An optimization method for the capacity reported by a group of fused magnesium furnaces participating in a frequency regulation

Abstract

The present invention provides a method for optimizing the capacity reported by a group of fused magnesium furnaces participating in primary frequency regulation on a certain day. The method belongs to the field of primary frequency regulation of power systems and is applied to the participation of high-energy-consuming fused magnesium furnace loads in primary frequency regulation of power grids. Steps: 1) Establishing an objective function with the goal of maximizing overall benefits; 2) Determining constraints, taking into account frequency regulation needs, energy demand limits, and product quality; 3) Processing the uncertainty of the adjustment capacity of the fused magnesium furnace group, allowing for the optimization solution of unsatisfied constraints between some cells, so as to achieve efficient processing of such uncertainty. The present invention reflects the uncertainty of the adjustment capacity of the fused magnesium furnace group in the form of probability through the method of chance constraints, and solves the optimal reported capacity for participating in the primary frequency regulation of the power grid in each time period on the certain day. It provides support for fused magnesium enterprises to reasonably participate in the primary frequency regulation of the power grid and report frequency regulation capacity on the certain day as a demand response resource on the load side.

Description

Technical Field

[0001] The present invention belongs to the field of primary frequency regulation of power systems, and relates to a method for optimizing the capacity reported by a group of fused magnesium furnaces participating in primary frequency regulation, and applies the method to the participation of high-energy-consuming fused magnesium furnace loads in primary frequency regulation of power grids. Background Art

[0002] The safe, efficient, green, and low-carbon transformation of power systems, coupled with digital and intelligent technological innovation, has become a global trend. my country is accelerating the construction of a new power system centered on renewable energy. In recent years, the large-scale development and utilization of renewable energy, represented by wind power and photovoltaics, has helped reduce reliance on traditional fossil fuels and promoted the transition of the energy structure toward a clean energy-based economy. Building a new power system dominated by renewable energy is an inevitable trend in promoting the low-carbon development of modern power systems. This low-carbon development of the system has resulted in the "double high" characteristics of the power grid, leading to an increasingly strong demand for primary frequency regulation. The shortage of frequency regulation resources will degrade the frequency quality of the power grid. Therefore, the power grid urgently needs to increase primary frequency regulation resources on all sides of the "source-grid-load" chain.

[0003] A large number of flexible resources on the load side can participate in system operations through various modes, such as peak shaving, frequency regulation ancillary services, medium- and long-term markets, and new energy trading. While rapidly developing, these flexible resources have also gained digital technology. By strengthening the integration of control theory with practical application, and through flexible, reliable, intelligent, and green management of load-side flexible resources, their utilization is further developing. High-energy-consuming industrial loads, with their large load capacity and high level of automation, are particularly suitable flexible resources for participating in primary frequency regulation. Fused magnesium loads are a typical example of high-energy-consuming industrial loads, but research on the participation of fused magnesium furnaces in grid primary frequency regulation is currently scarce, necessitating further research in this area.

[0004] Because the primary objective of fused magnesium furnaces is to smelt high-quality magnesium oxide crystals, rather than participate in the grid's primary frequency regulation, they must simultaneously monitor their own power margins while responding to primary frequency regulation signals or demands. This makes the implementation of fused magnesium furnaces participating in primary frequency regulation essentially an optimization process. Balancing the power consumption of fused magnesium furnaces with the grid's primary frequency regulation requirements presents significant challenges in optimizing operations. Fused magnesium furnace operation is subject to uncertainties, such as shifts in operating modes and random production conditions. This uncertainty contributes to the uncertainty of the primary frequency regulation capability of the fused magnesium load, significantly increasing the difficulty of optimizing operations.

[0005] With the steady advancement of the new power system, primary frequency regulation resources are becoming increasingly scarce and frequency response capabilities are becoming increasingly weak. Relying on a market-based paid service mechanism, the huge potential of load-side resources in participating in the primary frequency regulation of the power grid has been realized. However, due to the combined effects of complex factors such as load modeling, functional objectives, and uncertain information, the participation of load-side resources in grid frequency regulation is facing major challenges. Therefore, it is urgent to explore coordinated control strategies for load-side resources in the primary frequency regulation of the power grid, thereby improving the safe and stable operation capabilities of the grid frequency while enhancing the economic benefits of load-side resources. Under the single-system load-side resource primary frequency regulation ancillary service compensation mechanism, flexible resource entities report their primary frequency regulation adjustable capacity for the operating day (D-day) to the system as a market commodity on D-1. Summary of the Invention

[0006] In order to solve the problem of optimizing the capacity reported on the day before, the present invention provides a method for optimizing the capacity reported on the day before for a fused magnesium furnace group participating in a frequency modulation.

[0007] First, determine the composition of the objective function. Research has revealed that over 60% of the production costs of fused magnesium furnaces come from electricity consumption. Therefore, fused magnesium companies choose to perform smelting at night when electricity prices are relatively low, smelting for 10.5 hours from 21:00 to 07:30 the next day. The remaining costs mainly include raw materials and labor costs. To simplify the problem, this invention only considers electricity costs. Therefore, the daily revenue is the revenue from producing crystalline magnesium oxide minus the electricity cost. However, when fused magnesium companies participate in the primary frequency modulation of the power grid, they can obtain primary frequency modulation compensation. At the same time, the frequency modulation process will cause production losses, and at certain times, they will also be subject to insufficient frequency modulation penalties. Therefore, after fused magnesium companies participate in primary frequency modulation, the total revenue is equal to the revenue from producing high-purity crystalline magnesium oxide plus the primary frequency modulation compensation minus the electricity cost, production losses, and possible insufficient frequency modulation penalties.

