A scheduling method and device of a hydrogen production system

Abstract

This invention discloses a scheduling method and apparatus for a hydrogen production system, belonging to the field of hydrogen production technology. The scheduling method includes: constructing an uncertainty set including uncertainties in biomass water content and photovoltaic power generation; constructing a hydrogen production system scheduling model considering the constraints of complementary utilization of materials and energy among hydrogen production units and system operation constraints, the objective function of which is to minimize the first-stage cost and the second-stage cost corresponding to the uncertainty set; solving the hydrogen production system scheduling model to obtain day-ahead scheduling decisions; and using the day-ahead scheduling decisions for hydrogen production scheduling. This invention, by constructing uncertainties in photovoltaic and biomass water content, compensates for the neglected or difficult-to-estimate influence of biomass uncertainty in the multi-energy coupled complementary hydrogen production optimization scheduling problem. Furthermore, by utilizing the constraints of complementary utilization of materials and energy among hydrogen production units, it can obtain scheduling decisions that meet stable hydrogen demand under uncertain environments, thereby improving the robustness of system scheduling.

Description

Technical Field

[0001] This invention belongs to the field of hydrogen production technology, and more specifically, relates to a scheduling method and apparatus for a hydrogen production system. Background Technology

[0002] Hydrogen is an important raw material in industrial chemical processes and also a promising secondary energy source. Replacing fossil fuels with renewable energy for hydrogen production is a crucial means of reducing carbon emissions, but this process is highly uncertain and struggles to meet stable hydrogen demand.

[0003] Integrating different hydrogen production technologies is an effective solution to meet stable hydrogen demand, as it leverages the advantages of both renewable energy and fossil fuel-based hydrogen production. Currently, most research on multi-energy coupled hydrogen production focuses on energy aspects, neglecting the material coupling relationships between different energy sources. This may lead to relatively low efficiency and poor economic viability in hydrogen production schemes. Therefore, further exploration of complementary hydrogen production methods, especially in stable hydrogen production scenarios, is of great significance in fully utilizing the complementary effects of matter and energy.

[0004] Hydrogen production primarily driven by renewable energy sources is a hallmark of integrated hydrogen production systems, with water, solar energy, and biomass being typical sustainable sources. Compared to the deterministic process of hydrogen production from fossil fuels, the water content of biomass and the output of photovoltaic power are uncertain and difficult to predict accurately, posing significant challenges to system modeling and operation. Currently, research on photovoltaic uncertainty is relatively mature. Although experts have confirmed the uncertainty of biomass water content and its significant impact on the gasification process, the impact of biomass uncertainty on hydrogen production scheduling is rarely addressed in hydrogen production scheduling problems, yet this uncertainty leads to poor robustness in hydrogen production scheduling. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a scheduling method and apparatus for a hydrogen production system. Its purpose is to construct an uncertainty set of photovoltaic and biomass water content to compensate for the neglected or difficult-to-estimate impact of biomass uncertainty in the optimal scheduling problem of multi-energy coupled complementary hydrogen production. Furthermore, by utilizing the constraints of complementary material and energy utilization among various hydrogen production units, scheduling decisions that meet stable hydrogen demand can be obtained even under uncertain environments, thereby improving the robustness of system scheduling. This solves the technical problem of poor scheduling robustness caused by biomass uncertainty in existing hydrogen production scheduling processes.

[0006] To achieve the above objectives, according to one aspect of the present invention, a scheduling method for a hydrogen production system is provided, comprising:

[0007] S1: Analyze the gasification products of biomass hydrogen production units under different biomass moisture contents, and obtain the hydrogen production impact quantity corresponding to the uncertainty of biomass moisture content.

[0008] S2: The uncertainty set of biomass water content is characterized by the prediction error range of the biomass hydrogen production coefficient and the hydrogen production influence quantity;

[0009] S3: Construct a hydrogen production system scheduling model that considers the constraints of complementary utilization of materials and energy among hydrogen production units and system operation constraints. The objective function is to minimize the first-stage cost and the second-stage cost.

[0010] The hydrogen production units include photovoltaic water electrolysis hydrogen production units, biomass hydrogen production units, and natural gas hydrogen production units; the first-stage cost includes the start-up and shutdown costs and raw material costs of both the biomass hydrogen production units and the natural gas hydrogen production units; the second-stage cost includes the start-up and shutdown costs, curtailment penalty costs, and unstable hydrogen production penalty costs of the photovoltaic water electrolysis hydrogen production units under the worst-case scenario obtained based on the uncertainty set; the uncertainty set includes the uncertainty set of biomass water content and the uncertainty set of photovoltaic power generation;

[0011] S4: Solve the hydrogen production system scheduling model to obtain the day-ahead scheduling decision; use the day-ahead scheduling decision to schedule hydrogen production.

[0012] In one embodiment, S1 includes:

[0013] S11: The biomass hydrogen production unit is modeled using a thermodynamic equilibrium model, and the gasification products of the biomass hydrogen production unit under different biomass moisture contents are analyzed in order to calculate the biomass hydrogen production coefficient.

[0014] S12: Quantify the impact of hydrogen production corresponding to the uncertainty of biomass water content using the biomass hydrogen production coefficient.

[0015] In one embodiment, S11 includes: modeling the biomass hydrogen production unit using a thermodynamic equilibrium model to obtain the mapping relationship between biomass feed and oxygen consumption and gas production; and analyzing the biomass gasification products under different biomass moisture contents based on the mapping relationship to calculate the biomass hydrogen production coefficients corresponding to oxygen and air as gasifying agents.

[0016] The mapping relationship is expressed as follows: in, Biomass consumption These are the biomass consumed when oxygen and air are used as vaporizing agents, respectively. These represent the hydrogen production, oxygen consumption, methane production, and carbon dioxide production of the j-th hydrogen production unit at time t, respectively. These correspond to the hydrogen production coefficients when oxygen and air are used as vaporizing agents, respectively. These correspond to the oxygen consumption coefficients when oxygen and air are used as vaporizing agents, respectively. The methane production coefficients corresponding to oxygen and air as vaporizing agents, respectively; The carbon dioxide production coefficients correspond to oxygen and air as vaporizing agents, respectively.

