电力系统短期负荷预测毕业设计

本科生毕业设计(论文)开题报告
LOAD FORECASTING
Eugene A. Feinberg
State University of New York, Stony Brook
Eugene.Feinberg@
Dora Genethliou
State University of New York, Stony Brook
dgenethl@
Abstract Load forecasting is vitally important for the electric industry in the deregulated economy. It has many applications including energy purchasing and generation, load switching, contract evaluation, and infrastructure development. A large variety of mathematical methods have been developed for load forecasting. In this chapter we discuss various approaches to load forecasting.
Keywords: Load, forecasting, statistics, regression, artificial intelligence.
1. Introduction
Accurate models for electric power load forecasting are essential to the operation and planning of a utility company. Load forecasting helps an electric utility to make important decisions including decisions on purchasing and generating electric power, load switching, and infrastructure
development. Load forecasts are extremely important for energy suppliers,ISOs, financial institutions, and other participants in electric energy generation, transmission, distribution, and markets.Load forecasts can be divided into three categories: short-term forecasts which are usually from one hour to one week, medium forecasts which are usually from a week to a year, and long-term forecasts which are longer than a year. The forecasts for different time horizons are important for different operations within a utility company. The natures of these forecasts are different as well. For example, for a particular region, it is possible to predict the next day load with an accuracy ofapproximately 1-3%. However, it is impossible to predict the next year peak load with the similar accuracy since accurate long-term weather forecasts are not available. For the next year peak forecast, it is possible to provide the probability distribution of the load based on historical weather observations. It is also possible, according to the industry practice,to predict the so-called weather normalized load, which would take place for average annual peak weather conditions or worse than average peak weather conditions for a given area.
Weather normalized load is the load calculated for the so-called normal weather conditions which arethe average of the weather characteristics for the peak historical loads over a certain period of time. The duration of this period varies from one utility to another. Most companies take the last 25-30 years of data.Load forecasting has always been important for planning and operational
decision conducted by utility companies. However, with the deregulation of the energy industries, load forecasting is even more important.With supply and demand fluctuating and the changes of weather conditions and energy prices increasing by a factor of ten or more during peak
situations, load forecasting is vitally important for utilities. Short-term load forecasting can help to estimate load flows and to make decisions that can prevent overloading. Timely implementations of such decisions lead to the improvement of network reliability and to the
reduced occurrences of equipment failures and blackouts. Load forecasting is also important for contract evaluations and evaluations of various sophisticated financial products on energy pricing offered by the market.
In the deregulated economy, decisions on capital expenditures based on long-term forecasting are also more important than in a non-deregulated economy when rate increases could be justified by capital expenditure projects.
Most forecasting methods use statistical techniques or artificial intelligence algorithms such as regression, neural networks, fuzzy logic, and expert systems. Two of the methods,
so-called end-use and econometric approach are broadly used for medium- and long-term forecasting. A
variety of methods, which include the so-called similar day approach,various regression models, time series, neural networks, statistical learning algorithms, fuzzy logic, and expert systems, have been developed for short-term forecasting.
As we see, a large variety of mathematical methods and ideas have been used for load forecasting. The development and improvements of appropriate mathematical tools will lead to the development of more accurate load forecasting techniques. The accuracy of load forecasting
depends not only on the load forecasting techniques, but also on the accuracy of forecasted weather scenarios. Weather forecasting is an important topic which is outside of the scope of this chapter.
We simply mention significant progress in the development of computerized weather forecasting systems, including the Mesoscale Model MM5 developed and supported by a consortium of universities.
2. Important Factors for Forecasts
For short-term load forecasting several factors should be considered,such as time factors, weather data, and possible customers’classes. The medium- and long-term forecasts take into account the historical load and weather data, the number of customers in different categories, the appliances in the area and their characteristics including age, the economic and demographic data and their forecasts, the appliance sales data, and other factors.The time factors include the time of the year, the day of the week,and the hour of the day. There are important differences in load between weekdays and weekends. The load on different weekdays also can behave differently. For example, Mondays and Fridays being adjacent to weekends, may have structurally different loads than Tuesday through Thursday. This is particularly true during the summer time. Holidays
are more difficult to forecast than non-holidays because of their relative infrequent occurrence. Weather conditions influence the load. In fact, forecasted weather parameters are the most important factors in short-term load forecasts.Various weather variables could be considered for load forecasting. Temperature and humidity are the most commonly used load predictors. An
electric load prediction survey published in indicated that of the 22research reports considered, 13 made use of temperature only, 3 made use of temperature and humidity, 3 utilized additional weather parameters,and 3 used only load parameters.Among the weather variables listed above, two composite weather variable functions, the THI (temperature-humidity index) andWCI (wind chill index), are broadly used by utility companies. THI is a measure of summer
heat discomfort and similarly WCI is cold stress in winter.
Most electric utilities serve customers of different types such as residential,commercial, and industrial. The electric usage pattern is different for customers that belong to different classes but is somewhat alike for customers within each class. Therefore, most utilities distinguish load behavior on a class-by-class basis.
3. Forecasting Methods
