Power system optimal dispatch method with electrolytic aluminum load participating in demand response

Abstract

The application discloses a power system optimal scheduling method of electrolytic aluminum load participating in demand response, which comprises the following steps: firstly, constructing a double-layer optimal scheduling model with an upper-layer model of power system optimal scheduling of electrolytic aluminum load participating and a lower-layer model of an electrolytic aluminum enterprise optimal operation model; and secondly, solving the double-layer optimal scheduling model to obtain optimal scheduling results containing unit scheduling and electrolytic aluminum load scheduling. The application can effectively guarantee the maximization of the income of the electrolytic aluminum enterprise while meeting the system regulation and control demand and reducing carbon emission.

Description

Technical Field

[0001] This invention belongs to the field of power system demand-side dispatching, specifically relating to a power system optimization dispatching method that involves electrolytic aluminum loads participating in demand response. Background Technology

[0002] Aluminum has a wide range of applications, including electrical engineering, transportation, and construction. Electrolytic aluminum production is characterized by two significant features: high energy consumption and high emissions. High energy consumption means enormous electricity consumption, with a single electrolytic aluminum plant potentially having a capacity of hundreds of megawatts. High emissions mean huge amounts of carbon dioxide emissions.

[0003] Demand response is one of the effective measures to improve the reliability and flexibility of the power system. Integrating demand response into the electricity market, and coordinating the planning of power generation and demand-side resources through effective incentive and guidance measures, is the future direction of the electricity market. The high energy consumption of electrolytic aluminum also brings it enormous regulation potential. If electrolytic aluminum production is rationally guided, considerable response capacity can be provided. Furthermore, the highly automated systems and comprehensive data monitoring systems of the factories make load regulation convenient and flexible, and reduce equipment investment costs. For electrolytic aluminum enterprises themselves, participating in demand response is also a good measure to promote energy conservation and emission reduction, and is conducive to promoting the high efficiency, low carbon, and greening of industrial energy use. Therefore, the optimal dispatch problem of aluminum load-power system is particularly important. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems in the existing technology by providing a power system optimization scheduling method that allows electrolytic aluminum loads to participate in demand response while meeting the power system regulation needs, reducing carbon emissions, and maximizing the profits of electrolytic aluminum enterprises.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A power system optimization dispatching method for electrolytic aluminum loads participating in demand response includes the following steps:

[0007] Step A: Construct a two-layer optimal scheduling model. In the two-layer optimal scheduling model, the upper-layer model is a power system optimal scheduling model involving electrolytic aluminum loads, and the lower-layer model is an optimal operation model for electrolytic aluminum enterprises.

[0008] Step B: Solve the constructed two-layer optimal scheduling model to obtain the optimal scheduling results, which include unit scheduling results and electrolytic aluminum load scheduling results.

[0009] In step A, the power system optimization scheduling model involving the electrolytic aluminum load takes the minimum total operating cost of the power system as its objective function:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] In the above formula, The total number of time periods. , , , , These include thermal power units, electrolytic cell series, operating scenarios, load nodes, and the number of wind farms. , Let $t$ be the coal consumption cost and the start-up cost of the i-th thermal power unit during time period $t$. , The prices for providing upper and lower reserves for the i-th thermal power unit are respectively. , These represent the upper and lower reserve capacities provided by the i-th thermal power unit during time period t. For carbon emission costs, , These represent the energy compensation and standby capacity compensation obtained by the l-th electrolytic cell series during time period t, respectively. Let be the probability of scenario s. , The energy prices for providing upper and lower reserves to the i-th thermal power unit are respectively. , These refer to the upper and lower backup deployments provided for the i-th thermal power unit during time period t in scenario s. This is compensation for the actual backup deployment in scenario s. , These are the prices for involuntary load shedding and wind curtailment, respectively. , These represent the involuntary load shedding at the d-th node and the wind curtailment at the j-th wind farm, respectively, within time period t under scenario s. The energy compensation price of the power system for the l-th electrolytic cell series during time period t. The voltage of the l-th electrolytic cell series, The maximum allowable current to be supplied to the electrolytic cell, Let be the current intensity supplied to the l-th electrolytic cell series during time period t. , These are the standby capacity compensation price and the standby deployment compensation price for time period t, respectively. For the l-th electrolytic cell series in time period t, the current needs to be reduced to provide backup for deployment. For the l-th electrolytic cell series in scenario s during time period t, the actual reduced current is provided to provide deployment backup. For price coefficients, , Let be the carbon emissions and carbon emission allowance of the i-th thermal power unit during time period t, respectively. , Let be the carbon emission intensity and the baseline value for carbon quota allocation for the i-th thermal power unit, respectively. Let be the active power of the i-th thermal power unit during time period t. The duration of the time period;

[0018] The optimized operation model for electrolytic aluminum enterprises takes maximizing the net profit of the electrolytic aluminum enterprises as its objective function.

