Oil-immersed transformer allowable current prediction method based on environment temperature and load

Abstract

The invention discloses an oil-immersed transformer allowable current prediction method based on environment temperature and load, and the method comprises the steps: selecting an IEEE thermal model of an oil-immersed transformer, deducing an environment temperature and transformer load prediction model through employing a quantile regression model, and then carrying out the prediction of the allowable current of the oil-immersed transformer. According to the method, the probability that the allowable current is higher than a predicted dynamic rated value and the probability indexes of influence factors such as corresponding expected load reduction are introduced, and the allowable current of the transformer is predicted through the predicted distribution of the dynamic rated value of the transformer. Therefore, the transformer can run beyond the rated nameplate value in a short time without losing the rated service life or generating a fault, so that the running reliability of the transformer is improved.

Description

Technical Field

[0001] The invention belongs to the field of primary design of transformers for power transmission and distribution network equipment, and in particular relates to a method for predicting allowable current of an oil-immersed transformer based on ambient temperature and load. Background Art

[0002] In the framework of Smart Grid (SG), the optimal planning and operation of transmission and distribution systems is one of the main means to cope with the growing demand of electricity customers and not waste renewable power generation. As one of the most important basic equipment in the transmission and distribution system, the overload operation of the transformer leads to temperature rise, resulting in loss of rated life and even failure. The operating temperature mainly depends on the transformer load and heat dissipation capacity, while the transformer load and external temperature are inherently random. It is urgent to develop a method that can combine ambient temperature and transformer load to predict the allowable current of the transformer.

[0003] Under favorable thermal conditions, the transformer can be operated over the nameplate rating for a specified time. The maximum transformer load value that does not cause the hottest-spot temperature (HST) to exceed the given maximum allowable value is called the dynamic rating of the transformer. There are two methods for the dynamic rating of the transformer: directly monitoring the HST change and applying a thermal model to calculate the transformer HST based on the ambient temperature monitoring data. However, the HST of the transformer usually appears at an inaccessible position on the top of the winding, and it is impossible to install a temperature sensor. Therefore, developing a method that relies on weather sensors and current measurement units and is easily installed through non-invasive operations will be the most cost-effective solution. The literature [IEEE Guide for Loading Mineral-Oil-Immersed Transformers and Step-Voltage Regulators, IEEE Std. C 57.91-2011, 2012.] uses the dynamic thermal model reported in the IEEE Oil-Immersed Transformer Load Guide. Subsequently, many different thermal models were developed and tested based on this model. Due to the uncertainty of weather conditions and transformer parameters, the research on transformer dynamic ratings inevitably has uncertainty. The dynamic ratings must be regarded as random variables, and the probabilistic prediction method is more desirable than the deterministic prediction method. Reference [Wang Lujia, Zhou Lijun, Wang Dongyang, et al. Influence of overload starting on dynamic temperature rise of traction transformer hot spots [J]. Proceedings of the CSEE, 2017, 37(24): 7350-7358+7449.] built a transformer research form combining a temperature rise simulation platform and three-dimensional numerical simulation, and studied the relationship between the hot spot temperature rise rate and the top oil / winding time constant under different load factors, but the research object is railway traction transformer. Reference [Huang Yuanfang, Liu Yunkai, Zheng Shiming, et al. Heavy overload risk warning of distribution transformer considering load uncertainty [J]. Power Grid and Clean Energy, 2021, 37(10): 17-24.] Taking into account the load uncertainty factor, the gated cyclic unit quantile regression algorithm is used to calculate the load level of different quantiles, and then the kernel density estimation algorithm is used to evaluate the risk level of the transformer under overload conditions, but the influence of environmental conditions is not considered. Reference [Shan Shirui, Lv Zhenwei. Transformer probabilistic risk management assessment method based on dynamic capacity [J]. Journal of Xiangyang Vocational and Technical College, 2023, 22(1): 91-97.] Combining long short-term memory network and support vector machine, a dynamic probability prediction model for key components of the power grid is proposed, which can realize the active regulation of risk events.References [Xu Hao, Jiang Xinxiong, Liu Zhicheng, et al. Risk assessment and active control strategy of static safe operation of power grid based on probability prediction [J]. Automation of Electric Power Systems, 2022, 46(1): 182-191.] Based on the two evaluation indicators of the full life cycle and transformer failure cost, the Bayesian algorithm is used to build a transformer failure probability prediction model, which can more accurately predict the service life of the transformer. References [Guo Xiaohan, Niu Xin, Li Yongjie, et al. Prediction of the probability of failure of power transformers throughout their life cycle based on Bayesian algorithm [J]. Electronic Design Engineering, 2023, 31(13): 32-35+40.] In order to overcome the uncertainty of traditional single-point prediction, the conditional quantile regression algorithm is used to construct a probability prediction model, which can obtain the most likely prediction point and related distribution in the future. The literature [Han Yelin, Zhang Zhanyao, Yu Yili, et al. Prediction of distribution transformer heavy overload probability based on LSTM and quantile regression theory [J]. Electric Power Big Data, 2023, 26(6): 1-8.] proposed a transformer dynamic capacity evaluation method, and the hottest point temperature of the transformer was calculated using the quantile regression method and dynamic thermal model. However, the above literature did not simultaneously consider the impact of ambient temperature and transformer load on the dynamic rating of the transformer. Summary of the invention

[0004] The present invention provides a method for predicting the allowable current of an oil-immersed transformer based on ambient temperature and load, which can take into account the inevitable uncertainty in transformer thermal modeling, so that the transformer can operate beyond its nameplate rating for a short period of time without losing the rated life or causing failure, thereby improving the operational reliability of the transformer.

[0005] The technical solution adopted by the present invention is:

[0006] The method for predicting allowable current of an oil-immersed transformer based on ambient temperature and load includes the following steps:

[0007] Step 1: Select the IEEE thermal model of oil-immersed transformer and use the quantile regression model to derive the ambient temperature and transformer load prediction model;

[0008] Step 2: Introduce a probability index that takes into account the probability of the allowable current being higher than the predicted dynamic rating and the corresponding expected load reduction, and predict the transformer allowable current through the predicted distribution of the transformer dynamic rating.

[0009] In the step 1,

[0010] The prediction tool is set at the end of the time slot hk, aiming to predict the transformer allowable current within the required time frame h, as the lead time k, the lead time is set to be divided into equally spaced sub-intervals, and within each sub-interval, the environmental conditions and the transformer current are set to be constant, each sub-interval is set to 1 hour,

[0011] In the deterministic scenario, the transformer allowable current must be lower than / equal to the predicted value of the transformer dynamic rating. In order to obtain the dynamic rating I of the transformer in the required time period h h-max , we need to know the HST (θ H,h-1 ) and the maximum allowable HST(θ H-max ), once θ H,h-1 and θ H-max Known, I h-max It can be calculated by using the dynamic thermal model of the inversion transformer. Transformer HST(θ H,h-1 ) can be obtained by iteratively applying the transformer thermal model, making point predictions of the ambient temperature and transformer load for the intermediate time slots [h-k+1,h-1]. A thermal transient evaluation is performed for each considered intermediate time slot [h-k+1,h-k+2,…,h-1], taking into account the predictions of the ambient temperature and the transformer load, so as to predict the HST at the end of each intermediate time slot. The dynamic rating for a specific time slot h can be predicted, since the thermal state of the transformer at the end of the previous time slot h-1 is known, and the ambient temperature within the present time slot h can also be predicted. The "conventional" application of the thermal model is actually only used to predict the dynamic rating at the next step of the procedure, although the changes in the ambient temperature within the time slot h are taken into account. Note that the proposed procedure almost collapses into the "conventional" application of the thermal model only when a prediction for the next time slot is required.

