CN111368435B - Uncertain demand-oriented air separation pipe network device starting and stopping and load scheduling method - Google Patents
Uncertain demand-oriented air separation pipe network device starting and stopping and load scheduling method Download PDFInfo
- Publication number
- CN111368435B CN111368435B CN202010147968.2A CN202010147968A CN111368435B CN 111368435 B CN111368435 B CN 111368435B CN 202010147968 A CN202010147968 A CN 202010147968A CN 111368435 B CN111368435 B CN 111368435B
- Authority
- CN
- China
- Prior art keywords
- air separation
- pipe network
- stage
- air
- load
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Landscapes
- Separation By Low-Temperature Treatments (AREA)
Abstract
The invention discloses an uncertain demand-oriented method for starting, stopping and load scheduling of an air separation pipe network device. Dividing the devices in the air separation pipe network into different modes according to the operation conditions of the devices in the air separation pipe network, establishing a piecewise linear proxy model of the product yield of each production device in each mode, analyzing the flow balance, boundary conditions and the like of other devices in the pipe network, and establishing a scheduling optimization model of the whole pipe network from three layers of oxygen, nitrogen and argon; on the basis, aiming at the uncertainty of market demand, a two-stage random optimization model is adopted, a condition risk value model is introduced, and a production scheduling scheme is formulated with the aim of maximizing the two-stage profit and the condition risk value of the air separation pipe network. According to the invention, risk measurement can be carried out under the condition of uncertain market demand, and different scheduling schemes are formulated according to different risk levels, so that the conditions of low benefit and high risk are effectively avoided; meanwhile, the piecewise linear agent model can reduce the solving time and is convenient for solving and calculating the large-scale model.
Description
Technical Field
The invention relates to the field of scheduling optimization of an air separation pipe network, in particular to an uncertain demand-oriented method for starting, stopping and load scheduling of an air separation pipe network device.
Background
Air separation means that high-purity gas-liquid phase products such as oxygen, nitrogen, argon and the like are separated by utilizing the different physical properties of all components in air. Common air separation processes are cryogenic separation, adsorption, and membrane separation. Adsorption is generally preferred when oxygen demand is low and only gas phase products need to be produced. When the purity requirement is high and the production of gas-liquid phase products is also required, cryogenic separation is usually selected. Because the gas demand of iron and steel enterprises is large, a low-temperature separation method is generally adopted. The low-temperature separation method uses air as a raw material, the air is firstly changed into liquid state by a compression circulation and deep freezing method, and then gas-liquid phase products such as oxygen, nitrogen, argon and the like are gradually separated from the liquid air by rectification according to different boiling points of components such as oxygen, nitrogen and the like.
Most iron and steel enterprises in China are provided with air separation units, the iron and steel enterprises need to use a large amount of oxygen, nitrogen, argon and other industrial gases in the production and smelting processes, and the load of the air separation units needs to change frequently due to frequent fluctuation of the gas demand of the iron and steel plant. When the air separation device cannot adjust the capacity in time in the production process, a large amount of resource waste and economic loss can be caused. Meanwhile, the air separation process needs to consume a large amount of electric energy, and is a large power-consuming household in iron and steel enterprises. The energy consumption of an air separation plant is directly proportional to factors such as the scale of the plant, the pressure of the supplied air, the yield of the liquid product, and the like. In addition, the start-stop of the plant and the increase of the adjustment frequency of the load are also factors of the increase of the space division energy consumption. The difficulty of scheduling problems is greatly improved due to real-time change of requirements, and manual scheduling has the defects of strong subjectivity, poor reliability and the like, so that the scheduling optimization of the air separation pipe network is very important.
Disclosure of Invention
In order to solve the problems, the invention provides an air separation pipe network device starting and stopping and load scheduling method facing to uncertain demands, and when the market gas demand is uncertain, the method considers the influence caused by uncertain factors and considers the risk level. According to different risk preference settings, different production scheduling schemes are formulated, and the profit can be the maximum under the condition of lower risk.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an air separation pipe network device start-stop and load scheduling method for uncertain demands comprises the following steps:
step (1): the air separation pipe network device consists of an air separation device and an auxiliary device, and is divided into different modes according to the operation condition of the air separation device to obtain the production space of each air separation device in each mode;
step (2): establishing a material balance equation for an auxiliary device in the air separation pipe network, and combining the material balance equation with the production space of the air separation device to obtain a process balance equation of the air separation pipe network; the production space of the air separation device under each mode, the material balance equation of the auxiliary device and the process balance equation of the air separation pipe network form an integral model of the air separation pipe network;
and (3): the method comprises the following steps that a two-stage random planning model is adopted to divide an overall model of an air separation pipe network into two stages again, the first stage makes decisions on start-stop and nominal loads of an air separation device and a compressor, and the second stage makes decisions on incremental loads of the air separation device and the compressor, start-stop and overall loads of a liquefier, start-stop and overall loads of a gasifier and overall loads;
and (4): the conditional risk value CVaR is introduced on the basis of the two-stage random planning model, an uncertain scheduling model based on the CVaR is constructed, and under the condition that market demand uncertainty is considered, the profit and the conditional risk value CVaR in the two stages are maximized, so that an optimal scheduling scheme is obtained.
