Transformer economic evaluation and optimization method

Abstract

The invention discloses an economic evaluation and optimization method for a transformer, and the method achieves the dual optimization of a power transformer in the aspects of economy and technology through the construction of a detailed full-life-cycle cost model and an accurate life loss prediction model, and remarkably improves the economic benefits of a power grid company. According to the method, cost factors such as purchase, operation, maintenance and residual values of the transformer are comprehensively considered, and the service life loss of the transformer under different working conditions is accurately evaluated, so that a transformer use scheme with the minimum cost and the minimum service life loss is formulated. The investment and operation cost of a power grid company can be effectively reduced, the service life of the transformer is prolonged, and the stability and reliability of a power system are enhanced. Meanwhile, the method provides powerful support for a power grid company to formulate a scientific transformer management strategy, helps a decision maker to make a more intelligent choice, and ensures reasonable configuration and effective utilization of transformer resources.

Description

Technical Field

[0001] The present application relates to the technical field of transformer substations, and in particular to a transformer economic evaluation and optimization method. Background Art

[0002] As the core component of substations, power transformers play a vital role in the power system. They are responsible for converting electrical energy from one voltage level to another to meet the needs of different users. As the demand for electricity continues to grow, the load borne by power transformers is also increasing, providing a stable and reliable energy supply for all types of users.

[0003] Transformers generate high temperatures when running under load, which is the main cause of their aging. Long-term high temperature environment will accelerate the degradation of the internal materials of the transformer, which will in turn affect its performance and life. Aging not only leads to higher operation and maintenance costs, but also causes loss of life (LoL). In the most serious cases, it may even cause transformer failure and require replacement of new equipment. In the full life asset management, power grid companies have put forward strict requirements on the technical and economic performance of power equipment. For power transformers, if its relevant indicators are unclear or unreasonable at the economic level, even if it is technically feasible, it may be rejected by the power grid company. This requires us to fully consider both the economic and technical factors when formulating transformer management strategies.

[0004] In addition, the complex structure of power transformers and the large amount of materials used result in relatively high procurement costs. According to rough statistics, power transformers account for more than a quarter of the total cost of a new substation. This increases the investment pressure on power grid companies and also places higher demands on their asset management. In addition to procurement costs, a large amount of money needs to be invested each year in the operation and maintenance of transformers. This includes costs such as regular inspections, repairs, and replacement of parts. These costs will increase further as the transformer ages and reaches its expected lifespan.

[0005] Although some progress has been made in the research of power transformers, there are still the following major shortcomings:

[0006] First, current research often focuses on optimizing the technical performance of transformers, while ignoring the consideration of their economic performance. This results in some technically feasible solutions being abandoned in practical applications because they are not economically viable. Second, no effective economic evaluation model has been proposed based on the failure probability defined by the degree of aggregation. This makes it difficult for power grid companies to make reasonable decisions when conducting economic evaluations on transformers because of the lack of scientific basis.

[0007] In addition, current research fails to fully consider key aging factors when determining life loss and modification cost models. This results in limited practical application of the model and fails to accurately reflect the real condition of the transformer. Summary of the invention

[0008] The embodiment of the present application provides a transformer economic evaluation and optimization method, which can effectively optimize the technical and economic functions of the transformer.

[0009] In order to achieve the above object, the technical solution of the embodiment of the present invention is:

[0010] The embodiment of the present invention provides a transformer economic evaluation and optimization method, including: constructing a transformer life cycle cost model, the cost model includes purchase cost, no-load loss cost, load loss cost, maintenance cost and the residual value of a damaged transformer; constructing a transformer life loss model based on transformer hot spot temperature data and in combination with material aging theory; constructing a multi-objective optimization model based on the cost model and the life loss model, the multi-objective optimization model includes a transformer life loss objective function and a transformer cost objective function; solving the multi-objective optimization model through a preset genetic algorithm to obtain a Pareto optimal set of the multi-objective optimization model; the Pareto optimal set includes an optimal solution set that simultaneously satisfies the minimum life loss and the minimum transformer cost; according to the Pareto optimal set, comprehensively considering the requirements of technical feasibility and economic rationality, formulate and implement an optimization strategy for the transformer use plan.

[0011] In some possible implementations, the transformer life cycle cost model is expressed as:

[0012] LCC=PP+C NLL ×P0+C LL ×P L +CM-CR,

[0013] in, PP is the purchase cost, CM is the maintenance cost (including labor costs, repair costs, etc.), CR is the residual value of the scrapped transformer, M is the number of cycles (years), C NLL is the no-load loss, C LL is the load loss, the no-load loss represents the core loss, and the load loss represents the winding loss, which is proportional to the square of the load rate K.