[0012] The ambient temperature and transformer load of each time slot are actually random variables. Therefore, the above method has great limitations in the deterministic framework, and the probabilistic method is the most feasible. In this paper, we propose a probabilistic method, which uses the probabilistic prediction of ambient temperature and transformer load to establish HST (θ H,h-1 ) and then the dynamic rating of the transformer I h-max Make a probability prediction. Once I h-max Based on the predicted distribution, the permissible current can be selected through a probability index, which takes into account the probability of the permissible current being higher than the predicted dynamic rating and the corresponding load reduction, which is a risk-based framework.

[0013] In the proposed 4-step procedure,

[0014] In the first step, a probabilistic forecast of ambient temperature and transformer load is developed. The first step is generated at the end of each intermediate time slot hk until the end of time slot h(h-1). The input is the hourly ambient temperature measurement dataset [θ A,1 ,θ A,2 ,θ A,3 ,…,θ A,h-k] and hourly transformer load data set [I1,I2,I3,…,I h-k ] until the end of time slot hk. These data sets and further quantitative and qualitative predictors are the input to two quantile regression (QR) models that provide the ambient temperature over the entire forecast lead time k. and transformer load The prediction quantile set is obtained, and the prediction samples of ambient temperature and transformer load can be extracted from the interpolated prediction cumulative distribution through the inversion method.

[0015] Step 2 uses the predicted samples up to time slot h-1 in the Monte Carlo simulation to evaluate the transformer thermal transient scenario by applying the transformer dynamic thermal model. The output of this step is the sample distribution prediction of the transformer HST at the end of time slot h-1.

[0016] Step 3: Given the maximum allowed HST(θ H,max ) and the predicted distribution forecast of ambient temperature Monte Carlo simulation is used to invert the transformer dynamic thermal model to obtain the predicted sample distribution of the transformer dynamic rating within one hour. It is worth noting that the maximum allowable HST is the temperature that will not cause the transformer to lose its rated life. Unless the insulation breakdown temperature is reached, higher values ​​do not necessarily lead to insulation degradation.

[0017] In step 4, the present value of the transformer allowable current is inferred through a probability indicator, namely the hourly expected perunit rating (HEPR). HEPR is a normalized index that takes into account both the probability of allowing current to be higher than the predicted dynamic rating and the corresponding load reduction.

[0018] The thermal model proposed in the IEEE Oil-Immersed Transformer Loading Guide is selected for this paper. According to the IEEE and IEC Oil-Immersed Transformer Loading Guide, the HST of the transformer is the thermal parameter that mainly affects the transformer aging effect. The HST achieved in one time slot depends on the ambient temperature, the final load, and the initial condition of the transformer (if the time slot considered is less than the thermal time constant, which usually occurs at hourly time slots). A common universal HST value of 110°C is expected to provide a uniform aging factor and is therefore selected as the maximum allowable HST for each time slot (θ H-max ). HST(θ H,h ) is calculated as shown in formula (1):

[0019] θ H,h =θ A,h +ΔθO,h +Δθ H,h (1)

[0020] Where: θ A,h is the ambient temperature of time slot h; Δθ O,h is the top oil temperature rise above the ambient temperature at time interval h; Δθ H,h is the hot spot temperature rise exceeding the top oil temperature at time slot h.

[0021] The solution formula for the top oil temperature rise exceeding the ambient temperature caused by the step load change is shown in formula (2):

[0022]

[0023] Where: L is the temperature rise of top oil relative to ambient temperature under rated load; u,h , L i,h are the final and initial loads of time slot h and the nameplate current I n R is the ratio of the loss under rated load to the loss under no-load; n is an empirical parameter based on the cooling type, ranging from 0.8 to 1; τ O,h For the initial load ratio L i,h To the final load ratio L u,h The time constant for the transition process that occurs during oil flow, measured in hours. The values ​​of R and n can be obtained from the transformer parameters and characteristics in the literature [Wang Lin, Ju Yuntao, Wu Wenchuan, et al. Optimal design of inertia damping parameters of virtual synchronized microgrid for frequency stability improvement [J]. Proceedings of the CSEE, 2021, 41(13): 4479-4490.].

[0024] The winding time constant τ should be solved w Another transient state of control is used to calculate the hottest point temperature rise Δθ above the top oil temperature H,h If this time constant is not available, the IEEE guide recommends conservatively calculating the hottest temperature rise above the top oil temperature as its steady-state value. In the proposed method, this choice is reasonable because the winding time constant rarely exceeds a few minutes. Considering the hourly discretization method adopted in this paper, the transient can be considered to be completed within the hourly time slot and the steady-state value can be consistently used as the solution. This is a conservative choice in terms of transformer aging effects. Therefore, the hottest temperature rise Δθ above the top oil temperature is H,h The calculation formula is shown in formula (3):

[0025]

[0026] Where: m is an empirical parameter, and its value range is 0.8 to 1 according to different cooling methods; Or 65℃, it varies with the increase of average winding temperature.

[0027] Therefore, given the transformer characteristics, ambient temperature value and initial load value, HST is a function of the final load ratio, and the calculation formula is shown in formula (4):

[0028] θ H,h =θ H,h (L u,h |θ A,h ,L i,h ) (4)

[0029] The ambient temperature θ A,h As a random variable, the time slot h prediction is provided by the QR method, and the initial load rate L i,h It can be calculated as the equivalent thermal load rate for the first 10-12 hours. Therefore, if the prediction lead time is 1 hour, it is assumed to be completely known, because the historical operation record of the transformer is completely known, and when multi-step prediction of thermal transient is performed by formula (2), the intermediate load step must be predicted. Then, the fixed maximum allowable HST (θ H-max ), the corresponding final ratio L can be obtained numerically from the inversion of equation (1) u,h-max , and by dividing by I n To obtain the dynamic rating I h-max The dynamic rating obtained by the proposed procedure can be enforced to not exceed 3 times (2 times) the nameplate rating of distribution (power) oil-immersed transformers.

[0030] Despite the different regressors, the forecasts of ambient temperature and transformer load are obtained by means of QR models, but this choice is not the only solution, since there are a large number of probabilistic models in the literature that can produce ambient temperature and load forecasts. However, in order to have a procedure that does not depend on very specific conditions and availability, we decided to apply simple, complete statistical models that can be adjusted case by case depending on the available input conditions. In the proposed procedure, the forecasts of the lead time are achieved by iteratively applying one-step-ahead models. For the ambient temperature QR model, the α-quantile of the ambient temperature at time h The prediction model is shown in formula (5):

[0031]

[0032] Where: and are P+1 model coefficients; x 1θ,t 、x Pθ,t is the P predictor variable.

[0033] The choice of predictor variables is obviously crucial. In such applications, typical quantitative predictor variables are historical values ​​of ambient temperature, historical values ​​of related weather variables and / or numerical weather forecasts of ambient temperature and related weather variables. It should be noted that these variables should be available at the specific location of the transformer and in a discrete 1-hour time span as input to the proposed procedure. The introduction of qualitative predictor variables is to take into account the daily and annual periodicity of ambient temperature; for example, the 24 binary predictor variables hod t-1 , hod t-2 , …, hod t-24 (If t is the i-th hour of the day, then hod t-i =1, otherwise hod t-i = 0) can simulate daily periodicity, while the 12 binary predictor variables (moy t-1 , moy t-2 ,..., moy t-12 (If t is the i-th month of the year, then moy t-i =1, otherwise moy t-i =0) can simulate the annual periodicity of ambient temperature.

