Refrigeration cycle device and optimization method

Abstract

This multi-type refrigeration cycle device comprises: a refrigerant circuit including a plurality of expansion valves; and a control device for setting an opening degree command value for the plurality of expansion valves. The control device, in an initial step, sets a target opening degree for each of the plurality of expansion valves to a plurality of provisional opening degrees, and, in a first step, determines whether the plurality of provisional opening degrees satisfy an inequality constraint condition. If the inequality constraint condition is not satisfied, the control device: in a second step, fixes one of the provisional opening degrees to an inequality constraint end; and, in a third step, orthogonally projects points representing the plurality of provisional opening degrees onto an affine hyperplane in a space that is reduced in dimension by removing the already-fixed provisional opening degree from the plurality of provisional opening degrees, the subtracted total opening degree obtained by subtracting the already-fixed provisional opening degree from the total opening degree being employed as a segment in the affine hyperplane, and resets the resulting points to a provisional opening degree and then returns the process to the first step. If the inequality constraint condition is satisfied, the control device sets the provisional opening degree at the present time to the opening degree command value in a fourth step.

Description

Refrigeration cycle device and optimization method

[0001] The present disclosure relates to a multi-type refrigeration cycle apparatus in which a plurality of utilization-side heat exchangers are connected to a heat source-side heat exchanger, and an optimization method applicable to the refrigeration cycle apparatus.

[0002] Japanese Patent No. 6910554 (Patent Document 1) discloses a multi-type air conditioner. This air conditioner includes a refrigerant circuit including a compressor, a heat source heat exchanger, multiple expansion valves connected in parallel to the heat source heat exchanger, and multiple user heat exchangers connected in series to the multiple expansion valves. This air conditioner optimizes refrigerant distribution among the user heat exchangers by controlling the apertures of the multiple expansion valves. Specifically, this air conditioner allocates the total aperture of the multiple expansion valves to the multiple expansion valves and calculates appropriate aperture command values ​​for the multiple expansion valves by solving an optimization problem with upper and lower aperture limits for the multiple expansion valves as constraints.

[0003] Japanese Patent No. 6910554 Japanese Patent Application Laid-Open No. 2017-133777

[0004] As described above, the air conditioner disclosed in Patent Document 1 calculates appropriate opening command values ​​for a plurality of expansion valves by solving an optimization problem.

[0005] However, Patent Document 1 does not mention any specific method for solving the optimization problem. If a general method for solving the optimization problem is used, problems such as an increase in the size of the computer, a longer calculation period, or a decrease in control performance may occur depending on the calculation load or calculation accuracy. In addition, the need to set design parameters may arise, which may increase the design load.

[0006] The present disclosure has been made to solve the above-mentioned problems, and its purpose is to obtain a solution to an optimization problem applicable to a multi-type refrigeration cycle device with high accuracy and a small computational load.

[0007] (Item 1) A refrigeration cycle apparatus according to the present disclosure includes a refrigerant circuit including a compressor, a heat source heat exchanger, multiple expansion valves connected in parallel to the heat source heat exchanger, and multiple user side heat exchangers connected in series to the multiple expansion valves, and a control device that controls the multiple expansion valves so that their openings correspond to multiple opening command values. The control device includes a total calculation unit that calculates a total opening of the multiple expansion valves, a target calculation unit that calculates multiple target openings representing target values ​​for the openings of the multiple expansion valves, a limit setting unit that sets multiple limit ranges defined by lower and upper limit values ​​for the openings of the multiple expansion valves, and an optimization unit that sets the multiple opening command values ​​using the total opening, the multiple target openings, and the multiple limit ranges. The target calculation unit calculates the multiple target openings so that the sum of the multiple target openings matches the total opening.

[0008] the optimization unit: in an initial step, sets a plurality of target openings to a plurality of provisional openings, respectively; in a first step, determines whether or not an inequality constraint condition that the plurality of provisional openings are within their corresponding limit ranges is satisfied; if the inequality constraint condition is not satisfied, in a second step, calculates and compares an upper limit exceedance index indicating the degree to which the plurality of provisional openings exceed their upper limit values ​​and a lower limit exceedance index indicating the degree to which they exceed their lower limit values, and fixes the provisional opening that deviates the most from the limit value with the larger index to the upper limit or lower limit value of that provisional opening; in a third step, in a space that has been reduced in dimension by removing the provisional openings that have already been fixed from the plurality of provisional openings, points representing the plurality of provisional openings are orthogonally projected onto an affine hyperplane whose intercept is the subtracted total opening obtained by subtracting the provisional openings that have already been fixed from the total opening, and sets the points as the plurality of provisional openings, and returns to the first step; and repeats the processing from the first step to the third step until the inequality constraint condition is satisfied; If the inequality constraint condition is satisfied, then in the fourth step, a plurality of provisional openings when the inequality constraint condition is satisfied are set as a plurality of opening command values, respectively.

[0009] (Section 2) A refrigeration cycle apparatus according to the present disclosure includes a refrigerant circuit including a compressor, a heat source heat exchanger, multiple expansion valves connected in parallel to the heat source heat exchanger, and multiple user side heat exchangers connected in series to the multiple expansion valves, and a control device that controls the multiple expansion valves so that their openings correspond to multiple opening command values. The control device includes a total calculation unit that calculates a total opening of the multiple expansion valves, a target calculation unit that calculates multiple target openings representing target values ​​for the openings of the multiple expansion valves, a limit setting unit that sets multiple upper limit openings representing upper limits of the openings of the multiple expansion valves and multiple lower limit openings representing lower limits of the openings of the multiple expansion valves, and an optimization unit that sets multiple opening command values ​​using the total opening, the multiple target openings, the multiple upper limit openings, and the multiple lower limit openings. The target calculation unit calculates the multiple target openings so that the sum of the multiple target openings matches the total opening.

[0010] In an initial step, the optimization unit divides a lower limit vector having elements of a plurality of lower limit openings, an upper limit vector having elements of a plurality of upper limit openings, and a target value vector having elements of a plurality of target openings by the total opening to obtain an adjustment lower limit vector a, an adjustment upper limit vector b, and an adjustment target value vector r. Ｓ and calculate the adjustment target value vector r from the adjustment lower limit value vector a. Ｓ and the vector obtained by subtracting the upper limit vector b from the adjustment target value vector r Ｓ The vector obtained by subtracting λ and the vector obtained by combining and sorting in ascending order is called the range vector λ ｒａｎｇｅ The index vector J is a vector whose first element is 1 and whose second element is twice the number N of the expansion valves, and the adjustment total range vector h is defined by the following equation (12):

[0011]

[0012] In the first step, it is determined whether J[2] - J[1], which is the value obtained by subtracting the value of the first element J[1] from the value of the second element J[2] of the index vector J, is equal to or less than 1. If J[2] - J[1] is not equal to or less than 1, in the second step, the value obtained by truncating the decimal point of the average value of the index vector J is used as the provisional index J. Ｐ The provisional adjusted total value h Ｐ is calculated using the following formula (14),

