[0087] Alternatively, in the case where the container is empty, Step 307 selects the best (partially resolved) solution from the queue and derives configuration data from this best solution. In this case, since the best solution does not cover the full range of the forecast period for which forecast data is available, uncertainty remains regarding whether the selected operating sequence can meet the forecast pressure and / or airflow demand. This problem can be resolved in the post-processing step of Step 307. In this post-processing step, a number of criteria may be applied to identify the risk that the forecast pressure and / or airflow demand will not be met due to an incomplete operating sequence. For example, it may be checked whether all compressors within the set can be loaded during the remainder of the forecast period for which the item is not fully resolved. If the selected best solution satisfies the post-processing criteria, that solution may be retained. Otherwise, that solution may be rejected, and another solution from the queue may be selected as the best solution.

[0088] Subsequently, configuration data is derived from this best solution, and in step 309, the compressor of the system is configured based on the configuration data. By this, one iteration of the method is completed.

[0089] When starting the second iteration of the above method, the first step is again the data collection step (301). However, at this time, the queue and the container are not necessarily empty. If the container contains an item, this item is added to the queue and the container is emptied. Subsequently, the items in the queue are shifted over time. If an item in the queue does not correspond to the updated state of the compressor, the item is removed from the queue. Finally, the items in the queue are updated using new prediction data.

[0090] FIG. 4b illustrates a flowchart of an embodiment of a branch and combine algorithm (305). The input to the branch and combine algorithm is a queue containing unsolved or partially solved problems (also referred to as items), each problem corresponding to a unique operating sequence of a compressor. The output of the branch and combine algorithm is an updated queue and container. The branch and combine algorithm depends on separate algorithms, namely a selection algorithm for selecting items from the queue, a branching algorithm for branching items, and a solution algorithm for solving items.

[0091] In step 400, the selection algorithm selects an item from the queue. To determine which item to select, the selection algorithm may use one of a number of criteria. Examples of such criteria are as follows.

[0092] ● Best First: The above selection algorithm always selects the item with the minimum value for the objective function f(x,y). This approach is simple to implement and can achieve the most optimal solution within minimal computation time without using heuristics. However, obtaining a feasible and fully resolved first solution over the entire forecast period may take longer than other criteria.

[0093] ● Alternating Best First: This is an algorithm built upon the best first algorithm. Instead of traversing the entire tree using the best first algorithm, the tree is partitioned, and the best first algorithm is applied alternately to all partitions of the tree. For trees with very long branches, this provides a good alternative for achieving a good solution in a shorter time than the 'best first' approach.

[0094] ● Breadth First: This algorithm selects the item at the beginning of the queue.

[0095] ● Depth First: This algorithm selects items that are partially solved, as they have already been solved over the longest time horizon. Once a feasible and fully solved solution is reached, this method can further explore the rest of the queue using different approaches.

[0096] ● Weight Depth and Cost: This algorithm balances the optimization of computational speed using a "depth-first" approach with the minimization of the cost function using a "best-first" approach. Typically, this approach will yield a solution that is faster but less optimized than a "depth-first" approach, and a solution that is slower but more optimized than a "depth-first" approach.

[0097] ● Heuristic: A heuristic is defined that attempts to estimate which direction the algorithm should proceed. Such a heuristic may be based on the present application.

[0098] The above algorithm may perform a transition between one or more of the above criteria during various iterations of the above method. The above algorithm may perform a transition between one or more of the above criteria or combine one or more of the above criteria during a single iteration of the above method.

[0099] In step (401), a branching algorithm creates a branch from an item selected from the queue in step (400). Thus, the created branch is a "child" of the originally selected item, i.e., the "parent." In this context, creating a branch involves the addition of a state transition to the operating sequence of the parent, thereby creating a new unique operating sequence and a new associated mathematical problem. Mathematically, the creation of a branch involves adding a set of equations representing time switches for the parent's constraint function g(x,y). These equations have been discussed in the context of FIGS. 3a and 3b.

[0100] State transitions that can be added to the existing sequence of operations are limited by the underlying state machine representation. It may be possible to generate multiple branches from a single parent. However, the branching algorithm is not required to generate all possible branches. For example, the branching algorithm may branch only from the compressor resolved in the shortest possible time, that is, from the machine that still has the largest region of state uncertainty over the prediction period. Alternatively, the branching algorithm may branch only from the machine responsible for maximum energy consumption. The branching algorithm may combine different branch generation strategies within a single iteration, or may switch branch generation strategies during the iteration of the method. The adopted branch generation strategy may be specifically applied to the underlying use case.