Further, the step (1) divides the air separation unit into different modes according to the operation condition of the air separation unit, the constant-load air separation unit is divided into two modes of shutdown and startup, and the variable-load air separation unit is divided into three modes of shutdown, low-load and high-load. After the operation modes are determined, historical operation data and a mechanism model are combined, and a piecewise linear agent model is built to describe the production space of each device in each mode. The method specifically comprises the following steps:
the air separation pipe network device comprises a plurality of air separation devices, compressors, liquefiers, gasifiers and liquid storage tanks, and the air separation devices are divided into constant-load air separation devices and variable-load air separation devices; according to the operating condition of the air separation device, dividing the constant-load air separation device into two modes of shutdown and startup, and expressing the following steps:
fu,m,g,t＝pru,m,gyu,m,t (1.2)
wherein, Fu,g,tRepresenting the yield of product g produced by unit u at time t, fu,m,g,tRepresenting the yield of product g produced by unit u in mode m at time t, yu,m,tIndicates whether the device u is at time tIn mode m, pru,m,gA fixed value representing the yield of unit u producing product g at modality m;
dividing the variable-load air separation device into three modes of shutdown, low load and high load:
fu,AIR,m,t＝(xu,m-1-xu,m)λu,m,t+xu,m*yu,m,t (1.6)
Qu,m,AIR,t＝(q(xu,m-1)-q(xu,m))λu,m,t+q(xu,m)*yu,m,t (1.7)
0≤λu,m,t≤yu,m,t(1.8)
wherein, Fu,AIR,tIndicating the amount of air entering the device u at time t, fu,m,AIR,tRepresenting the amount of air, Q, entering the device u in mode m at time tu,AIR,tRepresents the power consumption of the air compressor at the moment t, qu,m,AIR,tRepresenting the power consumption of the air compressor under the mode m at the moment t;
obtaining the production space of each air separation unit in each mode according to the divided different modes;
for the air separation device, logic constraint needs to be added to the switching of the modes, and a 0-1 variable z is introducedu,m',m,t， zu,m',m,t1 denotes that at time t-1 device u operates in mode m and at time t device u operates in mode m', which is expressed by the following logical relation:
the air separation device has different constraints on product yield under different modes:
wherein the content of the first and second substances,
represents the upper limit of the production of product g in the air separation unit u in mode m,
represents the lower limit of the production of product g in the air separation unit u in mode m.
Further, the flow balance equation of the air separation pipe network in the step (2) is divided into three layers of oxygen, nitrogen and argon, and comprises a flow balance equation of an oxygen pipe network, a flow balance equation of a nitrogen pipe network, a flow balance equation of an argon pipe network, a flow balance equation of a liquid oxygen storage tank, a flow balance equation of a liquid nitrogen storage tank and a flow balance equation of a liquid argon storage tank.
Further, the step (3) is specifically as follows:
the method comprises the following steps that a two-stage random planning model is adopted to subdivide an integral model of an air separation pipe network into two stages, a target function of the first stage is obtained by subtracting starting cost and power consumption of a compressor of the first stage from income of gas and liquid products of the first stage, and constraints of the first stage comprise a production space of a fixed-load air separation unit, a production space of a variable-load air separation unit and a flow balance equation of the air separation pipe network and are used for making decisions on starting and stopping of the air separation unit and the compressor and on a nominal load;
the objective function of the second stage is obtained by subtracting the power consumption of the compressor of the second stage from the income of gas and liquid products of the second stage, and the constraint of the second stage is an integral model which is used for making decisions on the increment load of the air separation device and the compressor, the start-stop and integral load of the liquefier, and the start-stop and integral load of the gasifier;
the two-stage stochastic optimization proposition is represented as follows:
s.t.Ax＝b
Tsx+Wsys＝hs
x≥0,ys≥0 (3.1)
where x is the decision variable of the first stage and ysIs a decision variable, p, of a second stage scenario ssRepresenting the probability of occurrence of scene s, N representing the number of scenes, cTx the objective function of the first stage,
the objective function of the second stage, Ax ═ b, denotes the constraint of the first stage, Tsx+Wsys＝hsRepresenting a second stage constraint, cT、
A、b、Ts、Ws、hsAre all coefficients.
Further, the step (4) is specifically as follows:
introducing a conditional risk value CVaR on the basis of a two-stage stochastic programming model, wherein the risk value VaR is the maximum possible loss value under a certain confidence level, and the conditional risk value CVaR gives an expected value of a part of loss amount exceeding the risk value VaR; from a profit perspective, VaR refers to the smallest possible profit value expected at confidence level α, CVaR gives the expected value for the portion with profit value less than VaR;
the CVaR optimization topic is:
s.t.zs≥ζ-f(x,y)
zs≥0 (4.1)
wherein p issRepresents the probability of occurrence of a scene s, ζ represents the minimum possible profit value expected at a confidence level α, N represents the number of scenes, f (x, y) represents a loss function, x is a decision variable, y is an uncertain parameter, and in different scenes, z is greater than f (x, y) when ζ is greater than fsDenotes the difference between ζ and f (x, y), and z is when ζ is smaller than f (x, y)sIs 0; converting the CVaR optimization problem into a linear programming problem through the formula (4.1), and solving the formula (4.1) to simultaneously obtain an approximate optimal VaR value and an approximate optimal CVaR value;
combining the profit value of the two-stage random planning with the conditional risk value CVaR, and constructing an uncertainty scheduling model based on the CVaR, wherein the uncertainty scheduling model is represented as follows:
wherein TP represents the sum of profits of the two stages, Profit represents the Profit of the first stage,
an expected value representing profit for the second stage;
for an objective function of the entire scheduling model, ηsS and delta are weight coefficients, the selection of delta reflects the preference degree of the risk, the larger the delta is, the higher the risk is, and the optimal production scheduling schemes under different risk levels can be obtained by setting different deltas, so that the risk can be avoided, and meanwhile, higher profit is obtained.