[0017] In one embodiment, the biomass hydrogen production coefficient when oxygen is used as the gasifying agent is... and biomass consumption product Characterize the impact of uncertain biomass water content on hydrogen production.

[0018] In one embodiment, S2 includes:

[0019] The prediction error range based on the hydrogen production impact of the uncertainty in biomass water content and the biomass hydrogen production coefficient. Robust adjustment factor Γ bio Set the uncertainty set Φ of biomass moisture content bio , represented as:

[0020]

[0021] in, Predicted hydrogen production coefficient for oxygen as a gasifying agent. The error, These are 0-1 variables representing the upper and lower bounds of the biomass hydrogen production coefficient.

[0022] In one embodiment, the constraints on the complementary use of materials and energy among the hydrogen production units include: material complementary use constraints, hydrocarbon fuel complementary use constraints, and energy complementary use constraints.

[0023] The constraints on the complementary utilization of materials include: the by-product oxygen of the photovoltaic water electrolysis hydrogen production unit is divided into: a portion stored in an oxygen storage device, a portion supplied to the biomass hydrogen production unit, and a portion supplied to the natural gas hydrogen production unit; the oxygen consumed by the biomass hydrogen production unit and the oxygen consumed by the natural gas hydrogen production unit are both provided by the photovoltaic water electrolysis hydrogen production unit and the oxygen storage device.

[0024] The constraints on the complementary use of hydrocarbon fuels include: the hydrocarbon fuel produced by the biomass hydrogen production unit includes a portion supplied to the natural gas hydrogen production unit and a portion stored in a gas storage device; the fuel required by the natural gas hydrogen production unit includes a portion purchased externally, a portion supplied by the biomass hydrogen production unit, and a portion supplied by the gas storage device;

[0025] The constraints on complementary energy utilization include:

[0026]

[0027] X∈{CO,CO2,H2O,CH4} bio ,Y∈{O2,H2O,CH4} gas

[0028] Where X and Y represent substances, C X C Y , respectively, are the specific heat capacities of substances X and Y; T represents the amount of gas produced (X) by the biomass hydrogen production unit and the amount of gas supplied (Y) by the natural gas hydrogen production unit, respectively; t gas T is the inlet gas temperature of the natural gas to hydrogen production unit. 0 The ambient temperature; T0 bio T is the gas production temperature of the biomass hydrogen production unit. bio T0 is the gas production temperature of the biomass hydrogen production unit after heat exchange. gas The inlet temperature of the natural gas to hydrogen production unit is before heat exchange.

[0029] In one embodiment, the system operation constraints include: hydrogen production unit operation constraints, energy storage hydrogen production unit operation constraints, stable hydrogen production constraints, carbon emission constraints, curtailment of solar power and unstable hydrogen production constraints, rescheduled power balance constraints, and rescheduled hydrogen balance constraints.

[0030] The constraints on wasted solar power and unstable hydrogen production are expressed as follows:

[0031]

[0032] The rescheduled power balance constraint is expressed as follows:

[0033] Among them, P t cur P represents the amount of light discarded. t pv For photovoltaic power generation, For the fluctuation of hydrogen demand, The threshold for hydrogen demand fluctuations. The hydrogen production power of the photovoltaic water electrolysis hydrogen production unit is given.

[0034] In one embodiment, S4 includes:

[0035] The nonlinear constraints in the hydrogen production system scheduling model are piecewise linearized to transform the solution problem of the hydrogen production system scheduling model into a mixed integer linear programming problem.

[0036] The mixed-integer linear programming problem is solved using a nested column and constraint generation algorithm to obtain the day-ahead scheduling decision; the day-ahead scheduling decision is then used for hydrogen production scheduling.

[0037] In one embodiment, the mixed-integer linear programming problem includes:

[0038] The current scheduling issue is used to decide the start-up mode of the biomass hydrogen production unit, the start-up mode of the natural gas hydrogen production unit, and the pre-scheduled output of the biomass hydrogen production unit;

[0039] The feasibility sub-problem is used to verify that the day-ahead scheduling decision can adapt to all photovoltaic power output and biomass moisture content scenarios.

[0040] According to another aspect of the present invention, a scheduling device for a hydrogen production system is provided, comprising:

[0041] The analysis module is used to analyze the gasification products of biomass hydrogen production units under different biomass moisture contents, and to obtain the hydrogen production impact quantity corresponding to the uncertainty of biomass moisture content.

[0042] The characterization module is used to characterize the uncertainty set of biomass water content using the prediction error range of the biomass hydrogen production coefficient and the hydrogen production influence amount; it is also used to characterize the uncertainty set of photovoltaic power generation using the prediction error range of photovoltaic power generation output.

[0043] A construction module is used to build a hydrogen production system scheduling model that considers the constraints of complementary utilization of materials and energy among various hydrogen production units and system operation constraints. The objective function is to minimize the first-stage cost and the second-stage cost. The hydrogen production units include photovoltaic water electrolysis hydrogen production units, biomass hydrogen production units, and natural gas hydrogen production units. The first-stage cost includes the start-up and shutdown costs and raw material costs of the biomass hydrogen production units and the natural gas hydrogen production units. The second-stage cost includes the start-up and shutdown costs, curtailment penalty costs, and unstable hydrogen production penalty costs of the photovoltaic water electrolysis hydrogen production units under the worst-case scenario obtained based on the uncertainty set. The uncertainty set includes the uncertainty set of biomass water content and the uncertainty set of photovoltaic power generation.

[0044] The scheduling module is used to solve the scheduling model of the hydrogen production system to obtain the day-ahead scheduling decision; and to use the day-ahead scheduling decision to perform hydrogen production scheduling.

[0045] According to another aspect of the present invention, a scheduling system for a hydrogen production system is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the scheduling method.

[0046] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the scheduling method.

[0047] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0048] (1) The scheduling method of the hydrogen production system provided by the present invention constructs an uncertainty set of photovoltaic and biomass water content to make up for the influence of the uncertainty of biomass in the optimization scheduling problem of multi-energy coupled complementary hydrogen production. Then, by utilizing the material and energy complementary utilization constraints among each hydrogen production unit, it ensures that a scheduling decision that meets the stable hydrogen demand can be obtained under uncertain environment, thereby improving the robustness of system scheduling. This solves the technical problem of poor scheduling robustness caused by biomass uncertainty in the existing hydrogen production scheduling process.

