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能源管理中的能源消耗预测模型构建方法随着全球对能源资源的需求不断增加，对能源管理的需求也越来越迫切。
能源消耗预测模型的构建对于合理规划能源供需、优化能源利用具有重要意义。
本文将介绍几种常用的能源消耗预测模型构建方法，包括传统的时间序列方法和机器学习方法。
1. 时间序列方法时间序列方法以时间为变量，通过分析和预测历史能源消耗数据的趋势和周期性变化来进行预测。
常用的时间序列方法包括：1.1 移动平均法移动平均法是最简单的时间序列方法之一。
它基于过去一段时间内的平均数据来预测未来的能源消耗。
通过选择适当的时间窗口长度，可以平滑掉数据的波动性，提高预测的稳定性。
1.2 指数平滑法指数平滑法是一种基于加权移动平均的方法。
它将较大的权重放在最近的观测值上，较小的权重放在较远的观测值上。
这样可以更好地适应数据的变化，并且对离群值更具有鲁棒性。
1.3 ARIMA模型ARIMA模型是一种常用的时间序列预测模型，它包括自回归（AR）部分、差分（I）部分和移动平均（MA）部分。
ARIMA模型能够处理具有非线性、非平稳特性的数据，适用于多种类型的时间序列数据。
2. 机器学习方法机器学习方法可以利用历史能源消耗数据中的特征和模式，通过构建合适的模型来进行未来能源消耗的预测。
常用的机器学习方法包括：2.1 回归模型回归模型是一种常用的机器学习方法，通过找到输入特征和输出目标之间的关系来进行预测。
对于能源消耗预测，可以选择线性回归、多项式回归或者其他非线性回归模型，根据实际情况选择最合适的模型。
2.2 支持向量回归（SVR）支持向量回归是一种非常适合处理非线性关系的回归方法，它通过在高维空间中构建一个最佳拟合超平面来进行预测。
SVR可以处理高维数据和大规模数据集，能够更准确地拟合能源消耗数据的特征。
2.3 集成学习方法集成学习方法将多个学习算法组合起来，通过集体决策来提高预测的准确性和稳定性。
常用的集成学习方法包括随机森林、梯度提升树等。
基于时间序列分析的能源消耗预测模型构建能源消耗预测模型是一个重要的研究领域，它对于有效管理能源资源、规划能源供应和促进能源可持续发展具有关键作用。
基于时间序列分析的能源消耗预测模型是其中的一种常用方法。
在构建能源消耗预测模型之前，我们需要收集历史能源消耗数据作为模型的训练集。
这些数据可以包括每日、每月或每年的能源消耗量。
除了能源消耗数据，还可以考虑与能源消耗相关的其他因素，如天气数据、经济指标等。
这些额外的因素可以帮助我们更准确地预测未来的能源消耗。
一种常见的基于时间序列分析的能源消耗预测模型是ARIMA模型（自回归综合移动平均模型）。
ARIMA模型是一种广泛应用于时间序列预测的统计模型。
它通过将时间序列中的趋势、季节性和随机性分解成不同的部分，并根据历史数据来拟合这些部分，从而进行未来预测。
ARIMA模型的建立包括三个主要步骤：模型选择、参数估计和模型验证。
首先，我们需要选择适合于能源消耗数据的ARIMA模型。
在选择模型时，可以根据能源消耗数据的平稳性、自相关性和偏自相关性来判断最合适的模型。
平稳性是ARIMA模型的前提条件，可以通过观察时间序列的均值、方差和自相关图来进行诊断。
自相关图可以用来判断模型的自相关性和偏自相关性。
在选择了ARIMA模型之后，我们需要根据历史能源消耗数据对模型的参数进行估计。
参数估计可以通过最大似然估计方法来进行。
最大似然估计方法的目标是找到可以最大程度地解释观测数据的模型参数。
完成参数估计后，我们需要对建立的模型进行验证。
这可以通过计算模型的残差（预测值与实际值之间的差异）来实现。
如果模型的残差是随机的，表示模型可以很好地拟合数据。
另外，可以使用一些统计检验方法，如Ljung-Box检验或DW 检验来验证模型的残差是否是随机的。
建立了能源消耗预测模型后，我们可以使用该模型来进行未来能源消耗的预测。
根据选择的时间跨度，我们可以预测未来一段时间内的能源消耗量。
预测结果可以帮助决策者制定有效的能源战略，合理规划能源供应和需求。
能源管理系统中的能耗预测方法及使用注意事项一、引言能源管理系统（Energy Management System，EMS）是为有效地控制和管理能源资源而设计的系统。
能耗预测是能源管理系统中的重要环节，通过对未来一段时间内的能耗进行预测，可以帮助企业制定合理的能源使用计划，提高能源利用效率，降低能源成本。
本文将介绍能耗预测的常用方法，以及在使用能源管理系统时的注意事项。
二、能耗预测的方法1. 基于统计模型的预测方法基于统计模型的能耗预测方法使用历史能耗数据进行建模，并通过统计分析来预测未来的能耗。
常用的统计模型包括ARIMA模型、灰色模型和回归模型等。
这些模型可以根据实际情况选择合适的变量和参数，进行能耗的预测。
2. 基于机器学习的预测方法基于机器学习的能耗预测方法通过训练模型来学习历史能耗数据中的模式和规律，并使用学习到的模型来进行未来能耗的预测。
常用的机器学习方法包括支持向量机（SVM）、人工神经网络（ANN）和随机森林等。
这些方法可以根据数据的特征选择合适的算法，并通过不断调整模型参数来提高预测的准确性。
3. 基于物理模型的预测方法基于物理模型的能耗预测方法通过对能源系统的建模，使用物理方程和实验数据来进行能耗的预测。
这种方法需要对能源系统的结构和参数有深入的了解，并进行系统的建模和模拟。
物理模型可以提供较为精确的能耗预测，但对于复杂的能源系统来说，建模和参数调整的难度较大。
三、能源管理系统的使用注意事项1. 数据质量的保证能耗预测的准确性与输入数据的质量密切相关。
在使用能源管理系统进行能耗预测时，需要确保能耗数据的准确性和完整性。
数据采集设备和传感器的运行稳定性和准确性对数据的质量有重要影响，需要定期检测和维护。
2. 模型的选择和参数的调整在进行能耗预测时，需要根据实际情况选择合适的预测模型，并进行模型的参数调整。
不同的模型适用于不同的能耗数据特征，所以需要根据实际情况选择合适的模型和算法，并对模型进行参数的优化和调整，以提高预测的准确性。
机器学习在能源消耗预测中的应用随着全球能源需求的不断增加，如何高效、准确地预测能源消耗成为了研究的热点。
机器学习（Machine Learning）作为一种新兴的信息处理技术，以其强大的数据分析能力和预测能力，越来越多地应用于能源消耗的预测中。
本文将探讨机器学习在这一领域的应用及其带来的影响。
一、能源消耗预测的重要性能源消耗预测对于各类机构和政府部门具有重要意义，因为它能够帮助实现以下目标：1.资源优化配置：准确的能源需求预测可以使电力公司及相关机构更有效地分配资源，防止资源的浪费。
2.供应链管理：在不同时间段内，如果能够准确预测需求，企业可以更好地管理库存，降低成本。
3.环境保护：通过合理的能源消耗预测，可以提前采取措施，减少碳排放，实现可持续发展。
二、机器学习的基本原理机器学习是一种通过自动分析和学习数据以进行预测的技术。
其基本原理包括：1.数据收集：通过传感器和其他数据收集设备，获取大量有关能源使用的数据。
2.特征提取：从收集的数据中提取能有效代表样本的信息，形成模型输入的数据结构。
3.模型建立：利用历史数据和提取的特征，选择适当的机器学习算法（如线性回归、支持向量机、神经网络等）建立预测模型。
4.模型评估与优化：通过交叉验证、精度测量等方法评估模型的有效性，并根据评估结果不断优化模型。
三、机器学习在能源消耗预测中的具体应用1. 负荷预测负荷预测是电力系统管理的重要环节。
机器学习通过分析历史负荷数据、天气因素、经济指标等多维信息，建立负荷预测模型。
例如，利用长短期记忆（LSTM）神经网络，能够有效捕捉时间序列数据的动态特征，从而提高短期负荷预测的准确性。
2. 能源消耗模式分析使用机器学习方法可以分析建筑物或工厂的能耗模式，通过聚类算法（如K均值聚类）将相似的用能模式分组，从而明确高耗能的区域或设备，有助于采取节能措施。
3. 智能家居中的应用智能家居系统可以根据用户的生活习惯和实时环境数据，通过机器学习算法预测未来的能源消耗。
统计学模型预测能源消耗趋势在当今全球能源不断紧张的背景下，预测能源消耗趋势变得尤为重要。
统计学模型成为了一种常用的方法，通过对历史数据的分析和预测，以及对相关因素的考虑，可以预测未来能源消耗的趋势。
本文将探讨统计学模型在预测能源消耗趋势中的应用，并介绍一些常用的统计学模型。
首先，我们需要明确能源消耗趋势预测的重要性。
能源是社会经济发展的基石，对于国家和地区的可持续发展至关重要。
准确预测能源消耗趋势，可以指导政府决策，合理配置和利用能源资源，降低能源消耗的压力，保障国家经济稳定运行。
接下来，我们将介绍几种常用的统计学模型。
首先是线性回归分析模型。
线性回归分析模型基于一个假设：能源消耗与一系列因素（如经济增长、人口变化、技术创新等）之间存在着线性关系。
通过收集和分析历史数据，可以建立一个数学模型，来描述能源消耗与这些因素之间的关系，并最终预测未来能源消耗趋势。
其次是时间序列模型。
时间序列模型是一种基于时间序列数据的分析方法。
该方法认为，能源消耗趋势具有一定的时间依赖性，即未来的能源消耗与过去的消耗密切相关。
时间序列模型可以通过分析和拟合历史数据中的周期性和趋势性，来预测未来的能源消耗趋势。
另外，非线性回归模型也是一种常用的预测能源消耗趋势的统计学模型。
不同于线性回归模型，非线性回归模型认为能源消耗与因素之间存在着非线性关系。
例如，能源消耗可能随着经济增长呈现指数级的增长趋势。
通过采集足够多的历史数据，并应用相应的非线性回归模型，可以更准确地预测未来能源消耗的趋势。
对于不同的统计学模型，我们需要选择合适的评估指标来评估模型的预测性能。
常见的评估指标包括均方根误差（RMSE）、平均绝对百分比误差（MAPE）等。
这些指标可以帮助我们衡量模型的准确性和可靠性，并选择最优的模型进行预测。
此外，统计学模型预测能源消耗趋势还需要考虑一系列外部因素。
例如，全球经济的发展状况、能源政策的调整、技术创新的进展等都会对能源消耗产生重要影响。
能源消耗模型与预测方法的比较分析随着全球能源需求的不断增长，能源消耗模型与预测方法的研究变得越来越重要。
通过对各种能源消耗模型和预测方法进行比较分析，可以更好地了解能源消耗的趋势和影响因素，为能源规划和政策制定提供科学依据。
一、定量模型定量模型是通过建立数学模型来预测能源消耗的方法。
常见的定量模型包括线性回归模型、ARIMA模型和灰色模型等。
线性回归模型是一种常用的预测方法，它基于历史数据，通过建立能源消耗与影响因素之间的线性关系来进行预测。
