Power system scheduling method considering large-scale advanced compressed air energy storage nonlinear variable working condition characteristics

Abstract

The invention discloses an electric power system scheduling method considering large-scale advanced compressed air energy storage nonlinear variable working condition characteristics, and belongs to the field of electric power system optimization scheduling. When a day-ahead economical efficiency scheduling model of an electric power system is established, key parameter change characteristics of A-CAES under variable working conditions are comprehensively considered; the change characteristics and the coupling relation of parameters such as the environment temperature, the isentropic efficiency, the compression ratio, the expansion ratio, the temperature of the air storage chamber and the temperature of the hot water tank in the A-CAES operation process are covered, so that the formulated scheduling plan better conforms to the actual operation conditions of the A-CAES, and the safety and the economical efficiency are both achieved; the defect that the existing linear fixed parameter model and piecewise linearization model are excessively optimistic and exaggerated for the A-CAES performance is overcome; and furthermore, rapid and accurate convergence of optimization is realized by adopting an iterative solution method, and efficient and accurate solution of the scheduling model is realized.

Description

Technical Field

[0001] The present invention belongs to the field of power system optimization and dispatching, and more specifically, relates to a power system dispatching method taking into account the nonlinear variable operating condition characteristics of large-scale advanced compressed air energy storage. Background Art

[0002] Promoting the large-scale development of clean energy such as wind and light is a key measure to achieve carbon neutrality and build a modern energy system. However, its inherent uncertainty characteristics pose severe challenges to the safe and stable operation of the power system. Against this background, advanced compressed air energy storage (A-CAES) came into being and is highly anticipated due to its advantages such as low investment, environmental friendliness, and flexible site selection.

[0003] A-CAES is a mechanical energy storage system that uses compressed air as the working medium. When charging, the compressor works to compress and store the air, while using circulating water and other heat carriers to absorb and store the compression heat. When discharging, high-pressure air is released to drive the expander and the generator, while the heat-absorbed circulating water is used to heat the air to improve the air's ability to do work. During the entire working process, A-CAES realizes the mutual conversion between electrical energy and the potential energy of compressed air and the thermal energy of circulating water.

[0004] In order to fully realize the value of large-scale energy throughput of A-CAES, accurate mathematical models and reasonable power plans are key. The existing dispatch models of power systems containing A-CAES usually adopt linear fixed parameter models or piecewise linearization models. However, in A-CAES, most state variables will deteriorate with the decrease of energy storage power, and their best working state is the rated state, at which the power is the rated value. Taking the isentropic compression efficiency of the compression condition as an example, when A-CAES works at the rated compression power, the isentropic compression efficiency usually reaches the maximum value. As the power decreases, the isentropic compression efficiency will decrease, and the change of isentropic compression efficiency with power is nonlinear. Therefore, in order to simplify the calculation difficulty in dispatch research, some studies assume that the isentropic compression efficiency is always the rated value and does not change with power. The model constructed in this way is a linear fixed parameter model; some studies also consider the change characteristics of the isentropic compression efficiency with power, but fit it to a piecewise linear function, and most of them are 2 to 3 segments, the fitting effect is very rough, and the model constructed in this way is a piecewise linearization model. The above models all more or less exaggerate the isentropic compression efficiency of A-CAES and underestimate the impact of power reduction on the deterioration of A-CAES working efficiency. They have the shortcomings of being overly optimistic and exaggerated about the performance of A-CAES, which leads to the formulated scheduling plan not meeting the safety regulations during the actual operation of A-CAES. If the scheduling instruction is sent to A-CAES, there is a risk of exceeding the pressure limit of the A-CAES gas storage chamber or the quality of the hot water tank. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a power system scheduling method taking into account the nonlinear variable operating condition characteristics of large-scale advanced compressed air energy storage. The method comprehensively covers the changing characteristics of parameters such as ambient temperature, isentropic efficiency, compression ratio, expansion ratio, air storage chamber and hot water tank temperature during the operation of A-CAES, and can make the formulated scheduling plan more in line with the actual operating conditions of A-CAES.

[0006] To achieve the above object, according to a first aspect of the present invention, a power system dispatching method considering the nonlinear variable operating condition characteristics of large-scale advanced compressed air energy storage is provided, comprising:

[0007] With the goal of minimizing the total operating cost of the power system, a day-ahead economic dispatch model of the power system considering the variable operating characteristics of A-CAES is established, and the model is solved under preset constraints to obtain the optimal dispatching scheme of the generator sets and A-CAES in the power system;

[0008] The preset constraints include: generator set constraints, power system constraints and A-CAES constraints; the A-CAES constraints include the state variable operation boundary constraints of A-CAES under various working conditions and the analytical expressions of the state variables;

[0009] The power system is a thermal power generation system, a new energy power generation system or a hydropower generation system.