The invention has the beneficial effects that:
the method combines historical operation data and a mechanism model, establishes a piecewise linear agent model, is more beneficial to describing the production space of each device under each mode, compares the solving time with the solving time of a pure mechanism model, reduces the solving time from more than 1 hour to 31 seconds, divides a large feasible region into a plurality of small feasible regions by the piecewise linear agent model, utilizes logic constraint to further reduce the feasible region range, and accelerates the solving speed of the large-scale model; the air separation pipe network is analyzed from the three layers of oxygen, nitrogen and argon, so that the description of an air separation pipe network scheduling model is more complete; the problem of uncertain scheduling is solved by combining a two-stage random planning model and a condition risk value model, and an optimal production scheduling scheme under different water risk levels can be obtained, so that the conditions of low benefit and high risk are effectively avoided.
Drawings
FIG. 1 is a flow diagram of an air separation network;
FIG. 2 is five scenarios of uncertain demand;
FIG. 3(a) is an optimal production scheduling scheme at low risk levels;
FIG. 3(b) is an optimal production scheduling scheme at moderate risk levels;
FIG. 3(c) is an optimal production scheduling scheme at high risk levels;
FIG. 4 is the variation of profit and conditional risk profit at different risk levels.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
In the example, an air separation pipe network of a Nanjing iron and steel plant is taken as an example, and a dispatching model of the pipe network is established. The specific process flow diagram of the air separation pipe network is shown in figure 1. The entire air separation system includes 4 large-scale air separation plants (a1 to a4), with No. 2 air separation plant being a constant load and No. 1, No. 3, and No. 4 air separation plants being variable loads. For an oxygen pipe network, the air separation plant No. 3 can directly generate high-pressure oxygen, the oxygen generated by the other three plants needs to be compressed by an oxygen compressor (OC1, OC2 and OC4) and then is transmitted to users through the pipe network, and if the oxygen is excessive, the oxygen can be diffused. For a nitrogen pipe network, nitrogen generated by the air separation device respectively enters the medium-pressure nitrogen pipe network and the low-pressure nitrogen pipe network through compression of the medium-pressure nitrogen press (M1-M5) and the low-pressure nitrogen press (N1-N3) and is conveyed to the steel plant through the pipe network so as to meet the real-time requirements of the steel plant. Liquid oxygen and liquid nitrogen produced by the air separation plant are stored in storage tanks No. 1 and No. 2 (T1, T2) for sale. When the pressure of the pipe network is low, the liquefying devices (L1, L2) can convert the gas with excess production into liquid to be stored in the storage tank, and when the pressure of the pipe network is high, the gasifying devices (V1-V3) can convert the liquid in the storage tank into gas to compensate. Liquid argon produced by the air separation plant is stored in a tank No. 3 (T3) and can be converted to gaseous argon by a liquid argon pump (P1-P4) for use by steel mills. R1-R5 are regulating valves. Specific parameters of the air separation plant of the plant are shown in table 1.
The air separation plant is divided into a constant-load air separation plant and a variable-load air separation plant, wherein the ASU1, the ASU3 and the ASU4 are variable-load plants, the oxygen production capacity under standard working conditions is 20000Nm3/h, 20000Nm3/h and 30000Nm3/h, and the ASU2 is a constant-load plant, and the oxygen production capacity is 20000Nm 3/h. Each air separation device is provided with a corresponding air compressor, an oxygen compressor, a nitrogen compressor and the like.
TABLE 1 specific parameters of the air separation plant
(1) In one embodiment of the present invention, the shutdown mode and the startup mode of the constant-load air separation unit are denoted as M1 and M2, respectively. The variable-load air separation device is characterized in that the starting mode is marked as M1, the low-load mode is marked as M2, and the high-load mode is divided into two sub-modes, namely M3 and M4. The amount of air entering the air separation unit in the different modes is shown in table 2.
TABLE 2 modes of air separation plant
After the operation modes are determined, historical operation data and a mechanism model are combined, and a piecewise linear agent model is built to describe the production space of each device in each mode.
For a constant-load air separation device, in a shutdown mode, all product yields are 0, a load of a startup mode is fixed, and a production space is described by formulas (1.1) to (1.3), which are expressed as follows:
fu,m,g,t＝pru,m,gyu,m,t (1.2)
wherein, Fu,g,tRepresenting the yield of product g produced by unit u at time t, fu,m,g,tRepresenting the yield of product g produced by unit u in mode m at time t, yu,m,tIndicates whether the device u is in the mode m at time t, pru,m,gA fixed value representing the yield of unit u producing product g at modality m;
for the variable-load air separation device, all the product yield is 0 in the shutdown mode, so the startup mode is divided into a low-load mode and a high-load mode, the device can only operate in one operation mode at each moment, and the production space in each operation mode is represented by a piecewise linear agent model. According to the air flow and air compressor power consumption data in different modes, the following piecewise linear agent model is established and expressed by adopting an extraction relational expression as follows:
wherein, yu,m,tIndicates whether the device u is in the mode m at time t, Fu,m,AIR,tRepresenting the amount of air, Q, entering the device u in mode m at time tu,m,AIR,tRepresenting the electric quantity consumed by the air compressor under the mode m by the device u at the moment t; x is the number ofu,mYield value, q (x), representing the operating point of device u on the boundary of modality mu,m) An electric quantity value, λ, representing an operating point of the device u on the boundary of the mode mu,m,tAre the weighting coefficients of the boundary points.