[0013]

[0014] In the third step, the provisional adjustment total value h Ｐ Determine whether or not h is equal to or greater than 1, and calculate the provisional adjusted total value h Ｐ If is 1 or more, the second element J[2] of the index vector J is assigned a temporary index J Ｐ and assign the provisional adjustment total value h to the second element h[2] of the adjustment total range vector h. Ｐ Substitute and return to the first step, and the provisional adjusted total value h Ｐ If is not equal to or greater than 1, the first element J[1] of the index vector J is assigned a provisional index J Ｐ and assign the provisional adjustment total value h to the first element h[1] of the adjustment total range vector h. Ｐ Substitute and return to the first step, repeat the processes from the first step to the third step until J[2] - J[1] is 1 or less, if J[2] - J[1] is 1 or less, in the fourth step, Lagrange multiplier λ ＊ is calculated using the following formula (16),

[0015]

[0016] The optimal solution calculated by the following equation (17) is set as a plurality of opening command values.

[0017]

[0018] (Clause 3) The optimization method according to the present disclosure, when a total value, a restriction vector including an upper limit value and a lower limit value, and a target value vector whose elements have the same total value as the total value are given to a computer or calculated by the computer's internal calculation, causes the computer to: in an initial step, set the provisional value vector as the target value vector; in a first step, determine whether or not an inequality constraint condition that the provisional value vector is within a restriction range defined by the restriction vector is satisfied; if the inequality constraint condition is not satisfied, in a second step, calculate and compare an upper limit exceedance index indicating the degree to which the element of the provisional value vector exceeds the upper limit value and a lower limit exceedance index indicating the degree to which the element exceeds the lower limit value; fix the element that deviates the most from the restriction value with the larger index to the upper limit value or the lower limit value of that element; In the third step, in a space that has been reduced in dimension by removing the already fixed elements from the provisional value vector, the point representing the provisional value vector is orthogonally projected onto an affine hyperplane whose intercept is the total value obtained by subtracting the already fixed elements from the total value, and the point is reset to the provisional value vector, and the process returns to the first step. The processes from the first step to the third step are repeated until the inequality constraint condition is satisfied, and if the inequality constraint condition is satisfied, in the fourth step, the provisional value vector when the inequality constraint condition is satisfied is output as a solution vector, and the process ends.

[0019] (4) The optimization method according to the present disclosure, when a total value, an upper limit value vector, a lower limit value vector, and a target value vector whose elements have a total value equal to the total value, are given to a computer or calculated by an internal calculation of the computer, performs the following steps in an initial step: Ｓ and calculate the adjustment target value vector r from the adjustment lower limit value vector a. Ｓ and the vector obtained by subtracting the upper limit vector b from the adjustment target value vector r Ｓ The vector obtained by subtracting λ and the vector obtained by combining and sorting in ascending order is called the range vector λ ｒａｎｇｅLet J be a vector whose first element is 1 and whose second element is twice the number of elements N of the target value vector, and define an adjustment total range vector h by the following formula (12):

[0020]

[0021] In the first step, it is determined whether J[2] - J[1], which is the value obtained by subtracting the value of the first element J[1] from the value of the second element J[2] of the index vector J, is equal to or less than 1. If J[2] - J[1] is not equal to or less than 1, in the second step, the value obtained by truncating the decimal point of the average value of the index vector J is used as the provisional index J. Ｐ The provisional adjusted total value h Ｐ is calculated using the following formula (14),

[0022]

[0023] In the third step, the provisional adjustment total value h Ｐ Determine whether or not h is equal to or greater than 1, and calculate the provisional adjusted total value h Ｐ If is 1 or more, the second element J[2] of the index vector J is assigned a temporary index J Ｐ and assign the provisional adjustment total value h to the second element h[2] of the adjustment total range vector h. Ｐ Substitute and return to the first step, and the provisional adjusted total value h Ｐ If is not equal to or greater than 1, the first element J[1] of the index vector J is assigned a provisional index J Ｐ and assign the provisional adjustment total value h to the first element h[1] of the adjustment total range vector h. Ｐ Substitute and return to the first step, repeat the processes from the first step to the third step until J[2] - J[1] is 1 or less, if J[2] - J[1] is 1 or less, in the fourth step, Lagrange multiplier λ ＊ is calculated using the following formula (16),

[0024]

[0025] The vector calculated by the following equation (17) is output as a solution vector and the process ends.

[0026]

[0027] The following process is executed.

[0028] According to the present disclosure, a solution to an optimization problem applicable to a multi-type refrigeration cycle device can be obtained with high accuracy and with a small calculation load.

[0029] 10 is a diagram schematically illustrating an example of the configuration of a multi-type refrigeration cycle device. FIG. 11 is a diagram schematically illustrating the configuration of a control device. FIG. 12 is a block diagram illustrating an example of the configuration of a portion of the control device that controls an expansion valve. FIG. 13 is a flowchart (part 1) illustrating an example of the processing procedure of an optimization unit. FIG. 14 is a diagram (part 1) conceptually illustrating the process of setting a command opening in a time series. FIG. 15 is a diagram (part 2) conceptually illustrating the process of setting a command opening in a time series. FIG. 16 is a diagram (part 3) conceptually illustrating the process of setting a command opening in a time series. FIG. 17 is a diagram (part 5) conceptually illustrating the process of setting a command opening in a time series. FIG. 18 is a diagram (part 1) conceptually illustrating the process of setting a command opening in a time series. FIG. 19 is a diagram (part 2) conceptually illustrating the process of setting a command opening in a time series.

[0030] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are designated by the same reference numerals, and description thereof will not be repeated.

[0031] FIG. 1 is a schematic diagram illustrating an example of the configuration of a multi-type refrigeration cycle apparatus 1 according to this embodiment. The refrigeration cycle apparatus 1 includes a control device 2, a compressor 3, a four-way valve 4, a heat source-side heat exchanger 5, multiple expansion valves 6a-6d installed in parallel branched pipes, and multiple user-side heat exchangers 7a-7d connected in series to the multiple expansion valves 6a-6d. A refrigerant circuit is formed by connecting the compressor 3, the heat source-side heat exchanger 5, each of the expansion valves 6a-6d, and each of the user-side heat exchangers 7a-7d via pipes. A refrigerant flows through the refrigerant circuit. The following description will be given using an example in which the refrigeration cycle apparatus 1 is an air conditioner, but the refrigeration cycle apparatus 1 is not limited to being an air conditioner.

[0032] The refrigeration cycle device 1 is configured to be switchable between cooling operation and heating operation. In Fig. 1, solid arrows indicate the direction of refrigerant flow during cooling operation, and dashed arrows indicate the direction of refrigerant flow during heating operation.