[0034] The estimate is then found by minimizing the Pinball Loss Function (PLF) during model training and The PLF of the ambient temperature at each time slot t is shown in equation (6):

[0035]

[0036] Several combinations of quantitative and qualitative predictors are trained, choosing those that result in PLF during validation t The model with the minimum (the average of all considered quantiles) is used for prediction during testing. The process is then iterated for the other quantiles to obtain a collection of ambient temperature quantile predictions The predicted cumulative distribution function of the ambient temperature is obtained by interpolating the quantiles, and the ambient temperature prediction samples are extracted by the inversion method. For the transformer load QR model, the α-quantile prediction of the transformer load at hour t is The model is established as shown in formula (7):

[0037]

[0038] Where: All are Q+1 load model coefficients; y 1I,t ,y QI,t is the Q predictor variable.

[0039] Typical quantitative predictors are past loads, ambient temperature and / or forecasts of ambient temperature and related weather variables if the total load delivered through the transformer is weather sensitive. In contrast, common qualitative predictors are related to weekdays (Wk) and Sundays (or holidays) (Su), further distinguishing between Mondays (or days after a holiday) (Mo) and Saturdays (or days before a holiday) (Sa). The transformers considered in the numerical application supply power to industrial facilities, introducing the predictor variable tod t-(Mo) 、tod t-(Wk) 、tod t-(Sa) 、tod t-(Su) To capture the load variations during the week and holidays, if time t occurs on Monday or the day after a holiday, then tod t-(Mo) =1, otherwise tod t-(Mo) = 0. Train multiple models with different combinations of predictive variables and select the model with the smallest value during the validation period for prediction during the test period. Then, interpolate the predicted quantiles Extract the prediction sample from the cumulative distribution function. Obviously, the sample prediction of transformer load ratio in hours is For thermal models.

[0040] In step 2, a probability index is introduced that takes into account the probability of the allowable current being higher than the predicted dynamic rated value and the corresponding expected load reduction and other influencing factors, and the transformer allowable current is predicted by the predicted distribution of the transformer dynamic rated value. h-max The predicted sampling distribution f Ih-max , the decision-making allowable current I of the transformer in the same hour can be obtained by calculating the index HEPR h-al HEPR is composed of hourly availability (HA), hourly average load reduction I mlc,h and weighted average load reduction I wmlc,h Calculated. HA is the transformer load I h The function is that the load does not exceed the transformer dynamic rating distribution f Ih-max The prediction sample {I lim,h1 , ..., I lim,hNs}, N s is the total number of samples drawn. Therefore, the HA calculation formula is shown in formula (8):

[0041]

[0042] In the formula: When i =0, otherwise λ i =1.

[0043] HA decreases as the transformer load increases, and (1-HA) is the hourly unavailability. By definition, for each I h-inf ≤min{I lim,h1 , ..., I lim,hNs}, HA(I h-inf )=1, and for each I h-sup >max{I lim,h1 , ..., I lim,hNs}, HA(I h-sup )=1.

[0044] I mlc,h The magnitude of the unavailability consequence is given in terms of transformer loading, which is the average difference between the transformer loading and the dynamic rating prediction samples. In practice, the average value of the current must be reduced in order to meet the thermal constraints of the transformer. mlc,h isI h The function is defined as shown in formula (9):

[0045]

[0046] Hourly weighted average load reduction required to avoid violating thermal constraints I wmlc,h (I h ) is I h The function is calculated as shown in formula (10):

[0047]

[0048] I wmlc,h The structure comes from the classic risk-based framework (probability of an event multiplied by the magnitude of the consequence).

[0049] HEPR is introduced to provide a more intuitive and flexible indicator. It is the normalized difference between a given transformer load and the hourly weighted average load reduction required to avoid violating the thermal constraint. Its percentage value is defined as shown in formula (11):

[0050]

[0051] When HEPR = 100%, it can be guaranteed that the thermal constraints are not violated under the dynamic rating prediction distribution. h-inf )=100%. On the contrary, the closer the HEPR is to 0%, the higher the product between the probability of a critical event and the load shedding consequence. Finally, the allowable current I based on the HEPR is defined h-al The criterion is to select the transformer load I associated with the specified HEPR level h Several strategies can be adopted. SG operators can choose I h-al for:

[0052] 1) Safety value I h-al(100％) , which is the maximum possible load to return a 100% HEPR level, i.e. I h-al(100％) =min{I lim,h1 , ..., I lim,hNs}. This value is considered safe because I h-al(100％) Out of sample prediction lim,h1 , ..., I lim,hNs} is 0. In this case, the hourly availability HA(I h-al(100％) )=1,hourly weighted average load reduction I wmlc,h (I h-al(100％) ). Obviously, this option is only feasible if the SG operator fully trusts the probabilistic predictions of dynamic ratings;

[0053] 2) Conservative value I h-al(cons) , even less than I h-al(100％) (i.e. I h-al(cons) <I h-al(100％) , as an extremely safe allowable current. This choice is conservative with respect to unavoidable dynamic rating prediction errors. In fact, the probabilistic prediction of the dynamic rating for a particular hour may be poor (i.e. biased) due to unexpected weather or load conditions, a poorly performing prediction model, or poor modeling of transformer parameters. To take these possibilities into account, the SG operator can h-al(cons) h-al(100％) to reduce the transformer load. It should also be noted that in this case, HA(I h-al(cons) )=1,I wmlc,h (I h-al(cons) )=0 and HEPR(I h-al(cons) )=100%.

[0054] If SG operators are willing to take the risk, they can also choose to:

[0055] 3) Value I corresponding to HEPR level p < 100 h-al(p％) As a less safe allowable current. According to the definition of HEPR, I h-al(p％) ≥I h-al(100％) , so choosing is definitely better than choosing I h-al(100％) More conservative and reliable. This level p < 100 may also be a "subjective allocation" made by the SG operator based on his personal experience, information and belief about the impact of load reduction. Alternatively, if a load utility function is provided, the transformer allowable current can be selected by considering the economic losses associated with load reduction caused as a critical event, rather than the load reduction itself, which will lead to the use of probability index in an economic environment, making some trade-off between economic benefits and safety.

[0056] ​Numerical simulations are carried out based on actual data, and the predicted allowable current is compared with the actual dynamic rated value, which proves the effectiveness of the proposed method.

[0057] The proposed method was tested on an actual 400 kVA medium / low voltage distribution transformer supplying power to an industrial facility. The meteorological observation station and the load monitoring system provided the ambient temperature and transformer load datasets from April 1, 2016 to January 31, 2017, respectively. The QR models were trained with different combinations of predictor variables, and the best performing QR model during the validation period (1 month) was selected to generate ambient temperature and transformer load forecasts. The transformer allowable current was then predicted for several months, but for the sake of brevity, only the results for the test period from September 1, 2016 to September 30, 2016 are shown in this paper. Among the many models for predicting ambient temperature, the selected QR model is shown in Equation (12):

[0058]

[0059] The QR model used for transformer load prediction is shown in formula (13):

[0060]

[0061] In the specific case considered, the transformer load is not sensitive to weather changes, so the ambient temperature does not appear in the prediction model. Both QR models are compared with the benchmark QR model (Benchmark QR, QR-B), where only one predictor variable is selected in the persistence framework, namely the last observed value of the ambient temperature or transformer load, and the calculation formulas are shown in Equations (14) and (15):

[0062]

[0063]

[0064] These QR-B model results are used to predict the dynamic rating of the transformer through the proposed procedure, in order to quantitatively evaluate the quality of the QR ambient temperature, QR transformer load and the corresponding QR-based transformer dynamic rating prediction, the corresponding PLF relationship with the prediction lead time, and the PLF value predicted by QR-B.

[0065] The evaluation procedure for allowing transformer current to pass is shown in detail for lead times of 1 hour and 10 hours. Two different load scenarios are considered: the first scenario S1 represents a real industrial facility and the second scenario S2 is obtained by increasing the real transformer load by 15%.