Using convex relaxation, the disjunctive relation is transformed into:
fu,AIR,m,t＝(xu,m-1-xu,m)λu,m,t+xu,m*yu,m,t (1.7)
Qu,m,AIR,t＝(q(xu,m-1)-q(xu,m))λu,m,t+q(xu,m)*yu,m,t (1.8)
0≤λu,m,t≤yu,m,t (1.9)
wherein, Fu,AIR,tIndicating the amount of air entering the device u at time t, fu,m,AIR,tRepresenting the amount of air, Q, entering the device u in mode m at time tu,AIR,tRepresents the power consumption of the air compressor at the moment t, qu,m,AIR,tRepresenting the power consumption of the air compressor under the mode m at the moment t;
and dividing the air separation unit into different modes according to the operating conditions of the air separation unit, and further obtaining the production space of each air separation unit in each mode.
The product yields in each mode are related as shown in the following formulas (1.11) to (1.15):
fu,m,AIR,t＝a1*fu,m,GOX,t+b1*fu,m,LIN,t+c1*yu,m,t (1.11)
a2*fu,m,AIR,t+b2*yu,m,t＝fu,m,LOX,t+fu,m,LIN,t (1.12)
a3*fu,m,AIR,t+b3*yu,m,t＝fu,m,GAN,t+fu,m,LIN,t (1.13)
a4*fu,m,AIR,t+b4*yu,m,t＝fu,m,LAR,t (1.14)
wherein f isu,m,GOX,t，fu,m,GAN,t，fu,m,LOX,t，fu,m,LIN,t，fu,m,LAR,tRespectively representing the yields of oxygen, nitrogen, liquid oxygen, liquid nitrogen and liquid argon produced by the air separation unit u under the mode m at the time t, Fu,g,tRepresents the yield of the product g produced by the air separation unit u at the time t; a is1，a2，a3，a4，b1，b2，b3，b4，c1The coefficients are obtained by regression of historical data, and the coefficients are different for different modes of different devices.
After establishing the operation modalities of each device, it is necessary to restrict the switching between modalities, and the rules of modality switching for each device are shown in table 3:
TABLE 3 Modal switching rules
For the air separation device, logic constraint needs to be added to the switching of the modes, and a 0-1 variable z is introducedu,m',m,t。 zu,m',m,tWhen t-1 is defined as t-1, the device u operates in the mode m, and when t is defined as t', the switching operation between the modes is represented by a logic relation:
the air separation device has different constraints on product yield under different modes:
wherein the content of the first and second substances,
represents the upper limit of the production of product g in the air separation unit u in mode m,
represents the lower limit of the production of product g in the air separation unit u in mode m.
(2) And establishing a dispatching model of the three large pipe networks of oxygen, nitrogen and argon. The pipe network comprises a plurality of air separation devices, compressors, liquefiers, gasifiers, liquid storage tanks and the like, and the flow balance and production constraints of the devices are analyzed from three layers of oxygen, nitrogen and argon, so that a production scheduling model of the whole air separation pipe network is established.
Firstly, establishing a material balance equation for an auxiliary device in an air separation pipe network device, and combining the material balance equation with the production space of the air separation device to obtain a process balance equation of the air separation pipe network;
the air separation pipe network also comprises a liquefier and a gasifier, and the material balance is as follows:
FLGOX,i,t＝2400*yLGOX,i,t (2.1)
FLGAN,i,t＝2200*yLGAN,i,t (2.2)
wherein, FLGOX,i,tRepresents the liquefied oxygen amount of the i-th liquefier at time t, yLGOX,i,tIndicating whether the ith liquefier liquefies oxygen at the time t; fLGAN,i,tDenotes the amount of liquefied nitrogen in the i-th liquefier at time t, yLGAN,i,tIndicating whether the ith liquefier liquefies nitrogen at time t.
FVLOX,i,t＝30000*yVLOX,i,t (2.3)
FVLIN,i,t＝20000-yVLIN,i,t (2.4)
Wherein, FVLOX,i,tDenotes the amount of gasified liquid oxygen of the i-th vaporizer at time t, yVLOX,i,tIndicating whether the ith gasifier gasifies liquid oxygen at the time t; fVLIN,i,tDenotes the amount of liquid nitrogen vaporized by the i-th vaporizer at time t, yVLIN,i,tIndicating whether the i-th gasifier gasifies the liquid at the time tAnd (3) nitrogen.
And gas produced by all the air separation units can enter a pipe network for gas supply after being gathered, so that the total amount of gas products produced by the air separation units at the time t and the total gasification amount of the gasification units minus the total liquefaction amount of the liquefaction units at the time t, the demand amount of the gas products and the diffusion amount are equal to the net increment of the gas in the pipe network at the time t.