[0101] In the context of Figures 3a and 3b, two types of time switches—namely, adjacent switches and free-floating switches—were introduced. The branch generation algorithm determines the type of switch to introduce to impose state transitions. In the context of model predictive control, adjacent switches are preferred. Since the initial state is known, using adjacent switches allows the solution to be switched from using a time-forward method, enabling the attainment of a feasible solution for an early part of the time horizon early in the computation phase. Consequently, the branching process can be halted before reaching a complete solution, provided that the feasibility of partially solved problems is guaranteed within the unresolved time horizon. In compressor control, this can be accomplished by post-processing that allows all compressors to be loaded within the unresolved time horizon.

[0102] In contrast, free-floating switches are computationally more expensive because they generate more branches. However, in some special cases, the use of free-floating switches can result in a faster solution. One such case is when the unconstrained state variables have already approached integer values ​​at a certain point in time. An additional disadvantage of using free-floating switches is the complexity of their implementation, which requires a dedicated algorithm to calculate possible switching paths between two different states to ensure that impossible subsolutions are not generated.

[0103] After the branch is created, the solution algorithm will attempt to resolve all branches. Step (402) checks whether all branches have been resolved. If all branches have been resolved, the branch and combine algorithm terminates, and the method returns to the time check step (303) of FIG. 4a. If all created branches have not been resolved, the method proceeds to the solution algorithm of step 403.

[0104] In step 403, the solution algorithm attempts to solve a specific problem associated with a unique sequence of operations. Mathematically, the problem is the minimization of the objective function f(x,y), which depends on the constraint lb ≤ g(x,y) ≤ ub, where , is. In this equation, X and are each and It is a polyhedral subset and a bounded polyhedral subset of, and the above objective function and the above constraint function It is assumed to be convex and twice consecutively differentiable. The unique order of operation associated with a particular problem is reflected in the constraint function through the addition of a set of time-switch equations for each transition imposed on every machine. The problem to be solved is a so-called Mixed Integer Non-Linear Problem (MINLP), which can be solved using existing solvers such as BARON, BONMIN, KNITRO, or NAG.

[0105] Typically, in the first substep of the solution algorithm, the linear relationship of MINLP is a relaxed variable and This will be performed by linearizing the objective function and constraint function centered on , and at this time is. Relaxed state variable Accordingly, is no longer limited to integers. If the relaxed problem is feasible (meaning the constraints can be satisfied), the relaxed state variable ...is restricted to an integer state variable y through rounding up or down. This restriction applies only within the constrained zone, and the problem is resolved over time intervals spanning said constrained zone, where the state of the machine is considered fixed. In the unconstrained zone, the machines are in an arbitrary state It can occupy. Subsequently, the original problem is, as starting values ​​for obtaining x, y (within the constrained region) and x (within the unconstrained region). It is resolved by using, and by using the switching time for the state transition in the operation sequence imposed accordingly.

[0106] In step 404, the algorithm checks whether the problem is also feasible as an integer (meaning that constraints can be satisfied when state variables are restricted to integer values). Additionally, step 404 also checks whether the cost of the branch's objective function is lower than the lowest objective cost achieved in another branch from other fully solved branches. If neither condition is satisfied, the specific branch is discarded in step 405. If both conditions are satisfied, the method checks in step 406 whether the branch is fully solved, that is, whether the machine's state is restricted over the entire time horizon of the prediction period during which prediction data was available. If the branch is fully solved, the associated operation sequence and objective cost are stored in a container in step 407. If the branch is not fully solved, the branch is added to a queue in step 408. In the next iteration of the branch and combine algorithm, the aforementioned branch can now be selected as the 'parent' from which the branch originates.

[0107] FIGS. 5a through 5h present the results of the execution of an embodiment of the method according to the present invention. In the embodiment of FIGS. 5a through 5h, the compressor set comprises three machines named U1, U2, and U3, each represented as a state machine (200, 200', and 200''). The machines (200, 200') are assumed to include three accessible states: a loaded state (201), an unloaded state (202), and a stopped state (203). The machine (200'') is assumed to include only two accessible states: a loaded state (201) and a stopped state (203). Predictive data for a compressed air network connected to the three compressors is available during a prediction period (126). The predictive data includes a prediction of future airflow demand (121) and predictions of future minimum pressure demand (123) and maximum pressure demand (124). To improve the readability of the drawing, it should be noted that not all drawing symbols have been added to all sub-graphs of the drawing.

[0108] FIG. 5a shows that, initially, the machine (200) and the machine (200') are in a loaded state (201) and the machine (200') is in a stopped state (203). The machine (200) must remain in the stopped state for at least one repetition. This may occur, for example, because the machine was previously in the stopped state and the minimum time of the machine in the stopped state has not yet expired. However, the machine (200, 200'') may change state from the beginning of the time horizon. The cross symbol indicates the values ​​calculated by the branch and combine algorithm for the calculated airflow (122), calculated pressure (125), and state variables. In the period of state certainty (222), the state of the machine is known, and the state variable being calculated is a bound state variable (131). In contrast, in the period of state uncertainty (223), the state of the machine is unknown, and the state variable being calculated is an unbound state variable (132).