[0008] When calculating electricity costs, it's important to note that fused magnesium producers are high energy consumers, so power companies adopt a two-part system for these enterprises. The electricity fee is based on the company's actual electricity usage, while the basic fee is based on the company's maximum electricity usage or the capacity of its transformer. Therefore, the basic fee is also called the maximum demand fee. The basic fee is affected by the company's peak load. The higher the peak load, the higher the basic fee charged by the power company. Before commencing production, fused magnesia producers sign an electricity contract with the local power company to constrain maximum electricity demand. This contract sets a maximum demand value. If the actual maximum production power exceeds this contracted value, penalties will be imposed.

[0009] Secondly, the various constraints in the optimization model were analyzed and determined. Power balance constraints are essential, reflecting the fact that fused magnesium enterprises divide their overall energy consumption into two major components: production completion and primary frequency regulation. Ensuring the economic benefits of fused magnesium production during operation is paramount, and therefore product quality must be guaranteed. This places certain demands on the operation of the fused magnesium furnace: The furnace temperature must be maintained, neither too high nor too low. This requires that the furnace's power regulation capacity should not be too large, and the duration should not be too long. Furthermore, the frequent operation of the motor inevitably causes additional losses to the equipment, all of which need to be considered in the modeling.

[0010] During normal production, a fused magnesium furnace cycles through the main melting, exhaust, and charging phases. The duration of each phase is not completely fixed, and the power during exhaust and charging fluctuates significantly, making it impossible to adjust the melting power. Only during the main melting phase can frequency modulation be implemented. Therefore, the regulation capacity of a fused magnesium cluster furnace is uncertain at different times. This uncertainty affects the modeling and solution for optimizing the frequency modulation capacity the previous day, and needs to be addressed.

[0011] In order to achieve the above object, the technical solution adopted in the present invention is:

[0012] A method for optimizing the capacity reported by a fused magnesium furnace group participating in a frequency modulation day includes the following steps:

[0013] Step 1: Establish the objective function;

[0014] With the goal of maximizing the total revenue of a fused magnesium enterprise within a day's production, while taking into account the completion of the primary frequency regulation task, the quality of the enterprise's products, and the power demand of the power grid, the primary frequency regulation capacity reported by the fused magnesium furnace group in each period is optimized. The total revenue of a fused magnesium enterprise per unit time mainly includes the production revenue of the fused magnesium furnace F1, the frequency regulation auxiliary service revenue F2, the enterprise's electricity cost F3, the penalty cost of insufficient frequency regulation F4, and equipment loss F5. Therefore, the objective function of the optimization model is:

[0015] max F=F1+F2-F3-F4-F5 (1)

[0016] The production income of the fused magnesium enterprise F1:

[0017]

[0018] Where, J represents the number of fused magnesium furnaces in the enterprise; T represents the scheduling period; α represents the profit per ton of magnesium oxide crystal produced (excluding electricity cost); P j,t represents the power of the j-th electric fused magnesium furnace in the t-th time period; Δt represents the duration of each 15-min reporting period; η represents the energy consumption per ton of the electric fused magnesium furnace.

[0019] The frequency regulation ancillary service income F2:

[0020]

[0021] Where ΔP t It represents the effective adjustable capacity reported by the fused magnesium furnace in the tth period; π represents the declared unit price.

[0022] For large industrial users, the power supply company charges electricity fee F3 in a two-part pricing method, and charges according to the actual maximum demand, which is divided into electricity fee and basic electricity charges Two parts. Electricity cost F3:

[0023]

[0024] In the formula, λ represents the electricity price; λ1 represents the electricity price during normal hours; λ2 represents the electricity price during off-peak hours; P M represents the maximum demand contract value; ω represents the maximum demand electricity price; Indicates the actual maximum demand during the production cycle. Under the two-part electricity pricing system, if the actual maximum demand of the electricity user exceeds 105% of the contracted value, the basic electricity fee will be doubled for the portion exceeding 105%.

[0025] When the reported frequency regulation capacity is higher than the adjustable power, the adjustable power of the fused magnesium furnaces in the area cannot reach the reported capacity. Then the enterprise will face the penalty F4 of insufficient frequency regulation points by the dispatching agency:

[0026]

[0027] Where, t up Indicates an increase in penalty time; Indicates that the power can be increased in the tth period; t down Indicates a reduction in penalty time; Indicates that the power can be reduced in the t-th period; ε represents the penalty unit price for insufficient frequency regulation.

[0028] Frequent and large-scale adjustments to the fused magnesium furnace in response to changes in grid frequency will affect the service life of the equipment and increase its failure rate. Therefore, the loss of the fused magnesium furnace in the primary frequency regulation equipment is F5:

[0029]

[0030]

[0031] Where, 3 represents the three-phase electrode; s j,t represents the number of adjustments of the j-th electric fused magnesium furnace in the t-th period; φ represents the unit price of loss of the equipment each time it is adjusted; Indicates the number of upward adjustments; Indicates the number of downgrades.

[0032] Step 2: Determine the constraints;

[0033] The fused magnesium furnace is subject to various production process restrictions during production. The following constraints should be considered during adjustment:

[0034] Power balance constraints:

[0035]

[0036] Where, It represents the smelting power of the jth electric fused magnesium furnace during normal production in the tth period.

[0037] Primary frequency regulation capacity constraints:

[0038] ΔP t ad ≥ΔP t (12)

[0039] Where ΔP t ad Indicates that the power of the fused magnesium furnace group can be adjusted in the tth period.

[0040] A single fused magnesium furnace cannot be adjusted too many times in the same scheduling cycle, and a single fused magnesium furnace should not be adjusted up or down continuously in two consecutive time periods.