[0066] Despite the limited range of the predicted distribution of the dynamic ratings, the differences between the choices of the allowable currents at different HEPR levels are evident. It is worth noting that the allowable current at the 100% HEPR level is very close to the actual dynamic rating, while in the case of 95% HEPR there is a non-negligible difference. The allowable current values ​​at the 95% and 100% HEPR levels are plotted over the same 40 h period in scenario S2. This is a tighter scenario than the one presented previously, however, the main consequence of these results is that the allowable current at the 100% HEPR level is still able to follow the actual dynamic rating and therefore does not lead to an overestimation.

[0067] If the SG operator selects the permissible current assuming 95% HEPR as the specified level, then following one of the above strategies, the actual dynamic rating will be greater than the permissible current only for 1 hour (i.e., hour 16). During the remaining time, the permissible current at the 95% HEPR level is typically about 40A greater than the actual dynamic rating.

[0068] I corresponding to 95%, 98% and 99% HEPR levels in scenarios S1 and S2 wmlc,h , although the size of the transformer load is different, but I wmlc,h The difference between the two cases is difficult to distinguish, with I at 99% and 98% HEPR levels. wmlc,h Slightly varies over time; at 95% level I wmlc,h Instead, it is close to the corresponding I at 95%. h-al This shows that by choosing a lower HEPR value, the expected load shedding tends to increase “slowly” as the transformer allowable current increases.

[0069] In scenarios S1 and S2 where the transformer allowable current is evaluated 10 hours in advance by HEPR, the allowable current I at 95% and 100% HEPR levels is h-alThe evaluation results are shown in Figure 2. As expected, the spread of allowable currents at different HEPR levels increases relative to the corresponding 1-hour-ahead results, due to the wider range of dynamic rating predictions, resulting in higher PLFs for longer lead times. In scenario S2, the allowable current at the 100% HEPR level is very close to the nameplate rating of the transformer for a long time interval (13-20 hours and 35-40 hours). In contrast to the 1-hour-ahead case, the allowable current at the 100% HEPR level does not seem to follow the actual dynamic rating but is always less than the rated value. Therefore, if the SG operator assumes 100% HEPR as the specified level and chooses the hourly allowable current according to the second strategy, no rating life loss will be incurred. In contrast, the allowable current at the 95% HEPR level is close to the actual dynamic rating for a few hours (10-11 hours and 31-36 hours), so the SG operator can also make different choices.

[0070] I corresponding to 95%, 98% and 99% HEPR levels in scenarios S1 and S2 wmlc,h , the result is very similar to the prediction result 1 hour ago. In fact, the difference between scenarios S1 and S2 is wmlc,h The differences in the two aspects are negligible and I wmlc,h The changes with respect to time are only evident at the 95% HEPR level. This suggests that lower quality probabilistic forecasts mitigate the impact of hourly weighted average load reduction.

[0071] Based on the thermal model detailed in the IEEE guide, the proposed method is considered to be extended to distribution and power dry-type transformers. Despite the obvious differences in transformer parameters and time constants, the treatment can be easily applied to distribution and power dry-type transformers with only minor modifications. In particular, the modifications required to the procedure only require changes to the transformer thermal model itself. The thermal model of the dry-type transformer during transients is actually simpler than the thermal model of the oil-immersed transformer in Eqs. (1) and (2) because it only considers the hot spot temperature rise above the ambient temperature and ignores the increase in the top oil temperature relative to the ambient temperature. The required inputs are still the predictions of the transformer load and ambient temperature over the entire prediction period, and the procedures for predicting the hourly transformer dynamic rating and the procedure for inferring the transformer allowable current using the probability index remain unchanged.

[0072] For oil-immersed power transformers as described in the IEEE Guide, the only difference is the maximum current and temperature that the transformer can withstand (lower for power transformers than for distribution transformers). In the proposed procedure, the maximum allowable HST is fixed at 110°C to ensure no loss of rated life, and the dynamic rating shall not exceed 3 times (2 times) the nameplate rating of the distribution (power) transformer, so that, apart from the obvious differences in transformer parameters and time constants, the proposed procedure can also be applied to oil-immersed power transformers.

[0073] When using thermal models not recommended by the IEEE guidelines, analytical thermal models for oil-immersed and dry-type transformers are very simple in the proposed procedure, as they only involve changes in the thermal model. In contrast, thermal models relying on the finite element method require further research work to be introduced into the proposed procedure, as these models are usually very well suited to a specific machine.

[0074] Finally, the proposed procedure can be applied not only to a single transformer but also to a group of transformers of the same or different types at the same time, with low cost and simple operation. The transformer load is actually monitored in real time and historical data can be easily collected, so the only input required for the widespread application of the proposed procedure is the ambient temperature, which can be simply monitored and collected by a temperature sensor. On the other hand, the electrical system in the SG mode is expected to be increasingly characterized by decentralized, complex and high-performance ICT-related infrastructure, which can easily meet the requirements of the proposed method.

[0075] The technical effects of the present invention are:

[0076] 1. The present invention starts with the SG dispatcher controlling the load reduction, selects the transformer allowable current by quantifying the consequences of abnormal load conditions, and incorporates the prediction problem of the allowable current of the oil-immersed distribution transformer into a probabilistic framework. The allowable current can be predicted within a specific time range, giving the SG dispatcher the opportunity to manage the transformer load dispatch within the specific time range;

[0077] 2. The probabilistic procedure is based on transformer load and environmental monitoring. The probabilistic indicator considers the probability of transformer load being higher than the predicted dynamic rating and load reduction. The allowable current is selected in a risk-based framework. The effectiveness of the method is verified through numerical simulations.

[0078] 3. Future research will aim to predict the permissible current of the transformer by using thermal models dedicated to a specific machine or to select the permissible current within an economic framework starting from the load utility function. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 is the time series of the transformer thermodynamics in the present invention;

[0080] Figure 2 It is the framework of the transformer allowable current prediction method in the present invention;

[0081] Figure 3 (a) is a graphical explanation of transformer load 1 in the present invention;

[0082] (b) is a graphical explanation of transformer load 2;

[0083] Figure 4 In the present invention, (a) is the relationship between the transformer load pinball loss function and the prediction lead time;

[0084] (b) is the relationship between the ambient temperature pinball loss function and the prediction lead time;

[0085] Figure 5 is the relationship between the pinball loss function for predicting the dynamic rating of the transformer and the prediction lead time in the present invention;

[0086] Figure 6 is the allowable current evaluation value of scenario S1 in the present invention;

[0087] Figure 7 is the allowable current evaluation value of scenario S2 in the present invention;

[0088] Figure 8 In the present invention, (a) is the weighted average load reduction change per hour in scenario 1;

[0089] (b) is the weighted average load reduction change per hour in scenario 2;

[0090] Fig. 9 is the allowable current evaluation value of scenario S1 in the present invention;

[0091] Fig.10 is the allowable current evaluation value of scenario S2 in the present invention;

[0092] Fig.11 In the present invention, (a) is the weighted average load reduction change per hour in scenario 1;

[0093] (b) is the change in the weighted average load reduction per hour in scenario 2. DETAILED DESCRIPTION

[0094] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0095] The method for predicting allowable current of an oil-immersed transformer based on ambient temperature and load includes the following steps:

[0096] Step 1: Transformer allowable current prediction method framework

[0097] Assume that the prediction tool aims to predict the transformer allowable current within the required time frame h, as the lead time k, at the end of the time slot hk. Assume that the lead time is divided into equally spaced subintervals, and within each subinterval, the environmental conditions and the transformer current are assumed to be constant, and for simplicity, each subinterval is set to 1 hour.