[0010] According to a second aspect of the present invention, there is provided an electronic device, comprising: a computer-readable storage medium and a processor;

[0011] The computer-readable storage medium is used to store executable instructions;

[0012] The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0013] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to cause a processor to execute the method as described in the first aspect.

[0014] According to a fourth aspect of the present invention, there is provided a computer program product, comprising a computer program or instructions, wherein when the computer program or instructions are executed by a processor, the method according to the first aspect is implemented.

[0015] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0016] 1. The method provided by the present invention comprehensively considers the changing characteristics of key parameters of A-CAES under variable operating conditions when establishing a day-ahead economic dispatch model for the power system, including the changing characteristics and coupling relationships of parameters such as ambient temperature, isentropic efficiency, compression ratio, expansion ratio, gas storage chamber and hot water tank temperature during the operation of A-CAES, so that the formulated dispatch plan is more in line with the actual operating conditions of A-CAES, and has both safety and economy, overcoming the shortcomings of existing linear fixed parameter models and piecewise linearization models that are overly optimistic and exaggerated about the performance of A-CAES.

[0017] 2. Furthermore, in view of the nonlinearity of the dispatching model, the method provided by the present invention proposes an iterative solution method with both accuracy and efficiency for solving the day-ahead economic dispatching problem of the power system. The application of this iterative solution method enables efficient and accurate solution even for the day-ahead economic dispatching model containing a large number of nonlinear factors, which fully meets the timeliness requirements of day-ahead dispatching; it is superior to the traditional piecewise linearization solution method in terms of solution efficiency and optimization performance; in addition, since the nonlinear model of A-CAES is not directly embedded in the dispatching optimization process, the solution efficiency of this iterative solution method is almost unaffected by the number of A-CAES and the complexity of the A-CAES model. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A-CAES structure diagram provided for an embodiment of the present invention;

[0019] Figure 2 The isentropic compression efficiency and isentropic expansion efficiency curves provided by the embodiments of the present invention;

[0020] Figure 3 A system topology diagram provided for an embodiment of the present invention;

[0021] Figure 4 The wind power, load power and ambient temperature prediction curves provided by the embodiment of the present invention;

[0022] Figure 5 A-CAES power schematic diagram of Case 1 and Case 2 provided in an embodiment of the present invention;

[0023] Figure 6 A schematic diagram of the pressure of the A-CAES gas storage chamber of Case 1 and Case 2 provided in an embodiment of the present invention;

[0024] Figure 7 Schematic diagram of the quality of the A-CAES hot water tank of Case 1 and Case 2 provided in the embodiments of the present invention. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0026] An embodiment of the present invention provides a power system dispatching method considering the nonlinear variable operating condition characteristics of large-scale advanced compressed air energy storage, including:

[0027] With the goal of minimizing the total operating cost of the power system, a day-ahead economic dispatch model of the power system considering the variable operating characteristics of A-CAES is established, and the model is solved under preset constraints to obtain the optimal dispatching scheme of the generator sets and A-CAES in the power system;

[0028] The preset constraints include: generator set constraints, power system constraints and A-CAES constraints; the A-CAES constraints include the state variable operation boundary constraints of A-CAES under various working conditions and the analytical expressions of the state variables;

[0029] The power system is a thermal power generation system, a new energy (wind power, photovoltaic) power generation system or a hydropower generation system.

[0030] Firstly, a nonlinear thermodynamic mathematical model of A-CAES is established, which covers the changing characteristics of key parameters such as ambient temperature, isentropic efficiency, final stage compression ratio, final stage expansion ratio, gas storage chamber temperature, and hot water tank temperature. That is, the model includes the analytical expressions of the state variables of A-CAES, and the nonlinear thermodynamic mathematical model of A-CAES is fully considered when establishing the day-ahead economic dispatch model of the power system, so as to obtain a power system dispatch scheme that takes into account the changing characteristics of key parameters of A-CAES under variable operating conditions.

[0031] A-CAES structure Figure 1 As shown, the variables are marked in red font; P C , P G are compression and power generation respectively; p atm 、T atm are ambient pressure and temperature respectively; N C 、N G are compression and expansion stages respectively; η C , η G are the isentropic efficiencies of compression and expansion, respectively; are the inlet working medium temperatures of the i-th stage compressor and the j-th stage expander respectively; π C.i is the compression ratio of the i-th stage compressor; π G.j is the expansion ratio of the j-th expander; ε, p loss are the efficiency coefficient and pressure loss rate of the heat exchanger respectively; m st 、p st , T st 、T ex are the working fluid mass, pressure, inlet temperature, internal temperature, and wall temperature of the gas storage chamber respectively; is the outlet heat medium temperature of the i-th stage heat exchanger in the compression section; are the working fluid flow rates of compression and power generation respectively; T hw 、T cw are the water temperatures of the hot water tank and the cold water tank respectively; m hw For the quality of hot water tank.

