翻譯-人工神經(jīng)網(wǎng)絡在短期負荷預測中的應用

1、目 錄外文文獻翻譯11 緒論12 各種影響負荷預測的因素23 混合神經(jīng)網(wǎng)絡33.1 線性神經(jīng)網(wǎng)絡33.2 非線性神經(jīng)網(wǎng)絡44 神經(jīng)網(wǎng)絡結(jié)構(gòu)的確定54.1 自動校正54.2 遺傳算法75 短期負荷預測系統(tǒng)76 仿真結(jié)果97 優(yōu)化處理107.1 基于規(guī)則系統(tǒng)107.2 模式識別系統(tǒng)10結(jié)論11外文文獻原文121.introduction122.variables afferting short-term load143. hybrid neurak networks153.1 linear neutal networks153.2 non-linear neural networks164. de

2、termination of network structure174.1 autocorrelation184.2 genetic algorithm195. short term load forecasting system206. simulation result217.enhancement227.1 rule-based system237.2 pattern recognition system23conclusion24外文文獻翻譯人工神經(jīng)網(wǎng)絡在短期負荷預測中的應用摘要：在本文，我們將討論如何利用人工神經(jīng)網(wǎng)絡對短期負荷進行預測。在這類系統(tǒng)中，有兩種類型的神經(jīng)網(wǎng)絡：非線性和線性

3、神經(jīng)網(wǎng)絡。非線性神經(jīng)網(wǎng)絡是用來捕獲負荷和各種輸入?yún)?shù)之間的高度非線性關(guān)系?；赼rma模型的神經(jīng)網(wǎng)絡，主要用來捕捉很短的時間期限內(nèi)負載的變化。我們的系統(tǒng)可以實現(xiàn)準確性高的短期負荷預測。關(guān)鍵詞：短期負荷預測，人工神經(jīng)網(wǎng)絡1 緒論短期（每小時）負荷預測對于電力系統(tǒng)的穩(wěn)定運行是必要的。準確的負荷預測對于高效的發(fā)電調(diào)度，開停機計劃，需求方的管理，短時維護安排或其他目的等是很必要的。改進短期負荷預測的準確性能為公共事業(yè)和聯(lián)合發(fā)電節(jié)省很多開支。很多種電力系統(tǒng)負荷預測方法在學術(shù)界已經(jīng)報導了。這些方法包括：多元線性回歸法，時間序列法，一般指數(shù)平滑法，卡爾曼濾波法，專家系統(tǒng)法和人工神經(jīng)網(wǎng)絡預測法。由于電力負荷和

4、各種參數(shù)（天氣的溫度，濕度，風速等）之間的高度非線性的關(guān)系，無論在電力負荷預測建?；蛟陬A測中都有重要的作用。人工神經(jīng)網(wǎng)絡就是這種具有潛力的非線性技術(shù)的代表，但是由于電力系統(tǒng)的復雜性，神經(jīng)網(wǎng)絡的規(guī)模會較大，所以，當終端用戶每天甚至每小時都在改變系統(tǒng)的運行時，訓練這個網(wǎng)絡將是一個重大的問題。在本文中，我們把這網(wǎng)絡看作是建立在負荷預測系統(tǒng)上的混合神經(jīng)網(wǎng)絡。這類網(wǎng)絡中包含兩類網(wǎng)絡：非線性神經(jīng)網(wǎng)絡和線性神經(jīng)網(wǎng)絡。非線性神經(jīng)網(wǎng)絡常用來捕獲負荷與各種輸入?yún)?shù)（如歷史負荷值、氣象溫度、相關(guān)濕度等）間的高度非線性關(guān)系。我們常用線性神經(jīng)網(wǎng)絡來建立arma模型。這種基于arma模型的神經(jīng)網(wǎng)絡主要用來捕獲負荷在很短時

5、間期限內(nèi)的變化。最終的負荷預測系統(tǒng)是兩種神經(jīng)網(wǎng)絡的組合。要用大量的歷史數(shù)據(jù)來訓練神經(jīng)網(wǎng)絡，以減小平均絕對誤差百分比 (mape)。一種改進的反向傳播學習算法已經(jīng)用來訓練非線性神經(jīng)網(wǎng)絡。我們使用widrow -霍夫算法訓練線性神經(jīng)網(wǎng)絡。當網(wǎng)絡結(jié)構(gòu)越簡單，那整個系統(tǒng)的訓練也就越快。為了說明這個基于實際情況的負荷預測系統(tǒng)的神經(jīng)網(wǎng)絡的性能，我們采用一個公共機構(gòu)提供的實際需求數(shù)據(jù)來訓練系統(tǒng)，利用三年（1989，1990，1991）中每小時的數(shù)據(jù)來訓練這個神經(jīng)網(wǎng)絡，用1992年每小時的實際需求數(shù)據(jù)用來驗證整個系統(tǒng)。這文章內(nèi)容安排如下：第一部分介紹本文內(nèi)容；第二部分描述了影響負荷預測結(jié)果的因素；第三部分介紹