[0019] In the above formula, This represents the profit price coefficient for aluminum products produced in the l-th electrolytic cell series. It is a constant. The coefficient of the quadratic term in the operation and maintenance cost function of an electrolytic aluminum enterprise.

[0020] The constraints of the power system optimal dispatch model involving electrolytic aluminum loads include:

[0021] Day-ahead scheduling phase constraints:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] In the above formula, Let be the predicted power of the j-th wind farm in time period t. Let be the predicted load power of the d-th node in time period t. The power of the l-th electrolytic cell series, , Let be the minimum and maximum active power output of the i-th thermal power unit, respectively. Let be the operating state variable of the i-th thermal power unit in time period t. , These are the uphill and downhill ramp rates of the i-th thermal power unit, respectively. for The operating status of the i-th thermal power unit in time period . This refers to the period during which thermal power units are subject to start-up and shutdown constraints. , Let be the minimum start-up and shutdown times for the i-th thermal power unit, respectively. This is the sensitivity matrix. , , , These are power matrices for thermal power units, wind farms, loads, and aluminum electrolysis cells, respectively. This is the matrix representing the maximum power flow of the line. The allowable value for carbon quota trading volume;

[0030] Intraday scheduling phase constraints:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] In the above formula, Let j be the actual power of the j-th wind farm in time period t under scenario s. This is a backup for the actual deployment of the l-th electrolytic cell series in time period t under scenario s. This represents the actual load power of the d-th node during time period t in scenario s. Let be the active power of the i-th thermal power unit in time period t under scenario s. , , , These are the power matrices for thermal power units, wind farms, loads, and aluminum electrolysis cells under scenario s. Here is the wind curtailment power matrix for wind farms in scenario s. The power matrix for involuntary load shedding in scenario s;

[0037] Association constraints:

[0038] .

[0039] The constraints of the optimized operation model for electrolytic aluminum enterprises include:

[0040] Day-ahead scheduling phase constraints:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] In the above formula, To be the minimum allowable current to flow into the electrolytic cell, , These are the Lagrange multipliers corresponding to the lower and upper power constraints of the l-th electrolytic cell series in time period t, respectively. , These are the Lagrange multipliers corresponding to the lower and upper limits of the reserve capacity constraints for the l-th electrolytic cell series during time period t. The electrolyte temperature of the l-th electrolytic cell series during time period t. , These are the minimum and maximum allowable temperatures for the electrolyte, respectively. , , For the Lagrange multipliers corresponding to temperature constraints, , , , , All are constants. This represents the minimum daily energy consumption of an electrolytic aluminum plant. For the Lagrange multiplier corresponding to the daily output constraint;

[0048] Deploy backup associated constraints:

[0049]

[0050] In the above formula, , These are the Lagrange multipliers corresponding to the lower and upper limits of the deployment reserve constraints, respectively.

[0051] Intraday scheduling phase constraints:

[0052]

[0053]

[0054]

[0055]

[0056] In the above formula, The electrolyte temperature is the value of the l-th electrolytic cell series in time period t under scenario s.

[0057] Step B specifically includes: first, transforming the two-level optimization scheduling model into a mixed-integer quadratic programming model based on KKT conditions, and then solving it.

[0058] The transformation of the two-level optimization scheduling model into a mixed-integer quadratic programming model based on KKT conditions includes:

[0059] For the power system optimal dispatch model involving electrolytic aluminum loads, the KKT conditions are applied to... Transform to obtain The equivalent expression is:

[0060] ;

[0061] For the optimized operation model of electrolytic aluminum enterprises, the constraints of the model are transformed into their KKT conditions using the Lagrange multiplier method, and the KKT conditions are linearized using the Big M method, resulting in the following constraints:

[0062]

[0063]

[0064]

[0065]

[0066]

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[0080] In the above formula, , , , , , , , , All of these are introduced auxiliary 0-1 variables. This characterizes whether the current flowing into the electrolytic cell is equal to its minimum current value. This indicates whether the current flowing into the electrolytic cell has reached its upper limit. This characterizes whether the reserve capacity provided by electrolytic aluminum has reached its lower limit. This characterizes whether the reserve capacity provided by electrolytic aluminum has reached its upper limit. This indicates whether the daily output of an electrolytic aluminum plant has reached its lower limit. , To characterize whether the electrolyte temperature in the tank has reached the lower limit. This characterizes whether the deployment reserve provided by electrolytic aluminum has reached its lower limit. This characterizes whether the deployment backup provided by electrolytic aluminum has reached its limit. It is a sufficiently large constant.