[0014] In some possible implementations, a transformer life loss model is constructed based on transformer hot spot temperature data and combined with material aging theory, including:

[0015] Determine the hot spot temperature of the transformer. The hot spot temperature is expressed as:

[0016]

[0017] Among them, θ h is the hot spot temperature, θ o is the top oil temperature, θ a is the top oil temperature, θ a is the ambient temperature, Δθ oi is the temperature rise of the top oil temperature during ambient startup, Δθ or is the top oil temperature rise temperature at rated loss in the stable state, x is the exponential function relationship between the total loss and the top oil (in the oil tank) temperature rise, y is the exponential function relationship between the current and the winding temperature, k 11 , k 21 , k 22 is the thermal model constant, H is the hot spot factor, g r is the gradient of the average winding to the average oil temperature at rated current, τ w is the winding time constant, τ0 is the oil time constant;

[0018] The transformer aging rate is determined based on the hot spot temperature. The aging rate is defined based on the hot spot temperature as:

[0019]

[0020] Among them, V θ is the relative aging rate within the time interval. Humidity and oxygen have a significant effect on the aging rate. The aging rate in the presence of moisture and oxygen is expressed as:

[0021]

[0022] Among them, V m is the aging rate in the presence of moisture and oxygen;

[0023] According to V θ and V m , calculate the relative aging rate, the relative aging rate is expressed as:

[0024]

[0025] In the relative aging rate formula, the exponent r represents the rated condition, and the life loss model is expressed as follows for the time period including F:

[0026]

[0027] In some possible implementations, the constraints of the multi-objective optimization model include: the total load of all substations is the same before and after the optimization, and the load of the transformer must not exceed its capacity.

[0028] In some possible implementations, when constructing the transformer life cycle cost model, the transformer life cycle cost model is also improved by considering the failure probability of the transformer, the actual expected life span, and the impact of inflation and interest rates on the cost of replacing the old transformer with a new transformer. The improved transformer life cycle cost model is expressed as:

[0029]

[0030] in,

[0031] MLCC is the improved full life cycle cost, D is the number of cycles for cost update, and EL is the actual expected life of the transformer.

[0032] In some possible implementations, the failure probability and actual expected life of the transformer are determined based on the degree of polymerization of the transformer insulation paper;

[0033] The actual expected life of the transformer is expressed as:

[0034]

[0035] Among them, DP start is the initial degree of polymerization, DP end is the degree of polymerization at the end of transformer life;

[0036] The transformer failure probability is expressed as:

[0037]

[0038] In some possible implementations, the method also includes comparing transformer operating data and economic indicators before and after optimization, evaluating the actual effect of the optimization scheme, and continuously improving the optimization strategy based on the evaluation results.

[0039] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:

[0040] The transformer economic evaluation and optimization method provided by the embodiment of the present invention realizes the dual optimization of power transformers at the economic and technical levels by constructing a detailed full life cycle cost model and an accurate life loss prediction model, thereby significantly improving the economic benefits of the power grid company. The method not only comprehensively considers cost factors such as the purchase, operation, maintenance and residual value of the transformer, but also accurately evaluates the life loss of the transformer under different working conditions, thereby formulating a transformer use plan with the lowest cost and the lowest life loss. It can not only effectively reduce the investment and operating costs of the power grid company, extend the service life of the transformer, but also enhance the stability and reliability of the power system. At the same time, the method provides strong support for the power grid company to formulate a scientific transformer management strategy, helps decision makers make more wise choices, and ensures the rational allocation and effective use of transformer resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention, the accompanying drawings required for use in the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying any creative work.

[0042] Figure 1 A schematic flow chart of an embodiment of a transformer economic evaluation and optimization method provided for the implementation of the present invention;

[0043] Figure 2 A schematic diagram of a multi-objective optimization framework structure in an embodiment of the present invention;

[0044] Figure 3 It is a schematic diagram of the flow chart of the NSGA-II algorithm in an embodiment of the present invention;

[0045] Figure 4 is a schematic diagram of the structure of the power transmission network architecture in an embodiment of the present invention;

[0046] Figure 5 Schematic diagram of the NSGA-II Pareto front of F1(K) and F2(K) in an embodiment of the present invention;

[0047] Figure 6 Schematic diagram of SLL and SLC values ​​in scheme A in an embodiment of the present invention;

[0048] Figure 7 Schematic diagram of cost values ​​in different scenarios in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0050] In the relevant description of this embodiment, the terms "including, containing, having" and the like are open terms and are generally understood to include but not be limited to; the term "at least one" is generally understood to mean one or more, where "plurality" refers to two or more; the term "at least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items, for example, "at least one of a, b or c", or "at least one of a, b and c", can all represent: a, b, c, ab (i.e., a and b), ac, bc, or abc, where a, b, c can be single or multiple, respectively; the symbol "A / B" is used to describe the selection relationship of associated objects, generally indicating an "or" relationship before and after.

[0051] In the following description of the present embodiment, the terms used in the embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The singular forms "a" and "the" used in the embodiments of the present application and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings.