[0033] First, the cooling operation will be described. The compressor 3 draws in a refrigerant, compresses it, and discharges it. The compressor 3 may be configured such that its capacity (the amount of refrigerant delivered per unit time) can be changed by, for example, arbitrarily changing the drive frequency using an inverter circuit (not shown). The four-way valve 4 switches the refrigerant flow path to switch between cooling operation and heating operation.

[0034] During cooling operation, the heat source-side heat exchanger 5 is installed on the discharge side of the compressor 3 and functions as a condenser. The condenser exchanges heat between the refrigerant and air, condensing and liquefying the refrigerant while heating the air. Multiple expansion valves 6a to 6d are respectively provided in the piping between the heat source-side heat exchanger 5 and the user-side heat exchangers 7a to 7d in the refrigerant circuit. Each of the expansion valves 6a to 6d is configured as a variable-opening expansion valve, such as an electronic expansion valve, and adjusts the pressure and flow rate of the refrigerant. During cooling operation, the user-side heat exchangers 7a to 7d are respectively installed on the piping on the discharge side of the expansion valves 6a to 6d and function as evaporators. The evaporators exchange heat between the refrigerant and air, evaporating the refrigerant and cooling the air. The vaporized refrigerant is drawn into the compressor 3.

[0035] Next, heating operation will be described. During heating operation, the refrigerant discharged from the compressor 3 flows in the direction of the dashed arrows due to switching of the refrigerant flow path by the four-way valve 4. The refrigerant discharged from the four-way valve 4 flows into each of the user-side heat exchangers 7a to 7d. During heating operation, each of the user-side heat exchangers 7a to 7d functions as a condenser. The heat-source-side heat exchanger 5 is installed in the piping on the discharge side of the expansion valves 6a to 6d and functions as an evaporator. Subsequent operation is the same as in cooling operation.

[0036] The refrigeration cycle apparatus 1 also includes, for example, temperature sensors 11, 12, 13a to 13d, 14a to 14d, and 17, and pressure sensors 15 and 16. Temperature sensor 17 is installed in the discharge piping of compressor 3 and detects the temperature of refrigerant discharged from compressor 3. Temperature sensor 11 is installed in the piping on the gas pipe side of heat source-side heat exchanger 5 and detects the temperature of refrigerant flowing into heat source-side heat exchanger 5 in cooling operation, and detects the temperature of refrigerant discharged from heat source-side heat exchanger 5 in heating operation. Temperature sensor 12 is installed in the piping on the liquid pipe side of heat source-side heat exchanger 5 and detects the temperature of refrigerant discharged from heat source-side heat exchanger 5 in cooling operation, and detects the temperature of refrigerant flowing into heat source-side heat exchanger 5 in heating operation. Temperature sensors 13a to 13d are installed on the piping on the liquid pipe side of the use-side heat exchangers 7a to 7d, and detect the temperature of refrigerant flowing into the use-side heat exchangers 7a to 7d in cooling operation, and the temperature of refrigerant discharged from the use-side heat exchangers 7a to 7d in heating operation. Temperature sensors 14a to 14d are installed on the piping on the gas pipe side of the use-side heat exchangers 7a to 7d, and detect the temperature of refrigerant discharged from the use-side heat exchangers 7a to 7d in cooling operation, and the temperature of refrigerant flowing into the use-side heat exchangers 7a to 7d in heating operation. Pressure sensor 15 detects the pressure of refrigerant discharged from compressor 3. Pressure sensor 16 detects the pressure of refrigerant flowing into compressor 3.

[0037] Although FIG. 1 illustrates a case in which four user-side heat exchangers 7a to 7d are connected in parallel to one heat-source-side heat exchanger 5, the number of user-side heat exchangers 7 connected to the heat-source-side heat exchanger 5 (i.e., the number of expansion valves 6) is not limited to four and may be two, three, or five or more. Furthermore, the refrigeration cycle apparatus 1 according to this embodiment is designed to function properly even when only one user-side heat exchanger 7 is connected to the heat-source-side heat exchanger 5. This is an important feature because even in multi-type refrigeration cycle apparatuses, single-unit operation is required. The refrigerant circuit shown in FIG. 1 is the minimum configuration required to realize the refrigeration cycle according to the present disclosure, and may include a capillary tube, an accumulator, a receiver, and the like, as necessary. Although the condenser and evaporator are described as exchanging heat between air and refrigerant, they do not necessarily have to exchange heat with air; they may exchange heat with water or geothermal heat.

[0038] 2 is a diagram showing a schematic configuration of the control device 2. The temperature sensors 11, 12, 13a to 13d, 14a to 14d, and 17 and the pressure sensors 15 and 16 are connected to the control device 2, and data such as temperature or pressure is input from each sensor. In addition, user commands are input to the control device 2 via an operation unit (not shown).

[0039] The control device 2 has a control processing device 21, a timing device 22, and a storage device 23. The control processing device 21 performs processes such as calculations and judgments based on input data such as temperature, and controls the devices of the refrigeration cycle device 1, such as the compressor 3 and the expansion valves 6a to 6d. The storage device 23 is a device that stores data required for the control processing device 21 to perform processing. The storage device 23 has a volatile memory (not shown) such as a random access memory (RAM) that can temporarily store data, and a hard disk, a non-volatile auxiliary memory (not shown) such as a flash memory that can store data for the long term. The timing device 22 is composed of, for example, a timer, and is used to measure time. The timing device 22 is used for judgments, etc. by the control processing device 21.

[0040] The control processing device 21 can be configured, for example, by a microcomputer having an arithmetic device such as a CPU (Central Processing Unit). The control processing device 21 executes processing based on program data to realize control. Note that the control performed by the control processing device 21 is not limited to processing by software such as a program, and can also be processed by dedicated hardware (electronic circuitry).

[0041] 3 is a block diagram showing an example of the configuration of the part that controls the expansion valves 6a to 6d in the control device 2. The control device 2 includes a total opening calculation unit 101, a target opening calculation unit 102, a limit opening setting unit 103, and an optimization unit 104.

[0042] The total opening calculation unit 101 calculates a total opening St, which is the sum of the openings of the expansion valves 6a to 6d. The total opening St is calculated, for example, by a PI (proportional-integral) controller for controlling the discharge temperature of the compressor 3 to a target discharge temperature. Note that the total opening St is not necessarily limited to a value for controlling the discharge temperature, and may be a value for controlling, for example, the degree of subcooling or the degree of superheating. Furthermore, the total opening St may be calculated to close or open at a constant speed. The total opening St calculated by the total opening calculation unit 101 is sent to the target opening calculation unit 102 and the optimization unit 104.

[0043] The target opening calculation unit 102 distributes the total opening St among the openings of the four expansion valves 6a to 6d and calculates multiple target openings Sm (=Sm1, Sm2, ... Sm4), each representing a target value for the opening of each of the expansion valves 6a to 6d. The distribution method may be, for example, equal or unequal distribution. In the case of unequal distribution, for example, the opening of an expansion valve connected to a large-capacity use-side heat exchanger is distributed so as to be greater than the opening of an expansion valve connected to a small-capacity use-side heat exchanger. Furthermore, the distribution ratio does not need to be a constant value but may be a variable value that changes depending on sensor values, etc. For example, the distribution ratio may be changed so as to reduce the opening of an expansion valve connected to a use-side heat exchanger installed in a room with a small difference between the indoor temperature and the set temperature (required load). Furthermore, for example, the distribution ratio may be changed so as to maintain the degree of superheating or subcooling within an appropriate range.