[0081] The solution was obtained using the Gurobi solver.

[0082] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0083] 1. The present invention discloses a power system optimal scheduling method for electrolytic aluminum load participation in demand response. First, a two-layer optimal scheduling model is constructed, with an optimal scheduling model of the power system involving electrolytic aluminum load as the upper layer model and an optimal operation model of electrolytic aluminum enterprises as the lower layer model. Then, the constructed two-layer optimal scheduling model is solved to obtain the optimal scheduling result including unit scheduling and electrolytic aluminum load scheduling. This two-layer optimal scheduling model can effectively ensure the maximization of the profits of electrolytic aluminum enterprises while meeting system regulation requirements and reducing carbon emissions, which is conducive to improving the enthusiasm of electrolytic aluminum loads to participate in demand response.

[0084] 2. The present invention provides a power system optimization scheduling method for electrolytic aluminum load participation in demand response. For both the power system optimization scheduling model and the electrolytic aluminum enterprise optimization operation model involving electrolytic aluminum load, a two-stage stochastic optimization method is adopted: a day-ahead scheduling stage and an intraday scheduling stage. The decision in the first stage is made in the day-ahead scheduling based on the predicted scenario, and its decision value is applicable to all scenarios in the second stage. In the second stage, intraday scheduling is performed under given uncertainty parameters, and its decision value depends on the decision value in the first stage and is scenario-dependent, in order to smooth out fluctuations in wind power and load within the scenario. This method enables the power system with electrolytic aluminum load participating in demand response to better cope with the uncertainties of wind power and load.

[0085] 3. The power system optimization scheduling method for electrolytic aluminum load participating in demand response in this invention transforms the two-level optimization scheduling model into a mixed integer quadratic programming model based on KKT conditions when solving the two-level optimization scheduling model. This model can be directly solved using the Gurobi solver, effectively reducing the difficulty of solving the model. Attached Figure Description

[0086] Figure 1 This is a topology diagram of the IEEE-39 node system used in Example 1.

[0087] Figure 2 This is the result of the electrolytic aluminum load scheduling for Case 3. Detailed Implementation

[0088] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0089] Example 1:

[0090] A power system optimal dispatching method for electrolytic aluminum load participating in demand response, the method using Figure 1 The IEEE-39 node system shown (containing 10 thermal power units, parameters as shown in Table 1, centrally connected to a wind farm at node 20, with a total capacity of 600MW; a certain aluminum electrolysis company has two aluminum electrolysis plants, located at node 2 and node 10 respectively, each plant containing one series of electrolytic cells, parameters as shown in Table 2) is used as the research object:

[0091] surface Thermal power unit parameters

[0092]

[0093] surface Electrolytic aluminum plant parameters

[0094]

[0095] The method is performed sequentially according to the following steps:

[0096] 1. First, generate 500 operating scenarios based on historical wind power data and load data, and set the probability of each scenario to 1 / 500. Then, merge similar scenarios through scenario reduction method to finally obtain 20 typical wind power and load scenarios. The probability of each typical wind power and load scenario is the number of merged similar scenarios divided by the total number of operating scenarios.

[0097] 2. Construct the upper-level model, namely the power system optimization scheduling model involving electrolytic aluminum load, whose objective function is as follows:

[0098]

[0099] In the above formula, The total number of time periods. , , , , These include thermal power units, electrolytic cell series, operating scenarios, load nodes, and the number of wind farms. , Let $t$ be the coal consumption cost and the start-up cost of the i-th thermal power unit during time period $t$. , The prices for providing upper and lower reserves for the i-th thermal power unit are respectively. , These represent the upper and lower reserve capacities provided by the i-th thermal power unit during time period t. For carbon emission costs, , These represent the energy compensation and standby capacity compensation obtained by the l-th electrolytic cell series during time period t, respectively. Let be the probability of scenario s. , The energy prices for providing upper and lower reserves to the i-th thermal power unit are respectively. , These refer to the upper and lower backup deployments provided for the i-th thermal power unit during time period t in scenario s. This is compensation for the actual backup deployment in scenario s. , These are the prices for involuntary load shedding and wind curtailment, respectively. , These represent the involuntary load shedding amount of the d-th node and the wind curtailment amount of the j-th wind farm, respectively, during time period t in scenario s.

[0100] Electrolytic aluminum enterprises incur dispatch costs when participating in demand response. Power system operators provide cost compensation to them based on the response of electrolytic aluminum loads, which includes three parts: energy compensation, reserve capacity compensation, and reserve deployment compensation.