[0052] Those skilled in the art should understand that in the following description of the embodiments of the present application, the order of serial numbers does not mean the order of execution, some or all of the steps can be executed in parallel or sequentially, and the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0053] Those skilled in the art will appreciate that the numerical ranges in the embodiments of the present application are to be construed as also specifically disclosing each intermediate value between the upper and lower limits of the scope. Each smaller range between the intermediate value in any stated value or stated range and any other stated value or intermediate value in the range is also included in the present invention. The upper and lower limits of these smaller ranges may be independently included or excluded in the scope.

[0054] Unless otherwise specified, the technical / scientific terms used herein have the same meanings as those generally understood by those skilled in the art to which this application belongs. Although this application only describes preferred methods and materials, any methods and materials similar or equivalent to these may also be used in the implementation or testing of this application. All documents mentioned in this specification are incorporated by reference to disclose and describe methods and / or materials related to the documents. In the event of a conflict with any incorporated document, the content of this specification shall prevail.

[0055] In order to illustrate the technical solution of the present invention, specific embodiments are provided below for illustration.

[0056] As the core component of substations, power transformers play a vital role in the power system. They are responsible for converting electrical energy from one voltage level to another to meet the needs of different users. As the demand for electricity continues to grow, the load borne by power transformers is also increasing, providing a stable and reliable energy supply for all types of users.

[0057] Transformers generate high temperatures when running under load, which is the main cause of their aging. Long-term high temperature environment will accelerate the degradation of the internal materials of the transformer, which will in turn affect its performance and life. Aging not only leads to higher operation and maintenance costs, but also causes loss of life (LoL). In the most serious cases, it may even cause transformer failure and require replacement of new equipment. In the full life asset management, power grid companies have put forward strict requirements on the technical and economic performance of power equipment. For power transformers, if its relevant indicators are unclear or unreasonable at the economic level, even if it is technically feasible, it may be rejected by the power grid company. This requires us to fully consider both the economic and technical factors when formulating transformer management strategies.

[0058] In addition, the complex structure of power transformers and the large amount of materials used result in relatively high procurement costs. According to rough statistics, power transformers account for more than a quarter of the total cost of a new substation. This increases the investment pressure on power grid companies and also places higher demands on their asset management. In addition to procurement costs, a large amount of money needs to be invested each year in the operation and maintenance of transformers. This includes costs such as regular inspections, repairs, and replacement of parts. These costs will increase further as the transformer ages and reaches its expected lifespan.

[0059] Although some progress has been made in the research of power transformers, there are still the following major shortcomings:

[0060] First, current research often focuses on optimizing the technical performance of transformers, while ignoring the consideration of their economic performance. This results in some technically feasible solutions being abandoned in practical applications because they are not economically viable. Second, no effective economic evaluation model has been proposed based on the failure probability defined by the degree of aggregation. This makes it difficult for power grid companies to make reasonable decisions when conducting economic evaluations on transformers because of the lack of scientific basis.

[0061] In addition, current research fails to fully consider key aging factors when determining life loss and modification cost models. This results in limited practical application of the model and fails to accurately reflect the real condition of the transformer.

[0062] In summary, power transformers play an important role in the power system, but they also face high temperature aging, economic and technical evaluation challenges, and high costs. Current research still has many deficiencies and needs further improvement and optimization. Therefore, formulating effective methods to rationally utilize and manage power transformers is of great significance to improving the stability and economy of the power system.

[0063] Based on this, an embodiment of the present invention provides a transformer economic evaluation and optimization method, which can effectively optimize the technical and economic functions of the transformer.

[0064] Figure 1 A schematic diagram of an embodiment of a transformer economic evaluation and optimization method provided for the implementation of the present invention is shown in FIG. Figure 1 As shown, the above transformer economic evaluation and optimization method may include:

[0065] S101, constructing a transformer life cycle cost model, which includes purchase cost, no-load loss cost, load loss cost, maintenance cost, and residual value of a damaged transformer;

[0066] It should be noted that the purpose of constructing a transformer life cycle cost model is to comprehensively and accurately evaluate all cost factors involved in the transformer during its entire service life. This cost model not only covers the direct cost of the initial purchase of the transformer, that is, the purchase cost, but also deeply considers the various indirect costs generated during the operation of the transformer.

[0067] Specifically, the purchase cost is the direct cost of the transformer when it is first purchased, including the price of the equipment itself, transportation costs, installation costs, and related taxes. No-load loss cost: The transformer will still consume a certain amount of electrical energy when it is no-load (that is, when it is not connected to the load). This part of the loss is converted into heat energy dissipation, and the resulting electricity cost is the no-load loss cost. It reflects the efficiency of the transformer design and is one of the important indicators for evaluating the economic efficiency of the transformer. Load loss cost: When the transformer is connected to the load, the electrical energy lost due to the resistance heat generated by the current passing through the winding is also converted into heat energy, and the corresponding electricity cost constitutes the load loss cost. Load loss is closely related to factors such as the load rate, winding resistance, and core structure of the transformer. Maintenance cost: includes regular inspection, testing, cleaning, maintenance, and replacement of aging parts. These costs gradually increase with the increase in the service life of the transformer, and are an indispensable part of ensuring the long-term stable operation of the transformer. The residual value of the damaged transformer: When the transformer is replaced due to failure or reaching the limit of its service life, its residual value (i.e., residual value) should be deducted from the full life cycle cost. The residual value depends on many factors, including the type, condition, market demand and recycling channels of the transformer.