Over the last few decades a number of forecasting methods have been developed. Two of the methods, so-called end-use and econometric approach are broadly used for medium- and long-term forecasting. A variety of methods, which include the so-called similar day approach, various regression models, time series, neural networks, expert systems,fuzzy logic, and statistical learning algorithms, are used for short-term forecasting. The development, improvements, and investigation of the appropriate mathematical tools will lead to the development of moreaccurate load forecasting techniques.Statistical approaches usually require a mathematical model that representsload as function of different factors such as time, weather, and
customer class. The two important categories of such mathematical models are: additive models and multiplicative models. They differ in whether the forecast load is the sum (additive) of a number of components or the product (multiplicative) of a number of factors.For example, Chen et al.presented an additive model that takes the form of predicting load as the function of four components:
L = Ln + Lw + Ls + Lr,
where L is the total load, Ln represents the “normal”part of the load,which is a set of standardized load shapes for each “type”of day that has been identified as occurring throughout the year, Lw represents the weather sensitive part of the load, Ls is a special event component that create a substantial deviation from the usual load pattern, and Lr is a completely random term, the noise.Chen et al. also suggested electricity pricing as an additional term that can be included in the model. Naturally, price decreases/increases affect electricity consumption. Large cost sensitive industrial and institutional loads can have a significant effect on loads. The study in [4] used Pennsylvania-New Jersey-Maryland (PJM) spot price data (as it related to Ontario Hydro load) as a neural network input. The authors report that accurate estimates were achieved more quickly with the inclusion of price data.A multiplicative model may be of the form
L = Ln ·Fw ·Fs ·Fr,
where Ln is the normal (base) load and the correction factors Fw, Fs, and Fr are positive numbers that can increase or decrease the overall load.
These corrections are based on current weather (Fw), special events (Fs),and random fluctuation (Fr). Factors such as electricity pricing (Fp) and load growth (Fg) can also be included. Rahman presented a rule based forecast using a multiplicative model. Weather variables and the base load associated with the weather measures were included in the model.
3.1 Medium- and long-term load forecasting methods
The end-use modeling, econometric modeling, and their combinations are the most often used methods for medium- and long-term load forecasting.Descriptions of appliances used by customers, the sizes of the houses, the age of equipment, technology changes, customer
behavior,and population dynamics are usually included in the statistical and simulation models based on the so-called end-use approach. In addition,economic factors such as per capita incomes, employment levels, andelectricity prices are included in econometric models. These models areoften used in combination with the end-use approach. Long-term forecasts include the forecasts on the population changes, economic development,industrial construction, and technology development.
End-use models. The end-use approach directly estimates energy consumption by using extensive information on end use and end users, such as appliances, the customer use, their age, sizes of houses, and so on.Statistical information about customers along with dynamics of change
is the basis for the forecast.End-use models focus on the various uses of electricity in the residential,commercial, and industrial sector. These models are based on the principle that electricity demand is derived from customer’s demand for light, cooling, heating, refrigeration, etc. Thus end-use models explain energy demand as a function of the number of appliances in the market.Ideally this approach is very accurate. However, it is sensitive to the amount and quality of end-use data. For example, in this method the distribution of equipment age is important for particular types of appliances. End-use forecast requires less historical data but more information about customers and their equipment.
Econometric models. The econometric approach combines economictheory and statistical techniques for forecasting electricity demand. The approach estimates the relationships between energy consumption (dependent variables) and factors influencing consumption. The relationships
are estimated by the least-squares method or time series methods.One of the options in this framework is to aggregate the econometric approach, when consumption in different
sectors(residential, commercial, industrial, etc.) is calculated as a function of weather, economic
and other variables, and then estimates are assembled using recent historical data. Integration of the econometric approach into the end-use approach introduces behavioral components into the end-use equations.
Statistical model-based learning. The end-use and econometric methods require a large amount of information relevant to appliances,customers, economics, etc. Their application is complicated and requires human participation. In addition such information is often not available regarding particular customers and a utility keeps and supports a pro-file of an “average”customer or average customers for different type of customers. The problem arises if the utility wants to conduct next-year forecasts for sub-areas, which are often called load pockets. In this case,
the amount of the work that should be performed increases proportionally with the number of load pockets. In addition, end-use profiles and econometric data for different load pockets are typically different. The characteristics for particular areas may be different from the average characteristics for the utility and may not be available.In order to simplify the medium-term forecasts, make them more accurate,and avoid the use of the unavailable information, Feinberg et al. developed a statistical model that learns the load model parameters from the historical data. Feinberg et al. studied load data sets provided by a utility company in Northeastern US. The focus of the study was the summer data. We compared several load
models and came to the conclusion that the following multiplicative model is the most accurate L(t) = F(d(t), h(t)) ·f(w(t)) + R(t),
where L(t) is the actual load at time, d(t) is the day of the week, h(t) is the hour of the day, F(d, h) is the daily and hourly component, w(t) is the weather data that include the temperature and humidity, f(w) is the weather factor, and R(t) is a random error.In fact, w(t) is a vector that consists of the current and lagged weather variables. This reflects the fact that electric load depends not only on the current weather conditions but also on the weather during the previous hours and days. In particular, the well-known effect of the so-called heat waves is that the use of air conditioners increases when the hot weather continues for several days.To estimate the weather factor f(w), we used the regression model