[0101]

[0102]

[0103]

[0104] In the above formula, The energy compensation price of the power system for the l-th electrolytic cell series during time period t. The voltage of the l-th electrolytic cell series, The maximum allowable current to be supplied to the electrolytic cell, Let be the current intensity supplied to the l-th electrolytic cell series during time period t. , These are the standby capacity compensation price and the standby deployment compensation price for time period t, respectively. For the l-th electrolytic cell series in time period t, the current needs to be reduced to provide backup for deployment. The current actually reduced for the l-th electrolytic cell series in scenario s during time period t to provide deployment backup.

[0105] The cost of carbon emissions can be expressed as:

[0106]

[0107] In the above formula, For price coefficients, , These represent the carbon emissions and carbon emission allowance of the i-th thermal power unit during time period t, respectively.

[0108] The carbon emissions of a thermal power unit are related to its output and can be expressed by the following formula:

[0109]

[0110] In the above formula, Let be the carbon emission intensity of the i-th thermal power unit. Let be the active power of the i-th thermal power unit during time period t. The duration of the time period.

[0111] Carbon emission quotas for thermal power units can be represented as follows:

[0112]

[0113] In the above formula, This is the baseline value for carbon quota allocation for the i-th thermal power unit, which represents the carbon emission quota per unit of electricity generated by the thermal power unit.

[0114] The constraints of this model are as follows:

[0115] Day-ahead scheduling phase constraints:

[0116] 1) Power balance constraints

[0117] Power balance is crucial for the safe and stable operation of a power system. The system power balance constraint requires that the sum of the output of thermal power units and the output of wind power units must equal the total load of the system, which can be expressed as:

[0118]

[0119] In the above formula, Let be the predicted power of the j-th wind farm in time period t. Let be the predicted load power of the d-th node in time period t. This represents the power of the l-th electrolytic cell series.

[0120] 2) Output constraints of thermal power units

[0121] Each thermal power unit has a maximum and a minimum output. The maximum output is generally the rated power, while the minimum output generally refers to the minimum power required to prevent the boiler from shutting down. The unit's output must fall between these two values, which can be expressed as:

[0122]

[0123] In the above formula, , Let be the minimum and maximum active power output of the i-th thermal power unit, respectively. Let be the operating status variable of the i-th thermal power unit in time period t. It is 0 when the unit is in the shutdown state and 1 when it is in the operating state.

[0124] 3) Gradient constraints of thermal power units

[0125] Due to inherent limitations, the output of thermal power units can only vary within a limited timeframe and cannot fluctuate drastically.

[0126]

[0127] In the above formula, , These represent the uphill and downhill ramp rates of the i-th thermal power unit, respectively.

[0128] 4) Minimum start-up / shutdown time constraints for thermal power units

[0129] To optimize economic efficiency and reduce damage to thermal power units, they must run continuously for a certain period after startup before being shut down; this period is called the minimum startup time. Similarly, after shutdown, thermal power units must remain shut down for a certain period before being restarted; this period is called the minimum shutdown time.

[0130]

[0131] In the above formula, for The operating status of the i-th thermal power unit in time period . This refers to the period during which thermal power units are subject to start-up and shutdown constraints. , These are the minimum start-up and shutdown times for the i-th thermal power unit, respectively.

[0132] 5) Reserve capacity constraints of thermal power units

[0133] To ensure the safe and stable operation of the power system, a certain amount of reserve capacity must be maintained to avoid power imbalances caused by load or wind power fluctuations, which could affect power supply.

[0134]

[0135] 6) Branch flow constraints

[0136] Branch power flow constraints, also known as branch capacity upper and lower limit constraints, indicate that each line in the system is limited by its maximum allowed power, and can be expressed as:

[0137]

[0138] In the above formula, This is the sensitivity matrix. , , , These are power matrices for thermal power units, wind farms, loads, and aluminum electrolysis cells, respectively. This is the matrix representing the maximum power flow value of the line.

[0139] 7) Carbon emission constraints

[0140] This constraint limits the amount of carbon allowances traded through the system to a certain range, essentially restricting the total amount of carbon emissions.

[0141]

[0142] In the above formula, This refers to the allowable volume of carbon quota trading.

[0143] Intraday scheduling phase constraints:

[0144] 1) Scene energy balance constraints

[0145] In the above formula, Let j be the actual power of the j-th wind farm in time period t under scenario s. This is a backup for the actual deployment of the l-th electrolytic cell series in time period t under scenario s. This represents the actual load power of the d-th node during time period t in scenario s.

[0146] 2) Scenarios Unit Ramp-up Constraints

[0147]

[0148] In the above formula, Let be the active power of the i-th thermal power unit in time period t under scenario s.