[0068] By comprehensively considering the above costs, the transformer life cycle cost model constructed in step S101 can provide a comprehensive and accurate cost assessment framework, providing solid data support for subsequent transformer selection, economic analysis and optimization decisions.

[0069] For example, the transformer life cycle cost model of the above-mentioned costs can be expressed by the following formula (1):

[0070] LCC=PP+C NLL ×P0+C LL ×P L +CM-CR (1)

[0071] Among them, PP is the purchase cost, CM is the maintenance cost (including labor costs, repair costs, etc.), CR is the residual value of the scrapped transformer, M is the number of cycles (years), C NLL is the no-load loss, C LL is the load loss, the no-load loss represents the core loss, and the load loss represents the winding loss, which is proportional to the square of the load rate K.

[0072] The no-load loss can be expressed by the following formula (2):

[0073]

[0074] The load loss can be expressed by the following formula (3):

[0075]

[0076] S102, constructing a transformer life loss model based on transformer hot spot temperature data and combined with material aging theory;

[0077] As is understandable, when the load on the transformer increases, the temperature of different parts of the active part (especially the windings) will increase. This is because the resistance heating generated when the current passes through the windings leads to temperature increase. As long as the transformer is under load, thermal tension will always exist in the active part, especially in the windings, and accelerate the aging process of the winding insulation material. The aging rate describes the rate at which a material ages over time. In the case of transformers, the aging rate is usually determined based on the aging process of the winding insulation paper. Since the heat distribution in the winding is not uniform, some points will have higher temperatures than others. These points with the highest temperatures are called hot spots. The hot spot temperature is a key factor in assessing the loss of transformer life. When building a transformer loss of life model, the hot spot temperature is usually used as the basis for calculation. This is because the hot spot temperature reflects the worst thermal stress conditions inside the transformer and has a decisive influence on the aging rate of the insulation material.

[0078] Specifically, step S102 first collects hot spot temperature data of the transformer in actual operation. Hot spot temperature refers to the temperature of the hottest point inside the transformer, which is usually determined by multiple factors, including load current, ambient temperature, cooling conditions, and the design and structure of the transformer itself. Excessive hot spot temperature will accelerate the aging process of the insulation material inside the transformer, resulting in performance degradation and shortened life.

[0079] In some embodiments, the hot spot temperature of the transformer can be expressed by the following formula (4):

[0080]

[0081] Among them, θ h is the hot spot temperature, θ o is the top oil temperature, θ a is the top oil temperature, θ a is the ambient temperature, Δθ oi is the temperature rise of the top oil temperature during ambient startup, Δθ or is the top oil temperature rise temperature at rated loss in the stable state, x is the exponential function relationship between the total loss and the top oil (in the oil tank) temperature rise, y is the exponential function relationship between the current and the winding temperature, k 11 , k 21 , k 22 is the thermal model constant, H is the hot spot factor, g r is the gradient of the average winding to the average oil temperature at rated current, τ w is the winding time constant, τ0 is the oil time constant;

[0082] Next, the material aging theory is used to analyze the impact of these hot spot temperature data on the life of the transformer. Material aging is a complex physical and chemical process involving the gradual change of material properties, such as the reduction of insulation strength and the weakening of mechanical strength. By deeply studying the aging rate and mechanism of materials at different temperatures, a mathematical relationship between material aging and temperature can be established.

[0083] Exemplarily, the transformer aging rate is determined according to the hot spot temperature. The aging rate can be defined according to the hot spot temperature as shown in the following formula (5):

[0084]

[0085] Among them, V θ is the relative aging rate within the time interval. Humidity and oxygen have a significant effect on the aging rate. The aging rate in the presence of moisture and oxygen can be expressed by the following formula (6):

[0086]

[0087] Among them, V m is the aging rate in the presence of moisture and oxygen; according to the above formula (5) and V θ and V m , calculate the relative aging rate, which can be expressed by the following formula (7):

[0088]

[0089] In the relative aging rate formula (7), the index r represents the rated condition. In the time period including F, the life loss model can be expressed by the following formula (8):

[0090]

[0091] In some embodiments, the cost model constructed by the above formula (1) can be applied to different research periods, but does not take into account the actual life expectancy and failure probability. Assuming that the transformer can work normally within a given time, the present invention can improve the LCC of the transformer group, and the improvements include: (1) considering the failure probability and actual life expectancy of the power transformer. That is, using load and aging factors such as load level, temperature, humidity, etc., calculate the actual life expectancy of the transformer and incorporate the result into the cost model. (2) It is proposed that when the research period is greater than the expected life of some transformers, it must be considered that after the expected life ends, the old transformer will be replaced with a new transformer, and due to the influence of inflation and interest rates, the different components of the cost model will be updated in the replacement year.