f(w) = β0 +_βjXj ,
where Xj are explanatory variables which are nonlinear functions of current and past weather parameters and β0, βj are the regression coef-ficients.The parameters of the model can be calculated iteratively. We start with F = 1. Then we use the above regression model to estimate f.
Then we estimate F, and so on.The described algorithm demonstrated rapid convergence on historical hourly load and weather data. We have applied it to many areas with population between 50,000 and 250,000 customers. Figure 12.1 presents an example of a scatter plot that compares the model and real parameters. Figure 12.2 demonstrates the convergence of the correlation
between the actual load and the model for the iteration process. Figure 12.3 demonstrates the convergence of the linear regression procedures in the algorithm.
Figure 12.1. Scatter plot of the actual load vs the model.
The software , that uses the described method, learns the model parameters and makes
next-year predictions based on the model loads for the last 25-30 years of data. Though historical loads may not available,the software applies the last year models to the historical weather data
to estimate the next year’s peak distribution.
Figure 12.2. Correlation between the actual load and the model.
Figure 12.3. Convergence of the R2 for the actual load vs the model.
The software generates several important characteristics. For example,for each load pocket and for the system, it calculates a weather normalization factor that is a ratio of the peak load to the load that would be observed under average peak conditions. It also produces probability distributions for the next year peaks.The described methods can be applied to both medium- and longterm forecasting. However, the long-term forecasts should incorporate economic and population dynamic forecasts as input parameters.
3.2 Short-term load forecasting methods
A large variety of statistical and artificial intelligence techniques have been developed for short-term load forecasting.
Similar-day approach. This approach is based on searching historical data for days within one, two, or three years with similar characteristics to the forecast day. Similar characteristics include weather, day of the week, and the date. The load of a similar day is considered as a forecast.
Instead of a single similar day load, the forecast can be a linear combination or regression procedure that can include several similar days.The trend coefficients can be used for similar days in the previous years.
4. Future Research Directions
In this chapter we have discussed several statistical and artificial intelligence techniques that have been developed for short-, medium-, and long-term electric load forecasting. Several statistical models and algorithms that have been developed though, are operating ad hoc. The accuracy of the forecasts could be improved, if one would study these statistical models and develop mathematical theory that explains the convergence of these algorithms.Researchers should also investigate the boundaries of applicability of the developed models and algorithms. So far, there is no single model or algorithm that is superior for all utilities. The reason is that utility service areas vary in differing mixtures of industrial, commercial, and residential customers. They also vary in geographic, climatologic, economic,and social characteristics. Selecting the most suitable algorithm by a utility can be done by testing the algorithms on real data. In fact,some utility companies use several load forecasting methods in parallel.As far as we know, nothing is known on a priori conditions that could detect which forecasting method is more suitable for a given load area. An important question is to investigate the sensitivity of the load forecasting
algorithms and models to the number of customers, characteristics of the area, energy prices, and other factors.As mentioned above, weather is an important factor that influences
the load. The usual approach to short-term load forecasting uses the forecasted weather
scenario as an input. However, one of the most important recent developments in weather forecasting is the so-called ensemble approach which consists of computing multiple forecasts. Then probability weights can be assigned to these ensembles.Instead of using the single weather forecast,weather ensemble predictions can be used as multiple inputs for load forecasts. These inputs generate multiple load forecasts. In recent papers, the authors describe ensemble load predictions based on weather ensembles and various statistical forecasting methods. There are two advantages of having load forecasts in the probabilistic form: (i) they can lead to a more accurate hourly forecast obtained by using multiple ensembles, for example, by averaging them; (ii) the probabilistic description of the future load can be used as an input to decision support systems to make important generation, purchasing, and switching decisions. In general, it is known from the appropriate mathematical models that the knowledge of the demand distribution leads to more cost efficient decisions than the knowledge of the expected demand. On a broader scale, we think that the important research and development directions are: (i) combining weather and load forecasting and (ii) incorporating load forecasting into various decision support systems.
5. Conclusions
Accurate load forecasting is very important for electric utilities in a competitive environment created by the electric industry deregulation.In this paper we review some statistical and artificial intelligence techniques that are used for electric load forecasting. We also discussed factors
that affect the accuracy of the forecasts such as weather data, time factors, customer classes, as well as economic and end use factors. Load forecasting methods use advanced mathematical modeling. Additional progress in load forecasting and its use in industrial applications can be achieved by providing short-term load forecasts in the form of probability distributions rather than the forecasted numbers; for example the so-called ensemble approach can be used. We believe that the progress in load forecasting will be achieved in two directions: (i) basic research in
statistics and artificial intelligence and (ii) better understanding of the load dynamics and its statistical properties to implement appropriate models.
负荷预测
尤金甲feinberg
纽约州立大学，石溪分校
eugene.feinberg @
多拉genethliou
纽约州立大学，石溪分校
dgenethl@
摘要负荷预测在电力行业是非常重要的，特别是在开放的经济体系有许多应用，包括能源采购与发电，负荷开关，合同评价，基础设施的发展。