[0149] 3) Scene branch flow constraints

[0150]

[0151] In the above formula, , , , These are the power matrices for thermal power units, wind farms, loads, and aluminum electrolysis cells under scenario s. Here is the wind curtailment power matrix for wind farms in scenario s. This is the power matrix for involuntary load shedding in scenario s.

[0152] 4) Curtailment of wind volume

[0153]

[0154] 5) Involuntary load shedding constraints

[0155]

[0156] Association constraints

[0157] .

[0158] 3. Construct the lower-level model, namely the optimized operation model of the electrolytic aluminum enterprise, whose objective function is as follows:

[0159] In the above formula, The profit generated from the production of electrolytic aluminum in the l-th electrolytic cell series during time period t. , The operating and maintenance costs and carbon emission costs of the l-th electrolytic cell series during time period t are respectively. This represents the actual profit obtained by the l-th electrolytic cell series from producing electrolytic aluminum during time period t under scenario s. This represents the actual operation and maintenance cost of the l-th electrolytic cell series during time period t under scenario s.

[0160] It can be represented as follows:

[0161]

[0162] In the above formula, This is the profit price coefficient for aluminum products produced in the l-th electrolytic cell series. It takes into account factors such as raw material costs and electricity costs. This price coefficient can be obtained by converting the profit per ton of aluminum.

[0163] Considering that electrolytic aluminum enterprises need to perform certain operations and maintenance to provide demand response, assuming that the operation and maintenance cost is a quadratic function of the provided response energy, it can be expressed as follows:

[0164]

[0165] In the above formula, The coefficient of the quadratic term in the operation and maintenance cost function of an electrolytic aluminum enterprise.

[0166] The carbon emission cost of electrolytic aluminum enterprises can be expressed as:

[0167]

[0168] In the above formula, , These represent the carbon emissions and carbon emission allowances for the l-th electrolytic cell series during time period t. It is a constant, with units of tCO2 / MWh.

[0169] In summary, the objective function of the optimized operation model for electrolytic aluminum enterprises can be further expressed as follows:

[0170] The constraints of this model are as follows:

[0171] Day-ahead scheduling phase constraints:

[0172] 1) Power Constraint

[0173]

[0174] In the above formula, To be the minimum allowable current to flow into the electrolytic cell, , These are the Lagrange multipliers corresponding to the lower and upper power constraints of the l-th electrolytic cell series during time period t.

[0175] 2) Reserve capacity constraints

[0176]

[0177] In the above formula, , These are the Lagrange multipliers corresponding to the lower and upper limits of the standby capacity constraints for the l-th electrolytic cell series during time period t.

[0178] 3) Temperature constraint

[0179]

[0180]

[0181]

[0182] In the above formula, The electrolyte temperature of the l-th electrolytic cell series during time period t. , These are the minimum and maximum allowable temperatures for the electrolyte, respectively. , , For the Lagrange multipliers corresponding to temperature constraints, , , , , All are constants.

[0183] 4) Daily output constraints

[0184]

[0185] In the above formula, This represents the minimum daily energy consumption of an electrolytic aluminum plant. The Lagrange multiplier corresponding to the daily output constraint.

[0186] Deploy backup associated constraints:

[0187]

[0188] In the above formula, , These are the Lagrange multipliers corresponding to the lower and upper limits of the deployment reserve constraint, respectively.

[0189] Intraday scheduling phase constraints:

[0190] 1) Scene temperature constraints

[0191]

[0192]

[0193]

[0194] In the above formula, The electrolyte temperature is the value of the l-th electrolytic cell series in time period t under scenario s.

[0195] If the backup capacity of the electrolytic aluminum load is less than or equal to the backup capacity it provides, then the power of the electrolytic cell in the scenario will be greater than or equal to the power of the electrolytic cell after considering the backup capacity, and the electrolyte temperature in the scenario will be greater than or equal to the electrolyte temperature after considering the backup capacity. That is, when the temperature constraint and the backup deployment constraint are satisfied, the scenario temperature constraint will naturally be satisfied.

[0196] 2) Daily output constraints in the scenario

[0197] .

[0198] 4. Based on KKT conditions, the two-level optimization scheduling model is transformed into a mixed-integer quadratic programming model, including:

[0199] For the power system optimization dispatch model involving electrolytic aluminum load, its objective function includes This term involves the multiplication of two different decision variables, making it difficult to directly solve the objective function. Therefore, the term is transformed using KKT conditions, thereby making the upper-level objective function convex. After transformation, we obtain... The equivalent expression is:

[0200] .

[0201] The convexized objective function is shown below:

[0202] .

[0203] For the optimization operation model of electrolytic aluminum enterprises, it is a continuous convex optimization problem. First, the lower-level optimization problem is transformed into its KKT conditions using the Lagrange multiplier method. Second, since there is a nonlinear structure in the KKT conditions, the KKT conditions are linearized using the Big M method.