[0044] In either case, the target opening calculation unit 102 makes the sum of the target openings Sm (= Sm1 + Sm2 + ... + Sm4) equal to the total opening St. Furthermore, each of the target openings Sm is clearly physically greater than or equal to 0. The target openings Sm calculated by the target opening calculation unit 102 are sent to the optimization unit 104.

[0045] The opening limit setting unit 103 sets a limit range for the opening of the expansion valves 6 a to 6 d. Specifically, the opening limit setting unit 103 sets a plurality of upper limit openings Su (=Su1, Su2, ...Su4) each representing an upper limit value of the opening of the expansion valves 6 a to 6 d, and a plurality of lower limit openings Sl (=Sl1, Sl2, ...Sl4) each representing a lower limit value of the opening of the expansion valves 6 a to 6 d.

[0046] The upper limit opening degree Su and the lower limit opening degree S1 may be constant values ​​determined by the upper and lower limit values ​​of the opening degree of each expansion valve in the specifications, or may be variable values ​​that change depending on the operating state. When the upper limit opening degree Su and the lower limit opening degree S1 are changed depending on the operating state, for example, the upper limit opening degree Su and the lower limit opening degree S1 may be changed so as to maintain the degree of superheat or subcooling within an appropriate range. However, the upper limit opening degree Su and the lower limit opening degree S1 are set to satisfy the following formula (a):

[0047] 0≦Sli≦Sui (i=1, 2, . . . , 4) (a) The total opening St is set so as to satisfy the following formula (b) with respect to the upper limit opening Su and the lower limit opening Sl.

[0048] Sl1 + Sl2 + ... + Sl4 ≦ St ≦ Su1 + Su2 + ... + Su4 ... (b) The upper limit opening Su (= Su1, Su2, ... Su4) and the lower limit opening Sl (= Sl1, Sl2, ... Sl4) set by the limit opening setting unit 103 are sent to the optimization unit 104.

[0049] The optimization unit 104 sets a plurality of command openings S (= S1, S2, ... S4) that respectively represent command values ​​for the openings of the expansion valves 6 a to 6 d using the total opening St, the target opening Sm, the upper limit opening Su, and the lower limit opening S1. Specifically, the optimization unit 104 sets the command openings S (= S1, S2, ... S4) that satisfy the following first to third conditions:

[0050] (First condition) The sum of the command openings S (= S1 + S2 + ... + S4) is equal to the total opening St. (Second condition) Each command opening S (= S1, S2, ... S4) is within the limited range between the corresponding upper limit opening Su and lower limit opening Sl.

[0051] (Third condition) Each command opening S (= S1, S2, ... S4) is closest to the corresponding target opening Sm within the range that satisfies the first and second conditions. Note that "closest" means that the Euclidean distance is the smallest.

[0052] In other words, the optimization unit 104 sets the command opening to a solution Si (i=1, 2, . . . , 4) of the optimization problem shown in the following equation (1).

[0053]

[0054] FIG. 4 is a flowchart showing an example of a processing procedure executed by the optimization unit 104 to efficiently solve the optimization problem shown in equation (1).

[0055] First, the optimization unit 104 initializes the provisional openings Sp (=Sp1, Sp2, ... Sp4) temporarily used in the process of solving the optimization problem to the target openings Sm (=Sm1, Sm2, ... Sm4) (step S00). Since the sum of the target openings Sm is the total opening St, the sum of the provisional openings Sp at the time of initialization is also equal to the total opening St.

[0056] Next, the optimization unit 104 determines whether all the provisional opening degrees Sp satisfy the inequality constraint condition shown in the above equation (1), i.e., whether each provisional opening degree Sp is within the restricted range between the corresponding upper limit opening degree Su and lower limit opening degree Sl (step S10).

[0057] If any of the provisional openings Sp does not satisfy the inequality constraint (NO in step S10), the optimization unit 104 calculates a lower limit exceedance index A, which indicates the degree to which all of the provisional openings Sp exceed their lower limits, and an upper limit exceedance index B, which indicates the degree to which all of the provisional openings Sp exceed their upper limits, and compares these in magnitude, selects an element to be constrained based on the comparison result, and fixes the element to be constrained to the inequality constraint end (step S20). Specifically, if the lower limit exceedance index A is greater than the upper limit exceedance index B, the optimization unit 104 selects, from among the elements of the provisional openings Sp that do not satisfy the lower limit constraint, the element that most deviates from the lower limit constraint end (lower limit opening S1), as the element to be constrained, and fixes the element to be constrained to the lower limit constraint end of that element. On the other hand, if the upper limit exceedance index B is greater than the lower limit exceedance index A, the optimization unit 104 selects the element that deviates most from the upper limit constraint end (upper limit opening Su) from among the elements of the temporary opening Sp that do not satisfy the upper limit constraint condition as the element to be constrained, and fixes the element to be constrained to the upper limit constraint end of that element. Hereinafter, the processing of step S20 will also be referred to as "constraining the solution element."

[0058] Next, the optimization unit 104 calculates a point representing the provisional opening Sp in a space reduced in dimension by removing the provisional openings that have already been fixed up to the present time from the four elements (= Sp1, Sp2, . . . Sp4) of the provisional opening Sp, and calculates the point representing the provisional opening Sp as a subtraction total opening S obtained by subtracting the provisional openings that have already been fixed from the total opening St. ｎｆThe point obtained by orthogonally projecting onto an affine hyperplane having an intercept of is set as the provisional opening Sp (step S30). Hereinafter, the process of step S30 will also be referred to as "orthogonal projection".

[0059] Thereafter, the optimization unit 104 returns the process to step S10. The optimization unit 104 repeats the constraint process of step S20 and the orthogonal projection process of step S30 until it is determined in step S10 that all the temporary opening degrees Sp satisfy the inequality constraint conditions.

[0060] Then, if all the provisional openings Sp satisfy the inequality constraints (YES in step S10), the current provisional openings Sp are the solution to the optimization problem, so the optimization unit 104 sets the current provisional openings Sp to the command openings S and terminates the processing (step S40).

[0061] 5 to 9 are diagrams conceptually illustrating, in time series, the process of setting the command opening S by repeating the processing of steps S10 to S30 in FIG. 4. To facilitate understanding, FIGS. 5 to 9 show an example in which three command openings S1, S2, and S3 are set using a three-dimensional space defined by three mutually orthogonal axes y1, y2, and y3 (i.e., an example in which there are three elements to be optimized). The axes y1, y2, and y3 are coordinate axes that represent the values ​​of the command openings S1, S2, and S3, respectively.