现在大量用于负荷预测的数学方法已经开发出来。

在这一章中我们讨论几种负荷预测的模式。

关键词：负荷，预报，统计，回归分析，人工智能。

1 。

导言
为电力负荷预测制定一个精确的模型对一个公用事业公司的运作和规划是必不可少的。

负
荷预测也可帮助电力事业来作出重大的决定，包括关于购买和发电，负荷开关，及基础设施的发展。

负荷预测对能源供应国，国际团结，金融机构，和其他与会者，在发电，输电，配电，和市场都是非常重要的。

负荷预测可分为三类：短期预测，这通常是由一小时到一周，中期预测，这通常是一个星期到一年，而长期预测是长于一年。

对于公用事业公司来说，预测不同的时间跨度对于不同的业务是重要的，当然这些预测的本质也一样是不同的。

例如，对于一个特定区域，我们可以预测第二天的负荷，准确性可达到1-3％。

但是，我们无法预测下一年度的高峰负荷，因为准确的长期天气预报到目前为止还是不可行的。

对于明年的高峰预测，我们可以根据历史上的气象观测来提供大概的负荷分布。

也有可以根据业界惯例，预测所谓天气正常化负荷，它将代替平均每年最高的气候条件或者比这个给定地区平均最高的天气条件差一些。

天气正常化负荷是对所谓的正常天气条件实施负荷计算，它是一定的时间内，历史高峰负荷的平均值。

这一时期从一个有用的点到另一个，多数公司采取过去25-30年的数据。

负荷预报对公用事业公司的运作和规划一直是重要的。

甚至，由于能源工业的不合理规划，负荷预测变得更加重要.随着供应和需求的波动变化和能源价格上升的因素，在十年或以上，在繁忙情况，负荷预测是制定水电费非常重要的依据。

