Method for optimal scheduling decision of air compressor group based on simulation technology

Abstract

The present invention provides a method for an optimal scheduling decision of an air compressor group based on a simulation technology, which belongs to the technical field of information. The present invention uses expert experience to construct an air compressor energy consumption model sample set, and applies a least squares algorithm to learn relevant parameters of an air compressor energy consumption model; uses maximum energy conversion efficiency and minimum economic cost based on an equivalent electricity as target functions, and applies the simulation technology and a depth first tree search algorithm to solve a multi-target optimal scheduling model of the air compressor group; and finally uses a fuzzy logic theory to describe the preferences of decision makers, and introduces the decision maker preference information into interactive decision making, thereby assisting production staff to formulate safe, economical, efficient and environmentally friendly operation schemes to achieve an operation mode of maximum resource utilization of the air compressor group. The method also has wide application value in different industrial fields.

Claims

1. A method for an optimal scheduling decision of an air compressor group based on a simulation technology, comprising the following steps: obtaining intake flow rate, diffusion flow rate and motor current of an air compressor within a time period from a database; based on experience, selecting part of samples from the time period to construct a sample set of an air compressor energy consumption model; and successively initializing a sample set of each air compressor energy consumption model in different air compressor groups; in one alternate operation cycle, setting an intake flow rate of the air compressor as υ; and representing energy consumption of the air compressor, which is different in three phases of start up phase, load phase and unload phase, by a piecewise function as follows: $\begin{array}{cc}E=\{\begin{array}{c}{E}^{\mathrm{start}\mathrm{up}}\\ E^{\mathrm{load}}=\sqrt{3}U\Psi \left(\upsilon \right)\cos \left(\phi \right)\\ E^{\mathrm{unload}}\end{array}& \left(1\right)\end{array}$ wherein the energy consumptions of the air compressor in a start-up phase E.sup.start up and an unload phase E.sup.unload are respectively obtained by integrating energy consumption during the start and stop time periods; U and φ respectively represent the voltage of the air compressor and a power factor of a drive motor; Ψ(υ) represents a relationship between the intake flow rate of the air compressor and motor current, and the relationship is obtained by using a least square algorithm to fit the sample set of the air compressor energy consumption model; determining comprehensive energy conversion efficiency maximization based on equivalent electricity from the following equation:
max J.sub.P.sub.sp=Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i.sub.ij.sup.load/Σ.sub.i=1.sup.mα.sub.1β.sub.1q.sub.iΣ.sub.j=1.sup.S.sup.iυ′.sub.ij  (2) wherein i and j respectively represent the label of air compressor in the air compressor group and the air compressor group located in an industrial park; J.sub.P.sub.sp represents a target function of energy conversion efficiency of the air compressor groups based on equivalent electricity; S.sub.i represents a starting strategy of the air compressors; .sub.ij.sup.load represents a loading power of the air compressor under the starting strategy S.sub.i; α.sub.1 and β.sub.1 respectively represent the coefficient of compressed air and equivalent electricity converted into standard coal; q.sub.i represents a loss coefficient of the air compressor; and υ′.sub.ij represents the intake flow rate of the air compressor under the starting strategy S.sub.i; determining minimal economic operation cost from the following equation:
min J.sub.P.sub.ec=ζ∫.sub.t0.sup.t1Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i.sub.ij.sup.loaddt+Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i(.sub.ij.sup.start up+.sub.ij.sup.unload+ε.sub.ij)  (3) wherein J.sub.P.sub.ec represents a target function of an economic cost of the air compressors; ζ represents a unit price of electric energy (kw/yuan); ∫.sub.t0.sup.t1Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i.sub.ij.sup.loaddt represents power consumption (kw) of m air compressor groups under the starting strategy S.sub.i within a (t.sub.0, t.sub.1) time period; .sub.ij.sup.start up, .sub.ij.sup.unload and ε.sub.ij respectively represent the starting cost, unloading cost and depreciation cost of the air compressor; wherein constraint conditions of target function are defined from the following formulas:
Q.sub.ij.sup.min≤Q.sub.ij≤Q.sub.ij.sup.max  (4) wherein the formula (4) defines gas production constraints of air compressor, where Q.sub.ij.sup.min and Q.sub.ij.sup.max respectively represent the maximum and minimum constraints on the outtake flow rate of the air compressor;
Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.iQ.sub.ij≥Q.sub.need  (5) wherein the formula (5) defines matching constraints of gas production and consumption of air compressor group, where Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.iQ.sub.ij represents the gas production of Σ.sub.i=1.sup.mS.sub.i air compressors in the air compressor groups, and Q.sub.need represents the demand of air users;
R.sub.ij.sup.min≤υ′.sub.ij≤R.sub.ij.sup.max  (6) wherein the formula (6) defines an opening constraint of intake flow rate of air compressor, where R.sub.ij.sup.min and R.sub.ij.sup.max respectively represent maximum and minimum constraints on the intake flow rate of the air compressor;
T.sub.ij.sup.L≤|T′.sub.ij,t−T′.sub.ij,t-1|≤T.sub.ij.sup.H  (7) wherein the formula (7) defines an operation time constraint of air compressor, where T.sub.ij.sup.L and T.sub.ij.sup.H respectively represent minimum and maximum operation time constraints of the air compressor, and the constraints aim to avoid frequent start and stop of the air compressor and long-term use of the air compressor, T′.sub.ij,t-1 and T′.sub.ij,t respectively represent the beginning and the end of operation time in the air compressor;
H.sup.L<H.sup.0+ΔH<H.sup.H  (8) wherein the formula (8) defines the constraints of pipe network pressure, where H.sup.L and H.sup.H respectively represent upper and lower pressure limits of a pipe network; H.sup.0 and ΔH respectively represent an initial state of outlet pressure of the air compressor group and a corresponding change amount; performing a depth first tree search algorithm based on the simulation technology and obtaining simulation results of a combined scheme of the air compressor group by: 1) initializing an operation state in which each air compressor of the air compressor group is regarded as a node; site personnel set a state of the node according to production conditions or production plan; the air compressor is in a normal state, a maintenance state or a fault state; the air compressor in the maintenance state or the fault state is not be used as an alternative device for combined scheduling optimal solution; 2) simulating a combined scheme in which each combined scheduling scheme is subjected to numerical simulation of economy and energy conversion efficiency; if the combined scheduling scheme is searched, a next combined scheduling scheme is simulated; 3) storing simulation results in which the simulation of economy and energy conversion efficiency of each combined scheduling scheme is stored; after all the combined scheduling schemes are traversed, an intelligent optimal decision analysis process based on decision maker preference information is conducted; setting two assessment indexes of the enemy conversion efficiency and the economy to assess k scheduling schemes, and setting an eigenvalue of a-th index of b-th assessment object as x.sub.ab to obtain a characteristic matrix X=(x.sub.ab).sub.2×k of the scheduling scheme; standardizing the obtained characteristic matrix to eliminate differences among indexes in different dimensions; obtaining matrix {circumflex over (X)} obtained after standardization based on the following equations: $\begin{array}{cc}{\hat{x}}_{ab}=\frac{x_{ab}-\underset{b}{\min }{x}_{ab}}{\underset{b}{\max }{x}_{ab}-\underset{b}{\min }{x}_{ab}},b\in \left[1,k\right],a\in I_1& \left(9\right)\\ {\hat{x}}_{ab}=\frac{\underset{b}{\min }{x}_{ab}-x_{ab}}{\underset{b}{\max }{x}_{ab}-\underset{b}{\min }{x}_{ab}},b\in \left[1,k\right],a\in I_2& \left(10\right)\end{array}$ wherein I.sub.1 and I.sub.2 respectively represent an energy conversion efficiency and an economy operation cost of the air compressor; by using a fuzzy rule of Mamdani model, which can be defined as:
Rule 1: IF {circumflex over (x)}.sub.k1 is A.sub.f1 and {circumflex over (x)}.sub.k2 is A.sub.f2,Then P is B.sub.f1  (11) wherein {circumflex over (x)}.sub.k1 and {circumflex over (x)}.sub.k2 respectively represent input of energy conversion efficiency and economic index standardization, and P represents an importance factor; A.sub.f1 and A.sub.f2 respectively represent fuzzy subsets of the energy conversion efficiency and the economic operation, and B.sub.f1 represents a fuzzy subset of an importance factor; calculating multi-target comprehensive evaluation indexes with preference information from the following equations:
y.sub.k={circumflex over (x)}.sub.k1P.sub.k+{circumflex over (x)}.sub.k2(1−P.sub.k)  (12)
y=Max(y.sub.1,y.sub.2, . . . y.sub.k)  (13) wherein a largest value of y represents a comprehensive optimal plan of a scheduling decision; y.sub.k represents a comprehensive assessment value of the k-th scheduling scheme; and P.sub.k represents the importance factor of the energy conversion efficiency.

Description

DESCRIPTION DRAWINGS

(1) FIG. 1 is a flow chart of each module in the present invention.

(2) FIG. 2 is a composition and plant area distribution diagram of an air compressor group in the present invention.