ARIMA模型是一种时间序列分析方法，它考虑了时间序列的趋势和季节性，能够更准确地预测能源消耗的变化。
灰色模型则是一种基于灰色系统理论的预测方法，它通过建立灰色微分方程来进行预测，适用于数据量较少或者不完整的情况。
二、系统动力学模型系统动力学模型是一种基于系统思维的预测方法，它考虑了能源消耗系统中各个因素之间的相互作用和反馈机制。
系统动力学模型常用于复杂的能源消耗系统，能够模拟系统的动态变化过程，并预测未来的发展趋势。
通过对系统动力学模型的建立和仿真，可以识别出系统中的关键影响因素，为能源消耗的调控和管理提供决策支持。
三、混合模型混合模型是将不同的预测方法进行组合，以提高预测的准确性和稳定性。
常见的混合模型包括ARIMA-GARCH模型和神经网络模型等。
ARIMA-GARCH模型将ARIMA模型和GARCH模型相结合，能够考虑到时间序列的波动性和非线性特征，提高了预测的精度。
神经网络模型则是一种基于人工神经网络的预测方法，通过学习历史数据的模式和规律来进行预测，适用于非线性和复杂的能源消耗系统。
四、优劣比较不同的能源消耗模型和预测方法各有优劣。
定量模型简单易用，适用于数据量较大和变化趋势较为稳定的情况，但对于非线性和复杂的系统往往预测效果较差。
系统动力学模型能够考虑到系统的动态变化和复杂性，但对于数据需求较高，建模和仿真过程较为复杂。
混合模型结合了不同的预测方法，能够充分利用各个方法的优势，提高预测的准确性和稳定性，但对于模型的选择和参数的确定较为困难。
基于机器学习的航空燃料消耗预测模型研究航空燃料消耗是航空运输行业中的一项重要指标，对于航空公司来说，准确预测航班的燃料消耗是管理航班成本、提高效率的关键。
机器学习作为一种可以自动学习和优化模型的方法，被广泛应用于各种领域，包括航空燃料消耗预测。
本文将探讨基于机器学习的航空燃料消耗预测模型的研究。
首先，我们需要了解机器学习在航空燃料消耗预测中的应用。
机器学习可以通过训练数据来学习和推断模型，然后利用学习到的模型对未知数据进行预测。
在航空燃料消耗预测中，机器学习模型可以通过历史航班数据和各种相关因素，如起飞重量、飞机型号、飞行距离等，来预测航班的燃料消耗。
通过构建一个精确可靠的预测模型，航空公司可以更好地规划飞行计划、提高航班效率，从而降低成本。
其次，我们需要挑选适合的机器学习算法用于航空燃料消耗预测模型的研究。
常见的机器学习算法有线性回归、支持向量机、决策树、随机森林等。
针对航空燃料消耗预测，我们可以使用回归算法。
回归算法旨在建立输入变量和输出连续变量之间的映射关系。
通过对历史数据的学习，回归模型可以预测未知数据的输出值。
在航空燃料消耗预测中，使用回归算法可以预测航班的燃料消耗值。
然而，在应用回归算法建立航空燃料消耗预测模型之前，我们首先需要对数据进行预处理。
数据预处理是机器学习中非常重要的一步，主要包括数据清洗、特征选择和特征标准化。
数据清洗可以排除异常值和缺失值，确保数据的质量和完整性。
特征选择是指从所有可能的特征中选择出对燃料消耗具有显著影响的特征，以减少模型复杂度和提高预测准确性。
特征标准化是指对不同特征进行缩放处理，以消除数据之间的量纲差异，使得模型更加稳定和可靠。
接着，我们可以开始构建基于机器学习的航空燃料消耗预测模型。
在模型构建过程中，我们使用历史航班数据作为训练集，通过学习历史数据中的模式和规律，建立起燃料消耗与相关因素之间的关系模型。
然后，通过对模型的测试和评估，选择最优的模型作为预测模型。
关于能源需求量预测常用模型及方法能源需求量的准确预测对于能源供应和能源政策的制定具有重要意义。
以下是常用的能源需求量预测模型和方法。
1.回归分析模型：回归分析是一种基于历史数据建立数学模型的方法。
通过将历史的能源需求量与各种相关因素（如人口、经济增长、工业生产等）进行回归分析，建立能源需求量的预测模型。
回归分析模型可以通过多元线性回归、非线性回归等方法来建立。
2.时间序列分析模型：时间序列分析是一种基于时间序列数据进行分析和预测的方法。
能源需求量的时间序列数据可以展示出一定的周期性和趋势性。
常用的时间序列分析方法包括移动平均、指数平滑、ARIMA模型等。
时间序列分析模型可以捕捉到能源需求量的趋势和季节性变化。
3.分类模型：分类模型是一种将样本划分到不同类别中的方法。
对于能源需求量预测，可以将其分为高、中、低等级别，然后根据历史数据和相关因素建立分类模型，预测未来的能源需求量所属的类别。
4.灰色系统理论：灰色系统理论是一种非常有用的预测方法，它是在样本数据有限或缺少信息的情况下进行预测的方法。
通过将数据序列分为灰色数据和白色数据两部分，利用已知数据序列来推断未知数据序列，进行能源需求量的预测。
5.智能算法：智能算法是一种模仿自然界生物演化过程的算法，如遗传算法、粒子群优化算法等。
这些算法不需要具体的数学模型，而是通过对算法参数的调整和结果的反馈来逐步寻找最优解。
智能算法可以应用于能源需求量的预测，帮助找到最优的预测模型。
除了以上的模型和方法，还可以采用数据挖掘、机器学习等技术来进行能源需求量的预测。
数据挖掘是一种从大规模数据集中提取有用信息的方法，机器学习是一种能够自动学习的算法。
这些方法可以综合考虑多个因素，构建更准确的能源需求量预测模型。
总之，能源需求量的预测是一个复杂的问题，需要综合考虑各种因素。
以上介绍的模型和方法是常用的能源需求量预测手段，但在实际应用中需要根据具体情况选择合适的方法。
在预测过程中，还需要不断更新数据和调整模型，以提高预测的准确性和实用性。
电力行业中的能源消耗预测模型研究能源消耗预测模型是电力行业中一项重要的研究课题。
准确预测电力行业的能源消耗对于电力公司、政府以及能源供应商来说至关重要。
通过建立能源消耗预测模型，可以提前做好能源供应和调度安排，以及优化能源的利用和分配，从而降低成本，提高能源利用效率。
在电力行业中，能源消耗预测模型通常基于历史数据和一系列的影响因素来进行建模。
以下是几种常见的能源消耗预测模型。
1. 时间序列模型时间序列模型是一种基于时间序列数据的预测方法，常用的有ARIMA模型（Autoregressive Integrated Moving Average，自回归移动平均模型）。
该模型通过分析历史数据中的趋势、季节性和周期性等特征，来预测未来的能源消耗。
ARIMA模型在许多实际应用中都表现出较好的预测准确度。
2. 回归模型回归模型是一种建立因变量与自变量之间关系的数学模型。
在能源消耗预测中，回归模型可以通过分析历史数据中的各种影响因素（如气温、季节、经济指标等）与能源消耗之间的相关性来建立模型。
常见的回归模型包括线性回归、多项式回归、岭回归等。
回归模型适用于具有一定规律性和可量化的影响因素的能源消耗预测。
3. 人工神经网络模型人工神经网络模型是模拟生物神经网络原理的一种数学模型。
在能源消耗预测中，人工神经网络模型可以通过学习历史数据中的模式和规律，来预测未来的能源消耗。
这种模型可以适应非线性和复杂的能源消耗数据，但需要较多的数据来训练网络结构。
4. 时间序列与回归模型的组合时间序列和回归模型可以结合使用，以提高能源消耗预测的准确性。
例如，可以先用时间序列模型预测能源消耗的趋势和季节性，然后将这些预测结果作为回归模型的自变量来预测未来能源消耗。
这种组合模型可以充分利用两种模型的优势，提高预测的准确度。
在建立能源消耗预测模型时，需要注意以下几点：1. 数据质量：准确的历史数据是建立预测模型的基础，要确保数据的完整性和准确性。
基于机器学习的能源消耗预测模型建立在当今日益增长的能源消耗中，精确预测能源的使用需求对于环境保护和经济发展至关重要。
传统的能源预测模型主要基于统计方法，受限于数据质量和数量，其精度有限。
而机器学习技术的应用使得能源预测变得更加准确和快速。
基于机器学习的能源消耗预测模型建立过程可以分为以下步骤：1. 数据收集和清洗能源消耗预测需要大量的历史数据，包括能源消耗量、天气情况、节假日、周末等。
这些数据需要经过整理清洗，确保数据的准确性和一致性。
同时，也需要考虑数据是否存在缺失或异常，需要进行适当的处理。
2. 特征工程特征工程是建立机器学习模型的关键步骤，它直接影响模型的性能和预测精度。
在特征工程中，我们需要从原始数据中提取出最相关的特征，以帮助机器学习模型进行预测。
比如，在能源消耗预测中，天气情况是一个重要的特征，可以通过提取温度、湿度、风力等信息来构建特征向量。
3. 模型选择和训练在选择合适的机器学习模型时，需要考虑不同模型的特点和适用范围。
常用的机器学习模型包括线性回归、决策树、神经网络等。
在训练模型时，我们需要使用历史数据进行训练，并通过交叉验证等方法来评估模型的性能和精度。
4. 预测和优化模型训练完成后，我们可以使用模型来预测未来的能源消耗情况。
同时，我们也需要不断优化模型，以提高预测精度。
优化方法包括不同的特征选择、模型参数调整等。
总的来说，基于机器学习的能源消耗预测模型是一种高效、准确的预测方法。
它能够帮助我们更好地了解能源消耗趋势，为能源管理提供科学参考，从而推动节能减排和可持续发展。