[0062] First, the optimization unit 104 initializes the target opening Sm (Sm1, Sm2, Sm3) to the first temporary opening Sp(1) in the three-dimensional space shown in FIG. 5 . The rectangular parallelepiped constraint region shown in FIG. 5 is a region satisfying the inequality constraint condition, i.e., a restricted range between the upper limit opening Su and the lower limit opening Sl (i.e., the range of Su1≦y1≦Sl1, Su2≦y2≦Sl2, and Su3≦y3≦Sl3). Also, the affine hyperplane shown in FIG. 5 , with the total opening St as its intercept, is a plane connecting points where the sum of the three command openings S1, S2, and S3 equals the total opening St. Therefore, in the three-dimensional space shown in FIG. 5 , searching for a point that is located on the affine hyperplane, is included in the rectangular parallelepiped constraint region, and is closest to the target opening Sm, corresponds to finding a solution to the optimization problem.

[0063] Since the sum of the three elements Sm1, Sm2, and Sm3 of the target opening Sm is the total opening St, the first provisional opening Sp(1) is placed on an affine hyperplane with the total opening St as its intercept. However, in the example shown in Figure 5, the first provisional opening Sp(1) is located outside the constraint region and does not satisfy the inequality constraint.

[0064] Of the three elements Sm1, Sm2, and Sm3 of the temporary opening Sp(1), the element constrained by the constraint on the solution element is element Sm3. Therefore, the optimization unit 104 sets a temporary fixed opening Sp(1)fix by fixing element Sm3 of the temporary opening Sp(1) to the upper limit opening Su3, which is the upper end of the inequality constraint, as shown in Figure 6. As a result, the three elements of the temporary fixed opening Sp(1)fix become (Sm1, Sm2, Su3). The temporary fixed opening Sp(1)fix is ​​a point representing the fixed opening Sp(1) in a two-dimensional space (= y1y2 plane) that has been reduced in dimension by removing axis y3 of the fixed element Sm3 from the three axes y1, y2, and y3.

[0065] Then, as shown in FIG. 7, in a two-dimensional space (=y1y2 plane) that has been reduced in dimension by removing the axis y3 of the fixed element Sm3 from the three axes y1, y2, and y3, the optimization unit 104 calculates a point representing the fixed opening Sp(1) (i.e., the provisional fixed opening Sp(1)fix) as a subtraction total opening S obtained by subtracting the fixed element Su3 from the total opening St. ｎｆ The point orthogonally projected onto an affine hyperplane (=straight line) with (1) as an intercept is set as the second provisional opening Sp(2). As a result, the three elements of the second provisional opening Sp(2) become the points (Sm1pro, Sm2pro, Su3) shown in FIG.

[0066] As shown in FIG. 7, the second provisional opening Sp(2) is still outside the constraint region and does not satisfy the inequality constraint.

[0067] Therefore, the optimization unit 104 sets a temporary fixed opening Sp(2)fix by fixing the element Sm2pro, which is out of the constraint region, of the three elements (Sm1pro, Sm2pro, Su3) of the second temporary opening Sp(2) to the upper limit opening Sl2, which is the lower end of the inequality constraint, as shown in Fig. 8. As a result, the three elements of the temporary fixed opening Sp(2)fix become (Sm1pro, Sl2, Su3).

[0068] Then, as shown in FIG. 9, the optimization unit 104 calculates a subtraction total opening degree S, which is obtained by subtracting the two fixed elements S, Su3 from the total opening degree St in a one-dimensional space (=y1 line) that has been reduced in dimension by removing the two fixed axes y2 and y3 from the three axes y1, y2, and y3. ｎｆ The point obtained by orthogonally projecting the provisional fixed opening Sp(2)fix onto an affine hyperplane (=point) with (2) as an intercept is set as the third provisional opening Sp(3).

[0069] 9, the third provisional opening Sp(3) is the optimal solution in which the sum of the three elements is the total opening St, does not deviate from the constraint region, and is closest to the target opening Sm. Therefore, the optimization unit 104 sets the third provisional opening Sp(3) as the command opening S and ends the process.

[0070] In this way, when there are three elements to be optimized, in this embodiment, the solution to the above optimization problem can be obtained by repeating the constraint process in step S20 and the orthogonal projection process in step S30 twice. Generalizing to the case where the number of elements to be optimized is "N", in this embodiment, the above optimization problem can be solved by repeating the processes in steps S10 to S30 "N-1" times.

[0071] Fig. 10 expresses the processing contents of the flowchart in Fig. 4 in mathematical form. For generalization, the dimension is set to "N" in Fig. 10. This dimension "N" corresponds to the number of elements to be optimized (the number of expansion valves) being "N".

[0072] First, in step S00, the optimization unit 104 initializes the vector variable f and the tentative solution vector y. Specifically, the optimization unit 104 sets f = 0 and y = r. Here, the tentative solution vector y is a vector whose elements are the tentative opening Sp. "r" is a target opening vector whose elements are the target opening Sm. Therefore, y = r means that the tentative opening Sp is set to the target opening Sm. Furthermore, the vector variable f is a vector variable in which the index of an element of the tentative solution vector y whose solution is not yet determined is assigned "0" and the index of an element whose solution is determined is assigned "1."

[0073] Next, in step S10, the optimization unit 104 determines whether ymin≦y≦ymax holds. Here, "ymin" is a lower limit vector whose elements are the lower limit opening S1, and "ymax" is an upper limit vector whose elements are the upper limit opening Su. Therefore, "ymin≦y≦ymax" means that all elements of the provisional solution vector y satisfy the inequality constraint.

[0074] If ymin≦y≦ymax is not satisfied (NO in step S10), the optimization unit 104 determines in step S20 whether to constrain the element that deviates from the upper limit value or the element that deviates from the lower limit value, and then selects the element of the provisional solution vector y that deviates the most from the inequality constraint end on the determined side as the element to be constrained, and fixes the element to be constrained to the inequality constraint end.

[0075] Specifically, first, in step S21, a process is executed to determine which element of the provisional solution vector y should be constrained and whether it should be constrained to an upper or lower limit. In step S21, an index j of the element to be constrained and a variable w indicating whether it should be constrained to an upper or lower limit are set. Details of step S21 will be described later. In the next step S22, it is determined whether the variable w is "1", which indicates that it should be constrained to an upper limit. If the variable w is "1", y[j] = ymax[j] is executed to constrain it to an upper limit, i.e., the element y[j] of the provisional solution vector y to be constrained is fixed to the upper limit ymax[j] (step S23). If the variable w is not "1", y[j] = ymin[j] is executed, i.e., the element y[j] of the provisional solution vector y to be constrained is fixed to the lower limit ymin[j] (step S24). Furthermore, in either case, in step S25, f[j]=1 is set, that is, the index of the fixed element in the vector variable f is set to "1".