[0049] (2) This scheme uses a thermodynamic equilibrium model to model the biomass hydrogen production unit. Based on this, it analyzes the impact of the uncertainty of biomass moisture content on biomass gasification. It uses the biomass hydrogen production coefficient to quantify the hydrogen production impact corresponding to the uncertainty of biomass moisture content, and determines the uncertainty set of biomass moisture content. This can ensure that scheduling decisions that meet the stable hydrogen demand are obtained under uncertain conditions.

[0050] (3) This scheme uses the biomass hydrogen production coefficient and biomass consumption when oxygen is used as a gasifying agent to characterize the hydrogen production impact of the uncertainty of biomass water content. This simplifies the determination process of the uncertainty set of biomass water content, thereby simplifying the solution process of the entire hydrogen production system scheduling model, reducing the computational complexity of the entire hydrogen production system scheduling method, and improving the scheduling efficiency while enhancing the robustness of hydrogen production scheduling.

[0051] (4) The constraints on the complementary use of materials and energy among the hydrogen production units in this scheme include: material complementary use constraints, hydrocarbon fuel complementary use constraints, and energy complementary use constraints. By fully exploring the complementary use of materials and energy among water electrolysis, biomass, and natural gas, the photovoltaic water electrolysis hydrogen production units, biomass hydrogen production units, and natural gas hydrogen production units can complement and balance each other according to hydrogen production demand, improving scheduling robustness and hydrogen production efficiency. In addition, it can also improve the conversion rate of biomass and natural gas, thereby significantly improving the economic efficiency of system operation.

[0052] (5) The system operation constraints mentioned in this scheme also include constraints on curtailment of solar power and unstable hydrogen production, as well as constraints on rescheduling power balance. The system power balance can be met through intraday rescheduling, and the rationality of the day-ahead scheduling results can be measured.

[0053] (6) In this scheme, the nonlinear constraints in the hydrogen production system scheduling model are piecewise linearized, which simplifies the solution process of the hydrogen production system scheduling model; the nested column and constraint generation algorithm is used to solve the hydrogen production system scheduling model, which reduces the computational complexity and improves the efficiency of the entire scheduling process.

[0054] (7) This scheme divides the mixed integer linear programming problem into day-ahead scheduling problem and feasibility subproblem, and can find a reasonable photovoltaic power output scenario and biomass moisture content scenario. In the next stage of the scenario, the day-ahead scheduling decision meets the operation requirements under the most severe scenario (maximum system relaxation), that is, the day-ahead scheduling decision has good robustness and can cope with the uncertainty of photovoltaic and biomass. Attached Figure Description

[0055] Figure 1 The flowchart is shown for the robust scheduling method of the integrated stable hydrogen production system provided in Embodiment 1 of the present invention.

[0056] Figure 2a This is a diagram of gasification products under different biomass moisture contents when air is used as a gasifying agent, as provided in Example 4 of the present invention.

[0057] Figure 2b This is a diagram of gasification products under different biomass moisture contents when oxygen is used as a gasifying agent, as provided in Example 4 of the present invention.

[0058] Figure 3 The flowchart of the NC&CG algorithm provided in Embodiment 8 of the present invention is shown.

[0059] Figure 4 This is a scatter plot of the total operating cost provided in Embodiment 8 of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0061] The embodiments of the present invention are all described in the following scenarios, as detailed below:

[0062] The hydrogen production system scheduling is based on a 1-hour interval, resulting in 24 scheduling periods per day. The system comprises three hydrogen production methods: one photovoltaic water electrolysis unit, three biomass hydrogen production units, two natural gas hydrogen production units, one oxygen storage unit, and one gas storage unit. The predicted hydrogen load demand is 1200 Nm³. 3 / h. The carbon emission limit factor is 8.5 kg CO2 / kg H2, the curtailment penalty cost is $80 / MWh, and the unstable hydrogen production penalty cost is $80 / MWh. The robust adjustment coefficient Γ is set to 24. The price of biomass pellets is $140 / ton, and the price of natural gas is $0.54 / m³. 3The main technical specifications of the photovoltaic water electrolysis hydrogen production unit, biomass hydrogen production unit, and natural gas hydrogen production unit are shown in Table 1. The maximum capacity of the oxygen storage device and the gas storage device are 4000 Nm³. 3 and 300Nm 3 A simulation model was built on the MATLAB R2021a platform and solved using the commercial software Gurobi.

[0063] Table 1 Main Technical Specifications of Hydrogen Production Units

[0064]

[0065]

[0066] Example 1

[0067] like Figure 1 As shown, this embodiment provides a scheduling method for a hydrogen production system, including: S1: Analyzing the gasification products of biomass hydrogen production units under different biomass moisture contents to obtain the hydrogen production impact quantity corresponding to the uncertainty of biomass moisture content. S2: Characterizing the uncertainty set of biomass moisture content using the prediction error range of the biomass hydrogen production coefficient and the hydrogen production impact quantity. S3: Constructing a hydrogen production system scheduling model considering the constraints of complementary utilization of materials and energy among hydrogen production units and system operation constraints, with the objective function being the minimization of the first-stage cost and the second-stage cost. The uncertainty set includes the uncertainty set of biomass moisture content and the uncertainty set of photovoltaic power generation. S4: Solving the hydrogen production system scheduling model to obtain the day-ahead scheduling decision. Hydrogen production scheduling is then performed using the day-ahead scheduling decision.

[0068] The hydrogen production system scheduling model includes constraints on three hydrogen production units: water electrolysis, biomass, and natural gas, as well as constraints on the complementary use of materials and energy among these units and system operation. The start-up and shutdown status of the biomass and natural gas hydrogen production units requires day-ahead scheduling decisions; the photovoltaic water electrolysis hydrogen production unit and energy storage are intraday adjustable devices. The objective function of the hydrogen production system scheduling model is to minimize the total system operating cost. The first-stage cost includes the start-up and shutdown costs of the biomass and natural gas hydrogen production units, as well as the costs of biomass and natural gas feedstocks. The second-stage cost includes the start-up and shutdown costs of the photovoltaic water electrolysis hydrogen production unit, as well as the penalties for curtailment and unstable hydrogen production. The objective function is as follows:

[0069]

[0070] in C represents the start-up and shutdown costs at time t for the j-th biomass hydrogen production unit, the n-th natural gas hydrogen production unit, and the i-th photovoltaic water electrolysis hydrogen production unit, respectively; bio C gas These are the prices of biomass pellets and natural gas, respectively. These represent the biomass consumed by hydrogen production unit j and the amount of purchased natural gas, respectively; C cur C flu These are the penalties for wasted solar power and unstable hydrogen production, respectively. These represent the amount of light wasted and the amount of hydrogen produced during time period t, respectively.