[0032] The modeling assumptions of the A-CAES nonlinear thermal mathematical model are as follows:

[0033] The model will be constructed from three aspects: compression condition, power generation condition and shutdown condition. During the modeling process, the following assumptions are considered:

[0034] (1) Air is used as the working fluid and is assumed to be an ideal gas;

[0035] (2) During the compression phase, the isentropic efficiency of all compressors is the same, and during the expansion phase, the isentropic efficiency of all expanders is the same;

[0036] (3) The wall temperature of the air storage chamber is constant;

[0037] (4) Circulating water is used as the heat carrier, which does not undergo phase change, all heat exchangers have the same efficiency coefficient, and there is no heat loss in the heat exchanger and hot water tank;

[0038] (5) During the expansion phase, the circulating water will pass through the radiator to return to normal temperature before returning to the cold water tank. Therefore, it is assumed that the temperature of the cold water tank is the ambient temperature;

[0039] (6) Throughout the day, the ambient temperature is predictable and the ambient pressure is constant.

[0040] The A-CAES nonlinear thermal mathematical model of the compression condition is as follows:

[0041] Under compression conditions, A-CAES consumes electrical energy to compress atmospheric pressure air into high-pressure air and store it in the air storage chamber. At the same time, circulating water is pumped out from the cold water tank, absorbs the heat generated by the compression process, and then flows into the hot water tank. After compression is completed, the electrical energy is converted into the pressure potential energy of the air and the thermal energy of the circulating water.

[0042] (1) Compression power

[0043]

[0044] In the formula, c p is the constant pressure specific heat capacity of air; γ is the specific heat ratio of air.

[0045] (2) Final stage compression ratio

[0046]

[0047] (3) Isentropic compression efficiency

[0048] The isentropic compression efficiency can be fitted as a function of the compression power, which shows Figure 2 The changing trend in the left figure.

[0049] (4) Compressor inlet working fluid temperature

[0050]

[0051]

[0052] (5) Inlet working fluid temperature of the gas storage chamber

[0053]

[0054] (6) Heat exchanger outlet heat medium temperature

[0055]

[0056] (7) Hot water tank temperature

[0057]

[0058] In the formula, the subscript "t" is the time subscript; Δt is the duration between adjacent moments; c w is the specific heat capacity of water.

[0059] (8) Hot water tank quality

[0060]

[0061] (9) Gas storage chamber pressure

[0062]

[0063] Where R is the gas constant of air; V st is the volume of the air storage chamber; α and β are the natural convection heat transfer coefficient and forced convection heat transfer coefficient between the air in the air storage chamber and the wall, respectively.

[0064] (10) Gas storage chamber quality

[0065]

[0066] (11) Gas storage chamber temperature

[0067] T st =p st V st / (m st R)

[0068] The A-CAES nonlinear thermal mathematical model for power generation conditions is as follows:

[0069] Under power generation conditions, A-CAES releases high-pressure air in the air storage chamber to drive the turbine to rotate, thereby driving the generator to work. At the same time, circulating water is pumped out from the hot water tank, releasing the compression heat absorbed previously to heat the air, improving the air's ability to do work, and then flows through the radiator and returns to the cold water tank. After power generation is completed, the pressure potential energy of the air and the thermal energy of the circulating water are converted into electrical energy.

[0070] (1) Power generation

[0071]

[0072] (2) Final stage expansion ratio

[0073]

[0074] (3) Isentropic expansion efficiency

[0075] The isentropic expansion efficiency can be fitted as a function of power generation, which shows Figure 2 The changing trend is shown in the right figure.

[0076] (4) Inlet working fluid temperature of the expander

[0077]

[0078]

[0079] (5) Hot water tank temperature

[0080] T hw.t+1 =T hw.t

[0081] (6) Hot water tank quality

[0082]

[0083] (7) Gas storage chamber pressure

[0084]

[0085] (8) Gas storage chamber quality

[0086]

[0087] (9) Gas storage chamber temperature

[0088] T st =p st V st / (m st R)

[0089] The A-CAES nonlinear thermal mathematical model of shutdown conditions is as follows:

[0090] Under shutdown conditions, the mass of the A-CAES gas storage chamber, the temperature and mass of the hot water tank remain unchanged. Since the gas in the gas storage chamber exchanges heat with the walls of the gas storage chamber, the pressure and temperature of the gas storage chamber change.

[0091] (1) Hot water tank temperature

[0092] T hw.t+1 =T hw.t

[0093] (2) Hot water tank quality

[0094] m hw.t+1 =m hw.t

[0095] (3) Gas storage chamber quality

[0096] m st.t+1 =m st.t

[0097] (4) Gas storage chamber pressure

[0098] p st.t+1 =p st.t -α(γ-1)(T st.t -T ex )Δt

[0099] (5) Gas storage chamber temperature

[0100] T st =p st V st / (m st R)

[0101] Then, a day-ahead economic dispatch model of a power system containing an A-CAES variable operating condition model (ie, an A-CAES nonlinear thermal mathematical model) is constructed, wherein the power system is a thermal power generation system, a new energy power generation system, or a hydropower generation system.