[0076] Next, in step S30, the optimization unit 104 calculates a point representing the provisional solution vector y in a space that has been reduced in dimension by removing the elements that have already been fixed up to the present time as the subtracted total opening S, which is the total opening S obtained by subtracting the fixed elements from the total opening S. ｎｆ The point obtained by orthogonally projecting onto an affine hyperplane having an intercept of is reset to the provisional solution vector y. Specifically, in step S30, the optimization unit 104 performs the following calculation.

[0077] First, the number of fixed elements N ｆ , and the number of unfixed elements N ｎｆ is calculated using the following equation (2).

[0078]

[0079] Furthermore, the determinant I that extracts the fixed elements ｆ , and a determinant I for extracting non-fixed elements ｎｆ is set as shown in the following equation (3).

[0080]

[0081] Furthermore, the fixed elements of the temporary solution vector y are converted to 0 to obtain a temporary fixed solution vector r ｔｍｐ , and the subtraction total opening S obtained by subtracting the fixed element from the total opening St ｎｆ is calculated using the following equation (4).

[0082]

[0083] Then, the provisional solution vector y is reset by the following equation (5): The provisional solution vector y reset by the equation (5) is calculated by subtracting the provisional fixed solution vector r from the provisional fixed solution vector r in a space that has been reduced in dimension by removing the elements that have already been fixed up to the present time. ｔｍｐ The point representing the total opening S is obtained by subtracting the fixed element from the total opening S. ｎｆ is a vector representing a point orthogonally projected onto an affine hyperplane with intercepts.

[0084]

[0085] After resetting the tentative solution vector y through the above calculations, the optimization unit 104 returns the process to step S10.

[0086] The optimization unit 104 repeats the processes of steps S20 and S30 until it is determined in step S10 that all elements of the provisional solution vector y satisfy the inequality constraints.

[0087] If all elements of the tentative solution vector y satisfy the inequality constraints (YES in step S10), the optimization unit 104 sets the current tentative solution vector y as the solution to the optimization problem and terminates the process (step S40).

[0088] FIG. 11 is a flowchart showing the detailed procedure of the process of step S21 in FIG. 10 (the process of setting the index j of the element to be constrained and the variable w indicating whether the element should be constrained to an upper limit or a lower limit).

[0089] First, the optimization unit 104 calculates a lower limit exceeding index A and an upper limit exceeding index B shown in the following formula (6) (step S211).

[0090]

[0091] Next, the optimization unit 104 determines whether the lower limit exceeding index A is greater than the upper limit exceeding index B (step S212).

[0092] If the lower limit exceeding index A is greater than the upper limit exceeding index B (YES in step S212), the optimization unit 104 sets the index j of the element to be constrained by the following equation (7) (step S213).

[0093]

[0094] Then, the optimization unit 104 sets the variable w to "-1", which indicates that it should be constrained to the lower limit (step S214).

[0095] On the other hand, if the lower limit overrun index A is not greater than the upper limit overrun index B (NO in step S212), the optimization unit 104 determines whether the upper limit overrun index B is greater than the lower limit overrun index A (step S215).

[0096] If the upper limit exceeding index B is greater than the lower limit exceeding index A (YES in step S215), the optimization unit 104 sets the index j of the element to be constrained by the following equation (8) (step S216).

[0097]

[0098] Then, the optimization unit 104 sets the variable w to "1" which indicates that the variable w should be constrained to the upper limit (step S217).

[0099] On the other hand, if the upper limit exceedance index B matches the lower limit exceedance index A (NO in step S215), the optimization unit 104 first defines the upper and lower limit difference vector dy by the following equation (9), and sets the element index j to be constrained by the following equation (10) (step S218).

[0100]

[0101]

[0102] Next, the optimization unit 104 determines whether the index j of the element to be constrained is greater than N (step S219). If the index j of the element to be constrained is equal to or less than N (NO in step S219), the optimization unit 104 sets the variable w to "-1" which indicates that the element should be constrained to the lower limit (step S214).

[0103] On the other hand, if the index j of the element to be constrained is greater than N (YES in step S219), the optimization unit 104 updates the index j of the element to be constrained to j-N (step S220), and sets the variable w to "1" indicating that the element should be constrained to the upper limit (step S217).

[0104] FIG. 12 shows an example of a simulation result of the control operation when the control device 2 performs the above process during cooling operation.

[0105] The graph in the upper left of Figure 12 is a time series graph of the target discharge temperature and discharge temperature of compressor 3. At the start of the simulation, the discharge temperature is 70°C and the target discharge temperature is 71°C, but as time passes, the discharge temperature converges to the target discharge temperature of 71°C. When the target discharge temperature is changed to 80°C at 90 minutes, the discharge temperature converges to the target discharge temperature of 80°C as time passes.

[0106] The graph at the bottom left of Figure 12 is a time-series graph of the degree of superheat at the outlet of each of the user-side heat exchangers 7a to 7d. In this simulation, the upper limit of the degree of superheat was set to 5°C, and at the start of the simulation, the degrees of superheat of two of the four user-side heat exchangers 7a to 7d, namely, the user-side heat exchangers 7c and 7d, exceeded the upper limit of 5°C. However, as time passed, all degrees of superheat became equal to or less than the upper limit of 5°C. At 90 minutes, when the target discharge temperature changed from 71°C to 80°C, the control device 2 performed the above-described process, causing the openings of the expansion valves 6a to 6d to fluctuate, resulting in a momentary degree of superheat exceeding the upper limit of 5°C. However, all degrees of superheat were again suppressed to or below the upper limit of 5°C.

[0107] The graph in the upper right of Fig. 12 is a time series graph of the opening degree of each of the expansion valves 6a to 6d. The graph in the lower right of Fig. 12 is a time series graph of the distribution ratio of the opening degrees of the expansion valves 6a to 6d. At the start of the simulation, the opening degrees of the expansion valves 6c and 6d of the user-side heat exchangers 7c and 7d, whose superheat degrees exceed the upper limit of 5°C, are relatively increased, but the opening degrees of the remaining expansion valves 6a and 6b are relatively decreased accordingly, so that the sum of the opening degrees of the four expansion valves 6a to 6d is maintained at the total opening degree St.

[0108] As described above, when the number of elements to be optimized is "N," the control device 2 according to this embodiment can solve the optimization problem shown in Equation (1) by simply repeating the constraints and orthogonal projection of the solution elements at most N-1 times. Furthermore, since the calculations performed by the optimization unit 104 are simple arithmetic operations, the calculation load is small and an optimal solution can be obtained with high accuracy. In other words, the control device 2 can be made smaller and the calculation period can be shortened, thereby improving control performance. The improved control performance means improved energy savings and comfort due to improved control performance of the discharge temperature, superheat degree, and subcooling degree.

[0109] It should be noted that the formulas and calculation methods described in this embodiment are merely examples, and are not limited to the formulas and calculation methods described in this embodiment, as long as it is possible to obtain a solution to an optimization problem by repeating the constraints on solution elements and the orthogonal projection.