[0041]

[0042] Where, τ represents the adjustment stage; Ω represents the maximum number of adjustments within 15 minutes for a single furnace; and They represent the 0-1 variables of the power adjustment of the fused magnesium furnace in the τth adjustment stage, Indicates an increase in the current stage. Indicates a downward adjustment at the current stage.

[0043] If the smelting power of the fused magnesium furnace is too high, the temperature of the molten pool will continue to rise, which may easily cause accidents such as furnace blowout. If the smelting power of the fused magnesium furnace is too low, the temperature in the furnace will not meet the production requirements, affecting the quality of magnesium oxide crystals. The smelting constraints of the fused magnesium furnace are:

[0044]

[0045] P min ≤P j,t ≤P max (18)

[0046] Where, N(t) represents the number of fused magnesium furnaces that can be adjusted in the tth period; P min and P maxRespectively represent the minimum and maximum power of the electric fused magnesium furnace.

[0047] After participating in the frequency regulation auxiliary service, the fused magnesium enterprise will generate greater economic benefits than when it does not participate in the frequency regulation auxiliary service. The total revenue F constraint is:

[0048]

[0049] Step 3: Dealing with uncertainty in the adjustment capacity of the fused magnesium furnace group;

[0050] Due to the uncertainty of the adjustment capacity of the fused magnesium furnace group within a day, in most cases, in order to ensure the validity of the constraint condition formula (12), the fused magnesium enterprise has to reduce the adjustment capacity of the fused magnesium furnace during the entire adjustment period due to local non-satisfaction of the constraints. Chance-constrained programming allows the optimization of the constraints that do not meet some small intervals by setting a reasonable confidence interval to achieve efficient processing of this uncertainty. The application of chance constraints requires calculating the probability of meeting the chance constraints, so it is necessary to clarify the probability that the fused magnesium furnace group can provide different adjustment capabilities in different time periods. The details are as follows:

[0051] To clarify the probability that a fused magnesium cluster can provide different adjustment capabilities at different times, we need to describe the timing characteristics of the adjustable power of the fused magnesium cluster. By drawing on the concept of sequential Monte Carlo simulation, we simulate the duration and melting power of each operating condition. Following the production sequence of the fused magnesium furnaces, we establish a virtual cyclic transition process for the fused magnesium cluster operating conditions within the production cycle, and calculate and analyze the adjustable power of each operating condition.

[0052] In step 3.1, each operating condition is first represented by a symbol: "0" represents the furnace start-up state, "1" represents the charging state, "2" represents the main melting state, and "3" represents the exhaust state. Considering the randomness of the fused magnesium load, the duration of each state is defined as an integer random distribution. The subroutine design for each state is based on the Monte Carlo method, and the furnace start-up stage and the smelting stage are connected using a Markov chain. The time required for the fused magnesium furnace start-up is t sf The time required for smelting is t sp , the furnace starting and smelting subroutine functions are:

[0053] S t+1 =start(t sf ,S t ,T rm ,j) (20)

[0054] S t+1 =smelting(t sp ,S t ,T rm ,j) (21)

[0055] Where S t+1represents the next state matrix; S t represents the current state matrix, T rm Represents the state time record matrix.

[0056] Step 3.2: During the smelting process of fused magnesium, the power cannot be adjusted during the furnace start-up phase, charging conditions and exhaust conditions. With adjustable power matrix The corresponding value is assigned to "0". Real-time mark of the fused magnesium furnace in the main melting state, the main melting state increases the power matrix The power of each furnace can be increased to 10% of the rated power, and the power matrix can be adjusted downwards The power of each furnace can be adjusted down to 15% of the rated power. The formula for calculating the rated power is:

[0057]

[0058] Step 3.3: Based on the idea of ​​probability theory, establish the Gaussian model corresponding to different time periods as follows:

[0059]

[0060] Where μ t represents the mathematical expectation of the adjustable power of the fused magnesium furnace group in the tth period; σ t It represents the standard deviation of the adjustable power of the fused magnesium furnace group in the tth period.

[0061] Step 3.4, the premise of using the idea of ​​chance constraints to deal with the uncertainty of the adjustment capacity of the fused magnesium furnace cluster is to set an appropriate relevant confidence level. The choice of confidence level directly affects the risk and benefit of the decision. Too high a confidence level may lead to overly conservative decisions and fail to fully utilize the adjustment capacity of the fused magnesium furnace cluster; while too low a confidence level may increase the decision risk and cause the fused magnesium furnace cluster to be unable to meet the primary frequency regulation requirements. Therefore, it is necessary to select an appropriate confidence level based on the decision maker's risk preference and actual needs, combined with the actual operation of the fused magnesium furnace cluster. The confidence level ξ of the adjustable power of the fused magnesium furnace cluster of the present invention is such that:

[0062] |ΔP t ad -ΔP t |<ξ (24)

[0063] Due to the limitation of adjustable power when operating Nichidai Magnesium Melting Furnace, there are:

[0064] ΔP t ad -ΔP t ≥0 (25)

[0065] To ensure that the intraday real-time adjustment phase can better match the capacity reported on the day before, γ is used to represent the opportunity constraint coefficient. The adjustable power is covered by the following opportunity constraints:

[0066] ρ(ΔP t ad -ΔP t ≥0)≥1-γ (26)

[0067] Where, 1-γ=ξ; ρ(ΔP t -ΔP t ad ≥0) represents the probability of reaching the reported capacity during a frequency modulation event. This is a nonlinear expression, making the optimization model unsolvable using an optimization solver. Considering that the random variables involved are single and normally distributed, they can be converted to a deterministic equivalence class to achieve linearization.