MODELS FOR ESTIMATING ENERGY CONSUMPTION OFELECTRIC TRAINSJyh-Cherng JONGPh. D., P.E., Research ScientistCivil, Hydraulics and Informatics Research CenterSinotech Engineering Consultants, Inc.171 Nanking E. RD. Sec. 5,Taipei 105, Taiwan(R.O.C.)Fax:+886-2-2765 5010E-Mail:jcjong@.tw En-Fu CHANGResearch ScientistCivil, Hydraulics and Informatics Research CenterSinotech Engineering Consultants, Inc.171 Nanking E. RD. Sec. 5,Taipei 105, Taiwan(R.O.C.)Fax:+886-2-2765 5010E-Mail:efchang@.twAbstract: Railway operators are heavy users of electric energy. To implement energy saving programs and to study economical operation strategies, an energy estimating model is required. In this paper, two models for estimating energy consumption of single train operation are presented. To verify the proposed models, a real railway link and an electric train from Taiwan Railway Administration (TRA) are selected for the experiment. The energy consumption estimated from the proposed model is then compared with that estimated by other commercial software. It is found that the difference is only 0.22%, demonstrating that the proposed models are accurate enough in practice for estimating energy consumption. The models can be further extended to develop models and algorithms for estimating power demand of multiple-train operation and minimizing energy consumption through different driving strategies.Key Words: Energy Consumption, Train Performance Simulator, Optimal Driving Strategy1.INTRODUCTIONEnergy resources are quite scarce in many countries. One of the most important energy resources is electricity. In the last few years, Taiwan has suffered from electricity shortage problem in summer. For this reason, the government has encouraged all public and private sectors to reduce electricity consumption.Railway operators are heavy users of electricity resource with the increasing use of electric trains. The water and power charge of Taiwan Railway Administration (TRA) has increased from 12.92% of total operating expense in 1998 to 13.32% in 2002. Similar situations can also be found in other countries. To implement energy cost reduction programs and study economical train operation strategies, a precise energy model for estimating train electricity consumption is required. In this paper, two models for estimating single train energy consumption are presented. Both require detailed train running states outputted from train performance simulator (TPS) or speed profile generator, including train velocity, running time, corresponding tractive effort and braking force. The first model estimates voltage and current usages via train velocity, and then computes electric power. The second model estimates electric power through train velocity, corresponding tractive effort and energy efficiency curve. Both models employ numerical integration method to estimate the overall energy consumption of a single train operation. Although the underlying concepts of the two models in calculating electric power are different, it is found that the first model is a special case of the second one from mathematical point of view. A mechanism is thus developed in this paper to convert voltage and current curve into a single efficiency curve that can be used in thesecond model. In addition, an error reduction algorithm is also developed to reduce the error in numerical integration for estimating energy consumption.To verify the proposed models, a real railway link and an electric train from TRA are selected as the test case. The energy consumption estimated from the proposed model is compared with other commercial software. At the end of this study, the effects of traction ratio and minimal allowable coasting speed on energy consumption are also analyzed. The proposed models can be further extended to develop models and algorithms for estimating power demand of multiple-train operation and minimizing energy consumption through different driving strategies.2. LITERATURE REVIEWEnergy saving is always an issue that draws much attention from rail authority. Previous researches and demonstrations have confirmed that energy consumption can be reduced through appropriate operation strategies. In Paul’s study (Paul, 1999), 5% extension on run time can produce energy savings up to 20% on a suburban system. Tomii (2003) develops a model which estimates power consumption at high precision with 2% deviation from real situation. It is found that reducing maximum speed and tactfully performing coasting can reduce energy consumption about 7% ~ 20%.TMG International Consultants proposes an optimal train performance simulator which gains a 13.7% reduction in traction energy consumption by the timetable optimization process without increase in running time. The simulator shows a reduction in traction energy consumption from 576 kWh per unit to 497 kWh per unit as a result of the timetable optimization process.In order to study energy saving problems, an accurate energy estimation model is necessary.As early as in 1985, Majumdar proposes four main stages of train movement including (1)acceleration, (2) balancing, (3) coasting, and (4) deceleration. Equation (1) is the summary of his ideas for calculating energy consumption. It shows that the total energy consumed in train operations is the product of force and displacement. Coefficients in the equation are energy efficiency and factors for converting the work done in ton-km into electric power units.Majumdar also proposes a statistical method for estimating energy. However, this approach is an actual measurement and thus, contributes less functions in energy saving.