[0102] Taking the power system as a thermal power generation system as an example, the day-ahead economic dispatch model of the power system containing A-CAES is as follows:

[0103] (1) Objective function

[0104]

[0105]

[0106]

[0107]

[0108] In the formula, are the operation and start-up and shutdown costs of thermal power units; C WF is the penalty cost for wind curtailment; T is the total number of dispatch periods; N TPU is the number of thermal power units; a TPU.k 、b TPU.k is the operating cost coefficient of the kth thermal power unit; is the output of the kth thermal power unit in period t; is the operating status of the kth thermal power unit in period t, 0 for shutdown and 1 for startup; c TPU.k is the single start-up and shutdown cost of the kth thermal power unit; N WF is the number of wind farms; c pen Penalty cost factor for wind curtailment; are the predicted output and dispatched output of the lth wind farm in period t respectively.

[0109] (2) A-CAES Constraints

[0110] A-CAES constraints include the analytical expressions of state variables for each operating condition and operating boundary constraints. The former has been introduced in the A-CAES nonlinear thermal mathematical model and will not be repeated here. The latter includes operating state constraints, power boundary constraints, air storage chamber pressure boundary constraints, hot water tank mass constraints, and compression / power generation condition duration constraints, as follows:

[0111] u C.t +u G.t ≤1

[0112] u C.t P C.min ≤P C.t ≤u C.t P C.max

[0113] u G.t P G.min ≤P G.t ≤u G.t P G.max

[0114] p st.min ≤p st.t ≤p st.max ,t=2,3,...,T

[0115] p st.ini ≤p st.T+1 ≤p st.max

[0116] m hw.min ≤m hw.t ≤m hw.max ,t=2,3,...,T

[0117] m hw.ini ≤m hw.T+1 ≤m hw.max

[0118]

[0119]

[0120] In the formula, u C.t 、u G.t are the compression and power generation states of A-CAES in period t, respectively. When in compression condition, the two are 1 and 0 respectively, and when in power generation condition, the two are 0 and 1 respectively; P C.max , P C.min are the maximum and minimum values ​​of compression power respectively; P G.max , P G.min are the maximum and minimum values ​​of the generated power respectively; p st.max 、p st.min 、p st.iniare the maximum, minimum and initial values ​​of the air storage chamber pressure respectively; m hw.max 、m hw.min 、m hw.ini are the maximum, minimum and initial values ​​of the hot water tank mass respectively; T C , T G They are the maximum continuous working time for compression and power generation conditions respectively.

[0121] (3) Other constraints

[0122] In addition to A-CAES constraints, the day-ahead economic dispatch model also includes thermal power unit constraints (thermal power unit power constraints, wind power constraints, ramp rate constraints, start and stop time constraints), power system constraints (flow constraints, line power constraints, power balance constraints, reserve constraints, etc.). These constraints are very mature and basic, and can be referred to in relevant materials, so they will not be repeated here.

[0123] It can be understood that since the power system includes A-CAES, the power balance constraint and the reserve constraint should both consider the output of the generator set and A-CAES at the same time. Taking the power system as a thermal power generation system as an example, the power balance constraint is:

[0124]

[0125] Where P L.t Forecast power for loads.

[0126] The positive spare constraints are:

[0127]

[0128] In the formula, is the rated output of the thermal power unit, E L.t are the power prediction errors of wind power and load respectively.

[0129] The negative spare constraint is:

[0130]

[0131] In the formula, It is the minimum technical output of thermal power units.

[0132] When solving the above scheduling model, existing methods can be used to solve it, such as the most common piecewise linearization solution method, or artificial intelligence algorithms such as particle swarm optimization algorithm.

[0133] Considering that A-CAES has complex variable-operating-condition electric-thermal-pneumatic coupling characteristics, its optimal scheduling is a nonlinear scheduling problem. There are two main existing methods for solving nonlinear scheduling problems, namely, piecewise linearization method and heuristic algorithm. Among them, the piecewise linearization method fits the nonlinear factors (such as continuous variable product, nonlinear function, etc.) of the A-CAES model in the original scheduling problem into piecewise functions, which reduces the difficulty of solving, but exaggerates the performance of A-CAES in scheduling, and will formulate a scheduling plan that does not meet the actual operation safety requirements of A-CAES; the heuristic algorithm can be summarized as a local directional traversal method. This method does not have rigorous analytical optimality and has problems such as local optimality and large solution time overhead. Based on this, as a further optimization of the present invention, the day-ahead economic scheduling model of the power system considering the variable operating characteristics of A-CAES is solved under preset constraints, including:

[0134] S1, let t = 1;