短期负荷预测方法可以帮助估计负荷流动，并作出决定，可以防止超载。

及时实施这样的决定可以改善网络的可靠性，并减少发生设备故障和停电的次数。

负荷预测也是一个重要的比较评价标准，为市场上提供的各种先进的金融产品在能源方面的价格提供一个标准。

在放松管制的经济下，基于长期预测的资本性支出的决定，比在那个加息有可能由资本开支项目决定的非开放的经济体系更加重要。

大多数预测方法利用统计技术或人工智能算法，如回归，神经网络，模糊逻辑和专家系统。

大致可分为两种方法，即所谓的最终用途法和计量经济学法，都已广泛用于中期和长期预测。

在这些方法中包括所谓的同类天法，就像回归模型，时间序列，神经网络，统计学习算法，模糊逻辑，专家系统一样已被短期预报而开发。

正如我们所见，大量的数学方法和思路已用于负荷预测。

发展和改善适当的数学工具，将促使开发更准确的负荷预测技术。

负荷预测的精度不仅取决于负荷预测技术，而且取决于预测天气的情况。

气象预报是一个重要话题，也是外界对本章议论的内容。

这里我们只是提了在发展计算机化的气象预报系统中的重大进展，其中包括由大学开发和支持的中尺度模式MM5。

2 重要因素预测
短期负荷预测的几个因素应予以考虑，例如时间因素，气象数据，并尽可能了解客户等级。

中期和长期预测应顾及历史负荷和天气数据，在家电领域不同类别的用户数目及其特点，包括年龄，经济和人口统计数据，以及他们的预测，家电销售数据，和其他因素都要予以考虑。

时间因素，包括这一年里，一周的某一天，某一小时。

在平日和周末，负荷之间有重大差别。

平时的负载也可以有所不同。

举例来说吧，在星期一和星期五，被周末隔开的两天，负荷是不同的。

而且由周二到周四也可能有很大的不同。

在今年夏天的时候尤为如此。

假期比非假期更难预测，因为他们相对显得不规则。

气象条件影响负荷。

事实上，预测天气的参数是最重要的，在短期负荷预测.各种天气变数应考虑进来。

温度和湿度是最常用的负荷预测因子。

一个电力负荷预测调查表示，13个利用温度，而只有3个利用了温度和湿度，3个利用额外的气象参数，3个只用于负荷.在以上列举的天气变数中，两种复合天气变函数，thi （温度，湿度指数）和wci （风寒冷指数），已广泛用于公用事业公司。

thi是衡量酷暑的热度，而相反wci是衡量冬季冷度。

大部分电力客户提供服务的类型不同，如住宅，商业及工业生产等对不同类别的客户，电力的使用模式不同，对同一个阶层的客户是一样。

因此，大部分公用事业按阶级基础区分负荷
是否为一类。

3 。

预测方法
在过去的几十年中，一些预报方法已经开发出来。

有两个方法，即所谓的最终用途法和计量经济学法，它们都已广泛用于中期和长期预测，而且采取了多种方式，其中包括所谓的同类天法，像各回归模型，时间序列，神经网络，专家系统，模糊逻辑，统计学习算法都是用于短期预测的。

开发，改进，并深入调查适当的数学工具，将促使发展更准确的负荷预测技术.统计办法通常需要一个数学模型来表示。

负荷由于功能不同的因素，如时间，天气，以及顾客阶层。

共有两个重要的类别，如数学模型，分别是：加模型和乘法模型。

他们对是否为负荷总和（添加剂）的一些组件或产品（乘）的若干因素各有不同的预测. 例如，Chen等。

介绍了一种添加剂的模式，采取的形式为预测负荷作为函数的四个组成部分：
L = Ln + Lw + Ls + Lr,
其中L是总负荷，LN代表"正常"的一部分负荷，这是一套标准化的负荷形状来衡量每一个"型"，已被确定为发生在整个一年中任一天，Ls代表着天气敏感的部分负载，LS是一项特别活动的组成部分，创造偏离了正常负荷的可观模式，及LR ，是一个随机参数.chen等人。