()úúûùêêëé÷÷øöççèæ+×+úûùêëé×+×=ååååD D C C a B B A A T v d v d P d T d T W 964.0814.0725.2(1)where T W =total power energy consumption (kWh)T =force in tones due to tractive effort (ton)d =distance traveled in km at that speed range (km)a P =power consumption by all auxiliaries (kWh)D C B A ,,,= Acceleration, Balancing, Coasting and Deceleration stage, respectivelyGoodman (1987) develops single train and multi train simulation programs. The voltage received by a train will vary with position and the simultaneous action of other trains in multi train model, while it remains a constant in single train model. This is the main differencebetween two models in estimating energy consumption. Goodman considers detailed factors in his model, including substation, feeder cable and volt-drop, etc.Recently, Caputo (2000) develops a model that considers not only power supply parameters,but also energy storage devices, such as accumulator, flywheels or capacitors. The expected benefits of the energy storage devices are the reduction in energy consumption as well as line peak loads. This becomes a new trend in saving electric energy for train operations.Estimation of energy consumption can be categorized mainly into electric-power approach and kinematics approach. Generally, the electric-power method calculates electric energy that is directly imported into the train. The kinematics method estimate energy consumption via kinetic energy and efficiency factor. The two models are explained more detailed in the following subsections.2.1 Electric-Power Based ModelWardrop (1989) proposes an electric-power based model to estimate energy consumption.The basic calculation, as shown in equation (2), requires line voltage, current and motor combination code, etc. The k value is the number of parallel motor circuits. According to equation (2), this method contains an assumption that energy consumption has a linear relationship with the proportion between actual traction and maximum traction. Eash (1978)and Lee (2000) also use this approach in their models, but each uses different concept to determine voltage or current.dt r I V k dt r k I V E T m T m m ××××=×××××=òò6106.31360010001(2)where m E =main power energy consumption (kWh)V =voltage (V)m I =motor current (A)k =motor combination code, k ≧1T r =maxT T actual , the proportion between actual traction actual T and maximum traction max T ,0≦T r ≦1t =operation time (s)2.2 Kinematics Based ModelAs shown in Figure 1, after electric power inputs to rolling stocks, it will go through converter,motor, and mechanic devices to output traction power for train movements. The entire procedure involves more or less energy loss. The motor efficiency is defines as the division of out P over in P . In equation (3), motor efficiency, train traction, and speed are inputs for estimating input power. Energy consumption is estimated via equation (4).outP in P Figure 1 Energy Consumption Sketch Mapinin out P v T P P ××==72.0η(3)dt P E in m ò=(4)where η=motor efficiency, 0<η≤1out P =output power (kW)in P =Input power (kW)T =tractive effort (kN)v =train velocity (km/h)Uher (1987a, 1987b) develops EMM (Energy Management Model) and TOM (Train Operations Model ) which use above approach. Piotr (2001) presents a model on MATLAB environment. His study also utilizes kinematics based model. In addition, special attention is given to wheel slippage. Coefficients measured from real data are considered in his study to develop a customized model for SJ RC4 locomotive.2.3 SummaryAccording to the above literature, estimation of energy consumption for electric trains is widely applied to the planning/design of power supply systems and the study of optimal driving strategies. Research on optimal driving strategies requires higher precision than power system planning/design since the latter usually takes the worst case to consider safe margins.Note that both kinematics based and electric-power based models are broadly adopted