[0098] In the deterministic scenario, the transformer allowable current must be lower than / equal to the predicted value of the transformer dynamic rating. In order to obtain the dynamic rating I of the transformer in the required time period h h-max , we need to know the HST (θ H,h-1 ) and the maximum allowable HST(θ H-max ),like Figure 1 As shown, once θ H,h-1 and θ H-max Known, I h-max It can be easily calculated by reversing the dynamic thermal model of the transformer. Transformer HST(θ H,h-1 ) can be obtained by iteratively applying the transformer thermal model to make point predictions of the ambient temperature and transformer load for the intermediate time slot [h-k+1,h-1], such as Figure 1 , as shown by the solid red line in . In particular, by taking into account the predictions of the ambient temperature and the transformer load, a thermal transient evaluation is performed for each considered intermediate time slot [h-k+1,h-k+2,…,h-1] in order to predict the HST at the end of each intermediate time slot, and the dynamic rating for a specific time slot h can be predicted, since the thermal state of the transformer at the end of the previous time slot h-1 is known, and the ambient temperature within the present time slot h can also be predicted. The “traditional” application of the thermal model is actually only used to predict the dynamic rating at the next step of the procedure, although the changes in the ambient temperature within the time slot h are taken into account. Note that the proposed procedure almost collapses into a “traditional” application of the thermal model only when a prediction for the next time slot is required.

[0099] The ambient temperature and transformer load of each time slot are actually random variables. Therefore, the above method has great limitations in the deterministic framework, and the probabilistic method is the most feasible. In this paper, we propose a probabilistic method, which uses the probabilistic prediction of ambient temperature and transformer load to establish HST (θ H,h-1 ) and then the dynamic rating of the transformer I h-max Make a probability prediction. Once I h-max Based on the predicted distribution, the permissible current can be selected through a probability index, which takes into account the probability of the permissible current being higher than the predicted dynamic rating and the corresponding load reduction, which is a risk-based framework.

[0100] The proposed 4-step procedure is as follows Figure 2As shown, each step of the program corresponds to a dotted block.

[0101] The first step is to develop a probabilistic forecast of ambient temperature and transformer load, which is generated at the end of each intermediate time slot hk until the end of time slot h(h-1). The input is a dataset of hourly ambient temperature measurements [θ A,1 ,θ A,2 ,θ A,3 ,…,θ A,h-k ] and hourly transformer load data set [I1,I2,I3,…,I h-k ] until the end of time slot hk. These data sets and further quantitative and qualitative predictors are the input to two quantile regression (QR) models that provide the ambient temperature over the entire forecast lead time k. and transformer load The prediction quantile set is obtained, and the prediction samples of ambient temperature and transformer load can be extracted from the interpolated prediction cumulative distribution through the inversion method.

[0102] Step 2 uses the predicted samples up to time slot h-1 in a Monte Carlo simulation to evaluate the transformer thermal transient scenario by applying the transformer dynamic thermal model. The output of this step is the sample distribution prediction of the transformer HST at the end of time slot h-1. The transformer dynamic thermal model is given in Section 2.1.

[0103] Step 3: The maximum allowed HST(θ H,max ) and the predicted distribution forecast of ambient temperature Monte Carlo simulation is used to invert the transformer dynamic thermal model to obtain the predicted sample distribution of the transformer dynamic rating within one hour. It is worth noting that the maximum allowable HST is the temperature that will not cause the transformer to lose its rated life. Unless the insulation breakdown temperature is reached, higher values ​​do not necessarily lead to insulation degradation.

[0104] Step 4 will infer the present value of the transformer allowable current through a probability indicator, namely the hourly expected perunit rating (HEPR). HEPR is a normalized index that takes into account both the probability of allowing current to be higher than the predicted dynamic rating and the corresponding load reduction.

[0105] The thermal model proposed in the IEEE Oil-Immersed Transformer Loading Guide is selected for this paper. According to the IEEE and IEC Oil-Immersed Transformer Loading Guide, the HST of the transformer is the thermal parameter that mainly affects the transformer aging effect. The HST achieved in one time slot depends on the ambient temperature, the final load, and the initial condition of the transformer (if the time slot considered is less than the thermal time constant, which usually occurs at hourly time slots). A common universal HST value of 110°C is expected to provide a uniform aging factor and is therefore selected as the maximum allowable HST for each time slot (θ H-max ). HST(θ H,h ) is calculated as shown in formula (1):

[0106] θ H,h =θ A,h +Δθ O,h +Δθ H,h (1)

[0107] Where: θ A,h is the ambient temperature of time slot h; Δθ O,h is the top oil temperature rise above the ambient temperature at time interval h; Δθ H,h is the hot spot temperature rise exceeding the top oil temperature at time slot h.

[0108] The solution formula for the top oil temperature rise exceeding the ambient temperature caused by the step load change is shown in formula (2):

[0109]

[0110] Where: L is the temperature rise of top oil relative to ambient temperature under rated load; u,h , L i,h are the final and initial loads of time slot h and the nameplate current I n R is the ratio of the loss under rated load to the loss under no-load; n is an empirical parameter based on the cooling type, ranging from 0.8 to 1; τ O,h For the initial load ratio L i,h To the final load ratio L u,h The time constant for the transition process that occurs during oil flow, measured in hours. The values ​​of R and n can be obtained from the transformer parameters and characteristics in the literature [Wang Lin, Ju Yuntao, Wu Wenchuan, et al. Optimal design of inertia damping parameters of virtual synchronized microgrid for frequency stability improvement [J]. Proceedings of the CSEE, 2021, 41(13): 4479-4490.].

[0111] The winding time constant τ should be solved w Another transient state of control is used to calculate the hottest point temperature rise Δθ above the top oil temperature H,hIf this time constant is not available, the IEEE guide recommends conservatively calculating the hottest temperature rise above the top oil temperature as its steady-state value. In the proposed method, this choice is reasonable because the winding time constant rarely exceeds a few minutes. Considering the hourly discretization method adopted in this paper, the transient can be considered to be completed within the hourly time slot and the steady-state value can be consistently used as the solution. This is a conservative choice in terms of transformer aging effects. Therefore, the hottest temperature rise Δθ above the top oil temperature is H,h The calculation formula is shown in formula (3):

[0112]

[0113] Where: m is an empirical parameter, and its value range is 0.8 to 1 according to different cooling methods; or 65°C, varying with the average winding rise.

[0114] Therefore, given the transformer characteristics, ambient temperature value and initial load value, HST is a function of the final load ratio, and the calculation formula is shown in formula (4):

[0115] θ H,h =θ H,h (L u,h |θ A,h ,L i,h ) (4)

[0116] The ambient temperature θ A,h As a random variable, the time slot h prediction is provided by the QR method, and the initial load rate L i,h It can be calculated as the equivalent thermal load rate for the first 10-12 hours. Therefore, if the prediction lead time is 1 hour, it is assumed to be completely known, because the historical operation record of the transformer is completely known, and when multi-step prediction of thermal transient is performed by formula (2), the intermediate load step must be predicted. Then, the fixed maximum allowable HST (θ H-max ), the corresponding final ratio L can be obtained numerically from the inversion of equation (1) u,h-max , and by dividing by I n To obtain the dynamic rating I h-max The dynamic rating obtained by the proposed procedure can be enforced to not exceed 3 times (2 times) the nameplate rating of distribution (power) oil-immersed transformers.

[0117] Despite the different regressors, the forecasts of ambient temperature and transformer load are obtained by means of QR models, but this choice is not the only solution, since there are a large number of probabilistic models in the literature that can produce ambient temperature and load forecasts. However, in order to have a procedure that does not depend on very specific conditions and availability, we decided to apply simple, complete statistical models that can be adjusted case by case depending on the available input conditions. In the proposed procedure, the forecasts of the lead time are achieved by iteratively applying one-step-ahead models. For the ambient temperature QR model, the α-quantile of the ambient temperature at time h The prediction model is shown in formula (5):

[0118]

[0119] Where: and are P+1 model coefficients; x 1θ,t 、x Pθ,t is the P predictor variable.

