CONTROLLING VAPOR COMPRESSION COOLING IN A THERMAL SYSTEM

Abstract

A method of controlling vapor compression cooling in a thermal system comprises: changing, using a controller and according to a first function, a first operating parameter of a first actuator of the thermal system, the first function defined by performing fitting to data, the first actuator controlling one of a speed of a fan of a condenser or a speed of a compressor; and changing, using the controller, a second operating parameter of a second actuator of the thermal system, the second actuator controlling another of the speed of the fan of the condenser or the speed of the compressor, the second operating parameter changed according to a second function that at least in part depends on a capacity request for the vapor compression cooling.

Description

TECHNICAL FIELD

This document relates to controlling vapor compression cooling in a thermal system.

BACKGROUND

Vapor compression cooling has been used in vehicles and other types of systems. Vehicles can use a thermal system to control the temperature of a passenger compartment, battery, and/or drivetrain. In some electric vehicles, the thermal system has been controlled by applying an algorithm referred to as controlling to a predefined efficient state. The predefined efficient state reflects a state of the thermal system under a given condition that is believed to be the most efficient. However, such approaches may have a lack of robustness.

Other control algorithms exist, such as a real-time extremum seeking control, and a real-time model-based optimal control. These approaches may be associated with a lack of reliability and/or other disadvantages.

SUMMARY

In a first aspect, a method of controlling vapor compression cooling in a thermal system comprises: changing, using a controller and according to a first function, a first operating parameter of a first actuator of the thermal system, the first function defined by performing fitting to data, the first actuator controlling one of a speed of a fan of a condenser or a speed of a compressor; and changing, using the controller, a second operating parameter of a second actuator of the thermal system, the second actuator controlling another of the speed of the fan of the condenser or the speed of the compressor, the second operating parameter changed according to a second function that at least in part depends on a capacity request for the vapor compression cooling.

Implementations can include any or all of the following features. The first actuator controls the speed of the fan of the condenser, wherein changing the first operating parameter increases or decreases the speed of the fan of the condenser, wherein the second actuator controls the speed of the compressor, and wherein changing the second operating parameter increases or decreases the speed of the compressor. Changing the speed of the compressor according to the second function comprises taking into account a requested mass flow derived from the capacity request. The first actuator controls the speed of the compressor, wherein changing the first operating parameter increases or decreases the speed of the compressor, wherein the second actuator controls the fan speed of the condenser, and wherein changing the second operating parameter increases or decreases the speed of the fan of the condenser. Controlling the vapor compression cooling comprises minimizing a cost function regarding power consumption by the compressor and the power consumption by the fan. The cost function comprises a sum of the power consumption by the compressor and the power consumption by the fan. The cost function is minimized using (i) a first partial derivative of the power consumption by the compressor, and (ii) a second partial derivative of the power consumption by the fan. The first and second functions represent the first and second partial derivatives, respectively. The first partial derivative is decomposed into a first relative partial derivative, wherein the second partial derivative is decomposed into a second relative partial derivative. The first actuator controls the speed of the fan of the condenser, wherein changing the first operating parameter increases or decreases the speed of the fan of the condenser, the method further comprising decomposing the first relative partial derivative into a third partial derivative and a fourth partial derivative multiplied with each other. The third partial derivative corresponds to a change in relative compressor power with respect to a change in saturated discharge temperature, and wherein the fourth partial derivative corresponds to the change in saturated discharge temperature with respect to a change in the speed of the fan of the condenser. The first function defined by performing fitting to the data comprises: (i) a first model fitted to data reflecting the third partial derivative, (ii) a second model data reflecting the fourth partial derivative, and (iii) a third model fitted to data reflecting the second relative partial derivative. The changing of the first operating parameter is done based on multiplying the first and second relative partial derivatives with a gain. The data comprises simulated data. The thermal system includes a non-electronic expansion device, and wherein the first and second operating parameters are changed without changing the non-electronic expansion device. The non-electronic expansion device comprises a passive expansion device or a mechanically adjusted expansion device. The method further comprises changing, using the controller, a third operating parameter of an expansion device of the thermal system, the third operating parameter changed to obtain a predefined value in the thermal system. Changing the third operating parameter comprises using a feedback loop. The predefined value is at least one of a superheat value a subcooling value, a mass flow rate, a suction pressure, a capacity of the thermal system, a discharge air temperature for an evaporator of the thermal system, or a coolant temperature for a chiller of the thermal system. The thermal system is part of a vehicle. The thermal system is part of a stationary energy storage.

In a second aspect, a method of controlling vapor compression cooling in a thermal system, the method comprising: setting (i) a first operating parameter of a first actuator of the thermal system and (ii) a second operating parameter of a second actuator of the thermal system; performing realtime optimization of the first and second operating parameters during operation of the thermal system based on minimization of a cost function taking into account at least the first and second actuators; and adjusting the first and second operating parameters based on the realtime optimization.

Implementations can include any or all of the following features. The first actuator controls one of a speed of a fan of a condenser or a speed of a compressor, and wherein the second actuator controls another of the speed of the fan of the condenser or the speed of the compressor. The realtime optimization is performed using a function fitted to data reflecting relative partial derivatives. The method further comprises setting (iii) a third operating parameter of an expansion device of the thermal system, wherein the performing realtime optimization is performed also of the third operating parameter, and wherein the third operating parameter is also adjusted based on the realtime optimization.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows an example of a thermal system.

FIGS. 2-3 show examples of a vapor compression cooling cycle that can be performed in the thermal system of FIG. 1.

FIGS. 4-7 show examples of diagrams with cost functions having minima, and effects of a mismatch in scaling on the minima.

FIGS. 8-11 show graphs with examples of point cloud slices at fixed conditions.