to develop computer software. Although they are derived from different viewpoints, their accuracies are acceptable if suitable data are correctly inputted to the models.In early days, the developing tool of computer models for estimating train energy consumption is usually FORTRAN language. For the past few years, C++ language has replaced FORTRAN gradually. Some researches build energy model under applications like MATLAB. Although this solution seems convenient, the main disadvantages are computationally inefficiency and non-portable executable files.3. SIMULATION MODELAs described in the previous section, the computation of energy consumption requires the integration of input power over time, no matter which model is applied. Since the power does not have specific function form, the integration is usually solved numerically. In train simulation programs, the estimation of energy consumption is usually based on train movement module. In order to obtain the parameters for calculating energy consumption at every time step, a train dynamic model is required.A complete energy estimation model for electric trains includes at least three parts, i.e., the energy used by the traction motors, the energy consumption of auxiliary equipments, and the energy produced by regenerative braking. These three modules are introduced in the following sections:3.1 Energy Model for Traction MotorsThe energy consumed by traction motors is utilized to produce sufficient tractive effort for train movements. It is the majority of total energy consumption of electric trains. In the proposed model, the kinematics based approach is selected to estimate energy consumption.The reason is that the input data of electric-power based model implies the concept of motor efficiency. Through suitable transformation, the input of electric-power model can be converted into a single efficiency curve. Section 3.4 will explain the mechanism in more detailed.According to Equation (3), (4), energy consumption is calculated from train traction, speed,and motor efficiency at every time step. These variables are obtained from train performance simulator or speed profile generator except motor efficiency. Usually, motor efficiency is a function of tractive effort and velocity as shown in equation (5). An example measured from empirical data of Taipei Metro EMU is plotted in Figure 2. There are corresponding efficiency curves for different tractive efforts. It is possible that these efficiency curves intersect each other. After twice interpolations, efficiency value for a specific traction and velocity can be acquired. Whenever the tractive effort or velocity cannot be covered by the curves, boundary value is adopted instead of extrapolation to avoid unreasonable efficiency.),(v T f =η(5)Figure 2 Motor Efficiency Curves for Taipei Metro EMU3.2 Energy Model for Auxiliary EquipmentsAuxiliary equipments include lighting, air conditioning, etc. In general, their energy consumption rate is considered as a constant. Assume that auxiliary equipments work all the time in the simulation. Then the power consumption can be calculated by3600)(3600a t at m am a a a t n P n P t P E ××+×=×=(6)where a E =total energy consumption for auxiliary equipment (kWh)a P =total electric power for auxiliary equipment (kW)a t =train operating time (sec)am P =electric power per locomotive car (kW)m n =number of locomotive cars.at P =electric power per trailer cars (kW)t n =number of trailer car.3.3 Energy Model for Regenerative BrakingModern electric trains are usually equipped with regenerative braking. During braking period,electric power is generated from kinetic energy of the train. Note that the braking force of the train is composed of friction braking force and motor braking force. Only the latter can be used to produce electricity. Thus, equation (7) must be applied to determine the electric braking force first. Then the product of the motor braking force, velocity and regenerative efficiency yields the electric power produced by the regenerative braking, as expressed in equation (8).fe T B B B +=(7)B e r v B P η×××=6.31(8)Where T B =total braking force (kN)e B = electrical (regenerative) braking force (kN)f B = friction breaking force (kN)B η= regenerative system efficiencyr P =electric power of regenerative braking (kW)The logic behind the model is similar to the energy model for traction motors. However, this model is only optional since not all electric trains equipped with regenerative