[0120] The choice of predictor variables is obviously crucial. In such applications, typical quantitative predictor variables are historical values ​​of ambient temperature, historical values ​​of related weather variables and / or numerical weather forecasts of ambient temperature and related weather variables. It should be noted that these variables should be available at the specific location of the transformer and in a discrete 1-hour time span as input to the proposed procedure. The introduction of qualitative predictor variables is to take into account the daily and annual periodicity of ambient temperature; for example, the 24 binary predictor variables hod t-1 , hod t-2 , …, hod t-24 (If t is the i-th hour of the day, then hod t-i =1, otherwise hod t-i = 0) can simulate daily periodicity, while the 12 binary predictor variables (moy t-1 , moy t-2 ,..., moy t-12 (If t is the i-th month of the year, then moy t-i =1, otherwise moy t-i =0) can simulate the annual periodicity of ambient temperature.

[0121] The estimate is then found by minimizing the Pinball Loss Function (PLF) during model training and The PLF of the ambient temperature at each time slot t is shown in equation (6):

[0122]

[0123] Several combinations of quantitative and qualitative predictors are trained, choosing those that result in PLF during validation t The model with the minimum (the average of all considered quantiles) is used for prediction during testing. The process is then iterated for the other quantiles to obtain a collection of ambient temperature quantile predictions The predicted cumulative distribution function of the ambient temperature is obtained by interpolating the quantiles, and the ambient temperature prediction samples are extracted by the inversion method. For the transformer load QR model, the α-quantile prediction of the transformer load at hour t is The model is established as shown in formula (7):

[0124]

[0125] Where: All are Q+1 load model coefficients; y 1I,t ,y QI,t is the Q predictor variable.

[0126] Typical quantitative predictors are past loads, ambient temperature, and / or forecasts of ambient temperature and related weather variables if the total load delivered through the transformer is weather sensitive. In contrast, common qualitative predictors are related to weekdays (Wk) and Sundays (or holidays) (Su), further distinguishing between Mondays (or days after a holiday) (Mo) and Saturdays (or days before a holiday) (Sa)

[32] . The transformers considered in the numerical application supply power to industrial facilities, and the predictor variable tod is introduced. t-(Mo) 、tod t-(Wk) 、tod t-(Sa) 、tod t-(Su) To capture the load variations during the week and holidays, if time t occurs on Monday or the day after a holiday, then tod t-(Mo) =1, otherwise tod t-(Mo) = 0. Train multiple models with different combinations of predictive variables and select the model with the smallest value during the validation period for prediction during the test period. Then, interpolate the predicted quantiles Extract the prediction sample from the cumulative distribution function. Obviously, the sample prediction of transformer load ratio in hours is For thermal models.

[0127] Step 2: Probability Indicator

[0128] Once the transformer dynamic rated current I in time slot h is known h-max The predicted sampling distribution f Ih-max , the decision-making allowable current I of the transformer in the same hour can be obtained by calculating the index HEPR h-alHEPR is composed of hourly availability (HA), hourly average load reduction I mlc,h and weighted average load reduction I wmlc,h Calculated. HA is the transformer load I h The function is that the load does not exceed the transformer dynamic rating distribution f Ih-max The prediction sample {I lim,h1 , ..., I lim,hNs}, N s is the total number of samples drawn. Therefore, the HA calculation formula is shown in formula (8):

[0129]

[0130] In the formula: When i =0, otherwise λ i =1.

[0131] HA decreases as the transformer load increases, and (1-HA) is the hourly unavailability. By definition, for each I h-inf ≤min{I lim,h1 , ..., I lim,hNs}, HA(I h-inf )=1, and for each I h-sup >max{I lim,h1 , ..., I lim,hNs}, HA(I h-sup )=1.

[0132] I mlc,h The magnitude of the unavailability consequence is given in terms of transformer loading, which is the average difference between the transformer loading and the dynamic rating prediction samples. In practice, the average value of the current must be reduced in order to meet the thermal constraints of the transformer. mlc,h isI h The function is defined as shown in formula (9):

[0133]

[0134] Hourly weighted average load reduction required to avoid violating thermal constraints I wmlc,h (I h ) is I h The function is calculated as shown in formula (10):

[0135]

[0136] I wmlc,h The structure comes from the classic risk-based framework (probability of an event multiplied by the magnitude of the consequence). Figure 3The HA (red), hourly unavailability 1-HA (blue), I mlc,h and I wmlc,h 2 transformer loads are considered to show HA, I mlc,h and I wmlc,h Note that [1-HA(I h )] and I mlc,h (I h )With I h The increasing trend is not obvious.

[0137] HEPR is introduced to provide a more intuitive and flexible indicator. It is the normalized difference between a given transformer load and the hourly weighted average load reduction required to avoid violating the thermal constraint. Its percentage value is defined as shown in formula (11):

[0138]

[0139] When HEPR = 100%, it can be guaranteed that the thermal constraints are not violated under the dynamic rating prediction distribution. h-inf )=100%. On the contrary, the closer the HEPR is to 0%, the higher the product between the probability of a critical event and the load shedding consequence. Finally, the allowable current I based on the HEPR is defined h-al The criterion is to select the transformer load I associated with the specified HEPR level h Several strategies can be adopted. SG operators can choose I h-al for:

[0140] 1) Safety value I h-al(100％) , which is the maximum possible load to return a 100% HEPR level, i.e. I h-al(100％) =min{I lim,h1 , ..., I lim,hNs}. This value is considered safe because I h-al(100％) Out of sample prediction lim,h1 , ..., I lim,hNs} is 0. In this case, the hourly availability HA(I h-al(100％) )=1,hourly weighted average load reduction I wmlc,h (I h-al(100％) ). Obviously, this option is only feasible if the SG operator fully trusts the probabilistic predictions of dynamic ratings;

[0141] 2) Conservative value I h-al(cons) , even less than I h-al(100％) (i.e. I h-al(cons) <I h-al(100％), as an extremely safe allowable current. This choice is conservative with respect to unavoidable dynamic rating prediction errors. In fact, the probabilistic prediction of the dynamic rating for a particular hour may be poor (i.e. biased) due to unexpected weather or load conditions, a poorly performing prediction model, or poor modeling of transformer parameters. To take these possibilities into account, the SG operator can h-al(cons) h-al(100％) to reduce the transformer load. It should also be noted that in this case, HA(I h-al(cons) )=1,I wmlc,h (I h-al(cons) )=0 and HEPR(I h-al(cons) )=100%.

[0142] If SG operators are willing to take the risk, they can also choose to:

[0143] 3) Value I corresponding to HEPR level p < 100 h-al(p％) As a less safe allowable current. According to the definition of HEPR, I h-al(p％) ≥I h-al(100％) , so choosing is definitely better than choosing I h-al(100％) More conservative and reliable. This level p < 100 may also be a "subjective allocation" made by the SG operator based on his personal experience, information and belief about the impact of load reduction. Alternatively, if a load utility function is provided, the transformer allowable current can be selected by considering the economic losses associated with load reduction caused as a critical event, rather than the load reduction itself, which will lead to the use of probability index in an economic environment, making some trade-off between economic benefits and safety.

[0144] Step 3: Numerical calculation and application

[0145] The proposed method was tested on an actual 400 kVA medium / low voltage distribution transformer supplying power to an industrial facility. The meteorological observation station and the load monitoring system provided the ambient temperature and transformer load datasets from April 1, 2016 to January 31, 2017, respectively. The QR models were trained with different combinations of predictor variables, and the best performing QR model during the validation period (1 month) was selected to generate ambient temperature and transformer load forecasts. The transformer allowable current was then predicted for several months, but for the sake of brevity, only the results for the test period from September 1, 2016 to September 30, 2016 are shown in this paper. Among the many models for predicting ambient temperature, the selected QR model is shown in Equation (12):

[0146]

[0147] The QR model used for transformer load prediction is shown in formula (13): ​

[0148]

[0149] In the specific case considered, the transformer load is not sensitive to weather changes, so the ambient temperature does not appear in the prediction model. Both QR models are compared with the benchmark QR model (Benchmark QR, QR-B), where only one predictor variable is selected in the persistence framework, namely the last observed value of the ambient temperature or transformer load, and the calculation formulas are shown in Equations (14) and (15):

[0150]

[0151]

[0152] These QR-B model results are used to predict the dynamic rating of the transformer through the proposed procedure, in order to quantitatively evaluate the quality of the QR ambient temperature, QR transformer load and the corresponding QR-based transformer dynamic rating prediction, the corresponding PLF relationship with the prediction lead time, and the QR-B predicted PLF value as shown in Figure 4 and Figure 5 shown.