[0068] because Right now Its probability distribution function is Φ(·), which is:

[0069]

[0070] Then the deterministic equivalent expression of the opportunity constraint of the primary frequency regulation capacity constraint is:

[0071] ΔP t ≥μ t +Φ -1 (1-γ)σ t (30)

[0072] In summary, this paper considers the impact of uncertainty in the ability of a fused magnesium furnace cluster to adjust under various operating conditions on the solution of a day-ahead capacity optimization model. This uncertainty is expressed probabilistically through a chance constraint approach. Taking into account frequency regulation requirements, energy demand specifications unique to fused magnesium production, product quality requirements, and smelting characteristics, an optimization model for the day-ahead capacity of a cluster of furnaces participating in a single frequency regulation is established and solved.

[0073] The beneficial effects of the present invention are:

[0074] (1) As an effective frequency response control resource, the participation of high-energy-consuming fused magnesium furnaces in primary frequency regulation can effectively make up for the lack of primary frequency regulation resources under the new situation. Relying on a market-oriented paid service mechanism, the huge potential of load-side resources in participating in the primary frequency regulation of the power grid can be realized. The present invention aims to maximize the overall benefits of the enterprise, taking into account the frequency regulation needs, energy demand restrictions and product quality, and establishes an optimization model for the capacity reported by the group furnaces participating in the primary frequency regulation on the day before. This allows fused magnesium enterprises to obtain primary frequency regulation compensation by participating in the primary frequency regulation of the power grid, thereby improving their overall operating economy.

[0075] (2) The present invention reflects the uncertainty of the adjustment capacity of the fused magnesium group furnaces in the form of probability through the method of chance constraint, which can take into account the frequency regulation demand, the energy demand specification unique to the production of fused magnesium enterprises, the product quality requirements and the smelting characteristic constraints, establish and solve the optimization model of the capacity reported by the group furnaces participating in the primary frequency regulation on the day before, and solve the optimal capacity reported for participating in the primary frequency regulation in each period on the day before. The example shows that fused magnesium enterprises can obtain higher benefits by participating in the primary frequency regulation of the power grid than those who do not participate in the primary frequency regulation of the power grid, and provide support for fused magnesium enterprises to reasonably participate in the primary frequency regulation of the power grid and report the frequency regulation capacity on the day before as a demand response resource on the load side. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The relationship between the adjustable power of the fused magnesium furnace and the reported primary frequency regulation capacity;

[0077] Figure 2 This is a flow chart for calculating the adjustable power of an electric fused magnesium furnace;

[0078] Figure 3 (a) is the simulation result of the adjustable capacity of the fused magnesium furnace group; Figure 3 (b) Figure 3 (a) A local enlarged view of point A;

[0079] Figure 4 is the frequency distribution histogram of the capacity that can be increased;

[0080] Figure 5 The frequency distribution histogram of the adjustable capacity of the fused magnesium furnace group in different periods; (a) is the capacity that can be adjusted up in the first period; (b) is the capacity that can be adjusted down in the first period; (c) is the capacity that can be adjusted up in the second period; (d) is the capacity that can be adjusted down in the second period; (e) is the capacity that can be adjusted up in the 42nd period; (f) is the capacity that can be adjusted down in the 42nd period;

[0081] Figure 6 The change of profit of fused magnesium furnace group under different confidence levels;

[0082] Figure 7 The results of Scheme 1 are shown in Figure 1; (a) is the smelting income and adjustable power; (b) is the electricity cost; (c) is the equipment loss;

[0083] Figure 8 The results of Scheme 2 are shown in Figure 2; (a) is the smelting income and reported power diagram; (b) is the primary frequency regulation compensation; (c) is the electricity cost; (d) is the primary frequency regulation deficiency penalty; (e) is the equipment loss;

[0084] Figure 9 Flowchart of the present invention. DETAILED DESCRIPTION

[0085] The present invention will be further described below with reference to specific embodiments.

[0086] The frequency quality requirement for my country's power grid is 50 ± 0.2 Hz, and the dead zone for primary frequency regulation of thermal power units is 0.033 Hz. If the grid frequency deviation falls within this dead zone, the fused magnesium furnace cluster will not operate. The model developed using this invention can calculate different reported capacities for different compensation electricity prices. The capacity compensation unit price for the fused magnesium furnace cluster participating in primary frequency regulation is set at 2 yuan / kW·h. The CPLEX optimization solver is used to solve the day-ahead reported capacity optimization problem, using the actual parameters of a fused magnesium furnace at a plant in Anshan City, Liaoning Province as an example.

[0087] A method for establishing a frequency response model of a fused magnesium furnace based on electrode regulation comprises the following steps:

[0088] Step 1: Establishment of objective function;

[0089] With the goal of maximizing the total revenue of a fused magnesium enterprise within a day's production, while taking into account the completion of the primary frequency regulation task, the quality of the enterprise's products, and the power demand of the power grid, the primary frequency regulation capacity reported by the fused magnesium furnace group in each period is optimized. The total revenue of a fused magnesium enterprise per unit time mainly includes the production revenue of the fused magnesium furnace F1, the frequency regulation auxiliary service revenue F2, the enterprise's electricity cost F3, the penalty cost of insufficient frequency regulation F4, and equipment loss F5. Therefore, the objective function of the optimization model is:

[0090] max F=F1+F2-F3-F4-F5 (1)

[0091] The production income of the fused magnesium enterprise F1:

[0092]

[0093] Where J represents 30 fused magnesium furnaces; T represents a 10.5-hour dispatch cycle; α represents the profit (excluding electricity costs) of producing one ton of magnesium oxide crystals, which is 2,500 yuan / ton; and η represents the energy consumption per ton of the fused magnesium furnace, which is 2,460 kW·h / ton.