[0135] S2, under the target constraint, solves the power system day-ahead economic dispatch model to obtain the compressed power of period t and power generation Substitute the analytical expression of the state variable to obtain the air storage chamber pressure at time t+1 that satisfies the analytical expression: and hot water tank quality

[0136] The target constraint is obtained by replacing the analytical expression of the state variables of A-CAES under each working condition in the preset constraint with the linear A-CAES constraint set of the state variables;

[0137] S3, determine whether t is less than T, if so, go to S4, otherwise go to S6;

[0138] S4, determine whether or If any of the following conditions exists, then the corresponding constraint or After the target constraint is reached, return to S1, otherwise enter S5;

[0139] S5, set t = t + 1, return to S2, until t = T;

[0140] S6, determine whether or If any of the following conditions exists, then the corresponding constraint

[0141] After adding to the target constraint, return to S1, otherwise end, exit the iteration and output the solution result of the day-ahead economic dispatch model of the power system under the target constraint in S2.

[0142] Specifically, the embodiment of the present invention preferably adopts the following method to iteratively solve the above scheduling model:

[0143] The above original scheduling problem is divided into two parts: the main problem and the sub-problem. The main problem is still a scheduling problem, but the nonlinear A-CAES constraint set in the constraint conditions (that is, the analytical expression of the state variables of each working condition) is replaced by a more idealized linear A-CAES constraint set. The sub-problem is a verification problem, which is used to verify whether the scheduling instructions of the main problem to A-CAES can meet its operating requirements. The main problem and the sub-problem are interactively iterated to achieve the solution of the day-ahead economic scheduling model. That is, solving the main problem is to replace the analytical expression of the state variables of A-CAES under each working condition in the preset constraints with the linear A-CAES constraint set of state variables and then solve the scheduling model; solving the sub-problem is to solve the value of the state variables of A-CAES that conforms to the analytical expression according to the analytical expression of the state variables of A-CAES under each working condition.

[0144] (1) Main question

[0145] Compared with the original scheduling problem, the main problem deletes the analytical expression of the A-CAES nonlinear thermal mathematical model in the original scheduling problem and adds the following linear constraints:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156] In the formula, are the pressure change rates of the air storage chamber in period t under compression and power generation conditions respectively; They are the maximum and minimum values ​​of the pressure change rate of the air storage chamber under compression conditions; They are the maximum and minimum values ​​of the pressure change rate of the gas storage chamber under power generation conditions; are the mass change rates of the hot water tank in period t under compression and power generation conditions respectively; They are the maximum and minimum values ​​of the mass change rate of the hot water tank under compression conditions; They are respectively the maximum and minimum values ​​of the mass change rate of the hot water tank under power generation conditions; M is a sufficiently large positive number.

[0157] Boundaries of rate of change of pressure or mass They are all fitted as a linear function of power, that is, the upper and lower limit boundary functions of the pressure change rate of the air storage chamber and the upper and lower limit boundary functions of the mass change rate of the hot water tank. The fitting method is:

[0158] (1) Compression conditions

[0159] Set the initial pressure of the air storage chamber to the minimum value, the initial temperature to the air storage chamber wall temperature, and perform compression at a given power and ambient temperature until the air storage chamber pressure reaches the maximum value. By taking the derivative of the air storage chamber pressure and the hot water tank mass in this process, we can obtain the air storage chamber pressure change rate and the hot water tank mass change rate during the entire compression process. Find their maximum and minimum values, which are the upper and lower limits of the air storage chamber pressure change rate and the hot water tank mass change rate under the current power conditions. Change the compression power and repeat the above process to obtain the upper and lower limits of the air storage chamber pressure change rate and the hot water tank mass change rate as a function of power changes.

[0160] (2) Power generation conditions

[0161] Set the initial pressure of the air storage chamber to the maximum value, expand and generate electricity at a given power, air storage chamber temperature, and hot water tank temperature until the air storage chamber pressure reaches the minimum value. By taking the derivative of the air storage chamber pressure and the hot water tank mass in this process, we can get the air storage chamber pressure change rate and the hot water tank mass change rate in the entire power generation process. Find their maximum and minimum values, which are the upper and lower limits of the air storage chamber pressure change rate and the hot water tank mass change rate under the current power conditions. Change the power generation and repeat the above process to get the upper and lower limits of the air storage chamber pressure change rate and the hot water tank mass change rate as a function of the power change.

[0162] In the master problem, the rate of change of pressure or mass It can be freely selected within the boundary range, is a schedulable decision variable, and is only affected by power. In fact, these change rates are state variables and are affected by many factors including power. For example, the rate of change of the air storage chamber pressure under compression conditions is a function of compression power, air storage chamber pressure, and ambient temperature. The main problem's treatment of the pressure or mass change rate causes the performance of A-CAES to be overestimated during the scheduling process. In addition, the main problem ignores the heat exchange between the air in the air storage chamber and the wall. This also reflects the over-optimism of the performance of A-CAES. Therefore, after the main problem is solved, the sub-problem needs to be further verified to see whether the scheduling result exceeds the operating limit of A-CAES.