[0092] In some embodiments, the improved transformer life cycle cost model is expressed by the following formula (9):

[0093]

[0094] in,

[0095] MLCC is the improved full life cycle cost, D is the number of cycles for cost update, and EL is the actual expected life of the transformer.

[0096] In some embodiments, the expected life of the transformer is determined based on the degree of polymerization of the insulation paper. The degree of polymerization (DP) is the average number of monomer units in the cellulose macromolecule, and the degree of polymerization of unbleached softwood kraft paper before processing is between 1100 and 1400. To calculate the expected life of the transformer, the following formula (10) can be used:

[0097]

[0098] Among them, DP start is the initial degree of polymerization, DP end is the degree of polymerization at the end of transformer life.

[0099] In some embodiments, the failure of the transformer depends on the degree of aggregation. The failure probability is represented by different models, and the transformer failure probability can be expressed by the following formula (11):

[0100]

[0101] According to the above formula (11), if the DP value of the transformer is less than 200, the transformer will fail. This is because when the DP is less than 200, the paper insulation will become brittle and cannot withstand the short-circuit stress. By taking 200 as the DP end , the expected life of the transformer can be calculated. This fact shows the relationship between expected life and failure probability. It should also be noted that the failure probability determined based on DP is greatly affected by aging factors such as temperature, humidity and oxygen.

[0102] S103, constructing a multi-objective optimization model based on the cost model and the life loss model, the multi-objective optimization model including a transformer life loss objective function and a transformer cost objective function;

[0103] Among them, the transformer life loss objective function focuses on how to minimize the life loss of the transformer due to thermal stress during its entire service life. The transformer cost objective function focuses on how to minimize the full life cycle cost of the transformer.

[0104] Understandably, when constructing a multi-objective optimization model, it is necessary to balance the relationship between these two objective functions. Because in practical applications, there is usually a trade-off: reducing life loss may require increasing costs (for example, by improving cooling efficiency or using more advanced insulation materials), while reducing costs may come at the expense of a certain life. Therefore, the goal of the multi-objective optimization model is to find a balance point that achieves the best combination of economy and technology while meeting technical performance requirements.

[0105] See also Figure 2 As shown, the two objective functions of the multi-objective optimization model constructed by the present invention include the LoL function F1(K) and the transformer cost function F2(K). Wherein, both F1(K) and F2(K) are defined as functions of K. During the optimization process, K will change continuously to achieve the purpose of optimizing the two functions simultaneously.

[0106] Using the hot spot temperature, F1(K) is formed according to the above formula (4), where it is assumed that all parameters related to the hot spot temperature calculation are constants except K. The above formula (4) can be rewritten as the following formula (12):

[0107] θ h =45.47+46.3×K 1.6 +20.3×K 1.3 (12)

[0108] The LoL function of a transformer group with Q substations for one year can be expressed by the following formula (13):

[0109]

[0110] In addition, in order to calculate F2(K), the parameters of the above formula (9) can be defined as constants except K, and the above formula (9) can be rewritten as the following formula (14):

[0111]

[0112] In some embodiments, the constraints of the multi-objective optimization model include the following formula (15) and formula (16):

[0113]

[0114] K tq ×L t ≤C tq (16)

[0115] Among them, formula (15) stipulates that the total load of all substations before and after optimization is the same, and formula (16) indicates that the load of the transformer shall not exceed its capacity.

[0116] S104, solving the multi-objective optimization model by using a preset genetic algorithm to obtain a Pareto optimal set of the multi-objective optimization model; the Pareto optimal set includes an optimal solution set that simultaneously satisfies the minimum life loss and the minimum transformer cost;

[0117] In the embodiment of the present invention, a genetic algorithm is used to solve the multi-objective optimization model. A genetic algorithm is an optimization algorithm that simulates natural selection and genetic mechanisms. It simulates operations such as selection, crossover and mutation in the biological evolution process, continuously iterates and updates individuals in the population, and gradually approaches the optimal solution.

[0118] In some embodiments, the preset genetic algorithm can be any existing genetic algorithm, and can be selected based on the effectiveness in the actual calculation process. For example, the preset genetic algorithm can be a second-generation non-dominated sorting genetic algorithm (NSGA-II) to optimize the objective function, or it can also be a strength Pareto evolutionary algorithm (SPEA).