The flow equilibrium equation of the oxygen pipe network is expressed as follows:
DGOX,t+1-DGOX,t＝(FGOX,t+FVLOX,t-FLGOX,t-dGOX,t-Fvent,t)*δt (2.5)
wherein D isGOX,tRepresents the capacity of the oxygen pipe network at time t, FGOX,tDenotes the total amount of oxygen produced by the air separation plant, FVLOX,tRepresents the total gasification amount of the gasification apparatus, FLGOX,tRepresents the total liquefaction amount of the liquefaction apparatus, dGOX,tDenotes the oxygen demand, Fvent,tRepresents the amount of oxygen, δtIs a discretized time interval; the relation between the gas quantity and the pressure of the oxygen pipe network is shown in the formula (2.6), PGOX,tRepresenting the pressure of the oxygen network at time t; the upper formulas (2.7) and (2.8) respectively represent the upper and lower limit constraints of the gas quantity and the pressure of the oxygen pipe network;
the flow equilibrium equation for a nitrogen pipe network is expressed as follows:
DGAN,t+1-DGAN,t＝(FGAN,t+FVLAN,t-FLGAN,t-dGAN,t)*δt (2.9)
wherein D isGAN,tRepresents the capacity of the nitrogen pipe network at time t, FGAN,tDenotes the total amount of nitrogen produced by the air separation plant, FVLIN,tRepresents the total gasification amount of the gasification apparatus, FLGAN,tRepresents the total liquefaction amount of the liquefaction apparatus, dGAN,tIndicating the nitrogen demand; the above formula (2.10) shows the relationship between the amount of gas in the nitrogen network and the pressure in the nitrogen network, PGAN,tRepresenting the pressure of the nitrogen pipe network at the time t; the upper formulas (2.11) and (2.12) respectively represent the upper and lower limit constraints of the gas quantity and the pressure of the nitrogen pipe network;
the flow equilibrium equation of the argon pipe network is expressed as follows:
FGAR,t＝dGAR,t (2.13)
wherein, FGAR,tRepresents the total amount of argon produced by the air separation plant, dGAR,tRepresenting the required amount of argon;
the liquid product produced by the air separation unit can be stored in a storage tank for standby or takeout, and the quantity of the liquid product produced by the air separation unit and the liquefaction quantity of the liquefaction unit at the time t minus the gasification quantity of the gasification unit and the sales quantity of the liquid product at the time t is equal to the net increment of the storage tank at the time t.
The equation for the flow equilibrium of the liquid oxygen storage tank is expressed as follows:
InvLOX,t+1-InvLOX,t＝(FLOX,t+FLGOX,t-FVLOX,t-SLOX,t)*δt (2.14)
wherein, InvLOX,tDenotes the capacity of the liquid oxygen reservoir, FLOX,tDenotes the total amount of liquid oxygen produced by the air separation plant, SLOX,tRepresents the sales volume of liquid oxygen;
the equation for the flow equilibrium of a liquid nitrogen storage tank is expressed as follows:
InvLAN,t+1-InvLAN,t＝(FLAN,t+FLGAN,t-FVLAN,t-SLAN,t)*δt (2.16)
wherein, InvLIN,tDenotes the capacity of the liquid nitrogen reservoir, FLIN,tRepresents the total amount of liquid nitrogen produced by the air separation plant, SLIN,tRepresents sales of liquid nitrogen;
the equation for the flow equilibrium for the liquid argon storage tank is expressed as follows:
InvLAR,t+1-InvLAR,t＝(FLAR,t-FGAR,t-SLAR,t)*δt (2.18)
wherein, InvLIN,tDenotes the capacity of the liquid argon reservoir, FLAR,tDenotes the total amount of liquid argon, S, produced by the air separation plantLAR,tIndicating the sales of liquid argon.
In conclusion, the production space of the air separation device in each mode, the material balance equation of the auxiliary device and the process balance equation of the air separation pipe network form an integral model of the air separation pipe network.
(3) Assuming that market demand distribution in a 14-day scheduling time domain is shown in fig. 2, 5 possible demand scenarios are provided, the occurrence probability is different, the problem that the market demand is uncertain is considered, a two-stage random planning model is adopted to divide the whole decision process into two stages, the first stage makes decisions on start-stop and nominal load of an air separation device and a compressor under the condition that the value of uncertain parameters is not solved, and at the moment, the decision of an integer variable and the decision of a continuous variable are considered. And in the second stage, after the actual values of the uncertain parameters are known, decisions are made on the increment loads of the air separation device and the compressor, the start-stop and the loads of the liquefier and the gasifier, and the adverse effects brought by the decisions in the first stage are weakened through the decisions. The method specifically comprises the following steps:
the objective function of the first stage is obtained by subtracting the starting cost and the power consumption of the compressor of the first stage from the income of gas and liquid products of the first stage, and the constraint of the first stage comprises the production space of a fixed-load air separation unit, the production space of a variable-load air separation unit and a flow balance equation of an air separation pipe network, and is used for making decisions on starting and stopping of the air separation unit and the compressor and the nominal load;
the objective function of the second stage is obtained by subtracting the power consumption of the compressor of the second stage from the income of gas and liquid products of the second stage, and the constraint of the second stage is an integral model which is used for making decisions on the increment load of the air separation device and the compressor, the start-stop and integral load of the liquefier, and the start-stop and integral load of the gasifier;
the two-stage stochastic optimization proposition is represented as follows:
s.t.Ax＝b
Tsx+Wsys＝hs
x≥0,ys≥0 (3.1)
where x is the decision variable of the first stage and ysIs a decision variable, p, of a second stage scenario ssRepresenting the probability of occurrence of scene s, N representing the number of scenes, cTx the objective function of the first stage,
the objective function of the second stage, Ax ═ b, denotes the constraint of the first stage, Tsx+Wsys＝hsRepresenting a second stage constraint, cT、
A、b、Ts、Ws、hsAre all coefficients.
(4) And introducing a conditional risk value CVaR on the basis of a two-stage stochastic programming model to evaluate the risk caused by uncertain factors.
The Value of Risk (VaR) refers to the maximum possible loss Value that is expected with a certain probability (confidence level). The Conditional Value at Risk (CVaR) gives the expected Value of the portion of the loss that exceeds VaR.