FIGS. 12-13 show bar plots with examples of total power consumption.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

This document describes examples of systems and techniques that control vapor compression cooling in a thermal system. A robust real-time discharge pressure optimization for vapor compression cooling applications can be provided, and can be used for a thermal control system of a vehicle, or of a stationary energy storage, to name just two examples. In some implementations, a control method can adjust condenser fan speed and compressor speed to minimize a cost function indicative of the vapor compression cycle cooling efficiency. Optionally, the position of an expansion device can also be adjusted by the control method. The gradient of the cost function can be decomposed into multiple relative partial derivatives, fitted offline using simulation data, and stored to be used in real time. The function decomposition and application method can be designed to be robust to mismatches between model expectations and real-world performance. More specifically, a process can involve: (i) adjusting one actuator (e.g., for condenser fan speed) as determined by a precalculated function and (ii) using a model back solve to adjust another actuator (e.g., to change compressor speed). In some implementations, a non-electronic expansion valve (e.g., a mechanically controlled expansion device or a passive expansion device) can be used in the thermal system that is not adjusted as part of the process. In other implementations, the process can also include (iii) changing the position of an expansion device to maintain a predefined value (e.g., superheat value, subcooling value, a mass flow rate, a suction pressure, a capacity of the thermal system, a discharge air temperature for an evaporator of the thermal system, or a coolant temperature for a chiller of the thermal system). For example, a minimization can be done on the one actuator and a constrained model back solve can be done on one or more other actuators.

In the previous approach of controlling to a predefined efficient state, the system may be characterized to be most efficient at a certain state under a given condition. The points are stored in a table or fitted into a formula, and a feedback control method (such as a proportional-integral-derivative (PID) controller, or full state feedback control) can be used to control to those points. One problem with this approach is that it may be unable to account for system-to-system variability if testing was used for characterization, or for unmodeled system dynamics if simulation data was used. The approach can be harder to implement when the definition for the condition includes many variables. If the optimal point can be defined as a function of one or two variables, testing and fitting with those variables as inputs may be doable, but for coupled and highly non-linear systems like vapor compression cycles, the efficiency is a function of many more coupled variables. As such, accounting for their effects becomes very challenging.

The existing real-time extremum seeking control may not be suitable in many applications. If a cost function is easy to compute in real time, an extremum seeking controller can adjust its outputs to minimize it by measuring the effect of an oscillatory input on the cost. This form of control may not be suitable for a thermal system as it requires continually injecting noise into the inputs to figure out the direction and amplitude of the change needed to minimize the cost. For an application in a vehicle thermal system, in order to optimize fan and compressor speed, the controller would need to oscillate both fan and compressor at a high enough amplitude so that the effect on the cost is measurable. This can negatively affect performance, reliability, and/or noise, vibration, harshness (NVH) characteristics.

The existing real-time model-based optimal control also may not be suitable in many applications. If a simplified model of the system were created that could capture the system dynamics, an optimal controller may be used to improve efficiency in real time. However, the controller would be limited by the accuracy of the model. For example, with vapor compression, even a detailed discretized thermofluidic model can deviate significantly in behavior from the real system.

The present subject matter can provide the advantage of being able to drive the system to an optimal point even if the model it was fitted on does not match the real system. An additional advantage can be that a method does not require a model of the system to run in real time, and can instead rely on fitted relative gradients which makes it less computationally expensive to run. Compared to extremum seeking control, the present subject matter has smoother output signals and is less susceptible to process lag or limited measurement resolution.

Examples herein refer to a vehicle. A vehicle is a machine that transports passengers or cargo, or both. A vehicle can have one or more motors using at least one type of fuel or other energy source (e.g., electricity). Examples of vehicles include, but are not limited to, cars, trucks, and buses. The number of wheels can differ between types of vehicles, and one or more (e.g., all) of the wheels can be used for propulsion of the vehicle, or the vehicle can be unpowered (e.g., when a trailer is attached to another vehicle). A vehicle can have one or more traction motors. For example, a traction motor can be an electric motor. As another example, a traction motor can be an internal combustion motor. The vehicle can include a passenger compartment accommodating one or more persons.

FIG. 1 shows an example of a thermal system 100. The thermal system 100 can be used with one or more other examples described elsewhere herein. The thermal system 100 is schematically shown to be implemented as part of a system 102. The system 102 represents any system where the thermal system 100 can perform thermal operations such as vapor compression cooling. In some implementations, the system 102 is a vehicle (e.g., an electric vehicle). For example, the thermal system 100 can provide vapor compression cooling for a passenger compartment and/or a battery/drivetrain of the vehicle. In some implementations, the system 102 is a stationary energy storage. For example, the stationary energy storage can include multiple electrochemical cells and be configured for delivering electric energy upon demand.

The thermal system 100 includes a compressor 104 that acts on refrigerant gas. The compressor 104 has an inlet 106 and an outlet 108 each connected to one or more respective refrigerant conduits in the thermal system 100. The compressor 104 can operate at any of multiple speeds (e.g., within a range of operating speeds expressed in revolutions per minute or another unit). As another example, the operation of the compressor 104 can be characterized in terms of the mass flow rate. The compressor 104 can have at least one actuator to facilitate control of the operation. For example, the actuator is used when setting and changing the operation of the compressor 104.

The thermal system 100 includes at least one condenser 110 that condenses refrigerant gas to a liquid state. In some implementations, multiple condensers can be used in the thermal system 100. The condenser 110 has an input receiving refrigerant that was output at the outlet 108 of the compressor 104. When the system 102 is a vehicle, the condenser 110 can serve as part of the vehicle's air conditioning system. The condenser 110 can have a fan 112 that can be operated to control the condensation. For example, when multiple condensers are used, each condenser can have its own fan. The fan 112 can operate at any of multiple speeds (e.g., within a range of operating speeds expressed in revolutions per minute or another unit). The fan 112 can have at least one actuator to facilitate control of the operation. For example, the actuator is used when setting and changing the operation of the condenser 110.