[0109] The solution of FIG. 5a includes a period of state uncertainty (223) and is therefore only partially resolved. The branching algorithm assumes that the maximum gain can be achieved by adding state transitions to the machine (200''), and that the maximum gain is achieved by creating two branches (presented in FIG. 5b and 5c) from the existing partial solution of FIG. 5a and adding these branches to a queue. After the creation of the branches shown in FIG. 5b and 5c, the 'parent' shown in FIG. 5a is discarded.

[0110] In the branch of FIG. 5b, a transition (208) from a loaded state to a stopped state is imposed on the machine (200''). Because the machine (200'') is stopped, the machine (200'') needs to be kept in a stopped state for a minimum time (210). The solution algorithm determines that, due to the absence of a stopped state, the machine (200) needs to be constrained to a loaded state for the entire time horizon. Furthermore, the solution algorithm determines that even if the machine (200') transitions from a stopped state to a loaded state, the compressor set cannot meet the minimum pressure demand (123) for a period (127). Therefore, the branch of FIG. 5b is not feasible and is removed from the queue.

[0111] In contrast, in the branch of FIG. 5c, the machine (200'') is maintained in a loaded state (201). The solution algorithm determines that, under these conditions, it is optimal for the machine (200) to remain in a constrained state in a stationary state for approximately 300 seconds, and for the machine (200) to remain in a constrained state in a loaded state for approximately 600 seconds. Under this sequence of operation, the compressors can meet the predicted future airflow and pressure demands. Thus, the branch is feasible. Because the time horizon of the branch includes a region of state uncertainty (223), the branch is not fully resolved and remains in a queue. Since the state of the machine (200) is not constrained over any part of the time horizon, the machine (200) is minimally resolved. Accordingly, the branching algorithm assumes that the maximum gain can be achieved by adding a state transition to the machine (200), and that the maximum gain is created by generating two branches (shown in FIG. 5d and FIG. 5e) from the existing partial solution of FIG. 5c and adding these branches to a queue. After the creation of the branches shown in FIG. 5d and FIG. 5e, the 'parent' shown in FIG. 5c is discarded.

[0112] In the branch of FIG. 5d, the machine (200) is initially constrained in a loaded state, whereas in the branch of FIG. 5e, a state transition (205) to an unloaded state is imposed on the machine (200). After resolution, both branches are shown to be partially resolved and feasible and are maintained in a queue. Since the cost of the objective function is lower for the operation sequence of FIG. 5e than for the operation sequence of FIG. 5d (not shown in the drawing), the branch of FIG. 5d is discarded, and the branching algorithm decides to branch from the operation sequence of FIG. 5e. Since the machine (200) is still resolved as the least of the three machines, the branching algorithm decides to branch by imposing an additional state transition on the machine (200), which leads to the creation of two new branches presented in FIG. 5f and FIG. 5g. After the creation of the branches shown in FIG. 5f and FIG. 5g, the 'parent' shown in FIG. 5e is discarded.

[0113] In the branch of FIG. 5f, the aforementioned additional state transition is a transition from an unloaded state to a loaded state (204), whereas in the branch of FIG. 5g, the aforementioned additional state transition is a transition from an unloaded state to a stopped state (206). Both branches are feasible. The cost of the objective function is lower for the operation sequence of FIG. 5g than for the operation sequence of FIG. 5f (not shown in the drawing). Therefore, the branch of FIG. 5f is discarded, while the branch of FIG. 5g is added to the queue.

[0114] At this point, the maximum computation time for one iteration of the above method may be exceeded. None of the branches are completely resolved. Accordingly, the above method will select the item with the lowest objective cost from the queue, which is the operating sequence of FIG. 5g. This sequence will be applied to the compressors.

[0115] Subsequently, when the next iteration begins, all items in the queue need to be shifted in time so that the beginning of the time horizon of the corresponding item coincides with the beginning of the new time horizon of the prediction data. FIG. 5h illustrates the sequence of FIG. 5g shifted over time. Now, machine (200) and machine (200') are initially placed in a stopped state, and machine (200'') is initially placed in a loaded state. At this time, if any other sequence exists in the queue, these sequences are also shifted over time. However, if the new initial state of these other sequences does not coincide with the new initial state of the compressor, and thus the other sequences become impossible to realize, they are likewise discarded. The sequence of FIG. 5h currently applied to the compressors is the only item remaining in the queue. The branch and combine algorithm will create a branch from this item and attempt to resolve the branch. Explanation of the symbols