[0094] The frequency regulation ancillary service income F2:

[0095]

[0096] Where, π represents the declared unit price of 2 yuan / kW·h.

[0097] For large industrial users, the power supply company charges electricity fee F3 in a two-part pricing method, and charges according to the actual maximum demand, which is divided into electricity fee and basic electricity charges Two parts. Electricity cost F3:

[0098]

[0099] Where, λ1 represents the electricity price during normal hours, which is 0.58 yuan / kW·h; λ2 represents the electricity price during off-peak hours, which is 0.32 yuan / kW·h; P M represents the maximum demand contract value of 80MW; ω represents the maximum demand electricity price of 35.2 yuan / kW·month.

[0100] When the reported frequency regulation capacity is higher than the adjustable power, the adjustable power of the fused magnesium furnaces in the area cannot reach the reported capacity. Then the enterprise will face the penalty F4 of insufficient frequency regulation points by the dispatching agency:

[0101]

[0102] Where ε represents the penalty price of insufficient frequency regulation, which is 5 yuan / kW·h.

[0103] Frequent and large-scale adjustments to the fused magnesium furnace in response to changes in grid frequency will affect the service life of the equipment and increase its failure rate. Therefore, the loss of the fused magnesium furnace in the primary frequency regulation equipment is F5:

[0104]

[0105]

[0106] In the formula, φ represents the unit price of loss of equipment each time it is adjusted, which is 0.2 yuan per time.

[0107] Step 2: Determine the constraints;

[0108] The fused magnesium furnace is subject to various production process restrictions during production. The following constraints should be considered during adjustment:

[0109] Power balance constraints:

[0110]

[0111] Primary frequency regulation capacity constraints:

[0112] ΔP t ad ≥ΔP t (12)

[0113] A single fused magnesium furnace cannot be adjusted too many times in the same scheduling cycle, and a single fused magnesium furnace should not be adjusted up or down continuously in two consecutive time periods.

[0114]

[0115] Where Ω represents the maximum number of adjustments within 15 minutes for a single furnace, which is 10 times.

[0116] If the smelting power of the fused magnesium furnace is too high, the temperature of the molten pool will continue to rise, which may easily cause accidents such as furnace blowout. If the smelting power of the fused magnesium furnace is too low, the temperature in the furnace will not meet the production requirements, affecting the quality of magnesium oxide crystals. The smelting constraints of the fused magnesium furnace are:

[0117]

[0118] P min ≤P j,t ≤P max (18)

[0119] Where, P min Indicates the minimum power of the fused magnesium furnace is 2.2MW; P max It means the maximum power of the fused magnesium furnace is 2.7MW.

[0120] After participating in the frequency regulation auxiliary service, the fused magnesium enterprise will generate greater economic benefits F than when it does not participate in the frequency regulation auxiliary service. The total revenue constraint is:

[0121]

[0122] Step 3: Dealing with uncertainty in the adjustment capacity of the fused magnesium furnace group;

[0123] Due to the uncertainty of the adjustment capacity of the fused magnesium furnace group within a day, in most cases, in order to ensure the validity of the constraint condition formula (12), the fused magnesium enterprise has to reduce the adjustment capacity of the fused magnesium furnace during the entire adjustment period due to local non-satisfaction of the constraints. Chance-constrained programming allows the optimization of the constraints that do not meet some small intervals by setting a reasonable confidence interval to achieve efficient processing of this uncertainty. The application of chance constraints requires calculating the probability of meeting the chance constraints, so it is necessary to clarify the probability that the fused magnesium furnace group can provide different adjustment capabilities in different time periods. The details are as follows:

[0124] To clarify the probability that a fused magnesium cluster can provide different adjustment capabilities at different times, we need to describe the timing characteristics of the adjustable power of the fused magnesium cluster. By drawing on the concept of sequential Monte Carlo simulation, we simulate the duration and melting power of each operating condition. Following the production sequence of the fused magnesium furnaces, we establish a virtual cyclic transition process for the fused magnesium cluster operating conditions within the production cycle, and calculate and analyze the adjustable power of each operating condition.

[0125] In step 3.1, each operating condition is first represented by a symbol: "0" represents the furnace start-up state, "1" represents the charging state, "2" represents the main melting state, and "3" represents the exhaust state. Considering the randomness of the fused magnesium load, the duration of each state is defined as an integer random distribution. The subroutine design for each state is based on the Monte Carlo method, and the furnace start-up stage and the smelting stage are connected using a Markov chain. The time required for the fused magnesium furnace start-up is t sfThe time required for smelting is t sp , the furnace starting and smelting subroutine functions are:

[0126] S t+1 =start(t sf ,S t ,T rm ,j) (20)

[0127] S t+1 =smelting(t sp ,S t ,T rm ,j) (21)

[0128] Step 3.2: During the smelting process of fused magnesium, the power cannot be adjusted during the furnace start-up phase, charging conditions and exhaust conditions. With adjustable power matrix The corresponding value is assigned to "0". Real-time mark of the fused magnesium furnace in the main melting state, the main melting state increases the power matrix The power of each furnace can be increased to 10% of the rated power, and the power matrix can be adjusted downwards The power of each furnace can be adjusted down to 15% of the rated power. The formula for calculating the rated power is:

[0129]

[0130] Simulate the operating status of 30 electric fused magnesium furnaces, calculate the power that can be adjusted up and down for 30 electric fused magnesium furnaces, and analyze the adjustable capacity. Using the established time series production simulation method, the results of simulating the adjustable capacity of the electric fused magnesium furnace group are as follows: Figure 3 (a) Figure 3 (b) shown.