The thermal system 100 includes an expansion device 114 that controls the flow of refrigerant. The expansion device 114 can be an electronic expansion device or a non-electronic expansion device (e.g., a mechanically controlled expansion device or a passive expansion device). The expansion device 114 can be, but is not limited to, a thermal expansion valve, an electronic expansion valve, a thermostatic expansion valve, a fixed orifice, a capillary tube, or any other type of flow restriction. An inlet of the expansion device 114 can receive refrigerant that was output at an outlet of the condenser 110. The expansion device 114 can be adjusted to any of multiple operating positions (e.g., within a range of positions, each of which provides a greater or smaller flow of refrigerant). When the expansion device 114 is electronically controllable, it can have at least one actuator to facilitate control of the operating position.

The thermal system 100 includes at least one cooling device 116 for cooling one or more aspects of the system 102. For example, the cooling device 116 includes the component(s) for receiving the heat that is to be removed by way of the vapor compression cooling. In some implementations, the system 102 is a vehicle, and the cooling device 116 can then include an evaporator for cooling a passenger compartment. As another example, the cooling device 116 can include a chiller for a battery pack of an electric vehicle and/or for some aspect of the powertrain. As such, the thermal system 100 can include one or more return paths of refrigerant arriving at the inlet 106 of the compressor 104.

The thermal system 100 includes a controller 118 for controlling some or all aspects of the vapor compression cooling. The controller 118 can include any processor-based device or component that executes instructions. The controller 118 can generate control signals that are conveyed by wire or wirelessly in the thermal system 100. The controller 118 can control compression in the thermal system 100 by way of a signal 120 to the actuator of the compressor 104. The controller 118 can control condensation in the thermal system 100 by way of a signal 122 to the actuator of the fan 112 of the condenser 110. In implementations where the expansion device 114 is controlled as part regulating the vapor compression cooling, the controller 118 can control the position of the expansion device 114 by way of a signal 124 to the actuator of the expansion device 114. The controller 118 can additionally or instead control one or more other aspects of the thermal system 100. By contrast, the cooling device 116 may not be controlled by the controller 118.

The controller 118 can seek to optimize the operation of the thermal system 100 in terms of the power consumption. For example, running vapor compression cooling more efficiently will lower the energy consumption and therefore increase the range of an electric vehicle, or will improve the utility of a stationary energy storage. In some implementations, the controller 118 performs realtime optimization of respective operating parameters for the compressor 104 and the fan 112. Optionally, the controller 118 can also adjust the expansion device 114 as part of the realtime optimization. For example, the realtime optimization can be done in form of minimization of a cost function of at least compressor speed and fan speed by way of partial derivatives and at least one fitted function.

FIGS. 2-3 show examples of a vapor compression cycle 200 that can be performed in the thermal system 100 of FIG. 1. The vapor compression cycle 200 can be used with one or more other examples described elsewhere herein. The vapor compression cycle 200 is shown in a diagram having pressure indicated on the vertical axis and specific enthalpy indicated on the horizontal axis. The diagram includes isotherms 202, each of which marks respective states characterized in having a specific refrigerant temperature. The diagram includes an area 204 covering those states in the diagram where the refrigerant is a mixture of liquid and vapor. The vapor compression cycle 200 includes a step 206 where the compressor performs work to increase the pressure and temperature of the refrigerant; a step 208 where heat is transferred to the surroundings using the condenser with the help of the fan; a step 210 where the expansion device lowers the pressure and temperature of the refrigerant; and a step 212 where heat from the cooling device transfers to the refrigerant.

Multiple different versions of the vapor compression cycle 200 can satisfy a given requirement of cooling capacity. While these different solutions deliver the same thermal result, they may use different amounts of energy, meaning that the thermal system has higher or lower efficiency depending on which solution is being used. In FIG. 2, an arrow 214 schematically indicates a decrease of the compressor power in the step 206, and this is associated with an arrow 216 that schematically indicates an increase in the power used by the condenser fan in the step 208. By contrast, in FIG. 3 an arrow 300 schematically indicates an increase of the compressor power in the step 206, and this is associated with an arrow 302 that schematically indicates a decrease of the power used by the condenser fan in the step 208. As such, while operating at a given suction pressure with at least one fixed value (e.g., superheat, subcooling, a mass flow rate, a suction pressure, a capacity of the thermal system, a discharge air temperature for an evaporator of the thermal system, or a coolant temperature for a chiller of the thermal system), the effect of increasing the condenser fan speed (i.e., condenser air flow rate), e.g., as illustrated by the arrow 216, is a lower discharge pressure, which decreases the compressor power at the cost of a higher fan power, e.g., as illustrated by the arrow 214, and vice versa for a decrease in the condenser fan speed, e.g., as illustrated by the arrows 300 and 302. The reduction of the discharge pressure at constant subcooling and superheating increases the refrigeration effect (enthalpy difference across the evaporator/chiller). This can further reduce compressor power by reducing the required compressor speed to achieve the same cooling demand, which can be characterized as a secondary effect of fan adjustment. An additional secondary effect can also exist in the thermal system: when the fan adjusts, the compressor will adjust based on another controller, which affects total power.

As such, there exists an optimum operating condition that delivers the required cooling capacity at a minimum operating power. The present subject matter can seek to find and operate the thermal system at such an optimum operating condition by changing some or all characteristics of the vapor compression cycle 200, as schematically illustrated in FIGS. 2-3 by the arrows 214-216 and 300-302. Some examples will now be provided.

The power used for vapor compression cooling, the operating points at which the actuators run, and the provided cooling capacities are all coupled. Since the delivered cooling capacity is governed by the load, optimizing the cycle efficiency can be expressed in terms of minimizing component power under a fixed cooling capacity condition:

$\mathrm{minimize}\to {\mathrm{Power}}_{\mathrm{RfgCycle}}\left(\mathrm{Actuators}\right){|}_{\stackrel{.}{Q}=\mathrm{Demand}},$

where Power_RfgCycle represents the component power being minimized in the refrigeration cycle, Actuators signifies that the component power depends on the setting of multiple actuators during operation, and {dot over (Q)}=Demand represents the fixed cooling capacity condition under which the minimization is to be performed.