braking.Moreover, the power energy produced by regenerative braking is not utilized by the train itself unless it is equipped with energy storage devices, like accumulator or capacitors.3.4 Transformation of Input DataAs mentioned in section 2.2, motor efficiency is defined as the ratio of output power to input power. If only the input data for electric-power based model is available, then the efficiency curve for kinematics based model can be derived from the following equation:M v v M in out I V k T v T T I V k v T P P v T f ×××××=××××===6.310001000/)(6.3/)(),(max,max,η(9)For example, Figure 3 (a) ~ (c) are the motor characteristics of E200 electric locomotive from TRA. Following equation (9), these figures can be converted into Figure 3 (d), which can befurther used in kinematics based model. Thus, the electric-power based method can beconsidered as a special case of the kinematics based model from mathematic point of view.(c) Voltage-Current Curve Figure 3 The Input (a~c) & Output (d) for Data TransformationThere are several advantages for the data transformation. First, the energy consumption estimated from the kinematics based model is exactly the same as that from the electric-power based model. Second, the energy models for traction motor and for regenerative braking are both estimated from efficiency curve and have the same input format. Third, it will be easier to check whether the efficiency curve is reasonable since it must fall in between 0 and 1.Finally, it provides very useful information for studying optimal driving strategies.3.5 Error Reduction AlgorithmThe proposed model requires detailed train information at each time step, including tractive effort, braking force, velocity, etc. These data can be obtained from TPS or speed profile generators. The energy consumption is then estimated by numerical integration. As a result,the error is dependent on the interval of time step. A high precision can be expected if the time increment is very small. But this would increase computation time. Note that the error is not originated from the interval of time step, but also due to fixed tractive effort and velocity in estimating energy consumption at each computation cycle. It is possible, however, to reduce the error without decreasing time interval. This section introduces such an error reduction algorithm.Let T denote tractive effort (or braking force) and v be the velocity of the train. For any two successive states (n T , n v ) and (1+n T , 1+n v ), the average velocity (i.e., 2)(21v v +) can be used to estimate energy consumption instead of n v and 1+n v . However, the adjustment of T is a little complex since it may be positive (traction) or negative (braking). There are ninecombinations of n T and 1+n T (see Table 1), which can be further classified into five situations. The adjustment of T in calculating energy consumption is discussed as follows:Table 1 Combinations between T & T and Their Corresponding Situations1. Situation I: This situation happens frequently in the whole simulation. Traction shall usethe average of n T and 1+n T .2. Situation II: This situation indicates that train uses traction n T continuously until thenext running state. So we can estimate energy consumption by n T .3. Situation III: There is no energy consumption in this situation.4. Situation IV: There is no energy consumption in this situation either. But regenerativeenergy must be estimated with n T .5. Situation V: The average of n T and 1+n T is used to estimate regenerative energy in thissituation.Note that this proposed algorithm still has its limitation for error reduction due to time interval. If accuracy is a major concern, a smaller increment is suggested.4. CASE STUDYIn order to demonstrate the proposed model for estimating energy consumption of electric trains, a real rail link and an electric train from TRA are selected for the case study. The rail link is Taichung line, which consists of 17 stations and is about 85 km long. The electric train is made up by E200 electric locomotive and 15 passenger cars. The locomotive is equipped with 6 parallel DC motors without regenerative braking.As mentioned before, the estimation of energy consumption requires detailed train dynamics.These data is resulted from a train simulator “TrainSim” developed in Jong and Chang (forthcoming). The input data, simulation result, and sensitivity analysis for the case study are discussed in the following subsections:4.1 Input DataThere are