[0110] <Modification> The optimization unit 104 according to the above-described embodiment obtains a solution to the optimization problem shown in equation (1) by repeatedly constraining the solution elements and performing orthogonal projection. However, the optimization unit 104 can also obtain a solution to the optimization problem shown in equation (1) by performing the following processing.

[0111] 13 is a flowchart showing an example of a processing procedure executed by the optimization unit 104 according to this modification to efficiently solve the optimization problem shown in equation (1). Note that, for generalization, the dimension is also set to "N" in FIG.

[0112] First, in step S000, the optimization unit 104 performs initialization processing shown in the following equations (11) and (12).

[0113]

[0114]

[0115] Specifically, the optimization unit 104 divides the lower limit vector ymin, the upper limit vector ymax, and the target opening vector r by the total opening St to obtain the adjustment lower limit vector a, the adjustment upper limit vector b, and the adjustment target opening vector r. Ｓ are calculated respectively.

[0116] Then, the optimization unit 104 calculates the adjustment target opening vector r from the adjustment lower limit value vector a. Ｓ and the vector obtained by subtracting the adjustment upper limit vector b from the adjustment target opening vector r Ｓ The vector obtained by subtracting λ and the vector obtained by combining and sorting in ascending order is called the range vector λ ｒａｎｇｅ Note that "sort" in equation (11) is a function that sorts the input array in ascending order.

[0117] The optimization unit 104 then determines a vector whose first element is 1 and whose second element is twice the number N of use-side heat exchangers as the index vector J. The optimization unit 104 then defines the adjustment total range vector h by the above formula (12).

[0118] Next, in step S100, the optimization unit 104 determines whether the value obtained by subtracting the value of the first element J[1] from the value of the second element J[2] of the index vector J (= J[2] - J[1]) is less than or equal to 1.

[0119] If the determination in step S100 is NO, the optimization unit 104 performs the processes shown in the following equations (13) and (14) in step S200.

[0120]

[0121]

[0122] Specifically, the optimization unit 104 calculates the temporary index J by rounding down the average value of the index vector J to the nearest integer. Ｐ Then, the optimization unit 104 calculates the provisional adjusted total value h ｐis calculated using the above formula (14). Note that "clip" is a function defined by the following formula (15).

[0123]

[0124] Next, in step S300, the optimization unit 104 performs the following process. First, the optimization unit 104 calculates the provisional adjusted total value h ｐ Determine whether the provisional adjusted total value h is equal to or greater than 1. ｐ If is 1 or more, the second element J[2] of the index vector J is assigned a temporary index J Ｐ and assign the provisional adjustment total value h to the second element h[2] of the adjustment total range vector h. ｐ On the other hand, the provisional adjustment total value h ｐ If is less than 1, the first element J[1] of the index vector J is assigned a temporary index J Ｐ and assign the provisional adjustment total value h to the first element h[1] of the adjustment total range vector h. ｐ Substitute.

[0125] When the process of step S300 is completed, the optimization unit 104 returns the process to step S100. The optimization unit 104 repeats the processes of steps S200 and S300 until it is determined in step S100 that J[2]-J[1] is equal to or less than 1.

[0126] If it is determined in step S100 that J[2]-J[1] is equal to or less than 1 (YES in step S100), the optimization unit 104 performs the processes shown in the following equations (16) and (17) in step S400.

[0127]

[0128]

[0129] Specifically, the optimization unit 104 calculates the Lagrange multiplier λ ＊ is calculated using equation (16). Then, the optimization unit 104 outputs the optimal solution calculated using equation (17).

[0130] The processing according to this modification outputs a solution that satisfies the KKT condition (Karush-Kuhn-Tucker condition), and the convexity of the problem guarantees the output of an optimal solution. Furthermore, an optimal solution can be obtained even if the sum of the target openings Sm (= Sm1, Sm2, ...) of the expansion valves is not equal to the total opening St. Furthermore, an optimal solution can be obtained with a maximum of "ceil (log2(N) + 1)" iterations. Here, "ceil" means rounding up to an integer.

[0131] The processing according to this modification 1 determines the optimal Lagrangian multiplier by rearrangement and bisection, and outputs the optimal solution. More specifically, by utilizing the fact that the Lagrangian multiplier and the feasible solution S, and the sum of the Lagrangian multiplier and the feasible solution S, are piecewise linear in this optimization problem, the end points of the piecewise linear solution including the point where the optimal Lagrangian multiplier exists are identified by rearrangement and bisection, and a point on the piecewise linear solution that satisfies the equality constraint is found, thereby determining a point that satisfies the KKT condition. The formulas and calculation method described in this modification 1 are merely an example, and are not limited to these.

[0132] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present disclosure is defined by the claims, not the above description, and is intended to include all modifications within the meaning and scope of the claims.

[0133] 1 Refrigeration cycle device, 2 Control device, 11, 12, 13a to 13d, 14a to 14d, 17 Temperature sensor, 3 Compressor, 4 Four-way valve, 5 Heat source side heat exchanger, 6a to 6d Expansion valve, 7a to 7d Use side heat exchanger, 15, 16 Pressure sensor, 21 Control processing device, 22 Timing device, 23 Storage device, 101 Total opening calculation unit, 102 Target opening calculation unit, 103 Limit opening setting unit, 104 Optimization unit.

Claims

1. A refrigerant circuit including a compressor, a heat source side heat exchanger, a plurality of expansion valves connected in parallel to the heat source side heat exchanger, and a plurality of user side heat exchangers connected in series to each of the plurality of expansion valves; and a control device that controls the plurality of expansion valves so that the openings of the plurality of expansion valves respectively become a plurality of opening command values, wherein the control device has: a total calculation unit that calculates a total opening of the plurality of expansion valves; a target calculation unit that calculates a plurality of target openings that respectively represent target values ​​for the openings of the plurality of expansion valves; a limit setting unit that sets a plurality of limit ranges defined by lower limit values ​​and upper limit values ​​for the openings of the plurality of expansion valves, and an optimization unit that sets the plurality of opening command values ​​using the total opening, the plurality of target openings, and the plurality of limit ranges, wherein the target calculation unit calculates the plurality of target openings so that the sum of the plurality of target openings matches the total opening, and the optimization unit sets the plurality of target openings to a plurality of temporary openings in an initial step, in a first step, it is determined whether or not an inequality constraint condition that the multiple provisional openings are within their corresponding limit ranges is satisfied; if the inequality constraint condition is not satisfied, in a second step, an upper limit exceedance index indicating the degree to which the multiple provisional openings exceed their upper limit values ​​and a lower limit exceedance index indicating the degree to which the multiple provisional openings exceed their lower limit values ​​are calculated and compared, and the provisional opening that deviates the most from the limit value with the larger index is fixed to the upper limit value or the lower limit value of the provisional opening; in a third step, in a space that has been reduced in dimension by removing provisional openings that have already been fixed from the multiple provisional openings, points representing the multiple provisional openings are orthogonally projected onto an affine hyperplane whose intercept is the subtracted total opening obtained by subtracting the provisional openings that have already been fixed from the total opening, and the points are set as the multiple provisional openings, and the process returns to the first step; and the processes from the first step to the third step are repeated until the inequality constraint condition is satisfied; If the inequality constraint condition is satisfied, in a fourth step, a plurality of provisional opening degrees when the inequality constraint condition is satisfied are set as the plurality of opening degree command values, respectively.

