2021年美國HiMCM數學建模競賽A題中英文

中文賽題:儲存太陽

您的團隊正在計劃利用太陽能幫助一個(ge) 偏遠地區的1600平方英尺的房子提供電力。您的計劃應滿足該家庭在夜間和陰天的能量需求。您已經進行了一些研究,發現當您的太陽能電池板產(chan) 量不足時,您可以從(cong) 電網(即電力公司)購買(mai) 電量,或者使用儲(chu) 能係統。由於(yu) 房子在偏遠地區,接入電網的成本非常昂貴,因此您決(jue) 定不使用電網並投資儲(chu) 能(離網)。

背景: 能量存儲(chu) 係統可以讓您獲得電能,並將其存儲(chu) 為(wei) 另一種形式的能量(電池、熱能、機械能),然後在需要時使用。這些存儲(chu) 單元的目的是將晴天產(chan) 生的能量儲(chu) 存起來,以便在太陽能電池板不能產(chan) 生足夠的能量(夜間或雲(yun) 層覆蓋)時使用,或者用於(yu) 存儲(chu) 和轉移多餘(yu) 的能量。在使用儲(chu) 能係統的太陽能家庭中,大多數使用某種電池。一些房主隻有一個(ge) 大電池,而另外一些人可能使用“電池組”(連接兩(liang) 個(ge) 或多個(ge) 電池)。能量存儲(chu) 可能需要昂貴的成本,因此房主應該選擇適合他們(men) 情況的係統。圖 1 顯示了離網能源的簡單概念。

2021年美國中學數學建模競賽A題圖1: 離網能源係統示意圖

在選擇儲(chu) 能係統時,需要考慮很多準則。以下是一些最常見的決(jue) 策準則,以及對每種準則最重要的電池規格。

  • 要同時為(wei) 很多的家庭供電,您需要具有高連續額定功率的電池。

  • 要為(wei) 更耗能的設備供電(需要在短時間內(nei) 提供更多功率),您的電池應該具有較高的瞬時額定功率

  • 要想讓儲(chu) 能係統能為(wei) 您供電更長時間,請尋找具有更高可用容量的電池。

  • 如果您想充分利用輸入電池的電量,請尋找具有更高往返效率的電池。

其他注意事項適用於(yu) 電池類型。

  • 鉛酸(浸沒式或密封式)和鋰離子電池適用於(yu) 不同使用級別的全時離網供電。

  • 鉛酸電池已經存在很長時間,以其低廉的價(jia) 格和可靠性而聞名。

  • 鋰離子電池更貴,但無需維護。其他選項是鎳鎘電池和液流電池。

  • 磷酸鐵鋰 (LFP) 電池(一種鋰離子電池)具有最長的使用壽命和最多的循環次數。

  • 要獲得絕對最高的安全等級(盡管它們(men) 都是安全的),請查看 LFP 電池。

要求:

  1. 考慮您正在規劃的 1600 平方英尺的離網住宅。

    a. 首先確定您的能源需求需要列出問題列表,從(cong) 而分析您的太陽能存儲(chu) 需求。討論您的問題的可能答案範圍。為(wei) 了方便您開始研究,這裏提供幾個(ge) 問題:

    b. 使用您在第 1.a. 部分中的分析,考慮問題背景中的準則和因素以及您認為(wei) 重要的任何其他因素,建立數學模型或算法,為(wei) 您的離網家庭選擇“最佳”電池存儲(chu) 係統.

    c. 考慮可用的電池存儲(chu) 選項,並使用您的模型為(wei) 您的離網家庭選擇最佳選項。問題陳述末尾的圖表提供了幾個(ge) 電池選項(不局限於(yu) 這幾個(ge) 選項)。討論您的選擇。

    • 這個家有多少人會使用能源?
    • 家裏的哪些物品需要能源,需要多少能源?
    • 家裏的人什麽時候會使用能源?
  2. 調整並推廣您在問題一中所建立的模型,使其能適應個(ge) 人需求和偏好,可以為(wei) 任何家庭選擇最佳電池存儲(chu) 。討論您對模型所做的修改。評估您的模型。

  3. 最近,瑞典的研究人員發現水泥可以用來儲(chu) 存能量[1]。由水泥製成的混凝土用於(yu) 建造建築物、人行道、橋梁和無數其他結構。

    a. 確定使用水泥電池存儲(chu) 太陽能的一些優(you) 點和缺點。描述您如何將水泥用作離網家庭或任何家庭的電池?

    b. 確定並討論您需要的其他信息,以便您對水泥電池的使用進行建模並進行比較,並將其與(yu) 當前可用的太陽能存儲(chu) 電池進行比較。注意:您不需要創建模型。

  4. 寫(xie) 一篇一頁的非技術新聞稿,描述您的太陽能電池存儲(chu) 方案決(jue) 策模型。在您的文章中需包含有關(guan) 水泥電池未來可能性的一些建議。

您的PDF解決(jue) 方案(不超過 25 頁)應包括

  • 一頁摘要
  • 目錄
  • 完整的解決方案
  • 一頁新聞稿
  • 參考文獻

注意: HiMCM 競賽現在有 25 頁的限製。 您提交的所有內(nei) 容都計入 25 頁的限製(摘要表、目錄、參考列表和任何附錄)。

Glossary:

連續額定功率: 電池在電量耗盡之前可以連續提供的功率(千瓦 (kW) 或安培 (A) )。

儲(chu) 能係統: 可以捕獲電力以另一種形式存儲(chu) ,並可隨時用來供電的係統

瞬時額定功率: 電池可以在短時間內(nei) 提供的千瓦 (kW) 或安培 (A) 功率(但不能長期維持)。

使用壽命(電池): 您的電池能正常工作的時長,通過預期的運行年數、預期的吞吐量(kWh使用量)和預期的循環(充電和放電)次數來衡量。

離網:不使用或依賴公共電力供應(或其他公用事業(ye) )。

往返效率:你從(cong) 每一個(ge) 單位的電池中獲得的電量,以百分比來衡量。

可用容量:電池能夠儲(chu) 存和供應給您家的電量,以千瓦時 (kWh) 或安培小時 (Ah) 為(wei) 單位。

英文賽題:Storing the Sun

Your team is helping to plan the use of solar power to provide electricity to a 1600 square-foot home being built in a remote area. You need to plan for enough energy to support the energy requirements of the home at night and on a cloudy day. You have done some research and found that you can either pull energy from the grid (i.e. a power company) when your solar panels aren’t producing enough, or use an energy storage system. As the house is in a remote area, the cost of connecting to the grid is very expensive, so you decide to go off-the-grid and invest in energy storage.

Background: An energy storage system allows you to capture electricity, store it as another form of energy (battery, thermal, mechanical) and then have it available to use when needed. The purpose of these storage units is to store energy produced during sunny daylight hours for use when the solar panels do not produce enough energy for the demand (night or cloud covered), or for storage and transfer of excess energy. Of the solar-powered homes that use an energy storage system, most use some sort of battery. Some homeowners have only one large battery, while others may use a “bank of batteries” (two or more batteries connected). Energy storage can be expensive and so homeowners should choose a system that is appropriate for their situation. Figure 1 shows the general concept of off-the-grid energy.

2021年美國中學數學建模競賽A題Figure 1:Off-the-Grid Energy System

In choosing an energy storage system there are many criteria to consider. Here are a few of the most common decision criteria, as well as which battery specifications matter most for each criterion.

  • To power more of your home at once, you will want a battery with a high continuous power rating.
  • To power a more energy-intensive appliance (requiring more power in short bursts), your battery should have a high instantaneous power rating.
  • To run your home for a longer amount of time, look for a battery with a higher usable capacity.
  • If you want to get the most out of every kilowatt-hour of electricity you put into your battery, look for a battery with a higher round-trip efficiency.

Additional considerations apply for the type of battery.

  • Lead-acid (flooded or sealed) and lithium-ion batteries are ideal for a full-time, off-grid supply of different levels of use.
  • Lead-acid batteries have been around for a long time and are known for their low prices and reliability.
  • Lithium-ion batteries are more expensive, but require no maintenance. Other options are nickel cadmium and flow batteries.
  • Look for lithium iron phosphate (LFP) batteries (a type of lithium-ion battery) to get the longest lifetime that you can cycle the most times.
  • For the absolute highest safety rating possible (although they are all safe), look to LFP batteries.

Requirements:

  1. Consider the 1600 square-foot off-the-grid home you are planning.

    a. Analyze your solar-power storage requirements by first making a list of questions to determine your energy needs. Discuss the range of possible answers to your questions. To get you started, here are a few questions:

    b. Use your analysis from part 1.a., along with the criteria and considerations from the problem background and any other factors you consider important, to develop a mathematical model or algorithm for choosing the “best” battery storage system for your offthe- grid home.

    c. Consider available battery storage options and use your model to choose the best option for your off-the-grid home. The chart at the end of the problem statement provides several, but not all, battery options. Discuss your choice.

    • How many people will be using energy in this home?
    • What items in the home will need energy and how much energy will they need?
    • When will people in the home use energy?
  2. Adjust and generalize your model from Requirement 1 so that it is adaptable to individual needs and preferences to choose the best battery storage for any home. Discuss the changes you make to your model. Evaluate your model.

  3. Recently, researchers in Sweden discovered that cement could be used to store energy[1]. Concrete, which is made with cement, is used to build buildings, sidewalks, bridges, and countless other structures.

    a. Identify some of the advantages and disadvantages of using cement batteries to store solar power. Describe how might you incorporate cement as a battery for your off-the-grid home or for any home?

    b. Determine and discuss the additional information you would need in order for you to model and compare the use of cement batteries to currently available batteries for solarpower storage. Note: You are NOT required to create the model.

  4. Write a one-page non-technical news article describing your solar power battery storage decision model. Include in your article any recommendations for the future possibilities of a cement battery.

Your PDF solution of no more than 25 total pages should include:

  • One-page Summary Sheet.
  • Table of Contents.
  • Your complete solution.
  • One-page Article.
  • References list.

Note: The HiMCM Contest now has a 25-page limit. All aspects of your submission count toward the 25-page limit (Summary Sheet, Table of Contents, Reference List and any Appendices).

Glossary:

Continuous Power Rating: the kilowatts (kW) or Amps (A) of power that the battery can provide continuously (until the battery runs out of power).

Energy Storage System: a system that captures electricity, stores it in another form, and then retrieves it for use at a later time.

Instantaneous Power Rating: the kilowatts (kW) or Amps (A) of power that the battery can provide in short bursts (but not sustain over a long period).

Lifetime (of battery): the length of time your battery will continue working which is measured by expected years of operation, expected throughput (kWh of use), and expected number of cycles (charging and discharging).

Off-The-Grid: not using or depending upon public supply of electricity (or other utilities).

Round-Trip Efficiency: the number of units of electricity you’ll get out of a battery for every unit you put into it measured in a percentage.

Usable Capacity: the amount of electricity, in kilowatt-hours (kWh) or Amp-hours (Ah) that a battery is able to store and supply to your home.

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