[0116] 100: Compressed Air System 101 : Compressor 102 : Controller 103 : Courage 104 : Valve 105 : Client Network 106 : Master Controller 110: Feature data 120: Predicted data 121 : Estimated airflow demand 122 : Calculated airflow 123 : Estimated minimum pressure demand 124: Estimated maximum pressure demand 125 : Calculated pressure 126: Forecast period 127 : Time interval 130 : Configuration data 131 : Constraint State 132 : Unconstrained state 200: Status Machine 201 : Load status 202 : Unloaded status 203: Stopped state 204: Transition from unloaded state to loaded state 205: Transition from loaded state to unloaded state 206: Transition from unloaded state to stopped state 207: Transition from idle state to unloaded state 208: Transition from loaded state to stopped state 209: Transition from idle state to loaded state 210: Minimum time required in a specific state 220 : Switching time 221 : Next switching time 222 : Constrained zone 223 : Unconstrained zone 224 : Adjacent switch 225 : Free floating switch 300: Method initialization step 301: Data Collection Phase 302: Queue Update Phase 303: Time check phase 304: Queue Check Phase 305: Branch and Combine Algorithms 306: Container Inspection Steps 307: Select Solution from Queue Phase 308: Selecting a Solution from the Container Phase 309: Compressor Configuration Steps 400: Item Selection Algorithm 401: Branching Algorithm 402: Quarterly Check Phase 403 : MINLP Solver Step 404: Validity check stage 405: Branch Discard Step 406: Solution Check Phase 407: Additional steps for containers 408: Additional steps for the queue

Claims

Claim 1 A computer-implemented method for controlling a finite set of components flexibly connected to a common compressed air or gas distribution system, the computer-implemented method comprising: - receiving prediction data representing a predicted future pressure demand, a predicted future airflow demand, or both for the compressed air or gas distribution system, wherein the prediction data spans a prediction period; - receiving characteristic data for each component of the set of components, wherein the characteristic data includes at least airflow data, air pressure data, and energy consumption data; - determining a plurality of sets of continuously differentiable functions, wherein each set of functions includes a function describing the pressure, airflow, or both for the compressed air or gas distribution system and a function describing the energy consumption or energy efficiency for the compressed air or gas distribution system, and each set of functions represents a unique operating sequence of components in the set of components that satisfies the predicted future pressure demand, the predicted future airflow demand, or both for at least an early part of the prediction period; - selecting an optimal set of functions from the plurality of continuously differentiable functions, wherein by the optimal set of functions A computer-implemented method comprising: a step of satisfying the predicted future pressure demand, the predicted future airflow demand, or both during at least a second part of the predicted period; a step of deriving configuration data for the set of components from the optimal set of functions; and a step of repeatedly configuring each component of the set of components based on the configuration data. Claim 2 A computer implementation method according to claim 1, wherein each component of the set is represented by a state machine. Claim 3 A computer-implemented method according to paragraph 2, wherein the step of determining the plurality of sets of continuously differentiable functions comprises generating state-space data representing a possible order of operation of the set of components. Claim 4 A computer-implemented method according to paragraph 3, wherein the state space data is generated based on an acceptable state transition from a previous state of one or more components of the set of components to a subsequent state of one or more components of the set of components. Claim 5 A computer-implemented method according to claim 3 or 4, further comprising the step of pruning the state-space data based on at least one boundary condition or the value of an objective function. Claim 6 A computer-implemented method according to any one of claims 1 to 4, wherein each set of functions includes an objective function describing the energy use or energy efficiency of the compressed air or gas distribution system, and the step of selecting the optimal set of functions includes searching for at least a local minimum of the objective function. Claim 7 A computer implementation method according to claim 6, wherein the local minimum is sought using a branch and bound algorithm. Claim 8 A computer implementation method according to claim 6, wherein the local minimum of the objective function is sought by determining the time at which a component of the set of components undergoes a state transition of the operation sequence represented by the optimal set of functions. Claim 9 A computer-implemented method according to any one of claims 1 to 4, wherein the characteristic data further comprises one or more of minimum starting energy data for at least one component of the set of components, minimum activity period after starting data, and average maintenance time. Claim 10 A computer-implemented method according to any one of claims 1 to 4, wherein the repeated repetition includes repeating at separate fixed time intervals. Claim 11 A computer implementation method according to any one of claims 1 to 4, wherein the prediction period varies over time. Claim 12 A computer implementation method according to any one of claims 1 to 4, further comprising the step of determining the initial portion of the prediction period based at least on the maximum processing capacity of the data processing means executing the computer implementation method. Claim 13 delete Claim 14 A computer program stored on a medium, comprising a command that causes the computer to perform a method according to any one of claims 1 to 4 when the program is executed by the computer. Claim 15 A compressed gas system configured to be controlled according to a method according to any one of paragraphs 1 to 4.

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