(3) FIG. 3 shows description of fuzzy membership of expert preference information in the present invention; FIG. 3(a) shows a fuzzy membership function of input variable energy conversion efficiency; FIG. 3(b) shows a fuzzy membership function of input variable economic operation cost; FIG. 3(c) shows a fuzzy membership function of an output variable importance factor.

(4) FIG. 4 is a flow chart of specific implementation of the present invention.

DETAILED DESCRIPTION

(5) To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail in combination with FIG. 2 and FIG. 3 by taking scheduling of an air compressor group in a metallurgical enterprise as an example.

(6) A method for an optimal scheduling decision of an air compressor group based on a simulation technology comprises the following steps:

(7) Step 1: construction of an air compressor energy consumption model and parameter learning obtaining intake flow rate, diffusion flow rate and motor current of a j-th air compressor of an i-th air compressor group within a period of time from a database; based on expert experience, selecting part of samples from the above time period to construct a sample set of the air compressor energy consumption model; successively initializing the sample set of each air compressor in different air compressor groups according to the above mode;

(8) In one alternate operation cycle, setting the intake flow rate of the j-th air compressor of the i-th air compressor group as υ.sub.ij; and representing the energy consumption of the air compressor, which is different in three phases of start up phase, load phase and unload phase, by a piecewise function as follows:

(9) $\begin{array}{cc}{E}_{\mathrm{ij}}=\{\begin{array}{cc}{E}_{\mathrm{ij}}^{\mathrm{start}\mathrm{up}}& \begin{array}{c}\mathrm{the}\mathrm{air}\mathrm{compressor}\mathrm{is}\\ \mathrm{in}a\mathrm{start}\mathrm{up}\mathrm{phase}\end{array}\\ E_{\mathrm{ij}}^{\mathrm{load}}=\sqrt{3}{U}_{\mathrm{ij}}\Psi \left({\upsilon }_{\mathrm{ij}}\right)\cos {\phi }_{\mathrm{ij}}& \begin{array}{c}\mathrm{the}\mathrm{air}\mathrm{compressor}\\ \mathrm{is}\mathrm{in}a\mathrm{load}\mathrm{phase}\end{array}\\ E_{\mathrm{ij}}^{\mathrm{unload}}& \begin{array}{c}\mathrm{the}\mathrm{air}\mathrm{compressor}\mathrm{is}\\ \mathrm{in}\mathrm{an}\mathrm{unload}\mathrm{phase}\end{array}\end{array}& \left(1\right)\end{array}$

(10) wherein the power consumptions of the j-th air compressor of the i-th air compressor group in the start up phase E.sub.ij.sup.start up and the unload phase E.sub.ij.sup.unload are fixed values and can be respectively obtained by integrating energy consumption during the start and stop time periods; U.sub.ij and φ.sub.ij respectively represent the voltage of the j-th air compressor of the i-th air compressor group and a power factor of a drive motor; Ψ(υ.sub.ij) represents a relationship between the intake flow rate of the j-th air compressor of the i-th air compressor group and motor current, and the relationship therebetween is obtained by using a least square algorithm to fit the sample set of the energy consumption model of the air compressor group.

(11) Step 2: on line energy efficiency assessment and optimal scheduling system modeling of air compressor group

(12) 1) Target function {circle around (1)} Comprehensive energy conversion efficiency maximization based on equivalent electricity
max J.sub.P.sub.sp=Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i.sub.ij.sup.load/Σ.sub.i=1.sup.mα.sub.1β.sub.1q.sub.iΣ.sub.j=1.sup.S.sup.iυ′.sub.ij  (2)

(13) wherein J.sub.P.sub.sp represents a target function of energy conversion efficiency of m air compressor groups based on equivalent electricity; S.sub.i represents a starting strategy of the air compressors in the i-th air compressor group; .sub.ij.sup.load represents the loading power of the j-th air compressor of the i-th air compressor group under the starting strategy S.sub.i; α.sub.1 and β.sub.1 are respectively a coefficient of compressed air converted into standard coal and a coefficient of equivalent electricity converted from standard coal; q.sub.i is a loss coefficient of the air compressor in the i-th air compressor group; and υ′.sub.ij represents the intake flow rate of the j-th air compressor in the i-th air compressor group under the starting strategy S.sub.i; {circle around (2)} Minimal economic operation cost
min J.sub.P.sub.ec=ζ∫.sub.t0.sup.t1Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i.sub.ij.sup.loaddt+Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i(.sub.ij.sup.start up+.sub.ij.sup.unload+ε.sub.ij)  (3)
wherein J.sub.P.sub.ec represents the target function of the economic cost of the air compressors in m air compressor groups; ζ represents the unit price of electric energy (kw/yuan); ∫.sub.t0.sup.t1Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.i.sub.ij.sup.loaddt represents the power consumption (kw) of m air compressor groups under the starting strategy S.sub.i within a (t.sub.0, t.sub.1) time period, .sub.ij.sup.start up, and .sub.ij.sup.unload and ε.sub.ij respectively represent the starting cost, unloading cost and depreciation cost of the j-th air compressor in the i-th air compressor group.