[0131] Depend on Figure 3 (a) It can be found that the fused magnesium furnace group can provide relatively stable and continuous adjustable power during the entire smelting stage. In order to further clarify the timing characteristics of the furnace group, a probability analysis of the adjustable capacity curve during the smelting stage is performed. The frequency distribution histogram of the adjustable capacity is obtained as follows: Figure 4 Specific data are shown in Table 1.

[0132] Table 1 Probability statistics of capacity that can be increased during the smelting stage

[0133]

[0134] Depend on Figure 4 It can be found that the adjustable capacity of the group furnaces in the smelting stage has a normal distribution feature. It is necessary to further explore the distribution characteristics of the adjustable power in each 15-minute reporting period. The statistical results of the adjustable power and the adjustable power in some periods are as follows: Figure 5Specific data are shown in Table 2-Table 7.

[0135]

[0136]

[0137] Table 3 Probability statistics of capacity reduction in the first smelting phase

[0138]

[0139] Table 4 Probability statistics of capacity increase during the second smelting period

[0140]

[0141] Table 5 Probability statistics of capacity reduction in the second smelting period

[0142]

[0143] Table 6 Probability statistics of capacity increase during the 42nd period of smelting

[0144]

[0145] Table 7 Probability statistics of capacity reduction during the 42nd period of smelting

[0146]

[0147] Since the primary frequency regulation of the power grid requires the flexibility resources to provide the primary frequency regulation capability with symmetry, Figure 5 It can be found that the power that can be adjusted down in the fused magnesium group furnace at different time periods is significantly higher than the power that can be adjusted up. Therefore, the adjustable capacity of the fused magnesium group furnace in this paper is calculated based on the capacity that can be adjusted up in different time periods.

[0148] Step 3.3: Based on the idea of ​​probability theory, establish the Gaussian model corresponding to different time periods as follows:

[0149]

[0150] Step 3.4, the premise of using the idea of ​​chance constraints to deal with the uncertainty of the adjustment capacity of the fused magnesium furnace cluster is to set an appropriate relevant confidence level. The choice of confidence level directly affects the risk and benefit of the decision. Too high a confidence level may lead to overly conservative decisions and fail to fully utilize the adjustment capacity of the fused magnesium furnace cluster; while too low a confidence level may increase the decision risk and cause the fused magnesium furnace cluster to be unable to meet the primary frequency regulation requirements. Therefore, it is necessary to select an appropriate confidence level based on the decision maker's risk preference and actual needs, combined with the actual operation of the fused magnesium furnace cluster. The confidence level ξ of the adjustable power of the fused magnesium furnace cluster of the present invention is such that:

[0151] |ΔPt ad -ΔP t |<ξ (24)

[0152] Due to the limitation of adjustable power when operating Nichidai Magnesium Melting Furnace, there are:

[0153] ΔP t ad -ΔP t ≥0 (25)

[0154] To ensure that the intraday real-time adjustment phase can better match the capacity reported on the day before, γ is used to represent the opportunity constraint coefficient. The adjustable power is covered by the following opportunity constraints:

[0155] ρ(ΔP t ad -ΔP t ≥0)≥1-γ (26)

[0156] Considering that the random variables involved are single and obey the normal distribution, they can be converted into a deterministic equivalent class form to achieve the purpose of linearization.

[0157] because Right now Its probability distribution function is Φ(·), which is:

[0158]

[0159] Then the deterministic equivalent expression of the opportunity constraint of the primary frequency regulation capacity constraint is:

[0160] ΔP t ≥μ t +Φ -1 (1-γ)σ t (30)

[0161] The determination of the confidence level directly affects the risk and benefits of the decision. Different confidence levels will change the optimization model's solution to the reported capacity on the day before, and the reported capacity will affect the overall economic benefits. When the confidence level changes from 91% to 97%, the overall profit of the enterprise changes as follows: Figure 6 shown.

[0162] from Figure 6It can be found that when the confidence level increases from 91% to 95%, overall revenue can increase by more than 20,000 yuan. When the confidence level is between 91% and 95%, overall revenue shows an upward trend, indicating that lower confidence levels lead to larger reported capacities, increasing the time when the fused magnesium cluster furnace cannot meet the primary frequency regulation demand and increasing the penalties for insufficient primary frequency regulation imposed on the enterprise. As the confidence level increases, the reported capacity decreases, and the penalties for insufficient primary frequency regulation decrease. When the confidence level is greater than 95%, overall revenue shows a downward trend, indicating that excessively high confidence levels lead to overly conservative reported capacities, resulting in a significant decrease in overall revenue. Therefore, while ensuring the safe production of fused magnesium cluster furnaces, rationally selecting a confidence level can effectively improve overall economic benefits.

[0163] In order to reflect the economic changes of enterprises after participating in the primary frequency regulation, the reported capacity optimization scheme proposed in this chapter is compared with the benefits of enterprises that do not participate in the primary frequency regulation. The fused magnesium group furnace that does not participate in the primary frequency regulation is set as scheme 1, and the reported capacity optimization scheme proposed in this chapter is set as scheme 2. The overall power consumption of the two schemes is the same, and the results are as follows: Figure 7 and Figure 8 shown.

[0164] Depend on Figure 7 It can be found that the smelting income is lower in some time periods (such as 23:00-23:15). The smelting power of the electric fused magnesium furnace is relatively low during this period, so there will be more room for adjustment, that is, Figure 7 The purple curve in this period has a higher value. However, since the fused magnesium enterprises did not participate in the frequency regulation, they were unable to fully utilize the remaining adjustment space to obtain certain benefits, which was not conducive to the improvement of the overall benefits of fused magnesium. Figure 8 During the same time period, the remaining adjustment space is utilized to participate in the primary frequency regulation (the blue curve in the figure shows a higher primary frequency regulation power at this moment), resulting in primary frequency regulation benefits. The electricity cost curve (smelting stage) shows a significant difference between the electricity costs before 22:00 and between 05:00 and 07:30 the next day, compared to 22:00 and 05:00. This is due to time-of-use electricity prices. The electricity price between 22:00 and 05:00 is at its lowest point, at 0.32 yuan / kW·h, while the rest of the smelting period is at its normal price of 0.58 yuan / kW·h. This significant price difference leads to a significant difference in electricity costs during different time periods, which is a decisive factor in high-energy-consuming enterprises choosing nighttime production.