For the loss function f (x, y), where x is the decision variable and y is the uncertain parameter. f (x, y) obeys a certain probability distribution, ψ (x, ζ) denotes a cumulative distribution function of f (x, y), and ψ (x, ζ) ═ P { y | f (x, y) ≦ ζ }.
VaR：ζα(x) Min { ζ | ψ (x, ζ) ≧ α }, an α -VaR loss value for decision x at confidence level α.
CVaR：φα(x)＝E{f(x,y)|f(x,y)≥ζα(x) An α -CVaR loss value for decision x at confidence level α.
The CVaR model solves the problem of solving the minimum VaR value and the minimum CVaR value under known loss functions to characterize the minimum risk.
VaR, if considered from a profit perspective, refers to the minimum possible profit value expected at the confidence level α. CVaR gives the expectation for the portion with a profit value less than VaR.
The optimization problem is:
s.t.zs≥ζ-f(x,y)
zsnot less than 0 (4.1) wherein psRepresents the probability of occurrence of the scene s, ζ represents the minimum possible profit expected at a confidence level α, represents the value of the optimized VaR, α is set to 0.9; n represents the number of scenes, f (x, y) represents a loss function, x is a decision variable, y is an uncertain parameter, and in different scenes, when zeta is larger than f (x, y), z issDenotes the difference between ζ and f (x, y), and z is when ζ is smaller than f (x, y)sIs 0; the CVaR optimization problem is converted into a linear programming problem through the formula (4.1), and the approximate optimal VaR value and the CVaR value are simultaneously obtained by solving the formula (4.1).
(5) In the case of considering uncertainty in market demand, with the goal of maximizing the profit and conditional risk value (CVaR) of the two stages, which cannot be maximized at the same time, the weight is adjusted to change the risk level with the goal of weighted sum of the two. By solving the proposition, the optimal production scheduling scheme under different risk levels can be obtained. The method specifically comprises the following steps:
combining the profit value of the two-stage random planning with the conditional risk value CVaR, and constructing an uncertainty scheduling model based on the CVaR, wherein the uncertainty scheduling model is represented as follows:
wherein TP represents the sum of profits of the two stages, Profit represents the Profit of the first stage,
an expected value representing profit for the second stage;
for an objective function of the entire scheduling model, ηsS and epsilon are weight coefficients, the selection of epsilon reflects the preference degree of risk, epsilon is set to be 0.1, 0.2, 0.3 to 1, the larger epsilon is, the higher the risk is, and the optimal production scheduling scheme under different risk levels can be obtained by setting different epsilon, so that the risk can be avoided, and the higher the risk is obtained at the same timeThe profit of (1).
As shown in fig. 2, five scenes with different oxygen demands are respectively represented by five lines, the abscissa represents the scheduling time domain for 14 days, and the ordinate represents the oxygen demand, the five scenes are consistent in change in 1-6 days, and then the oxygen demand rises, but the uncertain oxygen demand specifically rises in the next day, so that the five possible situations are considered, the oxygen demand rises in 7 th, 8 th, 9 th, 10 th and 11 th days, and the occurrence probability is respectively 0.1, 0.2, 0.4, 0.2 and 0.1.
The scheduling result according to this example can roughly classify the risk levels into three categories, where epsilon is 0.1 to 0.2, low risk, epsilon is 0.3 to 0.4, medium risk, epsilon is 0.5 to 1, high risk, and the specific production scheduling schemes at the three risk levels are shown in fig. 3, where fig. 3(a) is the optimal production scheduling scheme at the low risk level; FIG. 3(b) is an optimal production scheduling scheme at moderate risk levels; FIG. 3(c) is an optimal production scheduling scheme at high risk levels; the black part represents that the air separation plant is in an open state, the blank part represents that the air separation plant is in a closed state, and the specific production scheduling scheme is different under different risk levels. The profit values and condition risk value changes under the three risk conditions are shown in fig. 4, higher profits can be obtained when the risk is high, the results are more conservative when the risk is low, and the profits are also low, so the risk can be avoided by adjusting the risk level, and higher profits can be obtained at the same time.
In the invention, the optimization propositions are solved by using CPLEX under a Pyomo platform and using a personal computer carrying Intel Core i7-8700K CPU and 32G memory.
The above-described embodiments are merely preferred embodiments of the present invention, which should not be construed as limiting the invention. Various changes and modifications may be made by one of ordinary skill in the pertinent art without departing from the spirit and scope of the present invention. Therefore, the technical scheme obtained by adopting the mode of equivalent replacement or equivalent transformation is within the protection scope of the invention.
Claims (5)
1. An air separation pipe network device start-stop and load scheduling method facing to uncertain demands is characterized by comprising the following steps:
step (1): the air separation pipe network device consists of an air separation device and an auxiliary device, and is divided into different modes according to the operation condition of the air separation device to obtain the production space of each air separation device in each mode;
step (2): establishing a material balance equation for an auxiliary device in the air separation pipe network, and combining the material balance equation with the production space of the air separation device to obtain a process balance equation of the air separation pipe network; the production space of the air separation device under each mode, the material balance equation of the auxiliary device and the process balance equation of the air separation pipe network form an integral model of the air separation pipe network;
and (3): the method comprises the following steps that a two-stage random planning model is adopted to divide an overall model of an air separation pipe network into two stages again, the first stage makes decisions on start-stop and nominal loads of an air separation device and a compressor, and the second stage makes decisions on incremental loads of the air separation device and the compressor, start-stop and overall loads of a liquefier, start-stop and overall loads of a gasifier and overall loads;
and (4): the conditional risk value CVaR is introduced on the basis of the two-stage random planning model, an uncertain scheduling model based on the CVaR is constructed, and under the condition that market demand uncertainty is considered, the profit and the conditional risk value CVaR in the two stages are maximized, so that an optimal scheduling scheme is obtained.