[0119] Exemplarily, the present invention uses NSGA-II as an optimization algorithm to find the Pareto optimal set for the objective function. The algorithm is used to find a set of equally sophisticated solutions close to the Pareto optimal frontier. By implementing the crowding distance, the diversity of Pareto optimal solutions is guaranteed. By allowing the parent and child populations to participate in the competition, the convergence of the optimization can be improved. The overall solution process of NSGA-II can be found in Figure 3 The specific parameters and values ​​of the NSGA-II algorithm are shown in Table 1 below.

[0120] Table 1:

[0121] parameter Parameter Value Maximum number of iterations 300 Population size 100 Cross ratio 0.7 Mutation rate 0.02 Mutation ratio 0.4

[0122] Through Figure 3 As well as the parameters and calculation process shown in Table 1, the constructed multi-objective optimization model is solved, and the obtained Pareto optimal set contains a set of optimal solutions that simultaneously meet the minimum life loss and the minimum transformer cost. These solutions are mutually non-dominated, that is, there is no situation where one solution is better than another solution in all objectives. Afterwards, the most appropriate solution can be selected from the Pareto optimal set according to actual needs.

[0123] S105, based on the Pareto optimal set, comprehensively consider the requirements of technical feasibility and economic rationality, formulate and implement the optimization strategy of transformer use plan.

[0124] It can be understood that through the above step S104, the Pareto optimal set of the multi-objective optimization model can be obtained. This set contains multiple solutions that achieve the best balance between life loss and transformer cost, and each solution represents a possible transformer usage plan. These solutions are technically feasible, but there may be differences in economics and other practical factors.

[0125] In some embodiments, in order to formulate an optimization strategy for the use of transformers, multiple requirements can be considered comprehensively. For example, technical feasibility, that is, the selected solution must meet the operating requirements of the power system, including voltage level, capacity, reliability and other aspects. The second is economic rationality, that is, the selected solution should reduce the life cycle cost as much as possible and improve economic benefits while ensuring technical performance. When formulating the optimization strategy, other practical factors need to be considered, such as the availability of the transformer, maintenance costs, environmental protection requirements, etc. These factors may have an important impact on the final choice. Therefore, solutions that meet the requirements of technical feasibility and economic rationality can be screened out from the Pareto optimal set, and the advantages and disadvantages of these solutions can be further analyzed. Through comparative analysis, one or more optimal transformer use solutions can be determined.

[0126] In some embodiments, the above method may further include: comparing transformer operating data and economic indicators before and after optimization, evaluating the actual effect of the optimization solution, and continuously improving the optimization strategy based on the evaluation results.

[0127] It is understandable that after the optimization strategy is implemented, the comparison of transformer operation data and economic indicators before and after optimization is intended to quantify the actual benefits brought by the optimization strategy and ensure that the obtained optimization strategy can be transformed into actual results. Operation data can include but are not limited to transformer load rate, loss, failure rate and maintenance frequency, while economic indicators can cover key parameters such as life cycle cost, energy efficiency ratio, and return on investment.

[0128] In some embodiments, in order to make an accurate comparison, it is necessary to ensure that the same measurement methods and evaluation criteria are used before and after the optimization so as to be able to fairly and objectively reflect the effect of the optimization strategy. Professional monitoring equipment and data analysis tools can be used to ensure the accuracy and comparability of the data. After obtaining sufficient operating data and economic indicators, statistical and economic methods will be used to conduct in-depth analysis of these data to evaluate the actual effect of the optimization strategy. It can include calculating key indicators such as cost savings, energy efficiency improvement ratio, and failure rate reduction, as well as analyzing the impact of these indicators on the overall operating efficiency and economic benefits of the power system. The evaluation results can help understand the performance of the optimization strategy in actual applications and possible deficiencies. Based on these feedbacks, the optimization strategy can be continuously improved to further enhance its effect. Including adjusting the operating parameters of the transformer, optimizing the maintenance plan, introducing more advanced energy-saving technologies and other measures.

[0129] The transformer economic evaluation and optimization method provided in the embodiment of the present invention realizes the dual optimization of power transformers at the economic and technical levels by constructing a detailed full life cycle cost model and an accurate life loss prediction model, thereby significantly improving the economic benefits of the power grid company. The method not only comprehensively considers cost factors such as the purchase, operation, maintenance and residual value of the transformer, but also accurately evaluates the life loss of the transformer under different working conditions, thereby formulating a transformer use plan with the lowest cost and the lowest life loss. It can not only effectively reduce the investment and operating costs of the power grid company, extend the service life of the transformer, but also enhance the stability and reliability of the power system. At the same time, the method provides strong support for the power grid company to formulate a scientific transformer management strategy, helps decision makers make more wise choices, and ensures the rational allocation and effective use of transformer resources.

[0130] The method of the present invention is described below with reference to a specific embodiment.