[0165] Depend on Figure 8It can be seen that the reported power at different times determines the primary frequency regulation benefits during that period. The primary frequency regulation compensation is relatively high during periods with high reported power. The highest reported power, 5.18 MW, occurs between 23:15 and 23:30, resulting in a primary frequency regulation compensation of 2,590 yuan. Due to the uncertainty of the power regulation capacity of fused magnesium furnaces, fused magnesium companies face the risk of penalties for insufficient frequency regulation. The optimization model accounts for this uncertainty to ensure optimal overall economic performance.

[0166] contrast Figure 7 and Figure 8 It can be seen that no capacity declarations were made during the period of 21:30–21:45, when the capacity adjustment capability is available. This is consistent with actual production: the startup time of a fused magnesium furnace lasts approximately 30–40 minutes, and the period from 21:30–21:45 coincides with the first 15-minute melting period after startup. The optimization results during this period do not meet the power dispatching agency's requirement for primary frequency regulation (primary frequency regulation capacity must be no less than 5% of the total load), so fused magnesium companies do not declare adjustable capacity during this period. The smelting revenue of fused magnesium clusters participating in primary frequency regulation is significantly lower than when they do not participate. However, the fused magnesium companies receive primary frequency regulation compensation, which improves their overall revenue. For example, the overall revenue of fused magnesium furnaces participating in primary frequency regulation from 22:00–22:15 is 11,386 yuan, while the overall revenue without primary frequency regulation is 10,497 yuan, an increase of 889 yuan. A comparison of the revenue of the two schemes over the entire production cycle is shown in Table 8.

[0167] Table 8 Profits of the two schemes in the entire production cycle

[0168]

[0169] Comparing Schemes 1 and 2, we find that although Scheme 2 reduced production revenue by 49,260 yuan, under the final reported capacity results for each time period, the fused magnesium enterprise received 96,945 yuan in primary frequency regulation compensation. After accounting for insufficient frequency regulation penalties and equipment losses, Scheme 2's overall revenue was approximately 370,200 yuan, an increase of 30,009 yuan compared to not participating in primary frequency regulation. The proposed day-ahead reported capacity optimization model enables fused magnesium enterprises to obtain primary frequency regulation compensation by participating in primary frequency regulation, improving their overall operational economics.

[0170] In summary, the present invention considers the impact of the uncertainty of the adjustment ability of the various working conditions of the fused magnesium furnace group on the solution of the optimization model of the reported capacity on the day before, and reflects the uncertainty of the adjustment ability of the fused magnesium furnace group in the form of probability through the method of chance constraint. Taking into account the frequency regulation needs, the energy demand specifications unique to the production of fused magnesium enterprises, product quality requirements and smelting characteristics constraints, an optimization model for the capacity reported on the day before for the group furnaces participating in the primary frequency regulation is established and solved, and the optimal reported capacity for participating in the primary frequency regulation of the power grid in each period on the day before is solved. The example shows that fused magnesium enterprises can obtain higher benefits by participating in the primary frequency regulation of the power grid than those who do not participate in the primary frequency regulation of the power grid, and provides support for fused magnesium enterprises to reasonably participate in the primary frequency regulation of the power grid and report the frequency regulation capacity on the day before as a demand response resource on the load side.

[0171] The above-described embodiments merely express the implementation methods of the present invention, but should not be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for optimizing the capacity reported by a group of fused magnesium furnaces participating in a frequency modulation, characterized in that: The following steps are involved: Step 1: Establish the objective function; With the goal of maximizing the total revenue of the fused magnesium enterprise within a day's production time, taking into account the completion of the primary frequency regulation task, the quality of the enterprise's production products, and the power demand of the power grid, the primary frequency regulation capacity reported by the fused magnesium group furnaces in each period is optimized. The total revenue per unit time of the fused magnesium enterprise includes the production revenue of the fused magnesium furnace F1, the frequency regulation auxiliary service revenue F2, the enterprise's electricity cost F3, the penalty cost of insufficient frequency regulation F4, and the equipment loss F5. Therefore, the objective function of the optimization model is: max F=F1+F2-F3-F4-F5(1) Step 2: Determine the constraints; Power balance constraints; Primary frequency regulation capacity constraints; A single fused magnesium furnace cannot be adjusted too many times in the same scheduling cycle, and a single fused magnesium furnace should not be adjusted up or down continuously in two consecutive time periods. Where, τ represents the adjustment stage; Ω represents the maximum number of adjustments within 15 minutes for a single furnace; and They represent the 0-1 variables of the power adjustment of the fused magnesium furnace in the τth adjustment stage, Indicates an increase in the current stage. Indicates a downward adjustment at the current stage; Constraints of fused magnesium furnace smelting: P min ≤P j,t ≤P max (18) Where, N(t) represents the number of fused magnesium furnaces that can be adjusted in the tth period; P min and P max Respectively represent the minimum and maximum power of the electric fused magnesium furnace; Total income F constraint: Step 3: Dealing with uncertainty in the adjustment capacity of the fused magnesium furnace group; The probability that the electric fused magnesium furnace group can provide different adjustment capabilities in different time periods is clarified, the timing characteristics of the adjustable power of the electric fused magnesium furnace group are determined, and the duration and melting power of each working condition are simulated through the sequential Monte Carlo simulation method; according to the production timing of the electric fused magnesium furnace, a virtual electric fused magnesium furnace working condition cycle transfer process is established within the production cycle, and the adjustable power of each working condition is calculated and analyzed.