2. The uncertain-demand-oriented air separation pipe network device start-stop and load scheduling method according to claim 1, wherein the step (1) is specifically:
the air separation pipe network device comprises a plurality of air separation devices, compressors, liquefiers, gasifiers and liquid storage tanks, and the air separation devices are divided into constant-load air separation devices and variable-load air separation devices; according to the operating condition of the air separation device, dividing the constant-load air separation device into two modes of shutdown and startup, and expressing the following steps:
fu,m,g,t＝pru,m,gyu,m,t (1.2)
wherein, Fu,g,tRepresenting the yield of product g produced by unit u at time t, fu,m,g,tRepresenting the yield of product g produced by unit u in mode m at time t, yu,m,tIndicates whether the device u is in the mode m at time t, pru,m,gA fixed value representing the yield of unit u producing product g at modality m;
dividing the variable-load air separation device into three modes of shutdown, low load and high load:
fu,AIR,m,t＝(xu,m-1-xu,m)λu,m,t+xu,m*yu,m,t (1.6)
Qu,m,AIR,t＝(q(xu,m-1)-q(xu,m))λu,m,t+q(xu,m)*yu,m,t (1.7)
0≤λu,m,t≤yu,m,t (1.8)
wherein, Fu,AIR,tIndicating the amount of air entering the device u at time t, fu,m,AIR,tRepresenting the amount of air, Q, entering the device u in mode m at time tu,AIR,tWhen represents tThe power consumption q of the air compressoru,m,AIR,tRepresenting the power consumption of the air compressor under the mode m at the moment t; x is the number ofu,mA yield value, λ, representing the operating point of the device u on the boundary of the mode mu,m,tIs a weighting coefficient of the boundary point;
after the operation mode is determined, combining historical operation data with a mechanism model, and describing the production space of each air separation unit in each mode by establishing a piecewise linear agent model; for the air separation device, logic constraint needs to be added to the switching of the modes, and a 0-1 variable z is introducedu,m',m,t，zu,m',m,t1 denotes that at time t-1 device u operates in mode m and at time t device u operates in mode m', which is expressed by the following logical relation:
the air separation device has different constraints on product yield under different modes:
wherein the content of the first and second substances,
represents the upper limit of the production of product g in the air separation unit u in mode m,
represents the lower limit of the production of product g in the air separation unit u in mode m.
3. The method for starting and stopping and load scheduling of the air separation pipe network device facing the uncertain demands as recited in claim 1, wherein the flow balance equation of the air separation pipe network in the step (2) is divided into three layers of oxygen, nitrogen and argon, and comprises a flow balance equation of an oxygen pipe network, a flow balance equation of a nitrogen pipe network, a flow balance equation of an argon pipe network, a flow balance equation of a liquid oxygen storage tank, a flow balance equation of a liquid nitrogen storage tank and a flow balance equation of a liquid argon storage tank.
4. The uncertain-demand-oriented air separation pipe network device start-stop and load scheduling method according to claim 1, wherein the step (3) is specifically:
the method comprises the following steps that a two-stage random planning model is adopted to subdivide an integral model of an air separation pipe network into two stages, a target function of the first stage is obtained by subtracting starting cost and power consumption of a compressor of the first stage from income of gas and liquid products of the first stage, and constraints of the first stage comprise a production space of a fixed-load air separation unit, a production space of a variable-load air separation unit and a flow balance equation of the air separation pipe network and are used for making decisions on starting and stopping of the air separation unit and the compressor and on a nominal load;
the objective function of the second stage is obtained by subtracting the power consumption of the compressor of the second stage from the income of gas and liquid products of the second stage, and the constraint of the second stage is an integral model which is used for making decisions on the increment load of the air separation device and the compressor, the start-stop and integral load of the liquefier, and the start-stop and integral load of the gasifier;
the two-stage stochastic optimization proposition is represented as follows:
s.t.Ax＝b
Tsx+Wsys＝hs
x≥0,ys≥0 (3.1)
where x is the decision variable of the first stage and ysIs a decision variable, p, of a second stage scenario ssRepresenting the probability of occurrence of scene s, N representing the number of scenes, cTx the objective function of the first stage,
second oneThe objective function of the stage, Ax ═ b denotes the constraint of the first stage, Tsx+Wsys＝hsRepresenting a second stage constraint, cT、
A、b、Ts、Ws、hsAre all coefficients.