lots of input parameters for the simulation, including train properties, speed regulation rules, railway alignment, operation parameters, stopping patterns, etc. The major input data of the train is listed in Table 2. Tractive effort and motor efficiency curves are displayed in Figure 3 (a) and Figure 3 (d), respectively. The railway data includes station,grade, curve radius, the tunnel type. The operation parameters consist of origin and destination stations, dwell plans, coasting strategies, etc. In this case study, the dwell time are set to 60 seconds at all stations except Taichung station whose dwell time is 120 seconds dueto heavy passenger flow. The parameter of simulation time interval is set to 0.5 seconds in this case study.4.2Simulation ResultTable 3 shows the energy consumption of shortest time and proper time operation strategies. The proper operation time is estimated from the speed profile that is generated in a way to mimic TRA experts in preparing speed profiles. It is found that the shortest time operation consumes more energy but reduces journey time. Because the downward direction of Taichung line has more downgrade sections, the downward operation consumes less energy than upward direction in either one of the operation strategies.Since the real energy consumption is not available, the result obtained from the proposed model is compared with the statistical report of TRA. In recent 5 years (1998 ~ 2002), the average energy consumption rate for all rail railway lines and all electric locomotives is about 3.44 kWh/100 ton-km, whereas the consumption rate calculated from the proposed model is 3.62 kWh/100 ton-km for downward operation and 3.80 kWh/100 ton-km for upward operation, under proper time operation strategies. The results are quite consistent.4.3Sensitivity AnalysisThe factors that affect energy consumption are very complicated. Several factors including traction ratio, loading coefficient, minimal allowable coasting speed and train speed limit are selected for sensitivity analysis. It is found that each of the factors influences energy consumption significantly and energy consumption always trades off with running time. For real applications, rail authority usually looks for minimum energy consumption under a specific running time. Among these factors, traction ratio is one of the popular control options for optimal driving strategy. Its sensitivity analysis shows that energy consumption is a convex function (U shape) of traction ratio, and the optimal traction ratio to drive the train is around 0.82, as shown in Figure 4.Because traction ratio is the most important factor that affects energy consumption, the joint effects of traction ratio and other factors on energy consumption are analyzed. In Figure 5, the x-axis, y-axis and z-axis represent loading factor, traction ratio and energy consumption,respectively. It is found that for high loading factors, the effect of traction ratio on energy consumption is more significant. When traction ratio is small, the energy consumption is very sensitive to loading factor.Figure 4 Sensitivity Analysis of Traction RatioFigure 5 Relationship between Traction ratio, Loading Factor, and Energy Consumption The speed limit also has great impacts on energy consumption. Figure 6 shows that energy consumption decreases as the reduction of maximal train speed increases up to 40 km/h. After that, the energy consumption increases gradually. Figure 6 implies that a settle point exists in the middle of the surface.Figure 6 Relationship between Traction Ratio, Speed Limit Reduction, and EnergyConsumptionFigure 7 shows the joint effect of minimal allowable coasting speed and traction ratio on energy consumption. It is found that energy consumption decreases as allowable coasting speed decreases, and energy savings is insignificant for allowable speed lower than 30 km/h. The energy consumption looks like a convex function of traction ratio and minimal allowable coasting speed.Figure 7 Relationship between Traction Ratio, Minimal Allowable Coasting Speed, andEnergy Consumption5.MODEL VERIFICATION AND VALIDATIONThe most accurate method for model verification and validation is to compare the real energy consumption data with that estimated from models under the same conditions. However, the measurement of energy consumption in real operation is difficult. In addition, train operation pattern significantly differs from driver to driver, which causes remarkable differences