[0131] For example, the present invention is based on Figure 4 The case study shown is optimized for a real transmission network containing 15 substations. For the convenience of calculation, the following assumptions are made in this paper: (1) the paper moisture and oxygen levels of all transformers are 1.6% and 5000ppm respectively; (2) the total load value is 4100kVA; (3) the load factor of each transformer is assumed to remain unchanged during the study period; (4) the ambient temperature of all substations is 25℃; (5) the purchase price of all transformers is the same; (6) for substations containing parallel transformers, the total load of the transformers is used in the calculation. It should be added that the calculation can be performed without these assumptions, but this does not change the conclusions and contributions of this paper, but only makes the calculation unnecessarily complicated.

[0132] Solution A: Ignore the expected life and failure probability of the transformer and only study the operation of the system for one year. In order to show the diversity of results and better understand the Pareto frontier (such as Figure 5 As shown in Table 2, the embodiment of the present invention constructs two sets of scenarios, namely, scenario 1 and scenario 2. In scenario 1, the minimum value of SLL (sum of life losses) is obtained. In scenario 2, the minimum value of SLC (sum of total life cycle costs) is obtained. The minimization results of F1(K) and F2(K) are shown in Table 2. The detailed results of scenario 1 and scenario 2 are shown in Table 3 and Table 4, respectively. The result schematic diagram is shown in Figure 6 shown.

[0133] Table 2:

[0134]

[0135] Table 3:

[0136]

[0137]

[0138] Table 4:

[0139]

[0140] See Table 2 above and Figure 6 It can be seen that (1) in various scenarios, the model constructed by the present invention can reduce SLC and SLL. (2) In scenario 1, SLL dropped sharply from 29.553 years to 16.7116 years. On the other hand, SLC dropped from 18.8824 million yuan to 18.6159 million yuan. It can be seen that load management not only extends the life of the transformer, but also saves 266,500 yuan. (3) In scenario 2, STC is reduced from 18.8824 million yuan to 18.5654 million yuan, which saves 317,000 yuan, while SLL is reduced from 29.553 years to 21.47 years. Comparing scenario 1 and scenario 2, the SLL of scenario 1 is better, while the SLC of scenario 2 is better. It should be noted that some substations (such as substation No. 2) may have higher LoL values ​​or LCC values ​​after optimization because the objective function is defined in a way to reduce the SLC and SLL of the entire system, not just a single substation.

[0141] Option B: Consider the expected service life and failure probability of each transformer. To verify the efficiency of this method, the inventors studied the cost of the transformer over a 20-year period (the normal expected life of a transformer is about 20 years). When oxygen and moisture aging factors are taken into account, the expected life may be much shorter because these factors accelerate the aging process.

[0142] In conditions of high humidity or oxygen content, the expected 20-year life of the transformer may be shortened to 5 or 6 years. At the same time, these aging factors together with high load factors will lead to a shortened life. As shown in the previous table, the expected life of the transformer varies with the load factor. Therefore, during the study period of this invention, some transformers may fail earlier than other equipment, thereby incurring more costs to the power grid company. In order to implement this solution, the expected life is first calculated according to formula (16), and then the economic value is solved according to the above formula (9). The results of scenario 1 in scheme B are shown in Table 5, and the results of scenario 2 in scheme B are shown in Table 6.

[0143] Table 5:

[0144]

[0145] Table 6:

[0146]

[0147] In some embodiments, in order to accurately illustrate the difference between considering and ignoring the transformer failure probability and expected life, the cost of a 20-year cycle is calculated without considering the failure probability and expected life. The results are shown in Table 7 and Figure 7 shown.

[0148] Table 7:

[0149]

[0150]

[0151] See Table 5, Table 6, Table 7 and Figure 7 , we can draw the following conclusions:

[0152] (1) The model constructed by the present invention can reduce costs in various scenarios. For example, in scenario 1, the cost is reduced from 178.68 million yuan to 149.85 million yuan. In scenario 2, the cost is also reduced from 178.68 million yuan to 160.25 million yuan. When considering the fault-free probability analysis state, the cost of scenario 1 and scenario 2 is reduced from 134.23 million yuan to 129.46 million yuan and 127.99 million yuan respectively.

[0153] (2) Comparing MLCC with LCC before optimization, the cost of MLCC is higher. This means that MLCC makes the economic calculation of transformers more realistic because it takes into account the role of expected life and failure probability, which may bring more costs to the power grid company. The reason is that when the expected life is considered according to the degree of aggregation, the transformer may fail earlier than in normal conditions. For example, without considering the probability of failure, the total cost before optimization is 134.23 million yuan, while when considering the probability of failure, the total cost is 178.68 million yuan, a difference of 44.45 million yuan between the two cases. Even when comparing the results after optimization, the STC and MSTC in Scenario 1 and Scenario 2 differ by 20.39 million yuan and 32.26 million yuan, respectively.