2. A refrigerant circuit including a compressor, a heat source side heat exchanger, a plurality of expansion valves connected in parallel to the heat source side heat exchanger, and a plurality of user side heat exchangers connected in series to each of the plurality of expansion valves; and a control device that controls the plurality of expansion valves so that the openings of the plurality of expansion valves respectively become a plurality of opening command values, wherein the control device has: a total calculation unit that calculates a total opening of the plurality of expansion valves; a target calculation unit that calculates a plurality of target openings each representing a target value for the openings of the plurality of expansion valves; a limit setting unit that sets a plurality of upper limit openings each representing an upper limit value for the openings of the plurality of expansion valves and a plurality of lower limit openings each representing a lower limit value for the openings of the plurality of expansion valves; and an optimization unit that sets the plurality of opening command values ​​using the total opening, the plurality of target openings, the plurality of upper limit openings, and the plurality of lower limit openings, wherein the target calculation unit calculates the plurality of target openings so that the sum of the plurality of target openings matches the total opening, and the optimization unit performs the following in an initial step: The lower limit value vector having the elements of the plurality of lower limit openings, the upper limit value vector having the elements of the plurality of upper limit openings, and the target value vector having the elements of the plurality of target openings are divided by the total opening to obtain an adjustment lower limit value vector a, an adjustment upper limit value vector b, and an adjustment target value vector r. Ｓ and calculating the adjustment target value vector r from the adjustment lower limit value vector a. Ｓ and the vector obtained by subtracting the adjustment upper limit value vector b from the adjustment target value vector r Ｓ The vector obtained by subtracting λ and the vector obtained by combining and sorting in ascending order is called the range vector λ ｒａｎｇｅ An index vector J is a vector whose first element is 1 and whose second element is twice the number N of the plurality of expansion valves, and an adjustment total range vector h is defined by the following equation (12): In the first step, it is determined whether J[2]-J[1], which is the value obtained by subtracting the value of the first element J[1] from the value of the second element J[2] of the index vector J, is equal to or less than 1. If J[2]-J[1] is not equal to or less than 1, in the second step, the value obtained by truncating the decimal point of the average value of the index vector J is used as the provisional index J. Ｐ The provisional adjusted total value h Ｐ is calculated using the following formula (14), In a third step, the provisional adjustment total value h Ｐ is greater than or equal to 1, Ｐ is 1 or more, the second element J[2] of the index vector J is set to the temporary index J Ｐ and assign the provisional adjustment total value h[2] to the second element h[2] of the adjustment total range vector h. Ｐ and return to the first step, and the provisional adjustment total value h Ｐ is not equal to or greater than 1, the first element J[1] of the index vector J is assigned the temporary index J Ｐ and assign the provisional adjustment total value h to the first element h[1] of the adjustment total range vector h. Ｐ and return to the first step, repeat the processes from the first step to the third step until J[2]-J[1] becomes 1 or less, and if J[2]-J[1] becomes 1 or less, in the fourth step, ＊ is calculated using the following formula (16), The optimal solution calculated by the following equation (17) is set as the plurality of opening command values. Refrigeration cycle equipment.

3. When a total value, a restriction vector including an upper limit value and a lower limit value, and a target value vector whose elements have a total value equal to the total value are given to a computer or calculated by an internal calculation of the computer, the computer: sets a provisional value vector to the target value vector in an initial step; determines in a first step whether an inequality constraint that the provisional value vector is within a restriction range defined by the restriction vector is satisfied; if the inequality constraint is not satisfied, calculates and compares an upper limit exceedance index indicating the degree to which the elements of the provisional value vector exceed the upper limit value and a lower limit exceedance index indicating the degree to which the elements exceed the lower limit value; fixes the element that deviates the most from the limit value with the larger index to the upper limit value or the lower limit value of the element; In a third step, in a space reduced in dimension by removing elements that have already been fixed from the provisional value vector, a point representing the provisional value vector is orthogonally projected onto an affine hyperplane having an intercept equal to the total value obtained by subtracting the elements that have already been fixed from the total value, and the point is reset as the target value vector, and the process returns to the first step; the processes from the first step to the third step are repeated until the inequality constraint condition is satisfied; and when the inequality constraint condition is satisfied, in a fourth step, the provisional value vector when the inequality constraint condition is satisfied is output as a solution vector, and the process terminates.

4. When a total value, an upper limit value vector, a lower limit value vector, and a target value vector whose elements have a total equal to the total value are given to a computer or calculated by an internal calculation of the computer, the computer, in an initial step, calculates an adjustment lower limit value vector a, an adjustment upper limit value vector b, and an adjustment target value vector r by dividing the lower limit value vector, the upper limit value vector, and the target value vector by the total value. Ｓ and calculating the adjustment target value vector r from the adjustment lower limit value vector a. Ｓ and the vector obtained by subtracting the adjustment upper limit value vector b from the adjustment target value vector r Ｓ The vector obtained by subtracting λ and the vector obtained by combining and sorting in ascending order is called the range vector λ ｒａｎｇｅ A vector whose first element is 1 and whose second element is twice the number N of elements of the target value vector is defined as an index vector J, and an adjustment total range vector h is defined by the following formula (12): In the first step, it is determined whether J[2]-J[1], which is the value obtained by subtracting the value of the first element J[1] from the value of the second element J[2] of the index vector J, is equal to or less than 1. If J[2]-J[1] is not equal to or less than 1, in the second step, the value obtained by truncating the decimal point of the average value of the index vector J is used as the provisional index J. Ｐ The provisional adjusted total value h Ｐ is calculated using the following formula (14), In a third step, the provisional adjustment total value h Ｐ is greater than or equal to 1, Ｐ is 1 or more, the second element J[2] of the index vector J is set to the temporary index J Ｐ and assign the provisional adjustment total value h[2] to the second element h[2] of the adjustment total range vector h. Ｐ and return to the first step, and the provisional adjustment total value h Ｐ is not equal to or greater than 1, the first element J[1] of the index vector J is assigned the temporary index J Ｐ and assign the provisional adjustment total value h to the first element h[1] of the adjustment total range vector h. Ｐ and return to the first step, repeat the processes from the first step to the third step until J[2]-J[1] becomes 1 or less, and if J[2]-J[1] becomes 1 or less, in the fourth step, ＊ is calculated using the following formula (16), The vector calculated by the following equation (17) is output as a solution vector and the process ends. This is an optimization method that executes the following process.

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