Take a seat and start updating the idea code of the Electrician Cup Mathematical Modeling Competition in real time in this post, and get it at the end of the article!
A question thinking analysis
Question 1: 1 Analysis of power consumption behavior of typical household electric heating load
(1) Under the constraints of the temperature control interval, analyze the behavior of the steady-state solution of the differential equation in a typical room temperature change process, including heating power P heat ( t ) , indoor temperature q in ( t ) and wall temperature q wall ( t ) change characteristics, and analyze the influence of model parameters on the change law of the steady-state solution.
For this question, we need to establish a differential equation physical model describing the relationship between electric heating equipment and indoor temperature. Models based on thermodynamics and heat transfer equations are often available to describe how a device converts electrical energy into heat, and how that heat propagates and affects room temperature.
Then, the steady-state solution of this differential equation needs to be solved. This can usually be achieved by setting the derivative term to zero and then solving the resulting algebraic equation. This may require the use of numerical methods such as Newton's method or bisection.
(2) The initial indoor temperature is 20°C. Under the outdoor temperature given in Table 1, calculate and draw the indoor temperature change and the corresponding electric heating equipment switch status curve for 24 hours a day, and fill in Table 1 with statistics related characteristic quantities , and Analyze the influence of outdoor temperature on the operating characteristics and power consumption of electric heating equipment.
For this problem we need to use numerical simulation methods. A finite difference method or a finite element method can be used to simulate indoor temperature variation over a day. The calculation process requires the use of an iterative approach, and each iteration requires updating the temperature and checking whether the temperature constraints are met.
Statistically related characteristic quantities (such as heating time, cooling time, period, duty cycle, etc.) are usually a post-processing step for simulation results. These feature quantities may need to be calculated based on the working status of the electric heating equipment and the historical data of the indoor temperature.
(3) Assuming that the heating period is 180 days, and the average outdoor temperature and duration are shown in Table 2, try to calculate the electricity consumption and electricity cost of typical households during the heating period , and fill in Table 2.
The simulation in problem (2) above can be extended to the entire heating period, given the outdoor temperature and duration of days in Table 2 . You need to simulate the temperature change every day, and then calculate the total electricity consumption and electricity cost according to the working status of the equipment.
Question 2: Analysis of the ability of typical household electric heating loads to participate in power regulation
Due to the thermal inertia of the building, the downward power adjustment capability can be obtained by turning off the electric heating equipment in the heating state, and the duration of the downward adjustment is limited by the lower limit of the temperature control range; the upward adjustment can be obtained by turning on the electric heating equipment in the off state. The power adjustment capability of the device, the duration of the increase is limited by the upper limit of the temperature control range.
We need to understand and exploit the thermal inertia of buildings. Thermal inertia is a property of a building that enables it to maintain a stable temperature over a period of time, even if the temperature of the external environment changes. In this problem, we need to consider the working state of the electric heating equipment (on or off) and the upper and lower limits of the temperature control interval.
- Taking the electric heating load of a single household as the object, the outdoor temperature is -15°C, the initial indoor temperature is 20°C, and the initial state of the electric heating equipment switch is on, calculate the power of the electric heating load of a typical household at each time point (interval 1min) in 24 hours a day Up-regulation, down-regulation duration, and plot the calculated results.
The solution to this problem is to build a time series model, which is used to record the switch state of electric heating equipment, indoor temperature and outdoor temperature, and update it at intervals of 1 minute. The initial conditions of the model are that the outdoor temperature is -15°C, the initial indoor temperature is 20°C, and the initial state of the electric heating equipment is on.
We need to run the model for 24 hours and record every minute. For each update, it is necessary to calculate the current power (based on the state of the device and the temperature difference between indoor and outdoor) and the time the device can continue to increase or decrease power under the constraints of the temperature control interval.
Finally, a visualization is performed on the data to visually show the duration of power up and down at each time point of the day.
- (2) For the different outdoor temperatures given in Table 1, calculate the sustainable time of the electric heating load power up and down, and analyze the influence of different outdoor temperatures on the power up and down characteristics.
The solution to this problem is similar to the above, but you need to do the calculations separately for each outdoor temperature given in Table 1. This means you need to run the model once for each outdoor temperature, and record and plot the results.
When analyzing these results, you can observe and compare the change in the turn-up and turn-down duration of the electric heating device at different outdoor temperatures, so as to understand the effect of the outdoor temperature on the power regulation ability of the electric heating device.
Note that the above analysis assumes that other conditions (such as the initial temperature of the room and the initial state of the equipment) are fixed. In actual situations, these conditions may vary and more complex simulations and analyzes may be required.