In electric vehicles multiple cooling devices can be used in the thermal system. A chiller can be used to cool the powertrain and battery via a coolant, and an evaporator can be used to cool the cabin via air. Under most operating conditions where cooling is required, potential adjustments in the refrigerant conditions at the suction of the compressor are limited. For cabin cooling, the evaporator fan is controlled to target specific discharge air temperatures and flow rates based on user inputs. This limits the possibility of performing suction side optimization. For powertrain or battery cooling, the suction condition is a function of the coolant temperature entering the chiller and the coolant flow rate. Changes on the coolant flow rate are limited to meet thermal load distribution requirements (i.e., to prevent large deviations in battery cell temperatures). This makes the suction pressure highly coupled to temperatures in battery and drive unit components. The above circumstances can leave the compressor speed, the condenser fan speed, and (optionally) the position of the expansion device as the main three components with an effect on cooling efficiency. The above minimization can therefore be expressed as:

$\mathrm{minimize}\to {\mathrm{Power}}_{\mathrm{RfgCycle}}\left(\mathrm{FanSpd},\mathrm{CmprSpd},\mathrm{ExvPosn}\right){|}_{\stackrel{.}{Q}=\mathrm{Demand}},$

where FanSpd is the speed of the condenser fan, CmprSpd is the speed of the compressor, and ExvPosn is the position of the expansion device. In other implementations, one or more other properties can also or instead be used for defining the cost function. For example, measured current or mechanical power can be used.

In some implementations, the problem can be simplified further by defining the operating point for compressor speed and position of the expansion device as a function of an assumed optimized state and the fixed demand requirement. In other implementations, the operating point of another component can instead be used. This way, the optimization can be done through one actuator (e.g., fan speed adjustments) directly, and through another actuator (e.g., compressor speed and position of the expansion device) indirectly. As a more specific example, assuming that one wants to operate at given superheat and subcooling values, if the condenser fan is driving the discharge condition to an optimal value while accounting for the effect on the other components, the compressor speed would have a one-to-one mapping with requested capacity at any point. The position of the expansion device would then have a single solution that sets superheat at a required value. If multiple suction side paths are used, each with its own requested capacity, then there is only one set of expansion device restrictions that results in the correct capacity distribution between them at a given superheat value.

Excluding suction side components (e.g., a chiller pump and/or an evaporator fan), the power to be minimized from the compressor and the condenser fan can be used as the cost function:

$\begin{array}{cc}\mathrm{Cost}=\left({\mathrm{Power}}_{\mathrm{Cmp}}+{\mathrm{Power}}_{\mathrm{Fan}}\right){|}_{\stackrel{.}{Q}=\mathrm{Demand}},& \left(1\right)\end{array}$

where Cost is the cost function, Power_Cmp is the compressor power, and Power_Fan is the power of the condenser fan.

Optimization can be performed using one or more partial derivatives. To minimize the cost through fan speed adjustment directly, the partial derivative of the cost function in (1) with respect to fan speed can be used:

$\begin{array}{cc}\frac{\partial \mathrm{Cost}}{\partial \mathrm{Fanspd}}=\frac{\partial {\mathrm{Power}}_{\mathrm{cmp}}}{\partial \mathrm{Fanspd}}+\frac{\partial {\mathrm{Power}}_{\mathrm{fan}}}{\partial \mathrm{Fanspd}},& \left(2\right)\end{array}$

where

$\frac{\partial {\mathrm{Power}}_{\mathrm{cmp}}}{\partial \mathrm{Fanspd}}$

is the partial derivative of compressor power with respect to fan speed, and

$\frac{\partial {\mathrm{Power}}_{\mathrm{fan}}}{\partial \mathrm{FanSpd}}$

is the partial derivative of condenser fan power with respect to fan speed.

The two partial derivatives in (2) can be fitted offline using data (for example, simulation data). To make the minimization more robust to modeling uncertainties, the partial derivatives can be decomposed into relative partial derivatives with respect to offline power data multiplied by the measured power terms. The respective partial derivatives can be expressed as:

$\begin{array}{cc}\frac{\partial {\mathrm{Power}}_{\mathrm{cmp}}}{\partial \mathrm{FanSpd}}={\mathrm{Power}}_{\mathrm{cmp}}*\frac{\partial {\mathrm{RelativePower}}_{\mathrm{cmp}}}{\partial \mathrm{FanSpd}},\mathrm{and}& \left(3\right)\end{array}$ $\begin{array}{cc}\frac{\partial {\mathrm{Power}}_{\mathrm{fan}}}{\partial \mathrm{FanSpd}}={\mathrm{Power}}_{\mathrm{fan}}*\frac{\partial {\mathrm{RelativePower}}_{\mathrm{fan}}}{\partial \mathrm{FanSpd}},& \left(4\right)\end{array}$

where Power_Cmp is the measured compressor power,

$\frac{\partial {\mathrm{RelativePower}}_{\mathrm{cmp}}}{\partial \mathrm{FanSpd}}$

is the relative partial derivative of compressor power, Power_fan is the measured condenser fan power, and

$\frac{\partial {\mathrm{RelativePower}}_{\mathrm{fan}}}{\partial \mathrm{FanSpd}}$

is the relative partial derivative of condenser fan power.

Using relative partial derivatives, if there is a mismatch in scale (i.e., if the function is stretched by a scalar over the power axis), the partial derivative would still drive the system to its most optimal point after rescaling. Scale mismatch can have an effect on the optimal point, as will now be exemplified.