[0153] The evaluation procedure for allowing transformer current to pass is shown in detail for lead times of 1 hour and 10 hours. Two different load scenarios are considered: the first scenario S1 represents a real industrial facility and the second scenario S2 is obtained by increasing the real transformer load by 15%.

[0154] In scenario S1, where the transformer allowable current is evaluated 1 hour in advance by HEPR, the allowable current I at 95% and 100% HEPR levels for 40 consecutive hours in September is h-al The evaluation value of Figure 6 Nameplate rating I n and the actual dynamic rated value I h,act-max is shown in the same figure for reference. This figure should not be misinterpreted. In the next hour 1 rating limit current, the prediction of the dynamic rating at the 2nd hour obviously assumes that the transformer load at the 1st hour is the actual load, not the actual dynamic rating. In the latter case, the dynamic rating prediction at the 2nd hour will be significantly smaller than the value in the figure, although the physical meaning is lost.

[0155] Despite the limited range of predicted distribution of dynamic ratings, the differences between the selected allowable currents at different HEPR levels are evident. It is noteworthy that the allowable current at the 100% HEPR level is very close to the actual dynamic rating, while in the case of 95% HEPR, there is a non-negligible difference. In the same 40 hours in scenario S2, the allowable current values ​​at the 95% and 100% HEPR levels are shown in Figure 2. Figure 7 This is a more strained scenario than previously presented, however, the main consequence of these results is that the allowable current at 100% HEPR level is still able to follow the actual dynamic rating and therefore does not lead to an overestimation.

[0156] If the SG operator selects the permissible current assuming 95% HEPR as the specified level, then following one of the above strategies, the actual dynamic rating will be greater than the permissible current only for 1 hour (i.e., hour 16). During the remaining time, the permissible current at the 95% HEPR level is typically about 40A greater than the actual dynamic rating.

[0157] I corresponding to 95%, 98% and 99% HEPR levels in scenarios S1 and S2 wmlc,h like Figure 8 As shown, although the size of the transformer load is different, wmlc,h The difference between the two cases is difficult to distinguish, with I at 99% and 98% HEPR levels. wmlc,h Slightly varies over time; at 95% level I wmlc,h Instead, it is close to the corresponding I at 95%. h-al This shows that by choosing a lower HEPR value, the expected load shedding tends to increase “slowly” as the transformer allowable current increases.

[0158] In scenarios S1 and S2 where the transformer allowable current is evaluated 10 hours in advance by HEPR, the allowable current I at 95% and 100% HEPR levels is h-al The evaluation results are as follows: Fig. 9 and Fig.10 As expected, the spread of allowable currents at different HEPR levels increases relative to the corresponding 1-hour-ahead results, due to the wider range of dynamic rating predictions, resulting in higher PLFs for longer lead times. In scenario S2, the allowable current at the 100% HEPR level is very close to the nameplate rating of the transformer for a long time interval (13-20 hours and 35-40 hours). In contrast to the 1-hour-ahead case, the allowable current at the 100% HEPR level does not seem to follow the actual dynamic rating but is always less than the rated value. Therefore, if the SG operator assumes 100% HEPR as the specified level and chooses the hourly allowable current according to the second strategy, no rating life loss will be incurred. In contrast, the allowable current at the 95% HEPR level is close to the actual dynamic rating for a few hours (10-11 hours and 31-36 hours), so the SG operator can also make different choices.

[0159] I corresponding to 95%, 98% and 99% HEPR levels in scenarios S1 and S2wmlc,h like Fig.11 As shown in Figure 2, the results are very similar to the predictions made 1 hour ago. In fact, the difference between scenarios S1 and S2 is wmlc,h The differences in the two aspects are negligible and I wmlc,h The changes with respect to time are only evident at the 95% HEPR level. This suggests that lower quality probabilistic forecasts mitigate the impact of hourly weighted average load reduction.

[0160] Based on the thermal model detailed in the IEEE guide, the proposed method is considered to be extended to distribution and power dry-type transformers. Despite the obvious differences in transformer parameters and time constants, the treatment can be easily applied to distribution and power dry-type transformers with only minor modifications. In particular, the modifications required to the procedure only require changes to the transformer thermal model itself. The thermal model of the dry-type transformer during transients is actually simpler than the thermal model of the oil-immersed transformer in Eqs. (1) and (2) because it only considers the hot spot temperature rise above the ambient temperature and ignores the increase in the top oil temperature relative to the ambient temperature. The required inputs are still the predictions of the transformer load and ambient temperature over the entire prediction period, and the procedures for predicting the hourly transformer dynamic rating and the procedure for inferring the transformer allowable current using the probability index remain unchanged.

[0161] For oil-immersed power transformers as described in the IEEE Guide, the only difference is the maximum current and temperature that the transformer can withstand (lower for power transformers than for distribution transformers). In the proposed procedure, the maximum allowable HST is fixed at 110°C to ensure no loss of rated life, and the dynamic rating shall not exceed 3 times (2 times) the nameplate rating of the distribution (power) transformer, so that, apart from the obvious differences in transformer parameters and time constants, the proposed procedure can also be applied to oil-immersed power transformers.

[0162] When using thermal models not recommended by the IEEE guidelines, analytical thermal models for oil-immersed and dry-type transformers are very simple in the proposed procedure, as they only involve changes in the thermal model. In contrast, thermal models relying on the finite element method require further research work to be introduced into the proposed procedure, as these models are usually very well suited to a specific machine.

[0163] Finally, the proposed procedure can be applied not only to a single transformer but also to a group of transformers of the same or different types at the same time, with low cost and simple operation. The transformer load is actually monitored in real time and historical data can be easily collected, so the only input required for the widespread application of the proposed procedure is the ambient temperature, which can be simply monitored and collected by a temperature sensor. On the other hand, the electrical system in the SG mode is expected to be increasingly characterized by decentralized, complex and high-performance ICT-related infrastructure, which can easily meet the requirements of the proposed method.

Claims

1. A method for predicting allowable current of oil-immersed transformer based on ambient temperature and load, characterized in that The following steps are involved: Step 1: Select the IEEE thermal model of oil-immersed transformer and use the quantile regression model to derive the ambient temperature and transformer load prediction model; Step 2: Introduce a probability index that takes into account the probability that the allowable current is higher than the predicted dynamic rating and the corresponding expected load reduction influencing factors, and predict the transformer allowable current through the predicted distribution of the transformer dynamic rating.