[0163] It is necessary to make the A-CAES model in the main problem more idealized, which leaves room for the iterative convergence process. If the A-CAES model of the main problem is more conservative, the scheduling result of the main problem in the sub-problem verification must meet the operation requirements of A-CAES. However, this scheduling result is not the global optimal solution because the large-scale energy throughput of A-CAES is not fully utilized. Therefore, a more conservative A-CAES model is not advisable in the main problem.

[0164] (2) Sub-questions

[0165] Since the idealized A-CAES model of the main problem performs better than the original scheduling problem, the A-CAES charging and discharging power plan obtained by the main problem may be too optimistic and aggressive, causing the A-CAES gas storage chamber pressure or hot water tank mass to exceed the safety boundary during actual operation. Therefore, it is necessary to further verify the sub-problem before the power command is issued to ensure the operation safety of A-CAES. The verification steps of the sub-problem are as follows:

[0166] ①t is 1.

[0167] ②The main question will be Pass to subproblem. and are respectively the compression power and generation power in period t obtained from the solution of the main problem. and They are respectively the pressure of the air storage chamber and the mass of the hot water tank at period t+1 obtained from the solution of the main problem.

[0168] ③ Sub-question will be and Substitute into the A-CAES nonlinear thermal mathematical model in step A and calculate according to the analytical formula and and They are respectively the pressure of the air storage chamber and the mass of the hot water tank at period t+1 obtained from the solutions of the subproblems.

[0169] ④ If t < T, execute this step; otherwise, skip it.

[0170] If it indicates that A-CAES is overcharged, and the overcharge amount is To prevent the pressure in the gas storage chamber from exceeding the upper boundary during the (t + 1)-th period, in the next iteration, the master problem needs to add the following constraints:

[0171]

[0172] If occurs, it can also be processed according to the above method. In the next iteration, the constraints that the master problem needs to add are respectively:

[0173]

[0174]

[0175]

[0176] ⑤ If t = T, execute this step; otherwise, skip it.

[0177] For the convenience of use on the next scheduling day, at time T + 1, the lower boundary of the pressure in the gas storage chamber should be p st.ini instead of p st.min , and the lower boundary of the mass of the hot water tank is m hw.ini instead of m hw.min . Therefore, if occurs, in the next iteration, the constraints that the master problem needs to add are respectively:

[0178]

[0179]

[0180]

[0181]

[0182] ⑥ This step needs to be executed by choosing one of the following three cases:

[0183] [Case 1] If in ④ or ⑤, the sub-problem finds that the pressure in the gas storage chamber or the mass of the hot water tank exceeds the boundary at time t + 1, stop the verification. After adding the relevant constraints, start the next iteration.

[0184] [Case 2] If the pressure in the gas storage chamber and the mass of the hot water tank do not exceed the boundary at time t + 1 and t < T, let t = t + 1, and return to step ② to continue the verification.

[0185] [Case 3] If the air storage chamber pressure and the hot water tank mass do not exceed the boundary at time T+1, it means that the air storage chamber pressure and the hot water tank mass in all time periods meet the upper and lower limit constraints. At this point, the algorithm has converged, exits the iteration, and outputs the solution to the main problem.

[0186] The model solution results are as follows:

[0187] 1) Thermal power units: start / stop status, planned output

[0188] 2) Wind farm: planned output

[0189] 3) A-CAES: compression state, power generation state, compression power, power generation power, gas storage chamber pressure, hot water tank quality in each scheduling period

[0190] 4) Others: Total system cost

[0191] The method provided by the embodiment of the present invention is further illustrated by taking a specific example as follows.

[0192] This embodiment is developed around the power system day-ahead economic dispatch strategy considering the variable operating condition characteristics of large-scale A-CAES as described in the present invention, and the specific steps are as follows:

[0193] Step A: The model of this embodiment is constructed as follows.

[0194] (1) Taking into account the operation constraints of thermal power units, A-CAES, wind farms, and system operation constraints, a scheduling model is constructed with the minimum sum of the operation cost of thermal power units, the start-up and shutdown cost of thermal power units, and the penalty cost for wind power abandonment as the optimization objective.

[0195] (2) In the above model, the specific mathematical expressions are detailed in the A-CAES nonlinear thermal mathematical model and the day-ahead economic dispatch model of the power system containing A-CAES described in steps A and B of the invention content.

[0196] Step B: The parameters of this embodiment are set as follows.

[0197] (1) Example operating environment: The example is tested on a computer with a CPU model of Intel Xeon Gold 2.70 GHz and a memory of 256 GB. The scheduling model is solved by calling Yalmip through MATLAB R2022a, and Gurobi9.1 is selected as the solver.