还建议电价可以作为一项额外的方法列入这种模式。

当然，价格跌幅/增加影响用电。

大成本敏感的工业和体制荷载能对负荷有重大影响。

这项研究[ 4 ]用宾夕法尼亚-新泽西-马里兰（pjm ）现货价格数据（因为它与安大略水电负荷），作为神经网络的输入。

作者报告说，准确的估算的取得收益于价格数据.乘法模型，可采取这种形式
L = Ln ·Fw ·Fs ·Fr,
LN是正常的（基本）的负荷，FW，Fs是校正因子，Fr是一个确定的常数可以增加或减少总的负荷。

这些更正是基于当前的天气（Fw），特殊事件（Fs），以及随机波动（Fr）。

像电价（Fp）和负荷增长（Fg）这些因素也可以被包括在内。

拉赫曼介绍了一种用乘法模型基于理论的预测方法。

天气变化和基本负荷与恶劣天气的测量将包括在此模型中。

3.1中期和长期负荷预测方法
最终建模法，经济计量模型法，以及他们的组合在中期和长期负荷预测中是最常用的。

电器用户使用的房子大小，新装备的年龄，新技术的变化，客户行为，种群动态，通常包括在统计和模拟模型中，它是基于所谓的最终用途法。

此外，经济因素，如人均收入，就业水平，和电价是包括在计量经济模型中的。

这些模型经常结合最终建模法。

长期预测包括人口变化，经济发展，产业建设，科技的发展的预测。

最终使用法，直接估计能源消耗，利用从最终用途和最终用户得到的广泛的信息，如家电，顾客使用，年龄，房子的大小等等.客户的统计信息，随着动态变化是预测的基础.最终利用模式侧重于电力在住宅，商业和工业部门的各种用途。

这些模式是根据以下原则，即电力需求的增长是基于顾客对光，制冷，制热，制冷等的需求。

从而最终使用的模式解释对能源的需求时，将其作为一个电器在市场上数目的函数。

理想的说，这种做法是十分正确的。

但是，它对最终用途数据数量和质量是非常敏感的。

举例来说吧，在此方法中的分布设备年龄对特定类型的设备是很重要的。

最终用途预测需要较少的历史数据，但需要很多有关客户和装备的信息。

计量经济模型。

计量经济学的方法将经济学理论和统计技术结合起来预测电力需求。

该办法估计能源消耗（依变数）和影响消费的因素之间的关系。

这种关系由最小二乘法或时间序列方法来估计。

在这个框架内，其中一种选择是集料的计量方式，在不同的部门（住宅，商业，工业等）消费时，将作为一个天气，经济和其他变量函数的计算公式，然后用最近的历史数据来估计。

一体化的经济计量方法纳入最终使用的方法把行为组件和终端使用方程等价起来。

统计模型为基础的学习。

最终用途和电子方法，需要大量家电，顾客，经济学等的相关资
料，其应用比较复杂，需要人的参与。

此外，这类信息往往是不符合有关的特定客户及公用事业，并保持和支持"平均"客户或对不同类型的客户采取平均的做法。

如果公用事业要进行下一期的预测并分领域，问题就出现了，它通常被称为负载的口袋。

在这种情况下，
大量的工作将随着人数负荷的口袋增加而增加比例。

此外，对不同负载的口袋最终使用概况和计量数据通常是不同的。

对特定领域，与公用事业的平均特点可能有所不同，所以未必有用。

为了简化中期预测，使之更加准确，并避免使用没用的资料，feinberg等人制定了一个统计模型，从历史数据汲取负荷模型的方法。

feinberg等人，研究了由在美国东北部的公用事业公司提供的负载数据集。

研究的重点是夏季数据。

我们几个比较负荷模型，并得出结论，认为下列乘法模型是最准确的。

L(t) = F(d(t), h(t)) ·f(w(t)) + R(t),
其中L（t）是实际负荷，d(t)是一周的某一天，h(t)是一天的某个小时，F(d, h)是每天和每小时的组成部分，w(t)的天气资料，包括温度和湿度，f(w)是气象因素，与r（t）是一个随机变量.i事实上，w(t)是一个向量由当前和滞后天气许多变数构成。

这反映出一个事实，就是电力负荷不仅取决于目前的天气状况，而且还取决于在过去几小时或几天的天气。

特别的，著名的效应即所谓热浪说，在天气炎热时使用冷气机，持续数天来估计气象因子f(w)时，我们采用了回归模型
f(w) = β0 +_βjXj ,
XJ是目前和以往的气象参数非线性功能的解释性变量，β0，βj是回归系数.模型参数可以反复被计算出。