FIGS. 4-7 show examples of diagrams 400, 500, 600, and 700 with cost functions having minima, and effects of a mismatch in scaling on the minima. The cost functions can be used with one or more other examples described elsewhere herein. In each of the diagrams 400-700, power is indicated against the vertical axis and fan speed is indicated against the horizontal axis. A graph 402 represents measured compressor power, and a graph 404 represents modeled compressor power. A graph 406 represents measured fan power, and a graph 408 represents modeled fan power. A discrepancy can occur between modeled and measured values because of model uncertainties, system aging system variability, etc. For example, the graphs 402 and 404 here differ from each other (i.e., the graph 402 is scaled relative to the graph 404), as do the graphs 406 and 408 (i.e., the graph 406 is scaled relative to the graph 408). In the diagram 500, a graph 502 corresponds to the sum of the graphs 402 and 406 (i.e., a sum of measured power), and a graph 504 corresponds to the sum of the graphs 404 and 408 (i.e., a sum of modeled power). The graph 502 has a minimum at a fan speed 506, and the graph 504 has a minimum at a fan speed 508. The fan speeds 506 and 508 are different from each other, which means that an actual cost function minimum may not occur at the point indicated by the model. However, the present subject matter can optimize also when such discrepancies occur by using the gradients normalized by the compressor and fan powers.

To also account for a shift in the expected operating condition versus the model, the partial derivative of the compressor power in (3) can be decomposed into two partial derivatives:

$\begin{array}{cc}\frac{\partial {\mathrm{Power}}_{\mathrm{cmp}}}{\partial \mathrm{FanSpd}}={\mathrm{Power}}_{\mathrm{cmp}}*\frac{\partial {\mathrm{RelativePower}}_{\mathrm{cmp}}}{\partial T_{\mathrm{SDischarge}}}*\frac{\partial T_{\mathrm{SDischarge}}}{\partial \mathrm{FanSpd}},& \left(5\right)\end{array}$

where

$\frac{\partial {\mathrm{RelativePower}}_{\mathrm{cmp}}}{\partial T_{\mathrm{SDis}charge}}$

is the relative partial derivative of compressor power with respect to saturated discharge temperature, and

$\frac{\partial T_{\mathrm{SDis}charge}}{\partial \mathrm{FanSpd}}$

is the relative partial derivative of saturated discharge temperature with respect to fan speed. That way, if the saturated discharge temperature condition shifted from what the model is expecting, the gradient map would also shift based on real-time measurements. Diagrams 600 and 700 show examples of how shifting the compressor power cost and scaling the fan power cost can affect the location of the optimal point.

A graph 602 represents measured compressor power, and a graph 604 represents modeled compressor power. A graph 606 represents measured fan power, and a graph 608 represents modeled fan power. A discrepancy can occur between modeled and measured values. For example, the graphs 602 and 604 here differ from each other (i.e., the graph 602 is shifted relative to the graph 604), as do the graphs 606 and 608 (i.e., the graph 606 is scaled relative to the graph 608). In the diagram 700, a graph 702 corresponds to the sum of the graphs 602 and 606 (i.e., a sum of measured power), and a graph 704 corresponds to the sum of the graphs 604 and 608 (i.e., a sum of modeled power). The graph 702 has a minimum at a fan speed 706, and the graph 704 has a minimum at a fan speed 708. The fan speeds 706 and 708 are different from each other, which means that an actual cost function minimum may not occur at the point indicated by the model.

Therefore, whether discrepancies exist between the modeled and actual compressor and fan power, or between the modeled and actual saturated discharge temperatures, an optimization method can still robustly move the system towards the optimum point by using gradients that are normalized by the respective cost function component (i.e., compressor or condenser fan power).

The partial derivatives in (3), (4), and/or (5) can be used in seeking the optimum operating condition for the thermal system. To avoid having to provide the controller with significant volumes of preexisting data to be used during operation, one or more functions can be fitted to representative data, and the controller can then evaluate the function in real time.

To obtain the equations for the partial derivatives, a set of simulations covering the expected operating range can be executed, and the partial derivatives can be computed numerically. A reasonable equation form can be selected as a reduced order model of the gradient, and a minimization algorithm (e.g., using regression analysis) can be used to fit the parameters of the model. For the relative compressor power partial derivative with respect to saturated discharge temperature in (5), the model can have the following form:

$$\begin{gathered} \begin{array}{cc}\frac{\partial {\mathrm{RelativePower}}_{\mathrm{cmp}}}{\partial T_{\mathrm{SDis}charge}}=\frac{P6*\mathrm{PR}+P7*{\mathrm{FSpeed}}_{\mathrm{cmp}}}{\mathrm{DENOMINATOR}},\mathrm{with}\text{ \\ DENOMINATOR=P0+P⁢1*P⁢R+P⁢2*FSpeedcmp+P⁢3*P⁢R2+P⁢4*FSpeedcmp2+P⁢5*PR*FSpeedcmp,where⁢ \\ PR:Discharge⁢to⁢Suction⁢Pressure⁢Ratio=PD⁢i⁢s⁢c⁢h⁢a⁢r⁢g⁢ePS⁢u⁢c⁢t⁢i⁢o⁢n, \\ FSpeedcmp:Fractional⁢Compressor⁢Speed=SpeedcmpMaxSpeedcmp,}& \left(6\right)\end{array} \end{gathered}$$

andP0 through P7 are parameters that are to be fitted based on the data.

The fitting can be performed using multiple models. In some implementations, a compressor model, a condenser model, and/or a fan model can be used. For example, the compressor model can be based on efficiency maps to reflect isentropic efficiency and volumetric efficiency. Data for performing the fitting can be obtained by collecting performance data or by performing simulations. In some implementations, simulations are performed within respective ranges of cooling capacity targets, saturated suction temperatures, and saturated discharge temperatures. For the simulations, superheat and subcooling can be fixed. An example of the fitting will now be described.