[0198] (2) Optimization time scale of the embodiment: the total scheduling duration is 1 day, and the unit scheduling duration is 15 minutes.

[0199] (3) Implementation example topology diagram: Figure 3 shown.

[0200] (4) Example A-CAES parameters: as shown in Table 1.

[0201] Table 1

[0202]

[0203] (5) Parameters of thermal power plant in the embodiment: as shown in Table 2.

[0204] Table 2

[0205]

[0206] (6) Prediction curves of wind power, load power and ambient temperature in the embodiment: Figure 4 shown.

[0207] Step C: Optimize and solve this embodiment and analyze the results.

[0208] In order to verify the effectiveness of the day-ahead economic dispatch strategy for the power system considering the variable operating conditions of A-CAES and its rapid solution method proposed in the present invention, four groups of implementation cases are set: Case 1 contains one A-CAES and is solved by the iterative method proposed in the present invention; Case 2 contains one A-CAES and is solved by the traditional piecewise linearization method; Case 3 contains two A-CAES and is solved by the iterative method proposed in the present invention; Case 4 contains three A-CAES and is solved by the iterative method proposed in the present invention.

[0209] First, the results of Case 1 and Case 2 are compared to analyze the advantages of the iterative solution method. Figure 5 As shown, the pressure in the air storage chamber is Figure 6 As shown, the quality of the hot water tank is Figure 7 The total cost is shown in Table 3.

[0210] Table 3

[0211]

[0212] As shown in Table 3, the solution time of Case 2 is as long as 40,000 seconds, which is much longer than the 412 seconds of Case 1, and it does not meet the timeliness requirements of day-ahead economic scheduling at all. The fundamental reason why Case 2 is slow to solve is that when applying the piecewise linearization method to the thermal mathematical model of A-CAES, a large number of binary auxiliary variables are introduced, which makes the scheduling model too large and the difficulty of solving it increases sharply. From the perspective of total cost, it seems that Case 2 has a slight advantage. But in fact, this is an erroneous result obtained by Case 2 by overestimating the performance of A-CAES.

[0213] Depend on Figure 5It can be seen that, thanks to the powerful optimization capability of the iterative solution method, the energy throughput scale and operating time of A-CAES in Case 1 far exceed those in Case 2, which enables A-CAES to more thoroughly and fully exert the value of its energy storage.

[0214] Depend on Figure 6 It can be seen that the pressure of the gas storage chamber in Case 1 is always within the specified boundary. In contrast, in Case 2, the piecewise linearization method overestimates the performance of A-CAES. Specifically, under the same compression power, the pressure increase of "DispatchResults" is greater than that of "ActualResults"; under the same power generation power, the pressure consumption of "DispatchResults" is smaller than that of "ActualResults". After a day of error accumulation, when "DispatchResults" believes that the pressure at the first dispatch time of the next day meets the boundary constraint, "ActualResults" is already far lower than the initial pressure. This shows that using the piecewise linearization method to solve the dispatch model will result in an overly optimistic A-CAES power plan, and A-CAES cannot support the implementation of the plan during actual operation.

[0215] Figure 7 With Figure 6 The same rule applies. Since the quality of the hot water tank does not exceed the limit in Case 1 and Case 2, we will not repeat it here.

[0216] Secondly, the results of Case 1, Case 3, and Case 4 are compared to explore the influence of the scheduling problem scale on the solving efficiency of the proposed method. The results of the three cases are shown in Table 4.

[0217] Table 4

[0218]

[0219] As can be seen from Table 4, as the number of A-CAES in the scheduling model increases, the solution time is always maintained within 10 minutes. This is because, in the proposed method, the nonlinear model of A-CAES appears in the sub-problem verification process. This process is a simple formula calculation and does not involve optimization solution. It can be predicted that even if more A-CAES are connected to the system, the solution time will not increase excessively. If the existing piecewise linearization method is used, the number of binary auxiliary variables will increase sharply with the increase in the number of A-CAES, resulting in a slower solution of the scheduling model or even an inability to solve it.

[0220] An embodiment of the present invention provides an electronic device, including: a computer-readable storage medium and a processor;

[0221] The computer-readable storage medium is used to store executable instructions;

[0222] The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the method described in any of the above embodiments.

[0223] An embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method described in any of the above embodiments.

[0224] The embodiment of the present invention provides a computer program product, including a computer program or an instruction, which implements the method described in any of the above embodiments when executed by a processor. It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A power system dispatching method considering the nonlinear variable operating condition characteristics of large-scale advanced compressed air energy storage, characterized in that: include: With the goal of minimizing the total operating cost of the power system, a day-ahead economic dispatch model of the power system considering the variable operating characteristics of A-CAES is established, and the model is solved under preset constraints to obtain the optimal dispatching scheme of the generator sets and A-CAES in the power system; The preset constraints include: generator set constraints, power system constraints and A-CAES constraints; the A-CAES constraints include the state variable operation boundary constraints of A-CAES under various working conditions and the analytical expressions of the state variables; The power system is a thermal power generation system, a new energy power generation system or a hydropower generation system.