2. The method for predicting allowable current of an oil-immersed transformer based on ambient temperature and load according to claim 1 is characterized in that: In the step 1, The prediction tool is set at the end of the time slot hk, aiming to predict the transformer allowable current within the required time frame h, as the lead time k, the lead time is set to be divided into equally spaced sub-intervals, and within each sub-interval, the environmental conditions and the transformer current are set to be constant, each sub-interval is set to 1 hour, In the deterministic scenario, the transformer allowable current must be lower than / equal to the predicted value of the transformer dynamic rating in order to obtain the transformer dynamic rating I in the required period h. h-max , we need to know the HST (θ H,h-1 ) and the maximum allowable HST(θ H-max ), once θ H,h-1 and θ H-max Known, I h-max The transformer HST (θ H,h-1 ) can be obtained by iteratively applying the transformer thermal model, making point predictions of ambient temperature and transformer load for the intermediate time slot [h-k+1,h-1], performing a thermal transient evaluation for each considered intermediate time slot [h-k+1,h-k+2,…,h-1] taking into account the predictions of ambient temperature and transformer load in order to predict the HST at the end of each intermediate time slot, the dynamic rating for a specific time slot h can be predicted, In the proposed 4-step procedure scheme, In the first step, a probabilistic forecast of ambient temperature and transformer load is developed. The first step is generated at the end of each intermediate time slot hk until the end of time slot h(h-1). The input is the hourly ambient temperature measurement dataset [θ A,1 ,θ A,2 ,θ A,3 ,…,θ A,h-k ] and hourly transformer load data set [I1,I2,I3,…,I h-k ], until the end of time slot hk, these data sets and further quantitative and qualitative predictors are the input to a 2-quantile regression QR model that provides the ambient temperature over the entire forecast lead time k and transformer load The prediction quantile set of ambient temperature and transformer load can be extracted from the interpolated prediction cumulative distribution through the inversion method. Step 2 uses the predicted samples up to time slot h-1 in the Monte Carlo simulation to evaluate the transformer thermal transient scenario by applying the transformer dynamic thermal model. The output of this step is the sample distribution prediction of the transformer HST at the end of time slot h-1. Step 3: Given the maximum allowed HST(θ H,max ) and the predicted distribution forecast of ambient temperature Monte Carlo simulation is used to invert the transformer dynamic thermal model to obtain the predicted sample distribution of the transformer dynamic rating within one hour. In step 4, the present value of the transformer allowable current is inferred through a probability indicator, the expected hourly unit rating (HEPR). This method uses the thermal model proposed in the IEEE Oil-Immersed Transformer Load Guide. According to the IEEE and IEC Oil-Immersed Transformer Load Guide, the HST of the transformer is the thermal parameter that mainly affects the transformer aging effect. The HST achieved in a time slot depends on the ambient temperature, the final load, and the initial condition of the transformer. The universal HST value of 110°C is expected to provide a uniform aging factor, so it is selected as the maximum allowable HST (θ H-max ), HST(θ H,h ) is calculated as shown in formula (1): i H,h =θ A,h +Δθ O,h +Δθ H,h (1) Where: θ A,h is the ambient temperature of time slot h; Δθ O,h is the top oil temperature rise above the ambient temperature at time interval h; Δθ H,h is the temperature rise of the hot spot exceeding the top oil temperature at time slot h, The solution formula for the top oil temperature rise exceeding the ambient temperature caused by the step load change is shown in formula (2): Where: L is the temperature rise of top oil relative to ambient temperature under rated load; u,h , L i,h are the final and initial loads of time slot h and the nameplate current I n R is the ratio of the loss under rated load to the loss under no-load; n is an empirical parameter based on the cooling type, ranging from 0.8 to 1; τ O,h For the initial load ratio L i,h To the final load ratio L u,h The oil time constant, in hours, that occurs during the transition The temperature rise of the hottest point exceeding the top oil temperature Δθ H,h The calculation formula is shown in formula (3): Where: m is an empirical parameter, and its value range is 0.8 to 1 according to different cooling methods; or 65℃, changes with the average winding temperature rise, Given the transformer characteristics, ambient temperature and initial load value, HST is a function of the final load ratio, and the calculation formula is shown in formula (4): i H,h =θ H,h (L u,h |θ A,h ,L i,h ) (4) The ambient temperature θ A,h As a random variable, the time slot h prediction is provided by the QR method, and the initial load rate L i,h Calculated as the equivalent heat load rate for the first 10-12 hours, The lead time prediction is achieved by iteratively applying the one-step-ahead model. For the ambient temperature QR model, the α-quantile of the ambient temperature at time h The prediction model is shown in formula (5): Where: and are P+1 model coefficients; x 1θ,t 、x Pθ,t is the P predictor variable, The estimate is found by minimizing the marble loss function PLF during model training. and The PLF of the ambient temperature at each time slot t is shown in equation (6): Several combinations of quantitative and qualitative predictors are trained, choosing those that result in PLF during validation t The smallest model is used to make predictions during testing, and the process is then iterated for the other quantiles to obtain a collection of ambient temperature quantile predictions The predicted cumulative distribution function of the ambient temperature is obtained by interpolating the quantiles, and the ambient temperature prediction samples are extracted by the inversion method. For the transformer load QR model, the α-quantile prediction of the transformer load at hour t is The model is established as shown in formula (7): Where: All are Q+1 load model coefficients; y 1I,t ,y QI,t is the Q predictor variable.

3. The method for predicting allowable current of an oil-immersed transformer based on ambient temperature and load according to claim 1 is characterized in that: In the step 2, Once the transformer dynamic rated current I in time slot h is known h-max The predicted sampling distribution f Ih-max , the decision-making allowable current I of the transformer in the same hour can be obtained by calculating the index HEPR h-al HEPR is composed of hourly availability rate HA, hourly average load reduction I mlc,h and weighted average load reduction I wmlc,h Calculated, HA is the transformer load I h The function is that the load does not exceed the transformer dynamic rating distribution f Ih-max The prediction sample {I lim,h1 , ..., I lim,hNs }, N s is the total number of samples drawn, so the HA calculation formula is shown in formula (8): In the formula: When i =0, otherwise λ i =1, HA decreases as the transformer load increases, then (1-HA) is the hourly unavailability, and by definition, for each I h-inf ≤min{I lim,h1 , ..., I lim,hNs }, HA(I h-inf )=1, and for each I h-sup >max{I lim,h1 , ..., I lim,hNs }, HA(I h-sup )=1, I mlc,h The magnitude of the unavailability consequence is given by the transformer load, which is the average difference between the transformer load and the dynamic rating prediction sample. In fact, in order to meet the thermal constraints of the transformer, the average value of the current, I mlc,h isI h The function is defined as shown in formula (9): Hourly weighted average load reduction required to avoid violating thermal constraints I wmlc,h (I h ) is I h The function is calculated as shown in formula (10): I wmlc,h The structure of is derived from the classic risk-based framework, HEPR is introduced to provide a more intuitive and flexible indicator. It is the normalized difference between a given transformer load and the hourly weighted average load reduction required to avoid violating the thermal constraint. Its percentage value is defined as shown in formula (11): When HEPR = 100%, it can be guaranteed that the thermal constraints are not violated under the dynamic rating prediction distribution. Obviously, HEPR (I h-inf )=100%. On the contrary, the closer the HEPR is to 0%, the higher the product between the probability of critical events and the load shedding consequences. Finally, the allowable current I based on HEPR is defined. h-al The criterion is to select the transformer load I associated with the specified HEPR level h , several strategies can be adopted. SG operators can choose I h-al for: 1) Safety value I h-al(100％) , which is the maximum possible load to return a 100% HEPR level, i.e. I h-al(100％) =min{I lim,h1 , ..., I lim,hNs }, the value is considered safe because I h-al(100％) Out of sample prediction lim,h1 , ..., I lim,hNs } is 0, in which case the hourly availability HA(I h-al(100％) )=1,hourly weighted average load reduction I wmlc,h (I h-al(100％) ), obviously, this choice can only be established if the SG operator fully trusts the probability prediction of the dynamic rating; 2) Conservative value I h-al(cons) , even less than I h-al(100％) (i.e. I h-al(cons) <I h-al(100％) , as an extremely safe allowable current, SG operators can select I h-al(cons) h-al(100％) To reduce the transformer load, it should also be noted that in this case, HA (I h-al(cons) )=1,I wmlc,h (I h-al(cons) )=0 and HEPR(I h-al(cons) )=100%.​

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