FIGS. 8-11 show graphs 800, 900, 1000, and 1100 with examples of point cloud slices at fixed conditions. The fitted functions can be used with one or more other examples described elsewhere herein. Each of the graphs 800-1100 shows a three-dimensional diagram with two horizontal axes and one vertical axis. In the graph 800, one of the horizontal axes shows saturated discharge temperature, and the other horizontal axis shows saturated suction temperature. The vertical axis shows change in compressor (cmp) power due to change in saturated discharge temperature (SDT). The graph 800 includes points 802 (shown as crosses) that are the modeled (e.g., simulated) data. The parameters of the selected function (e.g., the parameters P0 through P7 in (6) above) can be selected so that the function closely fits to the points 802. Here, points 804 that conform to the points 802 represent the fitted function.

One or more other functions can be fitted. For the partial derivative of the saturated discharge temperature with respect to fan speed in (5), the following can be used:

$\begin{array}{cc}\frac{\partial T_{\mathrm{SDis}charge}}{\partial \mathrm{FanSpd}}=\left(\mathrm{P0}+P1*{\mathrm{Speed}}_{\mathrm{cmp}}+P2*\mathrm{FanSpd}+P3*{\mathrm{Speed}}_{\mathrm{cmp}}^2+P4*{\mathrm{FanSpd}}^2+P5*{\mathrm{FanSpd}}^3\right)*\left(1+P6*\Delta T_{\mathrm{SDT}\to Amb}+P7*\Delta T_{\mathrm{SDT}\to Amb}^2\right),& \left(7\right)\end{array}$

where

$\frac{\partial T_{\mathrm{SDis}charge}}{\partial \mathrm{FanSpd}}:$

Change in saturated discharge temperature due to a change in fan speed,

• • Speed_cmp: Compressor speed,
  • FanSpd: Condenser fan speed,
  • ΔT_SDT→Amb: Saturated discharge to ambient temperature delta=T_SDischarge−T_Ambient, and
  • P0 through P7 are parameters that are to be fitted based on the data.

The parameters in (7) can be fitted using a compressor model, a condenser model, an evaporator model, an expansion device model, and a condenser fan model. For example, the compressor model can be based on efficiency maps. As another example, the expansion device model can feature a flow coefficient map. Data for performing the fitting can be obtained by collecting performance data or by performing simulations. In some implementations, simulations are performed within respective ranges of cooling capacity targets, saturated suction temperatures, ambient temperatures, and fan duties. For the simulations, a value (e.g., superheat, subcooling, a mass flow rate, a suction pressure, a capacity of the thermal system, a discharge air temperature for an evaporator of the thermal system, or a coolant temperature for a chiller of the thermal system) can be fixed. An example of the fitting will now be described.

In the graph 900 of FIG. 9, one of the horizontal axes shows saturated discharge temperature, and the other horizontal axis shows compressor speed. The vertical axis shows change in saturated discharge temperature due to change in fan speed. The graph 900 includes points 902 (shown as crosses) that are the modeled (e.g., simulated) data. The parameters of the selected function (e.g., the parameters P0 through P7 in (7) above) can be selected so that the function closely fits to the points 902. Here, points 904 that conform to the points 902 represent the fitted function. If the data in the graph 800 (FIG. 8) were to be multiplied with the data in the graph 900, the product would indicate how the relative compressor power varies with changes in fan speed.

One or more other functions can be fitted. For the relative fan power partial derivative with respect to fan speed in (4), the following can be used:

$\begin{array}{cc}\frac{\partial {\mathrm{RelativePower}}_{Fan}}{\partial \mathrm{FanSpd}}=\frac{1}{\left(F0+F1*\mathrm{FanSpd}\right)},& \left(8\right)\end{array}$

where F0 and F1 are parameters that are to be fitted based on the data. Data for performing the fitting of (8) can be obtained by collecting performance data or by performing simulations. In some implementations, simulations are performed within a range of fan speeds.

After one actuator (e.g., condenser fan speed) has been adjusted, another actuator (e.g., for compressor speed) can be back solved to ensure that the requested cooling capacity is maintained. In some implementations, volumetric efficiency of the compressor can be fitted to data for use in back solving for compressor speed. The calculation of the gradient using the pre-fitted function to adjust the first controller can account for the change (secondary effect) in the second actuator as a result of the back solve. For example, when initially determining that fan speed will change compressor speed by a particular amount, this also accounts for the fact that compressor speed will change in response to fan speed, using models exemplified below.

Data for performing the fitting can be obtained by collecting performance data or by performing simulations. In some implementations, simulations are performed within respective ranges of compressor speeds, saturated suction temperatures, saturated discharge temperatures, and superheat values. A model can fit compressor volumetric efficiency as a function of saturated suction temperature and saturated discharge temperature:

$\begin{array}{cc}{\dot{m}}_{Cmp}=\rho \left(T_{SSuction},\mathrm{Superheat}\right)*\mathrm{SweptVolume}*\frac{{\mathrm{Speed}}_{\mathrm{cmp}}}{60}*{\eta }_{\mathrm{vol}}\left(T_{SSuction},T_{\mathrm{SDis}charge}\right),& \left(9\right)\end{array}$ $\begin{array}{cc}{\eta }_{vol}\left(T_{SSuction},T_{\mathrm{SDischarge}}\right)=E0+E1*T_{SSuction}+E2*T_{\mathrm{SDischarge}}+E3*T_{SSuction}^2+E4*T_{\mathrm{SDischarge}}^2+E5*T_{SSuction}{T}_{\mathrm{SDischarge}},\mathrm{and}& \left(10\right)\end{array}$ $\begin{array}{cc}\rho \left(T_{SSuction},\mathrm{Superheat}\right)=D0+D1*T_{SSuction}+D2*\mathrm{Superheat}+D3*T_{SSuction}^2+D4*{\mathrm{Superheat}}^2+D5*T_{SSuction}\mathrm{Superheat},& \left(11\right)\end{array}$

• • where
  • {dot over (m)}_cmp is compressor mass flow rate,
  • T_Ssuction is saturated suction temperature,
  • T_SDischarge is saturated discharge temperature,
  • Superheat is suction superheat,
  • ρ is refrigerant inlet density,
  • Speed_cmp is compressor speed,
  • η_vol is compressor volumetric efficiency, and
  • E0 through E5 and D0 through D5 are parameters that are to be fitted based on the data.