(14) 2) Constraint conditions of target function

(15) $\begin{array}{cc}s.t.\{\begin{array}{cc}{Q}_{\mathrm{ij}}^{min}\le Q_{\mathrm{ij}}\le Q_{\mathrm{ij}}^{\mathrm{ma}x}& \\ \underset{i=1}{\overset{m}{.Math.}}\underset{j=1}{\overset{S_i}{.Math.}}{Q}_{\mathrm{ij}}\ge Q_{need}& \\ R_{\mathrm{ij}}^{min}\le {\upsilon }_{\mathrm{ij}}^{\prime }\le R_{\mathrm{ij}}^{m\mathrm{ax}}& \\ T_{\mathrm{ij}}^L<.Math.U_{\mathrm{ij},t}-U_{\mathrm{ij},t-1}.Math.<T_{\mathrm{ij}}^H& \\ H^L<H^0+\Delta H<H^H& \end{array}& \left(4\right)\end{array}$ {circle around (1)} Opening constraint of intake flow rate of air compressor:

(16) R.sub.ij.sup.min and R.sub.ij.sup.max respectively represent maximum and minimum constraints on the intake flow rate of the j-th air compressor in the i-th air compressor group; {circle around (2)} Matching constraints of gas production and gas consumption of air compressor group:

(17) Σ.sub.i=1.sup.mΣ.sub.j=1.sup.S.sup.iQ.sub.ij represents the gas production of Σ.sub.i=1.sup.mS.sub.i air compressors in the m air compressor groups, and Q.sub.need represents the air demand of air demand users; {circle around (3)} Gas production constraints of air compressor

(18) Q.sub.ij.sup.min and Q.sub.ij.sup.max respectively represent maximum and minimum constraints on the outtake flow rate of the j-th air compressor in the i-th air compressor group; {circle around (4)} Operation time constraint of air compressor

(19) T.sub.ij.sup.L and T.sub.ij.sup.H respectively represent minimum and maximum operation time constraints of the j-th air compressor of the i-th air compressor group, and the constraints aim to avoid frequent start and stop of the air compressor and long-term use of the air compressor; {circumflex over (5)} Change constraints of pipe network pressure

(20) H.sup.L and H.sup.H are respectively upper and lower pressure limits of a pipe network; H.sup.0 represents an initial state of outlet pressure of the air compressor group; and ΔH is a corresponding change amount.

(21) Step 3: solving of an optimal scheduling model of the air compressor group based on a simulation technology and a depth first tree search algorithm

(22) The patent proposes a depth first tree search algorithm based on the simulation technology to quickly obtain the simulation results of a combined scheme of the air compressor group. The solving steps of the algorithm are as follows:

(23) 4) initializing an operation state: each air compressor of the air compressor group is regarded as a node; site personnel set the state of the node according to the production conditions or production plan; state State=1 represents that the air compressor is in a normal state; state State=0 represents that the air compressor is in a maintenance or fault state; the air compressor at State=0 shall not be used as an alternative device for combined scheduling optimal solution;

(24) 5) Simulating a combined scheme: each combined scheduling scheme is subjected to numerical simulation of economy and energy conversion efficiency; if the combined scheduling scheme is searched, a next combined scheduling scheme is simulated;

(25) 6) Storing simulation results: the simulation values of the economy and the energy conversion efficiency of each combined scheduling scheme are stored; after all the combined scheduling schemes are traversed, an intelligent optimal decision analysis process based on decision maker preference information is conducted.

(26) Step 4: intelligent optimal decision based on decision maker preference information

(27) setting two assessment indexes of energy conversion efficiency and economy to assess k scheduling schemes, and setting the eigenvalue of a-th index of b-th assessment object as x.sub.ab to obtain a characteristic matrix X=(x.sub.ab).sub.2×k of the scheduling scheme; standardizing the obtained characteristic matrix to eliminate differences among indexes due to different dimensions; obtaining the matrix {circumflex over (X)} obtained after standardization, with methods for standardizing the values of X as follows:

(28) $\begin{array}{cc}{\hat{x}}_{ab}=\frac{x_{ab}-\underset{b}{\min }{x}_{ab}}{\underset{b}{\max }{x}_{ab}-\underset{b}{\min }{x}_{ab}},b\in \left[1,k\right],a\in I_1& \left(5\right)\\ {\hat{x}}_{ab}=\frac{\underset{b}{\min }{x}_{ab}-x_{ab}}{\underset{b}{\max }{x}_{ab}-\underset{b}{\min }{x}_{ab}},b\in \left[1,k\right],a\in I_2& \left(6\right)\end{array}$
wherein I.sub.1 is an energy conversion efficiency index of the air compressor, and I.sub.2 is an economy operation cost index.