in the energy consumption. For these reasons, the proposed model is verified by comparing the results with other commercial software. The one adopted in this study is TOM (Train Operation Model) developed in Uher and Disk (1987), and Uher (1987). TOM has been applied in many projects, including Washington Metro, Metropolitan Atlanta and Baltimore Metro, etc. The largest difference was less than 10%.5.1Modification of Input Data to TrainSimThere are many differences in input format and calculation logic between models. TrainSim take account of some practice rules in TRA that TOM model does not consider. In order to make a fair and reasonable comparison, the input data for TrainSim must be properly modified to comply with the input of TOM. The modifications are explained as follows:1.Neutral Section Effect: When an electric train passes through a neutral section, the powermust be cut off to prevent pantograph sparkle. Because TOM does not consider this effect, the option in TrainSim is disabled.2.Starting Resistance: After a train starts to acceleration and before it runs up to a certainspeed, extra resistance is acting on the train in addition to running resistance. The TRA experience shows that starting resistance coefficient ranges from 5~10‰. The resistance is set to zero in TrainSim since TOM does not take this parameter.3.Curve Resistance: TrainSim has an interface for inputting curve resistance, but TOMuses a fixed coefficient (0.8 lbs/ton/degree of curvature). Thus, the curve resistance input to TrainSim is set to the same value in TOM.4.Tunnel Resistance: In this case study, there are 5 tunnels with total length longer than 9km. When a train runs into a tunnel, extra resistance is imposed on the train due to piston effect. Since TOM does not consider tunnel resistance, the parameter in TrainSim is set to zero.5.Simulation Point: TrainSim can simulate speed profiles based on the head, middle, or tailof the train. The option of head is selected to be consistent with TOM.6.Operation Objective: TrainSim provides option for selecting shortest or proper timeoperation. The option for proper time operation is not provided in TOM. Thus, both models estimate energy consumption under the strategy of shortest time operation.5.2Comparisons of ResultsTable 4 shows the energy consumption estimated from TOM and TrainSim for each section, as well as the difference between them. It is found that the results are quite close. The difference between the two models ranges from -0.23% to 1.59%. The largest difference (1.59%) happens in “Nan-shih to Tung-lo” section. The absolute error is about 0.31% on average, and the overall difference for the entire operation is only 0.22%. Note that the error is not completely ascribed to the proposed energy model. In fact, the estimated operation time from TrainSim is slightly different from TOM. The difference in journey time is about 0.16%(Jong and Chang, forthcoming in 2005). The results demonstrate that the proposed model is accurate enough for estimating energy consumption.6.CONCLUSION AND RECOMANDATIONSThe primary objective of the study is to build a simulation model for estimating the energy consumption of electric trains. The proposed model integrates two methods found in the literature by converting the input data. To increase the precision of the result, an error reduction algorithm is also introduced in this paper. The model is finally verified with commercial software. The results are consistent and the overall error is only 0.22%.The proposed model requires detailed train dynamics for estimating energy consumption. Therefore, any factors influencing train operation also affect the results. Some of them are inflexible for operations. For instance, loading factor and dwell plan are dependent on rider ship and passenger flow that cannot be determined by the operator. On the other hand, some factors can be regarded as control variables, for example, traction ratio, minimal coasting speed, reduction in train speed limit, etc. Through properly control, it is possible to reduce energy consumption to trade off with running time. It is recommended that a systematic driver command model should be developed to solve this optimization problem.REFERENCESCaputo L. (2000) Control of Energy Storage Device for Rail Vehicles. Department of Automatic Control Lund Institute of Technology, Lund Sweden.Eash R. W. (1978) Energy Efficient Rail Transit Operation, Transportation Research Record, Vol. 662, 1-7.。