[0071] The photovoltaic water electrolysis hydrogen production units are as follows:

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Equation (2) represents the photovoltaic power generation P. t pv That is, to provide power to the photovoltaic water electrolysis hydrogen production unit. Equation (3) represents the hydrogen production output power of the photovoltaic water electrolysis hydrogen production unit. and current The relationship between them is shown in Equation (4); Equation (5) represents the working voltage of the photovoltaic water electrolysis hydrogen production unit. Including Nernst voltage E and Ohmic overvoltage Activation overvoltage U rev Where is the reversible voltage, R is the ideal gas constant, and T is the reversible voltage. cell α represents the operating temperature of the electrolytic cell. an / α cat These are the anode / cathode charge transfer coefficients, respectively, where F is the Faraday coefficient, and i an / i cat These are the anode / cathode current densities, respectively; Equation (6) describes the relationship between current and current density. Let A be the current density of the i-th photovoltaic water electrolysis hydrogen production unit at time t. cell Effective reaction area; hydrogen production capacity of photovoltaic water electrolysis hydrogen production unit and oxygen production As shown in equation (7); k1 is the unit conversion factor (W→MW), and k2 is the unit conversion factor (mol / s→Nm). 3 / s); N cell h is the number of electrolysis chambers. F For Faraday efficiency.

[0079] The biomass hydrogen production units are as follows:

[0080] Biomass-based hydrogen production uses a gasifying agent to convert carbon-containing solid fuels into combustible gases. Oxygen, a byproduct of water electrolysis, can be used as a gasifying agent to improve the hydrogen production capacity, calorific value, and energy efficiency of biomass-based hydrogen production units. Wood is used as biomass, and the overall gasification reaction equation is listed below:

[0081]

[0082] In the formula, w is the water content per kmol of wood, m is the oxygen consumption per kmol of wood, and x and y are the number of hydrogen and oxygen atoms per mole of carbon atoms. These are the coefficients corresponding to the products such as hydrogen, carbon monoxide, carbon dioxide, water, and methane.

[0083] The natural gas-to-hydrogen units are as follows:

[0084] The natural gas hydrogen production unit adopts chemical loop autothermal reforming technology, which can achieve efficient, low-cost, and low-energy carbon dioxide separation during the hydrogen production process. Similar to the biomass hydrogen production process, oxygen or air is used as the oxidant in the reaction process. The product composition is calculated based on the reaction equilibrium, mass balance, and heat balance equations, and the output constraints of natural gas hydrogen production are obtained (9). Since the lower the inlet temperature, the greater the heat required to achieve autothermal operation, the greater the oxygen consumption, and the greater the CO2 and H2O production.

[0085] Therefore, coefficients need to be considered. The relationship with feed temperature.

[0086]

[0087]

[0088] In the formula, This refers to natural gas consumption. These represent the amount of natural gas consumed when oxygen and air are used as gasifying agents, respectively. These represent the hydrogen production, oxygen consumption, water production, and carbon dioxide production of the nth hydrogen production unit at time t. These correspond to the hydrogen production coefficients when oxygen and air are used as vaporizing agents, respectively. These correspond to the oxygen consumption coefficients when oxygen and air are used as vaporizing agents, respectively. These correspond to the water production coefficients when oxygen and air are used as the vaporizing agents, respectively. The carbon dioxide production coefficients correspond to oxygen and air as vaporizing agents, respectively.

[0089] Example 2

[0090] In this embodiment, the constraints on the complementary use of materials and energy among the hydrogen production units include: material complementary use constraints, hydrocarbon fuel complementary use constraints, and energy complementary use constraints.

[0091] The constraints of complementary utilization of materials include: the oxygen byproduct of the photovoltaic water electrolysis hydrogen production unit is divided into three parts: a portion stored in an oxygen storage device, a portion supplied to the biomass hydrogen production unit, and a portion supplied to the natural gas hydrogen production unit. The oxygen consumed by both the biomass and natural gas hydrogen production units is provided by the photovoltaic water electrolysis hydrogen production unit and the oxygen storage device.

[0092] Specifically, material complementarity includes the utilization of oxygen and hydrocarbon fuels. Oxygen coupling is the core and link of the complementary hydrogen production system. As shown in equation (11), oxygen is a byproduct of the photovoltaic water electrolysis hydrogen production unit. It can be divided into three parts: storage in the oxygen storage device. Direct supply to biomass hydrogen production units and direct supply of natural gas to hydrogen production units As shown in equations (12) and (13), the oxygen consumed by the biomass hydrogen production unit and the oxygen consumed by the natural gas hydrogen production unit are both provided by the photovoltaic water electrolysis hydrogen production unit and the oxygen storage device.

[0093]

[0094]

[0095]

[0096] In the formula, The amount of oxygen supplied by the oxygen storage device to the biomass hydrogen production unit and the natural gas hydrogen production unit, respectively.

[0097] Constraints on the complementary use of hydrocarbon fuels include: the hydrocarbon fuel produced by biomass hydrogen production units includes a portion supplied to natural gas hydrogen production units and a portion stored in gas storage facilities. The fuel required by natural gas hydrogen production units includes a portion purchased externally, a portion supplied by biomass hydrogen production units, and a portion supplied by gas storage facilities.

[0098] In the complementary utilization of hydrocarbon fuels, hydrocarbon fuels produced from biomass hydrogen production... A portion is directly supplied to natural gas-to-hydrogen units. A portion is stored in a gas storage device. As shown in equation (14). Equation (15) indicates that the fuel required for the natural gas-to-hydrogen unit is purchased externally. Biomass hydrogen production unit and gas storage device supply.