Question 3: Analysis of regulation capacity of multiple electric heating loads
Taking 6 electric heating households (serial numbers 1-6) as an example, assuming that the outdoor temperature is -20°C and the initial indoor temperature is evenly distributed within the temperature control range, select a set of initial states of the electric heating equipment switches:
(1) Calculate the 24-hour indoor temperature change and the switching status of electric heating equipment for 6 households during normal power consumption, and draw the total power consumption curve of 6 households.
We need to initialize the status of each resident, including the indoor temperature and the on/off status of electric heating equipment. Then, given the outdoor temperature and the state of each resident, you can use your model to predict their electricity demand and indoor temperature.
From this data, we can draw an electricity demand curve for each household, representing their electricity demand at each point of the day. These curves can then be added to obtain the total electricity demand curve for all households.
(2) Based on the above-mentioned total power consumption curves of the 6 households, calculate and draw the number of electric heating equipment that can be adjusted up and down at each time point (interval 1 min) within 24 hours of the day and the total power that can be adjusted up and down at each time point.
Based on the power demand and indoor temperature data we have calculated, we can calculate the power that can be adjusted up and down by each household's electric heating equipment at each point in time. Then, we can draw a graph for each time point, showing the serial numbers of the electric heating devices that can participate in the regulation and their total adjustable power.
(3) Under the given outdoor temperatures in Table 1 , re -analyze questions (1) and (2), and analyze the influence of different outdoor temperatures on the adjustable capacity of electric heating equipment.
For each outdoor temperature given in Table 1, you can repeat the above steps. Then, you can analyze and compare the regulation ability of the electric heating equipment at different outdoor temperatures, so as to understand the effect of the outdoor temperature on the regulation ability of the electric heating equipment.
The above calculation process will involve complex calculations and simulations, and may require specialized software and algorithms. The specific calculation methods and results depend on your specific needs and data, as well as the mathematical model and algorithm you choose.
Question 4: Analysis of the ability of electric heating load in residential areas to participate in power grid regulation
Taking 600 households in the electric heating residential area as the analysis object, assuming that the initial indoor temperature of each household is evenly distributed in the temperature control interval, under the average outdoor temperature shown in Table 1, select a group of initial states of the electric heating equipment switch , calculate the indoor temperature and the switch state of the electric heating equipment at each time point of 24 hours in a day, and draw the total power consumption curve of the electric heating equipment in the residential area. Based on the above-mentioned total electric power curve, calculate and draw the total power curve that the electric heating load of the residential area can participate in the up-regulation and down-regulation at each time point in 24 hours of the day.
We need to initialize the state for all 600 households. This includes the indoor temperature (assumed to be uniformly distributed over the temperature control interval) and the initial on-off state of the electric heating equipment.
Based on the given outdoor temperature and the initial state of each household in Table 1, we can use a suitable physical or statistical model to predict the electricity demand and indoor temperature of each household. Based on the electricity demand of each household, we can calculate the total electricity demand for the entire residential area and draw a curve representing the total electricity demand at each time point of the day. Based on each resident's power demand and indoor temperature, we can calculate the power available for scaling up and down at each point in time and draw a curve representing that power.
Question 5: Benefit Analysis of Electric Heating Load in Residential Area Participating in Power Grid Shaving and Valley Filling
The aggregator organizes 600 electric heating loads in residential areas to participate in peak-shaving and valley-filling of the power grid (see Appendix B for peak-shaving periods, valley-filling periods and compensation prices), and needs to determine the maximum regulated power value that can be continuously provided during peak-shaving or valley-filling periods. The results of power up and down at each time point solved in question 4 are determined based on the switch state of the electric heating equipment that simply satisfies the constraints of the temperature control interval. The participation of the electric heating load in power regulation will change its original switch state, thereby affecting Time-varying nature of subsequent adjustable power.
First, we need to calculate the maximum continuous downward and upward adjustment power values that can be provided by 600 electric heating loads during the peak-shaving and valley-filling periods, respectively. This may require the calculation of temperature changes within the house using a thermal model that will take into account the initial state of the occupants, temperature control interval constraints, the switching status of electric heating equipment, and its impact on subsequent adjustable power.
We also need to count the number of electric heating equipment whose on and off states change due to participation in grid regulation. This will involve making changes to the preset switching states of the electric heating equipment and observing the results.
It is necessary to check whether the indoor temperature of all residents meets the constraints of the temperature control interval. This may require additional simulations or calculations to determine room temperature changes after participating in grid regulation.
We need to estimate the total benefit of the electric heating load in residential areas participating in peak shaving and valley filling under various outdoor temperatures. Consider using dynamic programming to find the optimal switching strategy for electric heating equipment . This HIA involves calculating the annual residential area electric heating load participation in peak-shaving and valley-filling up-regulation and down-regulation benefits based on the auxiliary service compensation price, and calculating Average household benefits and percentage savings in heating costs.