我们用F =1开始。

然后，我们使用上述回归模型来估计f，然后，我们估计F 等等.描述算法表现出历史每小时的负荷和天气数据的快速收敛。

我们已应用到许多领域，用户在5万和25万之间。

图12.1给出的一个例子，一个散步图谋，比较模型与实际参数。

图12.2显示了实际负荷和模型迭代过程的收敛的相关性。

图12.3显示了收敛的线性回归程序算法。

图12.1 。

散布图的实际负荷与示范。

软件，即采用描述的方法，知道了该模型的参数，并基于过去25-30年的数据提出未来一年的预测模型。

虽然历史负荷可能没用，该软件适用于过去一年模式，以历史气象资料来估计明年的峰值分布。

图12.2 。

相关关系，实际负荷和示范。

图12.3 。

收敛的R2对实际负荷与示范。

该软件生成的几个重要特点。

举例来说，对于每个负荷包和系统，它计算出天气正常化的因素，是一个高峰负荷向将在平均峰值条件观察的负荷的比例。

它还为下一年的高峰产生概率分布。

描述的方法可以应用到中期和长期预测。

然而，长期预测应纳入经济和人口动态预测，作为输入参数。

3.2短期负荷预测方法
对于短期负荷预测大量统计和人工智能技术已经开发出来。

类似天的方法。

这种方法是基于寻找在一，二，或三年与所预测的一天具有类似特点的历史资料。

相似的特点，包括天气，一周中的某一天。

负载类似的一天被认为是一个预测。

而不是一个单一的同类日负荷，预测可以是一个线性组合或回归程序，也可以包括几个类似的疗程趋势系数，可用于在过去几年的类似的日子。

4 未来的研究方向
在这一章中我们已经讨论过几个统计与人工智能技术已经开发出来用于短期，中期和长期电力负荷预测。

几个统计模型和算法虽然已被开发，但经营专案。

如果有人研究这些统计模型并发展数学理论，以至于能解释这些算法，预测的准确性就可以得到改进。

研究人员也应调查适用于发达的模型和算法的范围。

至目前为止，没有一个单一的模式或算法是优于一切事业的，原因是公用事业的服务范围随着不同的混合的工业，商业和住宅用户而变化。

他们也各有不同的地理，气候，经济，社会等方面的特点。

为了能选择最合适的算法，公用事业部门可以去测试算法实时数据。

事实上，一些公用事业公司都使用几种负荷预测方法。

据我们所知，没有一个众所周知的先验条件，可以侦测可预测的方法更适合于某一特定的负荷区的。

一个重要的问题，是调查负荷预测算法和模式对顾客人数，地区的特点，能源价格，和其他因素的敏感性.如上所述，天气是一个影响负载的重要因素。

通常的做法是短期负荷预测的用途将预测天气的情况作为输入。

不过，在气象预报中最重要的是最近的事态发展，就是所谓合奏的方式，它由多运算的预测组成。

那么概率度量衡可以分配到这些预测中。

单一的天气预报可由多投入负荷预测来代替，并作为其输出。

这些投入产生多种负荷预测。

在最近的论文中，作者描述合奏负荷预测，根据天气预报乐队和各种统计预报方法。

有负荷预测有两个好处：用概率的形式：（一）能不能达到一个更准确的预测，每小时所得采用多种自由组合，例如，将他们平均;（二）用概率描述未来的负荷，可作为一项投入，决策支持系统作出采购和交换的决定。

总的来说，这是众所周知的。

从适当的数学模型，即知识的需求分布来产生比知识预期的需求更多的成本效益。

在更广泛的规模，我们认为，重要的研究和发展方向是：（一）结合天气和负荷预测及（二）将负荷预测包含到各种决策支持系统中。

5 。

结论
准确的负荷预测对在充满竞争的环境中所造成的电力行业不正常是非常重要的。

本文我们回顾一些统计和人工智能技术，都是用于电力负荷预测的。

我们还讨论了影响预测的准确性的因素，如气象资料，时间因素，顾客等级，以及经济和终端使用的因素。

负荷预测方法，利。