[0099]

[0100]

[0101] In energy complementary utilization, the high-temperature gas generated by biomass hydrogen production can preheat the feed gas of natural gas hydrogen production, achieving thermal balance between biomass hydrogen production and natural gas hydrogen production. Equation (16) indicates that the heat provided by the outlet gas of the biomass hydrogen production unit must be greater than the heat obtained by the feed gas of the natural gas hydrogen production unit. Equation (17) limits the range of feed temperature variation.

[0102]

[0103]

[0104] The formula already indicates the substances represented by X and Y, and C. X C Y , respectively, are the specific heat capacities of substances X and Y; T represents the amount of gas produced (X) from biomass hydrogen production and the amount of gas supplied (Y) from natural gas hydrogen production, respectively; t gas T is the inlet gas temperature for hydrogen production from natural gas. 0 The ambient temperature; T0 bio Temperature for hydrogen production from biomass; T bio T0 is the temperature of the gas produced by the biomass hydrogen production unit after heat exchange. gas The temperature of the gas entering the hydrogen production process from natural gas before heat exchange.

[0105] Example 3

[0106] In this embodiment, the system operation constraints include: hydrogen production unit operation constraints, energy storage hydrogen production unit operation constraints, stable hydrogen production constraints, carbon emission constraints, curtailment of solar power and unstable hydrogen production constraints, rescheduled power balance constraints, and rescheduled hydrogen balance constraints.

[0107] The constraints on curtailment and unstable hydrogen production are expressed as follows:

[0108]

[0109] The power balance constraint for rescheduling is expressed as:

[0110] Among them, P t cur P represents the amount of light discarded. t pv For photovoltaic power generation, For the fluctuation of hydrogen demand, The threshold for hydrogen demand fluctuations. The hydrogen production capacity of the photovoltaic water electrolysis hydrogen production unit.

[0111] The operating constraints of the hydrogen production units include:

[0112] The upper and lower limits of the output of the hydrogen production unit are constrained by formula (18). Formula (19) limits the maximum change in the input of the hydrogen production unit. Formula (20) is the maximum output constraint at the start / stop time of the hydrogen production unit, where M is a large constant. Formula (21) is the minimum start / stop time constraint of the hydrogen production unit. The minimum start / stop time constraint at the beginning of the simulation period needs to be constrained in conjunction with the initial start / stop state of the hydrogen production unit. If the hydrogen production unit is in the start state at the beginning of the period, the constraint is formula (22), otherwise it is formula (23). Formula (24) is the relaxation constraint of the start / stop cost of the hydrogen production unit.

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] In the formula s t The start-up and shutdown status of the unit at time t; R is the feed rate of the hydrogen production unit; ΔR max R is the maximum ramp vector of the device; min and R max S represents the maximum and minimum output of the device; U and S D T represents the maximum start-up and maximum shutdown power of the device. on T represents the minimum operating time vector required to maintain the hydrogen production unit. off T represents the minimum downtime vector that the hydrogen production unit needs to maintain; on0 T represents the duration during which the hydrogen production unit has been running before the simulation period; off0 C represents the duration during which the hydrogen production unit had been shut down prior to the simulation period. su C sd These are the costs for a single start-up and shutdown of the hydrogen production unit; The set of start-up and shutdown costs for the three devices at time t.

[0121] The operational constraints for energy storage devices include those for oxygen storage devices and those for gas storage devices. Specifically, the operational constraints for oxygen storage devices include:

[0122]

[0123] In the formula, This represents the current capacity of the oxygen storage device. This represents the upper limit of the oxygen storage device's capacity. For the oxygen storage device, the state is a 0-1 variable; N os_max This is the upper limit for the rate at which an oxygen storage device stores / releases oxygen.

[0124] Operating constraints for gas storage devices include:

[0125]

[0126] In the formula, This represents the current capacity of the gas storage device. This is the upper limit of the gas storage device's capacity; N represents the 0-1 state variable of the gas storage device. gs_max This is the upper limit of the rate at which a gas storage device stores / releases gas.

[0127] The constraints on stable hydrogen production include:

[0128] The combined hydrogen production capacity of different hydrogen production technologies should meet the stable hydrogen demand.

[0129]

[0130] In the formula, For the demand for hydrogen.

[0131] The carbon emission constraints include:

[0132]

[0133] The first term in the numerator of the formula represents the standard carbon emissions corresponding to the input raw materials, and the second term represents the total carbon emissions from the hydrogen production process products; the denominator represents the total hydrogen production. Where T is the total scheduling period. These are the densities of hydrogen and carbon dioxide, respectively. These are the carbon emission factor for natural gas and the carbon emission limit.

[0134] The constraints on wasted solar power and unstable hydrogen production include:

[0135] Formula (29) represents the amount of light wasted. It should be less than the photovoltaic power generation. Formula (30) represents the fluctuation in hydrogen demand. It should be within a certain range.

[0136]

[0137]

[0138] The rescheduled power balance and hydrogen balance constraints include:

[0139]

[0140]

[0141] Example 4

[0142] In this embodiment, S1 includes:

[0143] S11: A thermodynamic equilibrium model is used to model the biomass hydrogen production unit, and the gasification products of the biomass hydrogen production unit under different biomass moisture contents are analyzed in order to calculate the biomass hydrogen production coefficient.

[0144] S12: Quantify the impact of uncertainty in biomass water content on hydrogen production using the biomass hydrogen production coefficient.

[0145] Specifically, regarding the uncertainty of biomass water content, the calculation results of the thermodynamic equilibrium model are as follows: Figure 2a and Figure 2b As shown, the overall trend of gas composition changes is the same when air and oxygen are used as gasifying agents. The composition of H2 and CO2 increases continuously with the increase of biomass moisture content, while CH4 gas production and O2 consumption remain basically unchanged with the increase of biomass moisture content. Furthermore, when oxygen is used as the gasifying agent, the H2 yield is higher than when air is used, while O2 consumption and CO2 synthesis are lower. It is worth noting that the uncertainty of biomass yield due to changes in biomass moisture content is related to whether air or oxygen is used as the gasifying agent: the H2 production in both oxygen and air changes with the biomass moisture content, but the ratio between the two remains almost unchanged.

[0146] Example 5

[0147] In this embodiment, S11 includes: modeling the biomass hydrogen production unit using a thermodynamic equilibrium model to obtain the mapping relationship between biomass feed, oxygen consumption, and gas production. Based on the mapping relationship, the biomass gasification products under different biomass moisture contents are analyzed to calculate the biomass hydrogen production coefficients corresponding to oxygen and air as gasifying agents.

[0148] A thermodynamic equilibrium model was used to model the biomass hydrogen production unit. By solving the element conservation, heat conservation, and chemical equilibrium equations, the relationship between biomass feed, oxygen consumption, and gas production was obtained: the mapping relationship is expressed as:

[0149]

[0150] in, Biomass consumption These represent the biomass consumed when oxygen and air are used as vaporizing agents, respectively. These represent the hydrogen production, oxygen consumption, methane production, and carbon dioxide production of the j-th hydrogen production unit at time t, respectively. The hydrogen production coefficients correspond to oxygen and air as gasifying agents, respectively. These correspond to the oxygen consumption coefficients when oxygen and air are used as vaporizing agents, respectively. The methane production coefficients correspond to oxygen and air as vaporizing agents, respectively. The carbon dioxide production coefficients correspond to oxygen and air as vaporizing agents, respectively.

[0151] Example 6

[0152] In this embodiment, S12 includes: utilizing Characterizing the impact of uncertain biomass water content on hydrogen production. The biomass hydrogen production coefficient is denoted by oxygen as the gasifying agent.

[0153] Specifically, the constraint condition (34) for biomass hydrogen production is transformed to obtain the form of the continuous variable multiplied by the biomass feed decision variable in formula (35), and further processing yields formula (36). The first formula of formula (35) is added to formula (36) to obtain formula (37), which allows the influence of the uncertainty of biomass water content to be considered by the change of coefficients under the condition of oxygen as a gasifying agent.

[0154]

[0155]

[0156]

[0157]

[0158] Example 7

[0159] In this embodiment, S2 includes:

[0160] Prediction error range of hydrogen production impact and biomass hydrogen production coefficient based on the uncertainty of biomass water content. Robust adjustment factor Γ bio Set the uncertainty set of biomass moisture content Φ bio , represented as:

[0161]

[0162] in, Predicted hydrogen production coefficient for oxygen as a gasifying agent. The error, These are 0-1 variables representing the upper and lower bounds of the biomass hydrogen production coefficient.

[0163] Specifically, the prediction error of the biomass hydrogen production coefficient is within the range of... Inside, the predicted value is Robust adjustment factor Γ bio (Values ​​between 0 and T) are used to adjust the conservatism of the proposed robust scheduling method. The set of uncertainties is as follows:

[0164]

[0165] In the formula These are 0-1 variables representing the upper and lower bounds of the biomass hydrogen production coefficient.

[0166] Assuming the prediction error of photovoltaic power generation output is within an interval of [-Δpv] t ,Δpv t Its predicted value is The set of uncertainties is as follows:

[0167]

[0168] In the formula These are 0-1 variables representing the upper and lower bounds of photovoltaic data, respectively.

[0169] Example 8

[0170] In this embodiment, S4 includes: piecewise linearizing the nonlinear constraints in the hydrogen production system scheduling model to transform the solution problem of the hydrogen production system scheduling model into a mixed-integer linear programming problem. A nested column and constraint generation algorithm is used to solve the mixed-integer linear programming problem to obtain the day-ahead scheduling decision. The day-ahead scheduling decision is then used for hydrogen production scheduling.

[0171] Specifically, the output model of the photovoltaic water electrolysis hydrogen production unit is processed using a piecewise linearization method, as shown in the figure.

[0172]

[0173] In the formula, L is the total number of segments; g l,i and h l,i These are the principal coefficients and constant coefficients of each segment; δ l,i,t These are the state variables corresponding to each segment; These are the inflection points of the independent variables in each segment.

[0174] The multiplication terms of continuous variables in the constraints on hydrogen production from natural gas and the constraints on heat complementarity can be uniformly expressed as temperature T. t gas and input raw materials The product of the products can be piecewise linearized as shown in (41).

[0175]

[0176] In the formula, the symbols “+” and “-” represent the two quadratic terms in the first row of formula (41); δ λ,tand Δ λ,t These are the introduced continuous and binary auxiliary variables; ψ λ a λ and b λ It is a constant parameter.

[0177] The nested column-and-constraint generation (NC&CG) algorithm is used to solve the day-ahead robust scheduling problem of a multi-energy complementary hydrogen production system.

[0178] Two-stage robust optimization, using a max-min objective function, can find a photovoltaic output scenario and biomass moisture content where the system requires the maximum relaxation. This scenario is defined as the most severe scenario. If the day-ahead scheduling scheme in the first stage can meet the operational requirements under the most severe scenario, then the day-ahead scheduling scheme has good robustness and can cope with the uncertainties of photovoltaic and biomass.

[0179] The proposed hydrogen production system scheduling model, a two-layer robust day-ahead scheduling model, can be described as follows:

[0180]

[0181] In the formula, A, B, H, Z, h, W, X, Q, and Y are constant matrices; I b I is the set of 0-1 integer variables in one stage; C is the set of continuous variables in one stage; u Let be the set of two-stage 0-1 integer variables; P be the set of two-stage continuous variables; Φ be the uncertainty set; α be a random variable representing the uncertainty of photovoltaic and biomass water content; U·C+Z·I b ≤h is the first-stage constraint, including formulas (2)-(7) and (9)-(28); W·C+X·I b +Q·I u +Y·P≤α is the second stage constraint, including (29)-(32).

[0182] The proposed model's two-stage problem includes 0-1 integer variables (start-up and shutdown states of the photovoltaic water electrolysis hydrogen production unit, gas storage unit state, and oxygen storage unit state). Therefore, its innermost minimization problem is a mixed-integer linear programming problem, which is non-convex and cannot be transformed into a dual solution using strong duality theory. Therefore, NC&CG is used to solve the model, and the algorithm flowchart is as follows. Figure 3 As shown.

[0183] The system operating costs obtained from the solutions are shown in Table 2. Example 1 considers only deterministic scenarios, thus having the lowest total cost. Example 2 considers the uncertainty of renewable energy but does not utilize the material and complementary effects between different hydrogen production technologies, resulting in the highest total cost. The algorithm proposed in this paper, Example 4, considers the uncertainty of biomass water content in addition to Example 3, thus increasing the total cost. Examples 1 and 4 do not have a two-stage penalty cost, indicating that the day-ahead scheduling results given by the proposed algorithm can guarantee stable hydrogen production demand under all renewable energy fluctuation scenarios.

[0184] Table 2 Cost Distribution and Comparison under Different Schemes

[0185]

[0186] To further analyze the superiority of the proposed robust optimization scheduling method, 1000 random scenarios were generated using Monte Carlo simulation to compare the economics of the robust scheduling scheme and the deterministic scheduling scheme. Figure 4 The scatter plot shows the total operating cost for each scenario. Example 4 shows the highest scatter density and smallest fluctuation range for total cost across different scenarios, while Example 1 shows a larger fluctuation range for total cost across all scenarios. Compared to Example 3, Example 4 further improves the ability of day-ahead scheduling to cope with biomass uncertainty and enhances overall economic efficiency. The statistical results of the 1000 scenarios are shown in the table. Fluctuations exceeding 2% of hydrogen demand are considered unstable hydrogen production. Example 1 has a large number of scenarios involving curtailed solar power and unstable hydrogen production. Even considering photovoltaic uncertainty, more than half of the scenarios still involve curtailed solar power and more than 1 / 4 involve unstable hydrogen production. Example 4 has no curtailed solar power or unstable hydrogen production in any scenario. In summary, when photovoltaic power generation and biomass water content cannot be accurately predicted, the day-ahead scheduling plan proposed in this method can meet all constraints under different scenarios and ensure that the operating cost is close to the optimal solution for all scenarios.

[0187] Table 3 Carbon emission calculation results

[0188]

[0189] Example 9

[0190] In this embodiment, the mixed-integer linear programming problem includes a day-ahead scheduling problem (the main problem) and a feasibility subproblem. The day-ahead scheduling problem is used to decide the start-up methods for biomass hydrogen production units, natural gas hydrogen production units, and the pre-scheduled output of biomass hydrogen production units. The feasibility subproblem is used to verify that the day-ahead scheduling decisions can adapt to all photovoltaic output and biomass moisture content scenarios.

[0191] Example 10

[0192] This embodiment provides a scheduling device for a hydrogen production system, comprising:

[0193] The analysis module is used to analyze the gasification products of biomass hydrogen production units under different biomass moisture contents, and to obtain the impact of biomass moisture content uncertainty on hydrogen production.

[0194] The characterization module is used to characterize the uncertainty set of biomass water content using the prediction error range of the biomass hydrogen production coefficient and the amount of hydrogen production impact. It is also used to characterize the uncertainty set of photovoltaic power generation using the prediction error range of photovoltaic power generation output.

[0195] The module is used to construct a hydrogen production system scheduling model that considers the constraints of complementary utilization of materials and energy among various hydrogen production units and system operation constraints. The objective function is to minimize the first-stage cost and the second-stage cost. The hydrogen production units include photovoltaic water electrolysis hydrogen production units, biomass hydrogen production units, and natural gas hydrogen production units. The first-stage cost includes the start-up and shutdown costs and raw material costs of both the biomass and natural gas hydrogen production units. The second-stage cost includes the start-up and shutdown costs, curtailment penalty costs, and unstable hydrogen production penalty costs of the photovoltaic water electrolysis hydrogen production unit under the worst-case scenario obtained based on the uncertainty set. The uncertainty set includes the uncertainty set of biomass water content and the uncertainty set of photovoltaic power generation.

[0196] The scheduling module is used to solve the hydrogen production system scheduling model to obtain day-ahead scheduling decisions. These day-ahead scheduling decisions are then used for hydrogen production scheduling.

[0197] Example 11

[0198] This embodiment provides a scheduling system for a hydrogen production system, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the scheduling method.

[0199] Example 12

[0200] This embodiment provides a computer-readable storage medium storing a computer program thereon, wherein the computer program implements the steps of a scheduling method when executed by a processor.

[0201] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A scheduling method for a hydrogen production system, characterized in that, include: S1: Analyze the gasification products of biomass hydrogen production units under different biomass moisture contents, and obtain the hydrogen production impact quantity corresponding to the uncertainty of biomass moisture content. S2: The uncertainty set of biomass water content is characterized by the prediction error range of the biomass hydrogen production coefficient and the hydrogen production influence quantity; S3: Construct a hydrogen production system scheduling model that considers the constraints of complementary utilization of materials and energy among hydrogen production units and system operation constraints. The objective function is to minimize the first-stage cost and the second-stage cost. The hydrogen production units include photovoltaic water electrolysis hydrogen production units, biomass hydrogen production units, and natural gas hydrogen production units; The first-stage cost includes the start-up and shutdown costs and raw material costs of both the biomass hydrogen production unit and the natural gas hydrogen production unit; the second-stage cost includes the start-up and shutdown costs, curtailment penalty costs, and unstable hydrogen production penalty costs of the photovoltaic water electrolysis hydrogen production unit under the worst-case scenario obtained based on the uncertainty set; the uncertainty set includes the uncertainty set of biomass water content and the uncertainty set of photovoltaic power generation. S4: Solve the hydrogen production system scheduling model to obtain the day-ahead scheduling decision; use the day-ahead scheduling decision to perform hydrogen production scheduling; S1 includes: S11: Modeling the biomass hydrogen production unit using a thermodynamic equilibrium model, analyzing the gasification products of the biomass hydrogen production unit under different biomass moisture contents, and calculating the biomass hydrogen production coefficient; S12: Quantifying the hydrogen production impact corresponding to the uncertainty of biomass moisture content using the biomass hydrogen production coefficient. S11 includes: modeling the biomass hydrogen production unit using a thermodynamic equilibrium model to obtain the mapping relationship between biomass feed and oxygen consumption and gas production; analyzing the biomass gasification products under different biomass moisture content based on the mapping relationship, so as to calculate the biomass hydrogen production coefficients corresponding to oxygen and air as gasifying agents respectively. The mapping relationship is expressed as follows: ; in, Biomass consumption , These represent the biomass consumed when oxygen and air are used as vaporizing agents, respectively. , , , The first j One hydrogen production unit in t Real-time hydrogen production, oxygen consumption, methane production, and carbon dioxide production; , These correspond to the hydrogen production coefficients when oxygen and air are used as vaporizing agents, respectively. , These correspond to the oxygen consumption coefficients when oxygen and air are used as vaporizing agents, respectively. , The methane production coefficients corresponding to oxygen and air as vaporizing agents, respectively; , The carbon dioxide production coefficients corresponding to oxygen and air as vaporizing agents, respectively; S12 includes: the biomass hydrogen production coefficient when oxygen is used as a gasifying agent. and biomass consumption product Characterizing the impact of uncertain biomass water content on hydrogen production; S2 includes: the prediction error range based on the hydrogen production impact amount corresponding to the uncertainty of biomass water content and the biomass hydrogen production coefficient. Robust adjustment factor is adopted Set the uncertainty set of biomass moisture content , is represented as: ； in, Predicted hydrogen production coefficient for oxygen as a gasifying agent. The error, , These are 0-1 variables representing the upper and lower bounds of the biomass hydrogen production coefficient; The uncertainty set of photovoltaic power generation is characterized using the prediction error interval of photovoltaic power generation output; it is expressed as: ； In the formula, For photovoltaic power generation, , These are 0-1 variables representing the upper and lower bounds of photovoltaic data, respectively. This represents the predicted output value of photovoltaic power generation.

2. The scheduling method for a hydrogen production system as described in claim 1, characterized in that, The constraints on the complementary use of materials and energy among the various hydrogen production units include: constraints on complementary use of materials, constraints on complementary use of hydrocarbon fuels, and constraints on complementary use of energy. The constraints on the complementary utilization of materials include: the by-product oxygen of the photovoltaic water electrolysis hydrogen production unit is divided into: a portion stored in an oxygen storage device, a portion supplied to the biomass hydrogen production unit, and a portion supplied to the natural gas hydrogen production unit; the oxygen consumed by the biomass hydrogen production unit and the oxygen consumed by the natural gas hydrogen production unit are both provided by the photovoltaic water electrolysis hydrogen production unit and the oxygen storage device. The constraints on the complementary use of hydrocarbon fuels include: the hydrocarbon fuel produced by the biomass hydrogen production unit includes a portion supplied to the natural gas hydrogen production unit and a portion stored in a gas storage device; the fuel required by the natural gas hydrogen production unit includes a portion purchased externally, a portion supplied by the biomass hydrogen production unit, and a portion supplied by the gas storage device; The constraints on complementary energy utilization include: ； ； in, X and Y Represents matter, , They are substances X and Y Specific heat capacity; , The biomass hydrogen production unit produces gas respectively. X and the gas inlet of the natural gas to hydrogen production unit Y The amount; The inlet temperature of the natural gas-to-hydrogen unit; Ambient temperature; The gas production temperature of the biomass hydrogen production unit; The gas production temperature of the biomass hydrogen production unit after heat exchange; The inlet temperature of the natural gas-to-hydrogen unit before heat exchange.

3. The scheduling method for a hydrogen production system as described in claim 2, characterized in that, The system operation constraints include: hydrogen production unit operation constraints, energy storage hydrogen production unit operation constraints, stable hydrogen production constraints, carbon emission constraints, curtailment of solar power and unstable hydrogen production constraints, rescheduled power balance constraints, and rescheduled hydrogen balance constraints. The constraints on wasted solar power and unstable hydrogen production are expressed as follows: ； ； The rescheduled power balance constraint is expressed as follows: ; in, For the amount of light discarded, For photovoltaic power generation, For the fluctuation of hydrogen demand, The threshold for hydrogen demand fluctuations. The hydrogen production power of the photovoltaic water electrolysis hydrogen production unit is given.

4. The scheduling method for a hydrogen production system as described in claim 1, characterized in that, S4 includes: The nonlinear constraints in the hydrogen production system scheduling model are piecewise linearized to transform the solution problem of the hydrogen production system scheduling model into a mixed integer linear programming problem. The mixed-integer linear programming problem is solved using a nested column and constraint generation algorithm to obtain the day-ahead scheduling decision; the day-ahead scheduling decision is then used for hydrogen production scheduling.

5. The scheduling method for a hydrogen production system as described in claim 4, characterized in that, The mixed-integer linear programming problem includes: The current scheduling issue is used to decide the start-up mode of the biomass hydrogen production unit, the start-up mode of the natural gas hydrogen production unit, and the pre-scheduled output of the biomass hydrogen production unit; The feasibility sub-problem is used to verify that the day-ahead scheduling decision can adapt to all photovoltaic power output and biomass moisture content scenarios.

6. A scheduling device for a hydrogen production system, characterized in that, A scheduling method for executing the hydrogen production system according to any one of claims 1-5, comprising: The analysis module is used to analyze the gasification products of biomass hydrogen production units under different biomass moisture contents, and to obtain the impact of biomass moisture content uncertainty on hydrogen production. The characterization module is used to characterize the uncertainty set of biomass water content using the prediction error range of the biomass hydrogen production coefficient and the hydrogen production influence amount; it is also used to characterize the uncertainty set of photovoltaic power generation using the prediction error range of photovoltaic power generation output. A construction module is used to build a hydrogen production system scheduling model that considers the constraints of complementary utilization of materials and energy among various hydrogen production units and system operation constraints. The objective function is to minimize the first-stage cost and the second-stage cost. The hydrogen production units include photovoltaic water electrolysis hydrogen production units, biomass hydrogen production units, and natural gas hydrogen production units. The first-stage cost includes the start-up and shutdown costs and raw material costs of the biomass hydrogen production units and the natural gas hydrogen production units. The second-stage cost includes the start-up and shutdown costs, curtailment penalty costs, and unstable hydrogen production penalty costs of the photovoltaic water electrolysis hydrogen production units under the worst-case scenario obtained based on the uncertainty set. The uncertainty set includes the uncertainty set of biomass water content and the uncertainty set of photovoltaic power generation. The scheduling module is used to solve the scheduling model of the hydrogen production system to obtain the day-ahead scheduling decision; and to use the day-ahead scheduling decision to perform hydrogen production scheduling.

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