[0204] The KKT conditions for the constraints in this model are as follows:

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[0206]

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[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214] In the above formula, This indicates that the product of x and y is 0.

[0215] The various KKT constraints described above are in the form that the product of the Lagrange multiplier and the constraint is 0, and include a nonlinear term—the product of the Lagrange multiplier and the decision variable. This nonlinear structure can be transformed into mixed linear constraints by introducing auxiliary 0 / 1 integer variables and using the Big M method.

[0216] Taking the KKT condition of power constraint in the optimized operation model of an electrolytic aluminum enterprise as an example, the transformed mixed linear constraint is shown below:

[0217]

[0218]

[0219] In the above formula, The auxiliary 0-1 variable introduced is set to 0 when the current flowing into the electrolytic cell is less than its minimum value; in this case, the Lagrange multiplier... The value is 1 when the current flowing into the electrolytic cell is greater than or equal to its minimum current value. At this point, the Lagrange multiplier... Therefore, it can be concluded that and Since at least one term in the equation is equal to zero, and their product is always zero, the more equivalent the equations before and after the transformation are, the better. It is a sufficiently large constant.

[0220] Similarly, the remaining constraints can also be transformed into similar mixed linear constraints, as follows:

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[0237] In the above formula, , , , , , , , All of these are introduced auxiliary 0-1 variables. This characterizes whether the current flowing into the electrolytic cell is equal to its minimum current value. This indicates whether the current flowing into the electrolytic cell has reached its upper limit. This characterizes whether the reserve capacity provided by electrolytic aluminum has reached its lower limit. This characterizes whether the reserve capacity provided by electrolytic aluminum has reached its upper limit. This indicates whether the daily output of an electrolytic aluminum plant has reached its lower limit. , To characterize whether the electrolyte temperature in the tank has reached the lower limit. This characterizes whether the deployment reserve provided by electrolytic aluminum has reached its lower limit. This characterizes whether the deployment reserve provided by electrolytic aluminum has reached its limit.

[0238] As can be seen from the above equation, apart from some quadratic terms, all other terms in the objective function are linear. Therefore, the two-level optimization problem considering both price guidance and demand response is transformed into a MIQP problem.

[0239] 5. The transformed model is solved using the Gurobi solver to obtain the optimized scheduling results, which include unit scheduling results and electrolytic aluminum load scheduling results.

[0240] Without considering carbon emission reduction policies, Case 1 is a single-layer two-stage stochastic optimization scheduling scheme that does not consider price guidance mechanisms and the participation of electrolytic aluminum in demand response; Case 2 is a single-layer two-stage stochastic optimization scheduling scheme that considers the participation of electrolytic aluminum in demand response but does not consider price mechanisms; and Case 3 is the scheduling scheme of Example 1. The cost calculation results of the three are compared, and the results are shown in Table 3.

[0241] Table 3 Cost Calculation Results for Each Option

[0242]

[0243] It should be noted that the profit per ton of electrolytic aluminum in the single-layer optimization model only affects the revenue of electrolytic aluminum enterprises, and has no impact on the objective function, unit dispatch results, or electrolytic aluminum load dispatch results. As shown in Table 3, Case 2 did not consider a price-guided mechanism, and the power system operator forcibly dispatched electrolytic aluminum loads to participate in demand response. Although the total system operating cost was the lowest, the revenue of electrolytic aluminum enterprises was actually lower than when they did not participate in demand response (Case 1). Case 3 considered a price-guided mechanism, treating electrolytic aluminum enterprises as independent operators, and guiding electrolytic aluminum loads to participate in demand response with dynamic energy compensation prices. In this example, the electrolytic aluminum loads mainly participate in demand response by providing energy response; therefore, the coal consumption cost of thermal power units is the lowest among the three examples, and the corresponding total cost in the first stage is also the lowest. The dispatch results in the second stage are consistent with Case 1. Comparing total operating costs, Case 3 has a higher total cost than Case 2, which does not consider price guidance mechanisms. This is because in Case 2, the power system operator forcibly dispatches electrolytic aluminum loads at a low energy compensation price, ignoring the interests of electrolytic aluminum companies. However, considering price guidance mechanisms, both the operation of the power system and the revenue of electrolytic aluminum companies need to be taken into account, and appropriate prices should be used to guide the dispatch. Therefore, in the two-layer model of Case 3, the revenue of electrolytic aluminum companies is not damaged and is the highest. The corresponding cost is that the total cost will increase, but it is still lower than that of Case 1, which does not consider demand response.