(29) An intelligent optimal scheduling decision system of the air compressor group uses fuzzy reasoning to describe uncertain information such as index weight change caused by the preference information of scheduler and complex working conditions, thereby increasing the feasibility and validity of a scheduling decision plan. The present invention uses a Mamdani fuzzy model widely used to describe the uncertain information of an industrial production system, and fuzzy rules can be defined as:
Rule 1: IF {circumflex over (x)}.sub.k1 is A.sub.f1 and {circumflex over (x)}.sub.k2 is A.sub.f2,Then P is B.sub.f1  (7)
wherein {circumflex over (x)}.sub.k1 and {circumflex over (x)}.sub.f2 are respectively input values of energy conversion efficiency and economic operation index standardization, and P represents an importance factor; A.sub.f1, and A.sub.f2 respectively represent the fuzzy subsets of the energy conversion efficiency and the economic operation, and B.sub.f1, represents the fuzzy subset of the importance factor. The fuzzy rules are shown in Table 1:

(30) TABLE-US-00001 TABLE 1 Table of Fuzzy Rules Economy cost Very low Low OK High Very high Energy High Very high Very high OK Low Very low conversion OK High High OK High Very high efficiency Low OK OK OK Very high Very high

(31) Calculation formulas of multi-target comprehensive evaluation indexes with preference information are:
y.sub.k={circumflex over (x)}.sub.k1P.sub.k+{circumflex over (x)}.sub.k2(1−P.sub.k)  (8)
y=Max(y.sub.1,y.sub.2, . . . y.sub.k)  (9)
wherein a largest value of Y represents a comprehensive optimal plan of the scheduling decision; y.sub.k represents a comprehensive assessment value of the k-th scheduling scheme; and P.sub.k represents the importance factor of the energy conversion efficiency.

(32) By taking an air compressor group system of a metallurgical enterprise as an example, it is assumed that the compressed gas is transmitted in a pipeline in an ideal state. The total demand of air compressor users is set manually. Without considering the differences in the power consumption price of the air compressor groups at different times, the electricity price is calculated according to 0.458 yuan/kWh. Table 2 provides comparison of effects of the method of the present invention and a manual scheduling method.

(33) TABLE-US-00002 TABLE 2 provides comparison of effects of the method of the present invention and a manual scheduling method Comprehensive Total air demand energy of users Economic cost efficiency (kNm.sup.3/min) Method Selected scheduling scheme (yuan/h) (%) 160 Manual 1# air {circle around (1)}{circle around (6)} 1645.86 89.25 scheduling compressor station 2# air {circle around (2)}{circle around (3)}{circle around (5)} compressor station 3# air {circle around (1)}{circle around (2)}{circle around (5)}{circle around (6)} compressor station 4# air {circle around (1)}{circle around (2)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station The 1# air {circle around (1)}{circle around (6)} 1633.17 92.12 present compressor invention station 2# air {circle around (2)}{circle around (3)} compressor station 3# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (6)} compressor station 4# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station 170 Manual 1# air {circle around (1)}{circle around (6)} 1773.98 88.7 scheduling compressor station 2# air {circle around (2)}{circle around (3)}{circle around (5)} compressor station 3# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (6)} compressor station 4# air {circle around (2)}{circle around (3)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station The 1# air {circle around (1)}{circle around (6)} 1749.58 91.34 present compressor invention station 2# air {circle around (3)}{circle around (5)} compressor station 3# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (6)} compressor station 4# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station 180 Manual 1# air {circle around (1)}{circle around (6)} 1885.4 89.32 scheduling compressor station 2# air {circle around (2)}{circle around (3)}{circle around (4)} compressor station 3# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station 4# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (5)}{circle around (6)} compressor station The 1# air {circle around (1)}{circle around (6)} 1873.8 91.32 present compressor invention station 2# air {circle around (2)}{circle around (6)} compressor station 3# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station 4# air {circle around (1)}{circle around (2)}{circle around (3)}{circle around (4)}{circle around (5)}{circle around (6)} compressor station