In the graph 1000 of FIG. 10, one of the horizontal axes shows saturated discharge temperature, and the other horizontal axis shows saturated suction temperature. The vertical axis shows mass flow rate. The graph 1000 includes points 1002 (shown as crosses) that are the modeled (e.g., simulated) data. The parameters of the selected function (e.g., the parameters E0 through E5 in (10) above, and D0 through D5 in (11) above) can be selected so that the function closely fits to the points 1002. Here, points 1004 that conform to the points 1002 represent the fitted function.

As mentioned above, a controller can perform optimization in real time using measurement data and one or more functions fitted as exemplified herein. In some implementations, a real-time optimization technique can make discrete calls to a controller in which a cost gradient is calculated and at least one actuator is adjusted. For example, fan speed can be adjusted in a negative direction of the slope of the cost function:

$\begin{array}{cc}\frac{\partial \mathrm{FanSpd}}{\partial t}=-K*\frac{\partial \mathrm{Cost}}{\partial \mathrm{FanSpd}},& \left(12\right)\end{array}$

where K is a tunable gain that can change the speed of fan speed adjustment.

Combining (12) with (5), (4), and (2) gives:

$\begin{array}{cc}\frac{\partial \mathrm{FanSpd}}{\partial t}=-K*\left({\mathrm{Power}}_{\mathrm{cmp}}*\frac{\partial {\mathrm{RelativePower}}_{\mathrm{cmp}}}{\partial T_{\mathrm{SDis}charge}}*\frac{\partial T_{\mathrm{SDis}charge}}{\partial \mathrm{FanSpd}}+{\mathrm{Power}}_{\mathrm{fan}}*\frac{\partial {\mathrm{RelativePower}}_{\mathrm{fan}}}{\partial \mathrm{FanSpd}}\right)& \left(13\right)\end{array}$

In the graph 1100 of FIG. 11, one of the horizontal axes shows saturated discharge temperature, and the other horizontal axis shows saturated suction temperature. The vertical axis shows power. The graph 1100 includes points 1102 (shown as dots) that are the fan power, points 1104 (shown as crosses) that are compressor power, and points 1106 (shown as crosses) that are the sums of respective ones of the points 1102 and 1104. The graph 1100 includes arrows 1108 that schematically illustrate operations of iteratively stepping toward a minimum according to (13). The algorithm can seek to move in state space along the slope toward a minimum of the points 1106. This slice reflects an assumption that superheat is steady. Also, saturated suction temperature may not be controlled directly, so the saturated suction temperature can be considered to be fixed and the optimization can move in two dimensions toward the minimum of the points 1106. The actual slope can adapt to real time measurements of the actual costs. For example, the respective derivatives of the points 1102 and 1104 can be stretched in real time to account for system-to-system differences versus a model. As another example, scaling can be performed. As another example, a partial derivative can be decomposed to improve the optimization.

In some implementations, the compressor speed can be optimized indirectly through fan speed adjustments. As the fan speed is modified to minimize the cost, the suction and discharge conditions can also change; to keep the supplied cooling capacity constant, the compressor speed can be back solved using a fitted compressor model. The compressor speed can be solved as a function of requested mass flow, which can be derived from a capacity request through inlet and outlet enthalpies:

${\dot{m}}_{Cmp}=\frac{{\mathrm{Demand}}_{\mathrm{cmp}}}{\left(h_{\mathrm{evapInlet}}\left(\mathrm{subc}\mathrm{ool},T_{\mathrm{SDis}charge}\right)-h_{\mathrm{evapOutlet}}\left(\mathrm{superheat},T_{SSuction}\right)\right)},$ $\mathrm{and}$ ${\mathrm{Speed}}_{\mathrm{cmp}}=\frac{60*\left({\stackrel{.}{m}}_{\mathrm{Cmp}}\right)}{\rho \left(T_{SSuction}\mathrm{Superheat}\right)*\mathrm{SweptVolume}*{\eta }_{\mathrm{vol}}\left(T_{SSuct\mathrm{ion}},T_{\mathrm{SDis}charge}\right)}.$

A position of an expansion device can be optimized indirectly. Optimization gradient fits can be evaluated at an assumed fixed superheat. In some implementations, a feedback loop is used. For example, the expansion device can be feedback controlled using a PID controller to maintain superheat around that target. In some implementations, the position of the expansion device is not adjusted as part of the optimization.

FIGS. 12-13 show bar plots 1200 and 1300 with examples of total power consumption. Each of the bar plots 1200-1300 shows, on the vertical axis, a simulation of energy used during a charging session, and on the horizontal axis, ambient temperature. The charging sessions in the bar plots 1200 and 1300 occurred for the same length of time, and the charging session in the bar plot 1200 was performed at a higher power rate than the charging session in the bar plot 1300. At each ambient temperature, the bar on the right shows the power used according to an implementation of the present subject matter, and the bar on the left (having a thicker outline) shows the power used according to a reference procedure at the same ambient temperature. Thus, the bar plot 1200 shows, at six different ambient temperatures, the power used by the reference procedure and the present implementation, respectively. The bar plot 1300 shows, at four different ambient temperatures, the power used by the reference procedure and the present implementation, respectively. Here, the reference procedure involved predefining optimal condenser and suction pressure points, and controlling the expansion device proportionally as a function of battery temperature.

Each bar in the bar plots 1200 and 1300 shows the distribution of energy consumed in the thermal system. At each ambient temperature in the bar plots 1200 and 1300, the present subject matter reduces the thermal power consumption compared to the reference procedure. At many of the ambient temperatures, the reduction is substantial. Similar optimizations can be obtained with cabin-only cooling and dual cabin and chiller cooling.