[0244] The electrolytic aluminum load scheduling results in Case 3 are as follows: Figure 2As shown in the figure, the proposed aluminum electrolysis cell heat conduction model effectively considers the impact of current changes on the electrolyte temperature within the cell. Therefore, the electrolyte temperatures of electrolysis cells 1 and 2 do not exceed the lower limit and remain within a reasonable range. During periods 1-4, the electrolyte temperature is highest, resulting in the largest adjustment space for the aluminum electrolysis load. Power system operators need to provide higher energy compensation prices to incentivize the aluminum electrolysis load to provide more response energy. During periods 8-10, the energy compensation price increases slightly because the net load increases rapidly, requiring power system operators to provide energy response from the aluminum electrolysis load to alleviate the ramp-up pressure on thermal power units. During periods 20-24, the aluminum electrolysis load temperature has reached the lower limit, leaving very little room for adjustment, and the corresponding energy compensation price is lowest. Comparing the scheduling results of electrolysis cell series 1 and 2, the power system operator provides a relatively higher energy compensation price to electrolysis cell series 1 and is more inclined to schedule electrolysis cell series 2. This is because the profit per ton of aluminum for electrolysis cell series 1 is higher than that for electrolysis cell series 2, so power system operators need to provide a higher compensation price to ensure that electrolysis cell series 1 has sufficient incentive to provide energy response.

[0245] The quadratic coefficient N in the operation and maintenance cost of electrolytic aluminum load is a crucial parameter, reflecting the sensitivity of the electrolytic aluminum load to power changes, which in turn affects the energy compensation price; therefore, N can also be called the sensitivity coefficient. Table 4 shows the impact of different sensitivity coefficients on the revenue of electrolytic aluminum enterprises and the total system operating cost. As N gradually increases, the operation and maintenance cost required for the same power change in electrolytic aluminum load also gradually increases, meaning that electrolytic aluminum enterprises become increasingly sensitive to power changes. To increase the enthusiasm of electrolytic aluminum loads to participate in demand response, power system operators need to offer higher energy compensation prices. Therefore, the revenue of electrolytic aluminum enterprises gradually increases, and the total system operating cost also increases accordingly.

[0246] Table 4. Impact of Sensitivity Coefficient on the Profitability and Total Operating Cost of Electrolytic Aluminum Enterprises

[0247] .

Claims

1. A power system optimal scheduling method for electrolytic aluminum load participating in demand response, characterized in that: the optimal scheduling method comprises the following steps in sequence: Step A, constructing a double-layer optimal scheduling model, wherein the upper-layer model is a power system optimal scheduling model with electrolytic aluminum load participating, and the lower-layer model is an electrolytic aluminum enterprise optimal operation model, wherein: the power system optimal scheduling model with electrolytic aluminum load participating takes the minimum total operation cost of the power system as an objective function: ； ； ； ； ； ； ； In the above formula, Total number of time periods , , , , These include thermal power units, electrolytic cell series, operating scenarios, load nodes, and the number of wind farms. , Let $t$ be the coal consumption cost and the start-up cost of the i-th thermal power unit during time period $t$. , The prices for providing upper and lower reserves for the i-th thermal power unit are respectively. , These represent the upper and lower reserve capacities provided by the i-th thermal power unit during time period t. For carbon emission costs, , They are respectively the t-th time period Energy compensation and standby capacity compensation obtained from each electrolytic cell series Let be the probability of scenario s. , The energy prices for providing upper and lower reserves to the i-th thermal power unit are respectively. , These refer to the upper and lower backup deployments provided for the i-th thermal power unit during time period t in scenario s. This is compensation for the actual backup deployment in scenario s. , These are the prices for involuntary load shedding and wind curtailment, respectively. , These represent the involuntary load shedding at the d-th node and the wind curtailment at the j-th wind farm, respectively, within time period t under scenario s. For the power system during time period t, the first Energy compensation price for a series of electrolytic cells For the first The voltage of each electrolytic cell series, The maximum allowable current to be supplied to the electrolytic cell, For time period t, the first The current intensity passed through each electrolytic cell series , These are the standby capacity compensation price and the standby deployment compensation price for time period t, respectively. For time period t, the first This series of electrolytic cells provides a reduced current for deployment backup. For the t-th time period under scenario s Each series of electrolytic cells provides a practically reduced current for deploying backup power. For price coefficients, , respectively carbon emission of the i th thermal power unit in the t time period and carbon emission quota, 、 respectively carbon emission intensity of the i th thermal power unit and carbon quota distribution reference value, is the active power of the i th thermal power unit in the t time period, is the length of the time period; the constraint conditions of the power system optimal scheduling model with electrolytic aluminum load participating include: day-ahead scheduling stage constraints: ； ； ； ； ； ； ； In the above formula, Let be the predicted power of the j-th wind farm in time period t. Let be the predicted load power of the d-th node in time period t. For the first The power of each electrolytic cell series, , Let be the minimum and maximum active power output of the i-th thermal power unit, respectively. Let be the operating state variable of the i-th thermal power unit in time period t. , These are the uphill and downhill ramp rates of the i-th thermal power unit, respectively. for The operating status of the i-th thermal power unit in time period This refers to the period during which thermal power units are subject to start-up and shutdown constraints. , Let be the minimum start-up and shutdown times for the i-th thermal power unit, respectively. This is the sensitivity matrix. , , , These are power matrices for thermal power units, wind farms, loads, and aluminum electrolysis cells, respectively. This is the matrix representing the maximum power flow of the line. The allowable value for carbon quota trading volume; intra-day scheduling stage constraints: ； ； ； ； ； In the above formula, is the actual power of the jth wind farm in the t period under the scenario s, is the actual deployment standby of the i th electrolytic cell series in the t period under the scenario s, is the actual load power of the dth node in the t period under the scenario s, is the active power of the ith thermal power unit in the t period under the scenario s, , , , are the power matrices of thermal power units, wind farms, loads and aluminum electrolytic cells under the scenario s respectively, is the wind power curtailment power matrix of the wind farm under the scenario s, is the involuntary load shedding power matrix under the scenario s;​ correlation constraints: ； the electrolytic aluminum enterprise optimal operation model takes the maximum net income of the electrolytic aluminum enterprise as an objective function: ； In the above formula, the profit price coefficient for the production of aluminum products in the first electrolytic cell series, is a constant, is the quadratic term coefficient of the function of the operating and maintenance costs of the aluminum electrolysis plant. the constraint conditions of the electrolytic aluminum enterprise optimal operation model include: day-ahead scheduling stage constraints: ； ； ； ； ； ； In the above formula, to allow the minimum current into the electrolytic cell, , respectively the lower and upper power constraints of the t-th electrolytic cell series, , , respectively the lower and upper reserve capacity constraints of the t-th electrolytic cell series, , the electrolyte temperature of the t-th electrolytic cell series, , respectively the minimum and maximum values allowed for the electrolyte temperature, , , , the Lagrange multiplier corresponding to the temperature constraint, , , , , are all constants, the minimum value of the daily energy consumption of the electrolytic aluminum plant, the Lagrange multiplier corresponding to the daily production constraint; deployment of standby correlation constraints: ； In the above formulae, , are the Lagrange multipliers corresponding to the deployment of lower and upper reserve constraints, respectively; intra-day scheduling stage constraints: ； ； ； ； In the above formula, For the t-th time period under scenario s Electrolyte temperature of each electrolytic cell series; Step B, solving the constructed double-layer optimal scheduling model to obtain an optimal scheduling result, wherein the optimal scheduling result includes unit scheduling results and electrolytic aluminum load scheduling results.

2. The power system optimal scheduling method for electrolytic aluminum load participating in demand response according to claim 1, characterized in that: the step B specifically includes: firstly, converting the double-layer optimal scheduling model into a mixed integer quadratic programming model based on KKT conditions, and then solving the model.

3. The power system optimal scheduling method for electrolytic aluminum load participating in demand response according to claim 2, characterized in that: the conversion of the double-layer optimal scheduling model into a mixed integer quadratic programming model based on KKT conditions includes: For the power system optimal scheduling model with electrolytic aluminum load participation, the KKT condition is used to transform the into the equivalent expression of . ； for the electrolytic aluminum enterprise optimal operation model, the constraint conditions of the model are converted into KKT conditions thereof by using a Lagrange multiplier method, and the KKT conditions are linearized by using a big M method to obtain the following constraint conditions: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； In the above formulae, , , , , , , , , are introduced auxiliary 0-1 variables, characterizes whether the current supplied to the electrolytic cell is equal to its minimum value, characterizes whether the current supplied to the electrolytic cell reaches an upper limit, characterizes whether the reserve capacity provided by the electrolytic aluminum reaches a lower limit, characterizes whether the reserve capacity provided by the electrolytic aluminum reaches an upper limit, characterizes whether the daily production of the electrolytic aluminum plant reaches a lower limit, , characterizes whether the temperature of the electrolyte in the cell reaches a lower limit, characterizes whether the deployment reserve provided by the electrolytic aluminum reaches a lower limit, characterizes whether the deployment reserve provided by the electrolytic aluminum reaches an upper limit, is a sufficiently large constant.

4. The power system optimal dispatch method for electrolytic aluminum load participation demand response according to claim 2, characterized in that: the solving is completed by using a Gurobi solver.

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