2. The method according to claim 1, characterized in that Solving the day-ahead economic dispatch model of the power system under preset constraints includes: S1, let t = 1; S2, under the target constraint, solves the power system day-ahead economic dispatch model to obtain the compressed power of period t and power generation Substitute the analytical expression of the state variable to obtain the air storage chamber pressure at time t+1 that satisfies the analytical expression: and hot water tank quality The target constraint is obtained by replacing the analytical expression of the state variables of A-CAES under each working condition in the preset constraint with the linear A-CAES constraint set of the state variables; S3, determine whether t is less than T, if so, go to S4, otherwise go to S6; S4, determine whether or If any of the following conditions exists, then the corresponding constraint or After the target constraint is reached, return to S1, otherwise enter S5; S5, set t = t + 1, return to S2, until t = T; S6, determine whether or If any of the following conditions exists, then the corresponding constraint After adding to the target constraint, return to S1, otherwise end; in, and are respectively the gas storage chamber pressure and hot water tank mass at time t+1 obtained by solving the day-ahead economic dispatch model of the power system under the target constraint, and p st.max 、p st.min 、p st.ini are the maximum, minimum and initial values ​​of the air storage chamber pressure, respectively. are respectively the compressed power of the T period obtained by solving the day-ahead economic dispatch model of the power system under the target constraint and power generation Substitute the analytical expression of the state variables to calculate the gas storage chamber pressure and the hot water tank mass in the T+1 period that satisfy the analytical expression.

3. The method according to claim 2, characterized in that The linear A-CAES constraint set of the state variables is: in, are the pressure change rates of the air storage chamber in period t under compression and power generation conditions respectively; They are the maximum and minimum values ​​of the pressure change rate of the air storage chamber under compression conditions; They are the maximum and minimum values ​​of the pressure change rate of the gas storage chamber under power generation conditions; are the mass change rates of the hot water tank in period t under compression and power generation conditions respectively; They are the maximum and minimum values ​​of the mass change rate of the hot water tank under compression conditions; are the maximum and minimum values ​​of the mass change rate of the hot water tank under power generation conditions; p st.t 、p st.t+1 are the pressure of the air storage chamber at time t and t+1, m hw.t+1 is the mass of the hot water tank in period t+1; M is a positive number.

4. The method according to claim 3, characterized in that All are fitted as a linear function of power, and the fitting process is: Under the compression condition, the initial pressure of the air storage chamber is set to the minimum value, and the initial temperature is the wall temperature of the air storage chamber. Compression is performed at a given power and ambient temperature until the air storage chamber pressure reaches the maximum value. The air storage chamber pressure and the mass of the hot water tank in this process are differentiated to obtain the air storage chamber pressure change rate and the hot water tank mass change rate in the entire compression process. The maximum and minimum values ​​are obtained, which are the upper and lower limits of the air storage chamber pressure change rate and the hot water tank mass change rate under the current power conditions. The compression power is changed, and the above process is repeated to obtain the upper and lower limits of the air storage chamber pressure change rate and the hot water tank mass change rate as a function of the power change. Under power generation conditions, the initial pressure of the gas storage chamber is set to the maximum value, and expansion power generation is carried out at given power, gas storage chamber temperature, and hot water tank temperature until the gas storage chamber pressure reaches the minimum value; the gas storage chamber pressure and the hot water tank mass in this process are differentiated to obtain the gas storage chamber pressure change rate and the hot water tank mass change rate of the entire power generation process, and their maximum and minimum values ​​are obtained, which are the upper and lower limits of the gas storage chamber pressure change rate and the hot water tank mass change rate under the current power conditions; the power generation power is changed, and the above process is repeated to obtain the upper and lower limits of the gas storage chamber pressure change rate and the hot water tank mass change rate as a function of power changes.

5. The method according to claim 1, characterized in that Under compression conditions, the state variables of the A-CAES include compression power, final stage compression ratio, isentropic compression efficiency, compressor inlet working medium temperature, air storage chamber inlet working medium temperature, heat exchanger outlet heat carrier medium temperature, hot water tank temperature and quality, air storage chamber pressure, quality and temperature; Under power generation conditions, the state variables of the A-CAES include power generation, final stage compression ratio, isentropic expansion efficiency, inlet working medium temperature of the expander, temperature and mass of the hot water tank, and pressure, mass and temperature of the gas storage chamber; Under shutdown conditions, the state variables of the A-CAES include the temperature and mass of the hot water tank, and the pressure, mass and temperature of the gas storage chamber.

6. An electronic device, characterized in that: include: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the method according to any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method according to any one of claims 1 to 5.

8. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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