[0154] (3) The total cost of Scenario 1 is lower (149.85 million yuan) compared to Scenario 2 (160.25 million yuan), while the opposite is true for Scenario A. This shows that if the probability of failure is taken into account, the total cost of Scenario 1 will eventually be lower than that of Scenario 2, because the lower SLL of Scenario 1 naturally indicates a longer life and lower procurement cost. This situation is another disadvantage of the method that does not consider the probability of failure in Scenario A: although the SLL of Scenario 1 is lower, the cost is higher. In other words, the longer the expected life, the lower the cost. On the other hand, in Scenario B, it can be seen that the cost of MLCC in Scenario 1 is lower than that in Scenario 2. This result is consistent with the view that the lower the SLL, the lower the cost.

[0155] In addition, it should be noted that the main part of the transformer cost is the purchase price, so if the transformer fails frequently, most of the cost will be used to purchase a new transformer. Therefore, it is reasonable to extend the life of the transformer to reduce its cost. It should be added that the above differences are for a regional transmission network consisting of 15 substations. For a grid company including a large number of substations, these numbers will be quite huge, so the method proposed in the present invention can effectively optimize the technical and economic functions of the transformer.

[0156] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other. Each embodiment focuses on the differences from other embodiments.

[0157] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit the present application. Although the present application has been described in detail with reference to the aforementioned embodiments, a person of ordinary skill in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present application.

Claims

1. A transformer economic evaluation and optimization method, characterized in that: include: Constructing a transformer life cycle cost model, the cost model including purchase cost, no-load loss cost, load loss cost, maintenance cost and residual value of a damaged transformer; Based on the transformer hot spot temperature data and combined with the material aging theory, a transformer life loss model is constructed; Constructing a multi-objective optimization model based on the cost model and the life loss model, wherein the multi-objective optimization model includes a transformer life loss objective function and a transformer cost objective function; Solving the multi-objective optimization model by a preset genetic algorithm to obtain a Pareto optimal set of the multi-objective optimization model; the Pareto optimal set includes an optimal solution set that simultaneously satisfies the minimum life loss and the minimum transformer cost; According to the Pareto optimal set, the optimization strategy of transformer use plan is formulated and implemented by comprehensively considering the technical feasibility and economic rationality requirements.

2. The method according to claim 1, characterized in that The transformer life cycle cost model is expressed as: LCC=PP+C NLL ×P0+C LL ×P L +CM-CR, in, PP is the purchase cost, CM is the maintenance cost (including labor costs, repair costs, etc.), CR is the residual value of the scrapped transformer, M is the number of cycles (years), C NLL is the no-load loss, C LL is the load loss, the no-load loss represents the core loss, and the load loss represents the winding loss, which is proportional to the square of the load rate K.

3. The method according to claim 2, characterized in that The transformer life loss model is constructed based on the transformer hot spot temperature data and combined with the material aging theory, including: Determine the transformer hot spot temperature, which is expressed as: Among them, θ h is the hot spot temperature, θ o is the top oil temperature, θ a is the top oil temperature, θ a is the ambient temperature, Δθ oi is the temperature rise of the top oil temperature during ambient startup, Δθ or is the top oil temperature rise temperature at rated loss in the stable state, x is the exponential function relationship between the total loss and the top oil (in the oil tank) temperature rise, y is the exponential function relationship between the current and the winding temperature, k 11 , k 21 , k 22 is the thermal model constant, H is the hot spot factor, g r is the gradient of the average winding to the average oil temperature at rated current, τ w is the winding time constant, τ0 is the oil time constant; The transformer aging rate is determined based on the hot spot temperature. The aging rate is defined based on the hot spot temperature as: Among them, V θ is the relative aging rate within the time interval. Humidity and oxygen have a significant effect on the aging rate. The aging rate in the presence of moisture and oxygen is expressed as: Among them, V m is the aging rate in the presence of moisture and oxygen; According to V θ and V m , calculate the relative aging rate, the relative aging rate is expressed as: In the relative aging rate formula, the exponent r represents the rated condition, and the life loss model is expressed as follows for the time period including F:

4. The method according to claim 3, characterized in that The constraints of the multi-objective optimization model include: the total load of all substations is the same before and after the optimization, and the load of the transformer shall not exceed its capacity.

5. The method according to claim 4, characterized in that When constructing the transformer life cycle cost model, the transformer life cycle cost model is improved by considering the failure probability of the transformer, the actual expected life span, and the impact of inflation and interest rates on the cost of replacing the old transformer with a new transformer. The improved transformer life cycle cost model is expressed as: in, MLCC is the improved full life cycle cost, D is the number of cycles for cost update, and EL is the actual expected life of the transformer.

6. The method according to claim 5, characterized in that The failure probability and actual expected life of the transformer is determined based on the degree of polymerization of the transformer insulation paper; The actual expected life of the transformer is expressed as: Among them, DP start is the initial degree of polymerization, DP end is the degree of polymerization at the end of transformer life; The transformer failure probability is expressed as:

7. The method according to any one of claims 1 to 6, characterized in that: The method also includes comparing transformer operating data and economic indicators before and after optimization, evaluating the actual effect of the optimization scheme, and continuously improving the optimization strategy based on the evaluation results.

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