5. The uncertain-demand-oriented air separation pipe network device start-stop and load scheduling method according to claim 1, wherein the step (4) is specifically:
introducing a condition risk value CVaR on the basis of a two-stage random planning model, wherein the CVaR optimization topic is as follows:
s.t.zs≥ζ-f(x,y)
zs≥0 (4.1)
wherein p issRepresents the probability of occurrence of a scene s, ζ represents the minimum possible profit value expected at a confidence level α, N represents the number of scenes, f (x, y) represents a loss function, x is a decision variable, y is an uncertain parameter, and in different scenes, z is greater than f (x, y) when ζ is greater than fsDenotes the difference between ζ and f (x, y), and z is when ζ is smaller than f (x, y)sIs 0;
combining the profit value of the two-stage random planning with the conditional risk value CVaR, and constructing an uncertainty scheduling model based on the CVaR, wherein the uncertainty scheduling model is represented as follows:
wherein TP represents the sum of profits of the two stages, Profit represents the Profit of the first stage,
an expected value representing profit for the second stage;
for an objective function of the entire scheduling model, ηsS and epsilon are weight coefficients.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010147968.2A CN111368435B (en) | 2020-03-05 | 2020-03-05 | Uncertain demand-oriented air separation pipe network device starting and stopping and load scheduling method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010147968.2A CN111368435B (en) | 2020-03-05 | 2020-03-05 | Uncertain demand-oriented air separation pipe network device starting and stopping and load scheduling method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111368435A CN111368435A (en) | 2020-07-03 |
| CN111368435B true CN111368435B (en) | 2022-03-22 |
Family
ID=71207034
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010147968.2A Active CN111368435B (en) | 2020-03-05 | 2020-03-05 | Uncertain demand-oriented air separation pipe network device starting and stopping and load scheduling method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111368435B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112651614B (en) * | 2020-12-21 | 2023-04-07 | 河南德尔液空科技有限公司 | Intelligent energy-saving method and system based on air separation equipment |
| CN112748666B (en) * | 2020-12-25 | 2022-07-01 | 国家能源集团宁夏煤业有限责任公司 | Adaptive scheduling control method for variable load of air separation equipment |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102520615A (en) * | 2011-12-28 | 2012-06-27 | 东方电气集团东方汽轮机有限公司 | Automatic load-variable multi-variable control method for air separation device |
| CN105629937A (en) * | 2016-02-19 | 2016-06-01 | 浙江大学 | Variable load dispatching method for combined production air separation unit |
| CN107392400A (en) * | 2017-09-04 | 2017-11-24 | 重庆大学 | Meter and real-time traffic and the EV of temperature charging load spatial and temporal distributions Forecasting Methodology |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6739359B2 (en) * | 2002-10-04 | 2004-05-25 | Shaw Aero Devices, Inc. | On-board inert gas generating system optimization by pressure scheduling |
-
2020
- 2020-03-05 CN CN202010147968.2A patent/CN111368435B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102520615A (en) * | 2011-12-28 | 2012-06-27 | 东方电气集团东方汽轮机有限公司 | Automatic load-variable multi-variable control method for air separation device |
| CN105629937A (en) * | 2016-02-19 | 2016-06-01 | 浙江大学 | Variable load dispatching method for combined production air separation unit |
| CN107392400A (en) * | 2017-09-04 | 2017-11-24 | 重庆大学 | Meter and real-time traffic and the EV of temperature charging load spatial and temporal distributions Forecasting Methodology |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111368435A (en) | 2020-07-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111368435B (en) | Uncertain demand-oriented air separation pipe network device starting and stopping and load scheduling method | |
| US6957153B2 (en) | Method of controlling production of a gaseous product | |
| CN101718270B (en) | Prediction and pressure regulation method for control system of air compressor | |
| He et al. | A novel air separation unit with energy storage and generation and its energy efficiency and economy analysis | |
| CN112418486B (en) | Data-driven scheduling method based on renewable energy consumption capability | |
| CN101901014A (en) | Method for controlling forecast pressure regulation in air compression stations | |
| Zhang et al. | MILP-based optimization of oxygen distribution system in integrated steel mills | |
| Kong et al. | A novel economic scheduling of multi-product deterministic demand for co-production air separation system with liquid air energy storage | |
| US20070186583A1 (en) | Method of controlling liquid production utilizing an expert system controller | |
| Dong et al. | Research on the optimal planning method of hydrogen-storage units in wind–hydrogen energy system considering hydrogen energy source | |
| JP4279540B2 (en) | Control method of air separation device | |
| CN111219596A (en) | Electricity cold production recycle system of hydrogenation station and natural gas pressure regulating station | |
| Li et al. | Optimization of oxygen system scheduling in hybrid action space based on deep reinforcement learning | |
| CN212273682U (en) | Electricity cold production recycle system of hydrogenation station and natural gas pressure regulating station | |
| CN110837938A (en) | Comprehensive energy system optimization operation method and system based on model prediction control framework | |
| Li et al. | Dynamic simulation for improving the performance of boil-off gas recondensation system at lng receiving terminals | |
| CN105629937B (en) | A kind of method for the scheduling of coproduction air separation unit varying duty | |
| Kong et al. | A Novel Economic Scheduling of Multi-Product Deterministic Demand for Co-Production Air Separation System with Liquid Air Energy Storage | |
| Zhang et al. | Oxygen demand forecasting and optimal scheduling of the oxygen gas system in the iron-and steel-making enterprises | |
| Tong et al. | Optimization strategy for contradiction between intermitting oxygen consumption in converter steelmaking and continuous oxygen production by air separation unit | |
| CN114219366A (en) | Iron and steel enterprise oxygen system scheduling method based on deep reinforcement learning | |
| CN114091784B (en) | Uncertain optimization scheduling method and system for oxygen system of iron and steel enterprise | |
| Gao et al. | A novel volatile organic compound cryogenic recovery system with cold energy storage | |
| Zhang et al. | Enhancing robustness: Multi-stage adaptive robust scheduling of oxygen systems in steel enterprises under demand uncertainty | |
| WO2013104840A1 (en) | Method for producing one or more air separation apparatuses, and equipment for air separation by cryogenic distillation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |