Optimal configuration method for photovoltaic park microgrid considering shared electricity-hydrogen hybrid energy storage

Abstract

The present invention discloses a two-stage optimization configuration method for a photovoltaic park microgrid considering shared electric-hydrogen hybrid energy storage. The photovoltaic park microgrid is composed of a photovoltaic power generation device, a DC / AC inverter and an AC load; the shared electric-hydrogen hybrid energy storage system includes a battery energy storage system and a hydrogen energy storage system, wherein the battery energy storage system is composed of battery energy storage and an energy storage converter, and the hydrogen energy storage system is composed of an electrolyzer, a hydrogen storage tank, a fuel cell, an AC / DC rectifier and a DC / AC inverter; the shared electric-hydrogen hybrid energy storage system, a number of photovoltaic park microgrids and a distribution network are interconnected through an AC bus. The optimization configuration method is divided into two stages. The first stage uses a step resolution to efficiently realize the annual capacity planning of shared hydrogen energy storage, and the second stage uses an hourly resolution to accurately realize the monthly capacity planning of shared battery energy storage. The method of the present invention can effectively reduce the operating cost of the photovoltaic park microgrid and promote the consumption of renewable energy.

Description

Technical Field

[0001] The present invention belongs to the technical field of microgrid planning and operation, and develops a two-stage optimization configuration method for a photovoltaic park microgrid with shared electricity-hydrogen hybrid energy storage that takes into account full life cycle cost service pricing for a high-proportion photovoltaic park microgrid. Background Art

[0002] In renewable energy microgrids, configuring a hybrid energy storage system (HESS) has become a practical solution to meet diverse energy storage needs. Existing studies have shown that hybrid energy storage systems achieve more economical and efficient operation than single energy storage devices by integrating the complementary characteristics of different types of energy storage, such as response speed, storage capacity, and cycle life. However, existing studies rarely focus on the key issue of the production and consumption balance of renewable energy microgrids over long time scales across seasons, and few studies have conducted large-scale simulation analysis throughout the year, resulting in the continuous characteristics of hydrogen storage in hydrogen energy transfer over long time scales being ignored. How to reduce operating costs and promote the long-term consumption of renewable energy while ensuring the stable operation of microgrids in parks with a high proportion of renewable energy has become an important issue currently faced. Summary of the invention

[0003] The present invention develops a two-stage optimization configuration method for photovoltaic park microgrids with shared electric-hydrogen hybrid energy storage considering full life cycle cost service pricing for high-proportion photovoltaic park microgrids. The photovoltaic park microgrid sharing architecture considering electric-hydrogen hybrid energy storage includes a photovoltaic park microgrid, a shared electric-hydrogen hybrid energy storage system and a distribution network. The photovoltaic park microgrid is composed of a photovoltaic power generation device, a DC / AC inverter and an AC load; the shared electric-hydrogen hybrid energy storage system includes a battery energy storage system and a hydrogen energy storage system, wherein the battery energy storage system is composed of a battery energy storage and an energy storage converter, and the hydrogen energy storage system is composed of an electrolyzer, a hydrogen storage tank, a fuel cell, an AC / DC rectifier and a DC / AC inverter; the shared electric-hydrogen hybrid energy storage system, several photovoltaic park microgrids and a distribution network are interconnected through an AC bus. The two-stage capacity optimization configuration method includes annual capacity planning and monthly capacity planning. The first stage uses step resolution to efficiently realize the annual capacity planning of shared hydrogen energy storage, and the second stage uses hourly resolution to accurately realize the monthly capacity planning of shared battery energy storage. The two-stage capacity optimization configuration cooperates to achieve a balance between fast and effective solution and simulation calculation accuracy. The method of the present invention can effectively reduce the operating cost of microgrids in high-proportion photovoltaic parks and improve the photovoltaic absorption effect, providing a reference for the planning, operation and scheduling of renewable energy microgrids considering electric-hydrogen hybrid energy storage.

[0004] In order to achieve the purpose of the present invention, the present invention provides a photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, comprising the following steps:

[0005] Step 1: Describe the photovoltaic park microgrid sharing architecture of electric-hydrogen hybrid energy storage; the photovoltaic park microgrid consists of photovoltaic power generation devices, DC / AC inverters and AC loads; the shared electric-hydrogen hybrid energy storage system includes a battery energy storage system and a hydrogen energy storage system, wherein the battery energy storage system consists of battery energy storage and energy storage converters, and the hydrogen energy storage system consists of an electrolyzer, a hydrogen storage tank, a fuel cell, an AC / DC rectifier and a DC / AC inverter; the shared electric-hydrogen hybrid energy storage system, several photovoltaic park microgrids and distribution networks are interconnected through AC busbars;

[0006] Step 2: Build a photovoltaic park microgrid operation model considering a shared electric-hydrogen hybrid energy storage system: establish a photovoltaic power generation model, a shared electric-hydrogen hybrid energy storage system model, and a power balance constraint model; the shared electric-hydrogen hybrid energy storage system model includes a monthly battery energy storage model and an annual hydrogen energy storage model; the annual hydrogen energy storage model includes an electrolyzer model, a fuel cell model, and a hydrogen storage tank model;

[0007] Step 3: Formulate a pricing method for shared electric-hydrogen hybrid energy storage services that takes into account throughput prices and capacity prices, including battery energy storage service pricing and shared hydrogen energy storage service pricing; the battery energy storage service pricing is used to calculate the monthly service cost of shared battery energy storage; the shared hydrogen energy storage service pricing is used to calculate the annual service cost of shared hydrogen energy storage;

[0008] Step 4: Propose a two-stage capacity optimization configuration method for shared electric-hydrogen hybrid energy storage, including annual capacity planning of hydrogen energy storage based on step resolution in the first stage and monthly capacity planning of battery energy storage based on hourly resolution in the second stage.

[0009] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein in step 2, the photovoltaic power generation model is:

[0010] (1)

[0011] in, For the park photovoltaic sky The power generated during the period; The unit capacity of photovoltaic sky The power generated during the period; The photovoltaic power generation installed capacity equipped for the park.

[0012] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein, in step 2, the shared electricity-hydrogen hybrid energy storage system model includes a monthly battery energy storage model and an annual hydrogen energy storage model;

[0013] The monthly battery energy storage model is:

[0014] (2)

[0015] (3)

[0016] (4)

[0017] (5)

[0018] (6)

[0019] (7)

[0020] (8)

[0021] in, To store energy in the battery sky State of charge during the time period; To store energy in the battery sky State of charge during the time period; To store energy in the battery sky State of charge during the time period; is the number of periods in a day, ; The daily initial state of charge for battery energy storage; The minimum state of charge for battery energy storage; The maximum state of charge for the battery energy storage; is the self-discharge coefficient of the battery energy storage; for The time interval between sessions; Battery storage for the park sky Charging power during the time period; Battery storage for the park sky Discharge power during the time period; Charging efficiency for battery energy storage; The discharge efficiency of the battery energy storage; For the park in Months of battery storage capacity; For the park in Maximum charging power of battery energy storage for one month; For the park in Maximum discharge power of battery energy storage for one month; Battery storage for the park sky 0 / 1 variables of the time period charge and discharge status, Indicates charging. Indicates discharge; The power capacity ratio of shared battery energy storage given by the operator; The annual maximum monthly rental capacity for shared battery energy storage in the park.

[0022] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein the annual hydrogen energy storage model includes an electrolyzer model, a fuel cell model and a hydrogen storage tank model;

[0023] The expression of the electrolytic cell model is:

[0024] (9)

[0025] (10)

[0026] (11)

[0027] in, For the park in sky The rate at which the electrolyzer outputs hydrogen during the period; For the park in sky The electrolytic power of the electrolytic cell during the period; The working efficiency of the electrolyzer; is the calorific value of hydrogen; Hydrogen energy storage for the park sky 0 / 1 variable of the charging and discharging status of the time period, Indicates hydrogen production / charging, Indicates release of hydrogen; The maximum electrolytic power of the electrolyzer in the park; The maximum annual rental capacity of shared electrolyzers in the park.

[0028] The expression of the fuel cell model is:

[0029] (12)

[0030] (13)

[0031] (14)

[0032] in, For the park in sky Output power of the fuel cell during the period; For the park in sky The rate at which the fuel cell consumes hydrogen during the period; For the efficiency of fuel cells; The maximum output power of the park's fuel cells; The maximum annual rental capacity of shared fuel cells in the park.

[0033] The expression of the hydrogen storage tank model is:

[0034] (15)

[0035] (16)

[0036] (17)

[0037] (18)

[0038] in, For the hydrogen storage tank sky The hydrogen charge state of the time period, For hydrogen storage tank sky The hydrogen charge state during the time period; is the natural hydrogen release rate of the hydrogen storage tank; The compression and hydrogen filling efficiency of the hydrogen storage tank; is the hydrogen release efficiency of the hydrogen storage tank; hydrogen storage tank capacity leased for the park; The maximum annual rental capacity of shared hydrogen storage tanks for the park; is the minimum hydrogen charge state of the hydrogen storage tank; is the maximum hydrogen charge state of the hydrogen storage tank; The hydrogen charge status of the hydrogen storage tank at the end of the year; is the initial hydrogen charge state of the hydrogen storage tank; is the number of days in a year, .

[0039] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein in step 2, the expression of the power balance constraint model is:

[0040] (19)

[0041] (20)

[0042] (twenty one)

[0043] (twenty two)

[0044] (twenty three)

[0045] (twenty four)

[0046] in, For the park in sky The power purchased during the time period; is the photovoltaic power consumption; is the abandoned optical power; For the park in sky 0 / 1 variable of the power purchase status during the time period, Indicates the purchase of electricity; The maximum power purchased by the park; The maximum abandoned optical power in the park; For the park in sky The battery storage power during the period; For the park in sky Hydrogen storage power during the period; For the park in sky The load power of the time period.

[0047] The photovoltaic park microgrid optimization configuration method considering shared electric-hydrogen hybrid energy storage, wherein, in step 3, the shared electric-hydrogen hybrid energy storage service pricing method considering throughput price and capacity price includes shared battery energy storage service pricing and shared hydrogen energy storage service pricing.

[0048] The calculation expression for the total life cycle cost of battery energy storage, hydrogen energy storage and photovoltaic power generation per unit capacity in the photovoltaic park microgrid is as follows:

[0049] (25)

[0050] (26)

[0051] (27)

[0052] in, The total life cycle cost of a unit capacity battery energy storage / electrolyzer / fuel cell / hydrogen storage tank or photovoltaic power generation device; is the initial investment cost of the equipment; The operating life of the equipment; For the device Annual operation and maintenance costs; For the device Depreciation expense for the year; is the residual value of the equipment system; is the tax rate; is the discount rate; The residual value rate of the system for battery energy storage / electrolyzer / fuel cell / hydrogen storage tank or photovoltaic power generation device; These are the codes for the components of the shared electric-hydrogen hybrid energy storage system. BES stands for battery energy storage, EC stands for electrolyzer, FC stands for fuel cell, HST stands for hydrogen storage tank, and PV stands for photovoltaic power generation device.

[0053] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein the pricing method of the shared battery energy storage service is as follows:

[0054] (28)

[0055] in, Monthly service costs for battery storage; To store energy in the battery Daily charging and discharging costs of the day; For battery storage in the month Capacity leasing costs; For the month the start date of For the month End date of

[0056] (29)

[0057] (30)

[0058] (31)

[0059] in, Energy throughput for battery storage; The price of battery energy storage unit throughput service; Throughput profit factor for shared battery storage; is the energy throughput of the unit capacity battery energy storage life cycle; The total life cycle cost of battery energy storage per unit capacity;

[0060] (32)

[0061] (33)

[0062] in, is the battery energy storage capacity rental price coefficient; The annual value of the life cycle cost of battery energy storage; is the number of months in a year, .

[0063] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein the pricing method of the shared hydrogen energy storage service is as follows:

[0064] (34)

[0065] in, The annual service cost of each component of hydrogen energy storage; For hydrogen energy storage components The cost of work done per day; The annual capacity leasing cost of each component of hydrogen energy storage; the components of hydrogen energy storage include electrolyzer, fuel cell and hydrogen storage tank;

[0066] (35)

[0067] in, is the daily work done by the electrolytic cell; is the daily work done by the fuel cell; is the daily throughput of hydrogen storage tanks; The service price per unit of work done by the electrolyzer; The price of fuel cell service per unit of work done, The price of hydrogen storage tank unit throughput service;

[0068] (36)

[0069] (37)

[0070] (38)

[0071] in, Profit coefficient for shared hydrogen energy storage; is the total work done during the life cycle of the electrolyzer per unit capacity; is the total work done per unit capacity during the life cycle of the fuel cell; is the total throughput of the hydrogen storage tank per unit capacity during its life cycle;

[0072] (39)

[0073] (40)

[0074] (41)

[0075] in, is the capacity rental price coefficient of the electrolyzer; is the capacity rental price coefficient of the fuel cell; is the capacity rental price coefficient of the hydrogen storage tank; is the equivalent annual value of the electrolyzer life cycle cost; is the equivalent annual value of the fuel cell life cycle cost; It is the annual value of the life cycle cost of the hydrogen storage tank.

[0076] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein, in step 4, the first stage is based on the hydrogen energy storage annual capacity planning model of step resolution:

[0077] Different from hourly resolution, a day is divided into In order to improve the feasibility of full-year simulation analysis, this paper proposes a step resolution that follows the time-of-use electricity price. According to the changing characteristics of the time-of-use electricity price, the step resolution divides a day into unequal time periods, of which: , , , , , ;

[0078] (42)

[0079] (43)

[0080] (44)

[0081] (45)

[0082] (46)

[0083] (47)

[0084] in, is the total annual energy cost; is the annual electricity purchase cost; is the annual shared battery energy storage service cost; The annual shared hydrogen storage service cost for the park; is the annual carbon trading cost; Discounted cost for annual PV configuration; For the park The electricity purchase price during the time period; is the carbon trading price; is the carbon emission factor; It is the annual carbon quota of the park.

[0085] In summary, the objective function and constraints of the campus microgrid hydrogen energy storage capacity planning model based on annual historical data are shown in formula (48):

[0086] (48)

[0087] in, Express Find the minimum value.

[0088] The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, wherein, in step 4, the second stage is based on the battery energy storage monthly capacity planning model with hourly resolution:

[0089] (49)

[0090] (50)

[0091] (51)

[0092] (52)

[0093] (53)

[0094] in, is the total monthly energy cost; is the monthly electricity purchase cost; The monthly shared hydrogen storage service cost; is the monthly carbon trading cost; Discounted cost for monthly PV configuration; It is the monthly carbon quota of the park.

[0095] In summary, the objective function and constraints of the battery energy storage monthly capacity planning model based on hourly resolution are shown in formula (54):

[0096] (54)

[0097] in, Express Find the minimum value.

[0098] Compared with the prior art, the present invention can achieve at least the following beneficial effects:

[0099] The present invention develops a two-stage optimization configuration method for photovoltaic park microgrids with shared electric-hydrogen hybrid energy storage that takes into account the full life cycle cost service pricing for high-proportion photovoltaic park microgrids. In terms of the shared operation mechanism, a photovoltaic park microgrid shared electric-hydrogen hybrid energy storage operation architecture is built: a shared electric-hydrogen hybrid energy storage system, a number of photovoltaic park microgrids and a distribution network are interconnected through an AC bus. In terms of pricing for shared electric-hydrogen hybrid energy storage services, based on the full life cycle costs of battery energy storage and hydrogen energy storage, both the throughput price and the capacity rental price of shared energy storage are considered. In terms of the optimization configuration method, the present invention proposes a two-stage optimization configuration method including annual capacity planning and monthly capacity planning. The former is committed to efficiently realizing the annual capacity planning of shared hydrogen energy storage, and the latter is committed to accurately realizing the monthly capacity planning of shared battery energy storage. The two stages cooperate to obtain the optimal capacity combination of annual hydrogen energy storage and monthly battery energy storage. Therefore, the present invention is suitable for park microgrids with a high proportion of renewable energy, which helps to match and transfer the production and consumption imbalance of the park microgrid on a long time scale across seasons and a short time scale within a day, realize the low-carbon and economical operation of the park microgrid, and provide a reference for the planning, operation and scheduling of the park microgrid. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 Schematic diagram of a photovoltaic park microgrid with shared electricity-hydrogen hybrid energy storage provided by the present invention.

[0101] Figure 2 It is a schematic diagram of the step resolution of the present invention that dynamically adapts to the time-of-use electricity price. DETAILED DESCRIPTION

[0102] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0103] The present invention provides a photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, including:

[0104] Step 1: Describe the photovoltaic park microgrid sharing architecture with electricity-hydrogen hybrid energy storage.

[0105] See also Figure 1The photovoltaic park microgrid sharing architecture of electric-hydrogen hybrid energy storage includes a shared electric-hydrogen hybrid energy storage system, several photovoltaic park microgrids and distribution networks. The photovoltaic park microgrid rationally utilizes the site space to equip itself with a certain capacity of photovoltaic power generation devices, which are connected to the AC load and AC bus through a DC / AC inverter; the shared electric-hydrogen hybrid energy storage system includes a battery energy storage system and a hydrogen energy storage system, wherein the battery energy storage system is composed of battery energy storage and energy storage converter, and the hydrogen energy storage system is composed of an electrolyzer, a hydrogen storage tank, a fuel cell, an AC / DC rectifier and a DC / AC inverter; the photovoltaic park microgrid can rent battery energy storage and hydrogen energy storage capacity on demand from the operator of the shared electric-hydrogen hybrid energy storage system, and control the charging and discharging actions of the shared electric-hydrogen hybrid energy storage system by sending dispatch instructions to the operator, thereby realizing energy interaction and economic operation; the operator receives and integrates the energy storage dispatch instructions of several photovoltaic park microgrids, avoids the redundant actions of the electric-hydrogen hybrid energy storage system through cluster optimization, and further improves the operator's operating economy; the photovoltaic park microgrid is interconnected with the distribution network, and when the photovoltaic park microgrid is short of power, it purchases electricity from the distribution network to ensure its own safe and reliable power demand.

[0106] Specifically, in some embodiments of the present invention, the proposed photovoltaic park microgrid sharing architecture of electric-hydrogen hybrid energy storage is as follows: Figure 1 As shown. The photovoltaic power generation device provides electricity for the park microgrid. When the photovoltaic power generation power is greater than the load power, the electric-hydrogen hybrid energy storage system stores electricity; when the photovoltaic power generation power is less than the load power, the electric-hydrogen hybrid energy storage system releases electricity. Among them, battery energy storage is used to improve the daily production and consumption balance of the photovoltaic park microgrid, and hydrogen energy storage is used to transfer and match the production and consumption balance of the photovoltaic park microgrid over a long time scale across seasons.

[0107] Step 2: Build a photovoltaic park microgrid operation model considering a shared electricity-hydrogen hybrid energy storage system.

[0108] In some embodiments of the present invention, the photovoltaic park microgrid operation model considering the shared electric-hydrogen hybrid energy storage system includes a photovoltaic power generation model, a shared electric-hydrogen hybrid energy storage system model and a power balance constraint model. The shared electric-hydrogen hybrid energy storage system model includes a monthly battery energy storage model and an annual hydrogen energy storage model; the annual hydrogen energy storage model includes an electrolyzer model, a fuel cell model and a hydrogen storage tank model.

[0109] In the present invention, step 2 specifically includes the following sub-steps:

[0110] Step 2.1: Establish a photovoltaic power generation model. Formula (1) is the photovoltaic power generation power expression of the photovoltaic park microgrid:

[0111] (1)

[0112] in, For the park photovoltaic sky The power generated during the period; The unit capacity of photovoltaic sky The power generated during the period; The photovoltaic power generation installed capacity equipped for the park.

[0113] Step 2.2: Establish a shared electricity-hydrogen hybrid energy storage system model, including a monthly battery energy storage model and an annual hydrogen energy storage model. In the photovoltaic park microgrid considering shared electricity-hydrogen hybrid energy storage proposed in the present invention, battery energy storage improves the daily production and consumption balance of the photovoltaic park microgrid, and hydrogen energy storage transfer matches the production and consumption balance of the photovoltaic park microgrid over a long time scale across seasons;

[0114] The energy conservation of battery energy storage charging and discharging is shown in equation (2); equations (3) and (4) are the state of charge constraints of battery energy storage; equations (5) and (6) limit the maximum charging and discharging power of battery energy storage; equation (7) defines the power capacity ratio of battery energy storage; equation (8) limits the maximum rental capacity of battery energy storage;

[0115] (2)

[0116] (3)

[0117] (4)

[0118] (5)

[0119] (6)

[0120] (7)

[0121] (8)

[0122] in, To store energy in the battery sky State of charge during the time period; To store energy in the battery sky State of charge during the time period; To store energy in the battery sky State of charge during the time period; is the number of periods in a day, ; The daily initial state of charge for battery energy storage; The minimum state of charge for battery energy storage; The maximum state of charge for the battery energy storage; is the self-discharge coefficient of the battery energy storage; for The time interval between sessions; Battery storage for the park sky Charging power during the time period; Battery storage for the park sky Discharge power during the time period; Charging efficiency for battery energy storage; The discharge efficiency of the battery energy storage; For the park in Months of battery storage capacity; For the park in Maximum charging power of battery energy storage for one month; For the park in Maximum discharge power of battery energy storage for one month; Battery storage for the park sky 0 / 1 variables of the time period charge and discharge status, Indicates charging. Indicates discharge; The power capacity ratio of shared battery energy storage given by the operator; The annual maximum monthly rental capacity for shared battery energy storage in the park.

[0123] The hydrogen energy storage model includes an electrolyzer model, a fuel cell model, and a hydrogen storage tank model. When photovoltaic power generation is in excess, the electrolyzer electrolyzes water to produce hydrogen. Equation (9) is the conversion function of the electrolysis process; Equation (10) limits the maximum electrolysis power of the electrolyzer; Equation (11) limits the maximum rental capacity of the electrolyzer;

[0124] (9)

[0125] (10)

[0126] (11)

[0127] in, For the park in sky The rate at which the electrolyzer outputs hydrogen during the period; For the park in sky The electrolytic power of the electrolytic cell during the period; The working efficiency of the electrolyzer; is the calorific value of hydrogen; Hydrogen energy storage for the park sky 0 / 1 variable of the charging and discharging status of the time period, Indicates hydrogen production / charging, Indicates release of hydrogen; The maximum electrolytic power of the electrolyzer in the park; The maximum annual rental capacity of shared electrolyzers in the park.

[0128] When photovoltaic power generation is insufficient, the fuel cell consumes hydrogen to generate electricity, and its output power is shown in formula (12); formula (13) limits the maximum output power of the fuel cell; formula (14) limits the maximum rental capacity of the fuel cell;

[0129] (12)

[0130] (13)

[0131] (14)

[0132] in, For the park in sky Output power of the fuel cell during the period; For the park in sky The rate at which the fuel cell consumes hydrogen during the period; For the efficiency of fuel cells; The maximum output power of the park's fuel cells; The maximum annual rental capacity of shared fuel cells in the park.

[0133] The hydrogen storage tank can store the hydrogen produced by the electrolyzer and provide hydrogen when the fuel cell is working. Equation (15) is the storage and release conservation model of the hydrogen storage tank for storing and releasing hydrogen; Equation (16) limits the maximum rental capacity of the hydrogen storage tank; Equations (17) and (18) are the hydrogen storage tank charge state constraints;

[0134] (15)

[0135] (16)

[0136] (17)

[0137] (18)

[0138] in, For hydrogen storage tank sky The hydrogen charge state of the time period, For hydrogen storage tank sky The hydrogen charge state during the time period; is the natural hydrogen release rate of the hydrogen storage tank; The compression and hydrogen filling efficiency of the hydrogen storage tank; is the hydrogen release efficiency of the hydrogen storage tank; hydrogen storage tank capacity leased for the park; The maximum annual rental capacity of shared hydrogen storage tanks for the park; is the minimum hydrogen charge state of the hydrogen storage tank; is the maximum hydrogen charge state of the hydrogen storage tank; The hydrogen charge status of the hydrogen storage tank at the end of the year; is the initial hydrogen charge state of the hydrogen storage tank; is the number of days in a year, .

[0139] In step 2, the expression of the power balance constraint model is:

[0140] (19)

[0141] (20)

[0142] (twenty one)

[0143] (twenty two)

[0144] (twenty three)

[0145] (twenty four)

[0146] in, For the park in sky The power purchased during the time period; is the photovoltaic power consumption; is the abandoned optical power; For the park in sky 0 / 1 variable of the power purchase status during the time period, Indicates the purchase of electricity; The maximum power purchased by the park; The maximum abandoned optical power in the park; For the park in sky The battery storage power during the period; For the park in sky Hydrogen storage power during the period; For the park in sky The load power of the time period.

[0147] Step 3: Develop a pricing approach for shared electric-hydrogen hybrid energy storage services that takes into account throughput prices and capacity prices.

[0148] In some embodiments of the present invention, the pricing of shared electric-hydrogen hybrid energy storage services that take into account throughput prices and capacity prices includes battery energy storage service pricing and shared hydrogen energy storage service pricing. The battery energy storage service pricing is used to calculate the monthly service cost of shared battery energy storage, and the shared hydrogen energy storage service pricing is used to calculate the annual service cost of shared hydrogen energy storage.

[0149] In the present invention, step 3 specifically includes the following sub-steps:

[0150] Step 3.1: Calculate the total life cycle cost of battery energy storage, hydrogen energy storage and photovoltaic power generation per unit capacity;

[0151] Formula (25) is the expression of the total cost of the equipment life cycle, including the initial investment cost, operation and maintenance cost, depreciation tax and system residual value; Formula (26) is the expression of annual depreciation amount; Formula (27) is the expression of system residual value;

[0152] (25)

[0153] (26)

[0154] (27)

[0155] in, The total life cycle cost of a unit capacity battery energy storage / electrolyzer / fuel cell / hydrogen storage tank or photovoltaic power generation device; is the initial investment cost of the equipment; The operating life of the equipment; For the device Annual operation and maintenance costs; For the device Depreciation expense for the year; is the residual value of the equipment system; is the tax rate; is the discount rate; The residual value rate of the system for battery energy storage / electrolyzer / fuel cell / hydrogen storage tank or photovoltaic power generation device; These are the codes for the components of the shared electric-hydrogen hybrid energy storage system. BES stands for battery energy storage, EC stands for electrolyzer, FC stands for fuel cell, HST stands for hydrogen storage tank, and PV stands for photovoltaic power generation device.

[0156] Step 3.2: Pricing of shared battery energy storage services;

[0157] Formula (28) defines the monthly service cost of shared battery energy storage; Formula (29) is the daily charging and discharging cost calculation formula for battery energy storage; Formula (30) is the energy throughput calculation formula for battery energy storage; Formula (31) is the unit throughput service price calculation formula for battery energy storage; Formula (32) is the battery energy storage capacity leasing cost calculation formula; Formula (33) is the annual value calculation formula for the life cycle cost of battery energy storage;

[0158] (28)

[0159] in, Monthly service costs for battery storage; To store energy in the battery Daily charging and discharging costs of the day; For battery storage in the month Capacity leasing costs; For the month the start date of For the month End date of

[0160] (29)

[0161] (30)

[0162] (31)

[0163] in, Energy throughput for battery storage; The price of battery energy storage unit throughput service; Throughput profit factor for shared battery storage; is the energy throughput of the unit capacity battery energy storage life cycle; is the total life cycle cost of battery energy storage per unit capacity;

[0164] (32)

[0165] (33)

[0166] in, is the battery energy storage capacity rental price coefficient; The annual value of the life cycle cost of battery energy storage; is the number of months in a year, .

[0167] Step 3.3: Pricing of shared hydrogen storage services.

[0168] Formula (34) defines the annual service cost of shared hydrogen energy storage; Formula (35) is the calculation formula for the daily work cost of each component of hydrogen energy storage; Formula (36) is the calculation formula for the daily work of electrolyzers and fuel cells; Formula (37) is the calculation formula for the daily throughput of hydrogen storage tanks; Formula (38) is the calculation formula for the service price per unit work of electrolyzers and fuel cells or the service price per unit throughput of hydrogen storage tanks; Formula (39) is the calculation formula for the annual capacity rental cost of electrolyzers and fuel cells; Formula (40) is the calculation formula for the annual capacity rental cost of hydrogen storage tanks; Formula (41) is the calculation formula for the annual value of the life cycle cost of unit capacity electrolyzers, fuel cells and hydrogen storage tanks;

[0169] (34)

[0170] in, The annual service cost of each component of hydrogen energy storage; For hydrogen energy storage components The cost of work done per day; The annual capacity leasing cost of each component of hydrogen energy storage; the components of hydrogen energy storage include electrolyzer, fuel cell and hydrogen storage tank;

[0171] (35)

[0172] in, is the daily work done by the electrolytic cell; is the daily work done by the fuel cell; is the daily throughput of hydrogen storage tanks; The service price per unit of work done by the electrolyzer; The price of fuel cell service per unit of work done, The price of hydrogen storage tank unit throughput service;

[0173] (36)

[0174] (37)

[0175] (38)

[0176] in, Profit coefficient for shared hydrogen energy storage; is the total work done during the life cycle of the electrolyzer per unit capacity; is the total work done per unit capacity during the life cycle of the fuel cell; is the total throughput of the hydrogen storage tank per unit capacity during its life cycle;

[0177] (39)

[0178] (40)

[0179] (41)

[0180] in, is the capacity rental price coefficient of the electrolyzer; is the capacity rental price coefficient of the fuel cell; is the capacity rental price coefficient of the hydrogen storage tank; is the equivalent annual value of the electrolyzer life cycle cost; is the equivalent annual value of the fuel cell life cycle cost; It is the annual value of the life cycle cost of the hydrogen storage tank.

[0181] Step 4: Propose a two-stage capacity optimization configuration method for shared electricity-hydrogen hybrid energy storage;

[0182] In some embodiments of the present invention, the two-stage capacity optimization configuration method for shared electricity-hydrogen hybrid energy storage performs annual capacity planning of hydrogen energy storage based on step resolution in the first stage, and performs monthly capacity planning of battery energy storage based on hourly resolution in the second stage.

[0183] In the present invention, step 4 specifically includes the following sub-steps:

[0184] Step 4.1: Annual capacity planning of hydrogen energy storage based on step resolution

[0185] The annual capacity planning of hydrogen energy storage adopts a full-year simulation analysis method to ensure the continuity of the hydrogen charge state during the long-term energy transfer across seasons. Compared with typical daily simulation analysis, full-year simulation analysis has the following challenges: 1) The computational complexity is significantly increased. The scale of the mixed integer nonlinear programming problem increases sharply with the widening of the time span, which leads to an exponential increase in computational complexity with the increase in the number of optimization variables and nonlinear constraints; 2) The demand for computing resources increases significantly, requiring a huge memory space to store massive data and its intermediate calculation results.

[0186] Different from hourly resolution, a day is divided into In order to improve the feasibility of full-year simulation analysis, this paper proposes a step resolution that follows the time-of-use electricity price, such as Figure 2 According to the changing characteristics of time-of-use electricity prices, the step resolution divides a day into unequal time periods, of which: , , , , , .

[0187] Formula (42) defines the annual total energy cost of the photovoltaic park microgrid; Formula (43) is the annual electricity purchase cost calculation formula; Formula (44) is the annual shared battery energy storage service cost calculation formula; Formula (45) is the annual shared hydrogen energy storage service cost calculation formula; Formula (46) is the annual carbon trading cost calculation formula; Formula (47) is the annual photovoltaic configuration discount cost calculation formula;

[0188] (42)

[0189] (43)

[0190] (44)

[0191] (45)

[0192] (46)

[0193] (47)

[0194] in, is the total annual energy cost; is the annual electricity purchase cost; is the annual shared battery energy storage service cost; The annual shared hydrogen storage service cost for the park; is the annual carbon trading cost; Discounted cost for annual PV configuration; For the park The electricity purchase price during the time period; is the carbon trading price; is the carbon emission factor; It is the annual carbon quota of the park.

[0195] In summary, the objective function and constraints of the campus microgrid hydrogen energy storage capacity planning model based on annual historical data are shown in formula (48):

[0196] (48)

[0197] in, Express Find the minimum value.

[0198] Step 4.2: Monthly capacity planning of battery energy storage based on hourly resolution;

[0199] The capacity planning of shared battery energy storage in the second phase adopts the "monthly capacity determination" approach, clustering the monthly load and photovoltaic power generation data to generate several typical days, and performing the second phase capacity determination of battery energy storage based on hourly resolution.

[0200] Formula (49) defines the monthly total energy consumption cost of the photovoltaic park microgrid; Formula (50) is the calculation formula for the monthly total electricity purchase cost; Formula (51) is the calculation formula for the monthly shared hydrogen energy storage service cost; Formula (52) is the calculation formula for the monthly carbon trading cost; Formula (53) is the calculation formula for the monthly photovoltaic configuration discount cost;

[0201] (49)

[0202] (50)

[0203] (51)

[0204] (52)

[0205] (53)

[0206] in, is the total monthly energy cost; is the monthly electricity purchase cost; The monthly shared hydrogen storage service cost; is the monthly carbon trading cost; Discounted cost for monthly PV configuration; It is the monthly carbon quota of the park.

[0207] In summary, the objective function and constraints of the battery energy storage monthly capacity planning model based on hourly resolution are shown in formula (54):

[0208] (54)

[0209] in, Express Find the minimum value.

[0210] Step 5: Apply the proposed photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage to a campus microgrid for simulation analysis.

[0211] This step specifically includes:

[0212] Step 5.1: Parameter settings

[0213] The time-of-use electricity price refers to the electricity price for industrial and commercial users in a certain area, as shown in Table 1.

[0214] Table 1 Time-of-use electricity price

[0215]

[0216] The prices and performance parameters of battery energy storage, electrolyzer, fuel cell, hydrogen storage tank and photovoltaic power generation device are shown in Table 2.

[0217] Table 2 Equipment price performance parameter settings

[0218]

[0219] Step 5.2: Scene setup

[0220] In order to verify the superiority of the two-stage optimization configuration method proposed in this invention, five scenarios are set for comparative analysis:

[0221] Scenario 1: No photovoltaics or energy storage.

[0222] Scenario 2: PV is configured but energy storage is not configured;

[0223] Scenario 3: Configure photovoltaics and fixed battery energy storage;

[0224] Scenario 4: Configure photovoltaics and shared battery energy storage;

[0225] Scenario 5: Configure photovoltaics and configure shared electricity-hydrogen hybrid energy storage.

[0226] Step 5.3: Simulate the five scenarios separately, and solve the model by calling GUROBI 10.0.3 solver based on MATLAB R2023b platform and YALMIP toolbox.

[0227] In the first phase of hydrogen energy storage annual capacity planning, the comparison of configuration models based on hourly resolution and step resolution is shown in Table 3.

[0228] Table 3 Comparison of annual shared hydrogen energy storage configuration models at different time resolutions

[0229]

[0230] The performance comparison of the PV park microgrid in 2016 shared electricity-hydrogen hybrid energy storage capacity planning results in five different scenarios is shown in Table 4.

[0231] Table 4 Comparison of simulation results of five scenarios

[0232]

[0233] According to the simulation results, the two-stage optimization configuration method of the photovoltaic park microgrid considering shared electric-hydrogen hybrid energy storage proposed by the present invention has the following benefits: 1) Enhance the feasibility of the full-year simulation model. When the step resolution of the dynamic adaptation time-of-use electricity price is applied, the model scale is effectively reduced. The model cannot be solved at the hourly resolution, but can be effectively solved at the step resolution; 2) Improve the economic efficiency of the park microgrid operation. When the energy storage is not configured, the annual total energy cost is 1.2430 million yuan. When the shared electric-hydrogen hybrid energy storage is configured, the annual total energy cost drops to 1.0531 million yuan, a decrease of 15.28%; 3) Promote the consumption of renewable energy power generation. The configuration of shared electric-hydrogen hybrid energy storage increases the photovoltaic utilization rate from 69.13% without energy storage to 99.97%, basically eliminating the phenomenon of abandoned light in the park. In summary, this method can effectively improve the economic efficiency of the operation of the microgrid in the photovoltaic park with a high proportion, and effectively promote the consumption of renewable energy, providing a practical way for the green and economic operation of the microgrid in the renewable energy park.

[0234] In terms of the shared operation mechanism, the present invention has built a photovoltaic park microgrid shared electric-hydrogen hybrid energy storage operation architecture: a shared electric-hydrogen hybrid energy storage system, a number of photovoltaic park microgrids and distribution networks are interconnected through an AC bus. In terms of the pricing of shared electric-hydrogen hybrid energy storage services, based on the full life cycle cost of battery energy storage and hydrogen energy storage, both the throughput price and the capacity rental price of shared energy storage are considered. In terms of the optimization configuration method, the present invention proposes a two-stage optimization configuration method including annual capacity planning and monthly capacity planning. The former is committed to efficiently realizing the annual capacity planning of shared hydrogen energy storage, and the latter is committed to accurately realizing the monthly capacity planning of shared battery energy storage. The two stages cooperate to obtain the optimal capacity combination of annual hydrogen energy storage and monthly battery energy storage. Therefore, the present invention is suitable for microgrids in parks with a high proportion of renewable energy, which helps to match the production and consumption balance of the long-term scale across seasons and the short-term scale within the day of the transfer park microgrid, realize the low-carbon and economic operation of the park microgrid, and provide a reference for the planning, operation and scheduling of the park microgrid.

[0235] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage, characterized in that: The following steps are involved: Step 1: Describe the photovoltaic park microgrid sharing architecture of electric-hydrogen hybrid energy storage; the photovoltaic park microgrid consists of photovoltaic power generation devices, DC / AC inverters and AC loads; the shared electric-hydrogen hybrid energy storage system includes a battery energy storage system and a hydrogen energy storage system, wherein the battery energy storage system consists of battery energy storage and energy storage converters, and the hydrogen energy storage system consists of an electrolyzer, a hydrogen storage tank, a fuel cell, an AC / DC rectifier and a DC / AC inverter; the shared electric-hydrogen hybrid energy storage system, several photovoltaic park microgrids and distribution networks are interconnected through AC busbars; Step 2: Build a photovoltaic park microgrid operation model considering a shared electric-hydrogen hybrid energy storage system: establish a photovoltaic power generation model, a shared electric-hydrogen hybrid energy storage system model, and a power balance constraint model; the shared electric-hydrogen hybrid energy storage system model includes a monthly battery energy storage model and an annual hydrogen energy storage model; the annual hydrogen energy storage model includes an electrolyzer model, a fuel cell model, and a hydrogen storage tank model; Step 3: Formulate a pricing method for shared electric-hydrogen hybrid energy storage services that takes into account throughput prices and capacity prices, including battery energy storage service pricing and shared hydrogen energy storage service pricing; the battery energy storage service pricing is used to calculate the monthly service cost of shared battery energy storage; the shared hydrogen energy storage service pricing is used to calculate the annual service cost of shared hydrogen energy storage; Step 4: Propose a two-stage capacity optimization configuration method for shared electric-hydrogen hybrid energy storage, including annual capacity planning of hydrogen energy storage based on step resolution in the first stage and monthly capacity planning of battery energy storage based on hourly resolution in the second stage; In step 2, the shared electricity-hydrogen hybrid energy storage system model includes a monthly battery energy storage model and an annual hydrogen energy storage model; The monthly battery energy storage model is: （2） （3） （4） （5） （6） （7） （8） in, To store energy in the battery sky State of charge during the time period; To store energy in the battery sky State of charge during the time period; To store energy in the battery sky State of charge during the time period; is the number of periods in a day, ; The daily initial state of charge for battery energy storage; The minimum state of charge for battery energy storage; The maximum state of charge for the battery energy storage; is the self-discharge coefficient of the battery energy storage; for The time interval between sessions; Battery storage for the park sky Charging power during the time period; Battery storage for the park sky Discharge power during the time period; Charging efficiency for battery energy storage; The discharge efficiency of the battery energy storage; For the park in Months of battery storage capacity; For the park Maximum charging power of battery energy storage for one month; For the park in Maximum discharge power of battery energy storage for one month; Battery storage for the park sky 0 / 1 variables of the time period charge and discharge status, Indicates charging. Indicates discharge; The power capacity ratio of shared battery energy storage given by the operator; The annual maximum monthly rental capacity for shared battery energy storage in the park; The expression of the electrolytic cell model is: （9） （10） （11） in, For the park sky The rate at which the electrolyzer outputs hydrogen during the period; For the park sky The electrolytic power of the electrolytic cell during the period; The working efficiency of the electrolyzer; is the calorific value of hydrogen; Hydrogen energy storage for the park sky 0 / 1 variable of the charging and discharging status of the time period, Indicates hydrogen production / charging, Indicates release of hydrogen; The maximum electrolytic power of the electrolyzer in the park; The maximum annual lease capacity for shared electrolyzers in the park; The expression of the fuel cell model is: （12） （13） （14） in, For the park sky Output power of the fuel cell during the period; For the park sky The rate at which the fuel cell consumes hydrogen during the period; For the efficiency of fuel cells; The maximum output power of the park's fuel cells; The maximum annual lease capacity for shared fuel cells in the park; The expression of the hydrogen storage tank model is: （15） （16） （17） （18） in, For the hydrogen storage tank sky The hydrogen charge state of the time period, For the hydrogen storage tank sky The hydrogen charge state during the time period; is the natural hydrogen release rate of the hydrogen storage tank; The compression and hydrogen filling efficiency of the hydrogen storage tank; is the hydrogen release efficiency of the hydrogen storage tank; hydrogen storage tank capacity leased for the park; The maximum annual rental capacity of shared hydrogen storage tanks for the park; is the minimum hydrogen charge state of the hydrogen storage tank; is the maximum hydrogen charge state of the hydrogen storage tank; The hydrogen charge status of the hydrogen storage tank at the end of the year; is the initial hydrogen charge state of the hydrogen storage tank; is the number of days in a year, .

2. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 1 is characterized in that: In step 2, the photovoltaic power generation model is: （1） in, For the park photovoltaic sky The power generated during the period; The unit capacity of photovoltaic sky The power generated during the period; The photovoltaic power generation installed capacity equipped for the park.

3. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 2 is characterized in that: In step 2, the expression of the power balance constraint model is: （19） （20） （21） （22） （23） （24） in, For the park sky The power purchased during the time period; is the photovoltaic power consumption; is the abandoned optical power; For the park sky 0 / 1 variable of the power purchase status during the time period, Indicates the purchase of electricity; The maximum power purchased by the park; The maximum abandoned optical power in the park; For the park sky The battery storage power during the period; For the park sky Hydrogen storage power during the period; For the park sky The load power of the time period.

4. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 3 is characterized in that: In step 3, the shared electricity-hydrogen hybrid energy storage service pricing method considering throughput price and capacity price includes shared battery energy storage service pricing and shared hydrogen energy storage service pricing; The calculation expression for the total life cycle cost of battery energy storage, hydrogen energy storage and photovoltaic power generation per unit capacity in the photovoltaic park microgrid is as follows: （25） （26） （27） in, The total life cycle cost of a unit capacity battery energy storage / electrolyzer / fuel cell / hydrogen storage tank or photovoltaic power generation device; is the initial investment cost of the equipment; The operating life of the equipment; For the device Annual operation and maintenance costs; For the device Depreciation expense for the year; is the residual value of the equipment system; is the tax rate; is the discount rate; The residual value rate of the system for battery energy storage / electrolyzer / fuel cell / hydrogen storage tank or photovoltaic power generation device; These are the codes for the components of the shared electric-hydrogen hybrid energy storage system. BES stands for battery energy storage, EC stands for electrolyzer, FC stands for fuel cell, HST stands for hydrogen storage tank, and PV stands for photovoltaic power generation device.

5. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 4 is characterized in that: The pricing method of the shared battery energy storage service is as follows: （28） in, Monthly service costs for battery storage; To store energy in the battery Daily charging and discharging costs of the day; For battery storage in the month Capacity leasing costs; For the month the start date of For the month End date of The total life cycle cost of battery energy storage per unit capacity; （29） （30） （31） in, Energy throughput for battery storage; The price of battery energy storage unit throughput service; Throughput profit factor for shared battery storage; is the energy throughput of the unit capacity battery energy storage life cycle; （32） （33） in, is the battery energy storage capacity rental price coefficient; The annual value of the life cycle cost of battery energy storage; is the number of months in a year, .

6. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 5 is characterized in that: The pricing method of the shared hydrogen energy storage service is as follows: （34） in, The annual service cost of each component of hydrogen energy storage; For hydrogen energy storage components The cost of work done per day; The annual capacity leasing cost of each component of hydrogen energy storage; the components of hydrogen energy storage include electrolyzer, fuel cell and hydrogen storage tank; （35） in, is the daily work done by the electrolytic cell; is the daily work done by the fuel cell; is the daily throughput of hydrogen storage tanks; The service price per unit of work done by the electrolyzer; The price of fuel cell service per unit of work done, The price of hydrogen storage tank unit throughput service; （36） （37） （38） in, Profit coefficient for shared hydrogen energy storage; is the total work done during the life cycle of the electrolyzer per unit capacity; is the total work done per unit capacity during the life cycle of the fuel cell; is the total throughput of the hydrogen storage tank per unit capacity during its life cycle; （39） （40） （41） in, is the capacity rental price coefficient of the electrolyzer; is the capacity rental price coefficient of the fuel cell; is the capacity rental price coefficient of the hydrogen storage tank; is the equivalent annual value of the electrolyzer life cycle cost; is the equivalent annual value of the fuel cell life cycle cost; is the annual value of the life cycle cost of the hydrogen storage tank.

7. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 6 is characterized in that: In step 4, the first stage is based on the annual capacity planning model of hydrogen energy storage with step resolution: The step resolution divides a day into time periods, of which: , , , , , ; （42） （43） （44） （45） （46） （47） in, is the total annual energy cost; is the annual electricity purchase cost; is the annual shared battery energy storage service cost; Annual shared hydrogen storage service costs for the park; is the annual carbon trading cost; Discounted cost for annual PV configuration; For the park The electricity purchase price during the time period; is the carbon trading price; is the carbon emission factor; The annual carbon quota for the park; In summary, the objective function and constraints of the campus microgrid hydrogen energy storage capacity planning model based on annual historical data are shown in formula (48): （48） in, Express Find the minimum value.

8. The photovoltaic park microgrid optimization configuration method considering shared electricity-hydrogen hybrid energy storage according to claim 7 is characterized in that: In step 4, the second stage is based on the battery energy storage monthly capacity planning model with hourly resolution: （49） （50） （51） （52） （53） in, is the total monthly energy cost; is the monthly electricity purchase cost; The monthly shared hydrogen storage service cost; is the monthly carbon trading cost; Discounted cost for monthly PV configuration; Monthly carbon quota for the park; In summary, the objective function and constraints of the battery energy storage monthly capacity planning model based on hourly resolution are shown in formula (54): （54） in, Express Find the minimum value.

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