Question 6: Prospects for temperature-controlled loads participating in power grid regulation
(1) Based on the above calculation results, analyze the potential of electric heating load participating in power grid regulation and possible problems encountered in the provincial area with a prospective area of 40 million m 2 , and give suggestions and solutions.
Possible problems:
Difficult to control: due to the dispersion of electric heating load, management and control are difficult. It is necessary to schedule the electric heating load under the premise of ensuring the user's temperature comfort.
User acceptance problem: Users may resist the frequent start and stop of electric heating equipment and scheduling behaviors that may affect temperature comfort.
Solutions and suggestions:
Establish an accurate load forecasting model to predict changes in electric heating load in advance to achieve more effective scheduling.
Improve the enthusiasm of users to participate, for example, by setting a reasonable electricity price mechanism, let users benefit from participating in grid regulation, and improve user acceptance.
(2) The temperature-controlled loads in the southern provinces are mainly air conditioners. The characteristics, potential and possible problems of air conditioner loads participating in grid regulation are analyzed and forecasted.
The air-conditioning load has obvious seasonal and temporal characteristics, and the grid load is heavy during the summer peak period and the daytime peak period.
The adjustment potential of load adjustment is huge. The on and off of the air conditioner can be used for frequency regulation and load balancing of the grid.
Possible problems:
The control of air-conditioning equipment is also difficult, and the user's comfort and the service life of the equipment need to be considered.
The change of air-conditioning load is greatly affected by the climate, so it is necessary to establish an accurate weather forecast and load forecast model.
Solutions and suggestions:
Establish accurate weather forecasting and load forecasting models to schedule power grids in advance.
Formulate reasonable electricity price policies and incentive mechanisms to encourage users to participate in grid regulation.
Analysis of problem B
Question B is an evaluation question, and the overall difficulty is much lower than question A. This question is mainly to evaluate the impact of artificial intelligence on college students' learning. We need to preprocess the provided data first, then establish evaluation indicators, then build a model, and finally write a report based on the model results and understanding of artificial intelligence. I will provide some possible solutions and models used for each problem.
Question 1: Analyze and numerically process the data given in Annex 2, and give a processing method;
We need to clean and preprocess the data. Some questions can be converted to binary variables, such as gender, use of learning software tools, etc. For questions with many categories, we can perform one-hot encoding, such as major, grade, personality, etc. For the duration of surfing the Internet, we can convert it into a numerical variable, which is convenient for subsequent calculation and analysis.
In the process of analysis, we need to use descriptive statistics methods to obtain the basic characteristics of the data, such as mean, median, mode, variance, frequency, etc. We may also use visualization tools such as boxplots, histograms, scatterplots, etc. to explore the distribution and relationships of the data.
Question 2: Select evaluation indicators based on your data analysis results, discuss their rationality in terms of priority, scientificity, and operability, and build an evaluation index system;
We can formulate corresponding evaluation indicators based on the data about the attitude and expectations of the use of AI tools, such as the acceptance of AI tools, the degree of dependence on AI tools, and the satisfaction with AI tools. The selection of evaluation indicators needs to be based on scientific reasons, such as the indicators' measurability, comparability, and importance in prediction and interpretation. At the same time, we need to consider the operability of indicators, such as whether the data is easy to obtain and whether it can reflect the real situation. The construction of the indicator system needs to take into account different aspects, and evaluate the impact of AI on learning as comprehensively as possible.
One possible way to establish an evaluation index system is to use the Analytic Hierarchy Process (AHP). AHP can be used to determine the weight of each indicator to reflect its relative importance.
Question 3: Establish a mathematical model, evaluate the impact of artificial intelligence on college students' learning, and give clear and convincing conclusions
We can consider the use of multiple linear regression models to assess the impact of AI on learning. In this model, the response variable could be the student's academic performance, while the predictor variables are the use of artificial intelligence and other factors that may affect academic performance (such as study time, learning method, etc.). Or use models such as decision trees and neural networks to make predictions and explanations .
Question 4: Based on the data of the questionnaire, combined with your understanding, cognition and judgment of artificial intelligence, and the prospect of future artificial intelligence development, write an analysis report on the impact of artificial intelligence on college students' learning, which can include but not limited to positive or negative effects.
The analysis report should first introduce the definition, development history and application of artificial intelligence in the field of education. Then, we should describe our data and analysis methods, including how we processed the data, selected evaluation indicators, and built models. Do as many visualizations as possible and explain the results. In doing so, we need to focus on how our models reveal the effects of AI on college student learning, and make clear whether those effects are good or bad .
At the end of the report, we will provide an outlook on the future development of artificial intelligence, discuss how artificial intelligence may continue to affect the learning of college students, and how we can use artificial intelligence to improve learning outcomes.