As such, the present subject matter can provide more efficient and/or faster charging; can provide an increased vehicle range when cabin cooling at low speeds; can provide an improved effective round-trip efficiency for a stationary energy storage and vehicle-to-grid applications; and can improve NVH characteristics by reducing compressor cabin noise and vibration in vehicle implementations.

The terms “substantially” and “about” used throughout this Specification are used to describe and account for small fluctuations, such as due to variations in processing. For example, they can refer to less than or equal to ±5%, such as less than or equal to ±2%, such as less than or equal to ±1%, such as less than or equal to ±0.5%, such as less than or equal to ±0.2%, such as less than or equal to ±0.1%, such as less than or equal to ±0.05%. Also, when used herein, an indefinite article such as “a” or “an” means “at least one.”

It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein.

A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the specification.

In addition, the logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. In addition, other processes may be provided, or processes may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Accordingly, other implementations are within the scope of the following claims.

While certain features of the described implementations have been illustrated as described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that appended claims are intended to cover all such modifications and changes as fall within the scope of the implementations. It should be understood that they have been presented by way of example only, not limitation, and various changes in form and details may be made. Any portion of the apparatus and/or methods described herein may be combined in any combination, except mutually exclusive combinations. The implementations described herein can include various combinations and/or sub-combinations of the functions, components and/or features of the different implementations described.

Claims

1. A method of controlling vapor compression cooling in a thermal system, the method comprising: changing, using a controller and according to a first function, a first operating parameter of a first actuator of the thermal system, the first function defined by performing fitting to data, the first actuator controlling one of a speed of a fan of a condenser or a speed of a compressor; andchanging, using the controller, a second operating parameter of a second actuator of the thermal system, the second actuator controlling another of the speed of the fan of the condenser or the speed of the compressor, the second operating parameter changed according to a second function that at least in part depends on a capacity request for the vapor compression cooling.

2. The method of claim 1, wherein the first actuator controls the speed of the fan of the condenser, wherein changing the first operating parameter increases or decreases the speed of the fan of the condenser, wherein the second actuator controls the speed of the compressor, and wherein changing the second operating parameter increases or decreases the speed of the compressor.

3. The method of claim 2, wherein changing the speed of the compressor according to the second function comprises taking into account a requested mass flow derived from the capacity request.

4. The method of claim 1, wherein the first actuator controls the speed of the compressor, wherein changing the first operating parameter increases or decreases the speed of the compressor, wherein the second actuator controls the fan speed of the condenser, and wherein changing the second operating parameter increases or decreases the speed of the fan of the condenser.

5. The method of claim 1, wherein controlling the vapor compression cooling comprises minimizing a cost function regarding power consumption by the compressor and the power consumption by the fan.

6. The method of claim 5, wherein the cost function comprises a sum of the power consumption by the compressor and the power consumption by the fan.

7. The method of claim 5, wherein the cost function is minimized using (i) a first partial derivative of the power consumption by the compressor, and (ii) a second partial derivative of the power consumption by the fan.

8. The method of claim 7, wherein the first and second functions represent the first and second partial derivatives, respectively.

9. The method of claim 7, wherein the first partial derivative is decomposed into a first relative partial derivative, wherein the second partial derivative is decomposed into a second relative partial derivative.

10. The method of claim 9, wherein the first actuator controls the speed of the fan of the condenser, wherein changing the first operating parameter increases or decreases the speed of the fan of the condenser, the method further comprising decomposing the first relative partial derivative into a third partial derivative and a fourth partial derivative multiplied with each other.

11. The method of claim 10, wherein the third partial derivative corresponds to a change in relative compressor power with respect to a change in saturated discharge temperature, and wherein the fourth partial derivative corresponds to the change in saturated discharge temperature with respect to a change in the speed of the fan of the condenser.

12. The method of claim 11, wherein the first function defined by performing fitting to the data comprises: (i) a first model fitted to data reflecting the third partial derivative, (ii) a second model data reflecting the fourth partial derivative, and (iii) a third model fitted to data reflecting the second relative partial derivative.

13. The method of claim 9, wherein the changing of the first operating parameter is done based on multiplying the first and second relative partial derivatives with a gain.

14. The method of claim 1, wherein the data comprises simulated data.

15. The method of claim 1, wherein the thermal system includes a non-electronic expansion device, and wherein the first and second operating parameters are changed without changing the non-electronic expansion device.

16. The method of claim 15, wherein the non-electronic expansion device comprises a passive expansion device or a mechanically adjusted expansion device.

17. The method of claim 1, further comprising changing, using the controller, a third operating parameter of an expansion device of the thermal system, the third operating parameter changed to obtain a predefined value in the thermal system.

18. The method of claim 17, wherein changing the third operating parameter comprises using a feedback loop.

19. The method of claim 17, wherein the predefined value is at least one of a superheat value a subcooling value, a mass flow rate, a suction pressure, a capacity of the thermal system, a discharge air temperature for an evaporator of the thermal system, or a coolant temperature for a chiller of the thermal system.

20. The method of claim 1, wherein the thermal system is part of a vehicle.

21. The method of claim 1, wherein the thermal system is part of a stationary energy storage.

22. A method of controlling vapor compression cooling in a thermal system, the method comprising: setting (i) a first operating parameter of a first actuator of the thermal system and (ii) a second operating parameter of a second actuator of the thermal system;performing realtime optimization of the first and second operating parameters during operation of the thermal system based on minimization of a cost function taking into account at least the first and second actuators; andadjusting the first and second operating parameters based on the realtime optimization.

23. The method of claim 22, wherein the first actuator controls one of a speed of a fan of a condenser or a speed of a compressor, and wherein the second actuator controls another of the speed of the fan of the condenser or the speed of the compressor.

24. The method of claim 22, wherein the realtime optimization is performed using a function fitted to data reflecting relative partial derivatives.

25. The method of claim 22, further comprising setting (iii) a third operating parameter of an expansion device of the thermal system, wherein the performing realtime optimization is performed also of the third operating parameter, and wherein the third operating parameter is also adjusted based on the realtime optimization.