2. The method for optimizing the capacity reported by a fused magnesium furnace group before participating in a frequency modulation according to claim 1, characterized in that: The step 3 is specifically as follows: Step 3.1: Each working condition is represented by a symbol, "0" represents the furnace start-up state, "1" represents the charging condition, "2" represents the main melting condition, and "3" represents the exhaust condition. Considering the randomness of the fused magnesium load, the duration of each state is defined as an integer random distribution. The subroutine design of each state is based on the Monte Carlo method, and the furnace start-up stage and the smelting stage are connected by a Markov chain. The time required for the fused magnesium furnace start-up is t sf The time required for smelting is t sp , the furnace starting and smelting subroutine functions are: S t+1 =start(t sf ,S t ,T rm ,j) (20) S t+1 =smelting(t sp ,S t ,T rm ,j) (21) Where S t+1 represents the next state matrix; S t represents the current state matrix, T rm represents the state time record matrix; Step 3.2: During the smelting process of fused magnesium, the power cannot be adjusted during the furnace start-up phase, charging conditions and exhaust conditions. With adjustable power matrix The corresponding value is assigned to "0" in the real-time mark of the fused magnesium furnace in the main melting state, and the power matrix is ​​adjusted upward in the main melting state. The power of each furnace can be increased to 10% of the rated power, and the power matrix can be adjusted downwards The power of each furnace can be adjusted down to 15% of the rated power; the rated power calculation formula is: Step 3.3: Based on probability theory, establish the Gaussian model corresponding to different time periods as follows: Where μ t represents the mathematical expectation of the adjustable power of the fused magnesium furnace group in the tth period; σ t It represents the standard deviation of the adjustable power of the fused magnesium furnace group in the tth period; In step 3.4, according to the risk preference and actual needs of the decision maker and the actual operation of the fused magnesium furnace cluster, an appropriate confidence level is selected; the confidence level ξ of the adjustable power of the fused magnesium furnace cluster is such that: Due to the limitation of adjustable power when operating Nichidai Magnesium Melting Furnace, there are: ΔP t ad -ΔP t ≥0 (25) To ensure that the intraday real-time adjustment phase can better match the capacity reported on the day before, γ is used to represent the opportunity constraint coefficient. The adjustable power is covered by the following opportunity constraints: ρ(ΔP t ad -ΔP t ≥0)≥1-γ (26) Where, 1-γ=ξ; ρ(ΔP t -ΔP t ad ≥0) represents the probability of reaching the reported capacity when participating in a frequency modulation. It is a nonlinear expression, which makes it impossible to directly apply the optimization solver to the optimization model; because Right now Its probability distribution function is Φ(·), which is: Then the deterministic equivalent expression of the opportunity constraint of the primary frequency regulation capacity constraint is: ΔP t ≥μ t +F -1 (1-c)s t (30).

3. The method for optimizing the capacity reported by a fused magnesium furnace group before participating in a frequency modulation according to claim 1, characterized in that: In step 1: The production income of the fused magnesium enterprise F1: Where J represents the number of fused magnesium furnaces in the enterprise; T represents the scheduling period; α represents the profit per ton of magnesium oxide crystal produced, excluding electricity costs; P j,t represents the power of the jth fused magnesium furnace in the tth period; Δt represents the duration of each 15-minute reporting period; η represents the energy consumption per ton of the fused magnesium furnace; The frequency regulation ancillary service revenue F2 is: Where ΔP t represents the effective adjustable capacity reported by the fused magnesium furnace in the tth period; π represents the reported unit price; The electricity cost F3 of the enterprise is calculated in a two-part electricity price, which is charged according to the actual maximum demand and is divided into electricity charges and basic electricity charges Two parts; electricity cost F3: In the formula, λ represents the electricity price; λ1 represents the electricity price during normal hours; λ2 represents the electricity price during off-peak hours; P M represents the maximum demand contract value; ω represents the maximum demand electricity price; Indicates the actual maximum demand during the production cycle; In the two-part electricity price billing method, when the actual maximum demand of the electricity user exceeds 105% of the contract value, the basic electricity fee for the part exceeding 105% will be doubled; The penalty cost F4 for insufficient frequency regulation: When the reported frequency regulation capacity is higher than the adjustable power, the adjustable power of the fused magnesium furnaces in the area cannot reach the reported capacity, and the dispatching agency will be penalized by the insufficient frequency regulation points F4: Where, t up Indicates an increase in penalty time; Indicates that the power can be increased in the tth period; t down Indicates a reduction in penalty time; Indicates that the power can be reduced in the t-th period; ε indicates the penalty unit price for insufficient frequency regulation; The equipment loss F5: Where, 3 represents the three-phase electrode; s j,t represents the number of adjustments of the j-th electric fused magnesium furnace in the t-th period; φ represents the unit price of loss of the equipment each time it is adjusted; Indicates the number of increases; Indicates the number of downgrades.

4. The method for optimizing the capacity reported by a fused magnesium furnace group before participating in a frequency modulation according to claim 1, characterized in that: In step 2: The power balance constraints are: Where, It represents the smelting power of the jth electric fused magnesium furnace during normal production in the tth period; The primary frequency regulation capacity constraint is: ΔP t ad ≥ΔP t (12) Where ΔP t ad Indicates that the power of the fused magnesium furnace group can be adjusted in the tth period.

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