6、了混合神經(jīng)網(wǎng)絡在系統(tǒng)中的應用；第四部分描述了找到最初網(wǎng)絡結(jié)構(gòu)的方法。第五部分詳細介紹了負荷預測系統(tǒng)；第六部分給出了一些仿真結(jié)果；最后，第七部分介紹了系統(tǒng)的優(yōu)化處理。2 各種影響負荷預測的因素以下是一些影響負荷預測的因素：溫度濕度風速云層日照時間地理區(qū)域假期經(jīng)濟因素顯然，這些因素的影響程度取決于負荷的類型。例如：溫度變化對民用和商業(yè)負荷的影響大于它對工業(yè)負荷的影響。相對較多民用負荷的區(qū)域的短期負荷受氣候條件影響程度大于工業(yè)負荷較多的區(qū)域。但是，工業(yè)區(qū)域?qū)τ诮?jīng)濟因素較為敏感，如假期。如下一個例子，圖2.1表示了午夜開始的一天中負荷的變化。圖2.1 一天中負荷變化的示例3 混合神經(jīng)網(wǎng)絡我們所研究的負

7、荷預測系統(tǒng)由兩類網(wǎng)絡組成：arma模型的線性神經(jīng)網(wǎng)絡和前饋非線性神經(jīng)網(wǎng)絡。非線性神經(jīng)網(wǎng)絡常用來捕獲負荷與各種輸入?yún)?shù)間的高度非線性關(guān)系。我們常用線性神經(jīng)網(wǎng)絡來建立arma模型，這種基于arma模型的神經(jīng)網(wǎng)絡主要用來捕獲負荷在很短時間期限（一個小時）內(nèi)的變化。3.1 線性神經(jīng)網(wǎng)絡一般的多元線性的調(diào)整參數(shù)p和獨立變量x的關(guān)系是：其中： -時刻的電力負荷 -時刻的獨立變量 -時刻的隨機干擾量 -系數(shù)線性神經(jīng)網(wǎng)絡能成功地學習歷史負荷數(shù)據(jù)和獨立變量中的系數(shù)和，widrow-hoff已經(jīng)決定了這些系數(shù)。這個模型包括了先前所以數(shù)據(jù)高達p的延遲，如上所示，這些數(shù)據(jù)不是獨立的，它與負荷有不用程度的相關(guān)性。相關(guān)性

8、學習用來決定模型中包含的最重要的參數(shù)，決定了許多參數(shù)會被去掉。這樣就減少了給定精度模型的大小和運算時間或是提高了給定規(guī)模大小的模型的精度。3.2 非線性神經(jīng)網(wǎng)絡為了能進行非線性預測，要建立一個類似線性模型的非線性模型，如下表示：其中：是由人工神經(jīng)網(wǎng)絡決定的非線性函數(shù)前饋神經(jīng)網(wǎng)絡用層來表示，通常有一個隱含層（在某些情況下有2層），層和層之間是充分聯(lián)系的，每一層有一個偏置單元（輸出層除外）。輸出是每個單元的加權(quán)輸入的總和（包括偏置），中間是通過指數(shù)激活函數(shù)來傳遞。我們已經(jīng)應用了修正的反向神經(jīng)網(wǎng)絡。錯誤的是定義了輸出單元的計數(shù)值和實際值或理想值之間的偏差的平方，這個定義使函數(shù)在微分的時候發(fā)生錯誤。不

9、像線性的時間序列模型那樣在每個滯后變量有一個裝有系數(shù)，非線性神經(jīng)網(wǎng)絡滯后輸入變量的選擇和裝有系數(shù)的數(shù)量是獨立的，而網(wǎng)絡的規(guī)模，是有由層數(shù)和隱含層單元的數(shù)目決定的。此外，在線性回歸模型中，如果輸入變量是無關(guān)的，那么它的回歸系數(shù)是零。但是在非線性神經(jīng)網(wǎng)絡中者不一定是真實的；一個輸入變量可能不重要但是仍可能有權(quán)重；這些權(quán)重將會影響到下層的傳遞，對于隱含單元來說也是重要的。所以，在傳統(tǒng)的反向傳播神經(jīng)網(wǎng)絡中，沒有自動消除無關(guān)輸入節(jié)點和隱含節(jié)點的功能。但是，在實際預測中有必要建立一個簡約模型，它能解決實際問題，但不會太簡單也不會太復雜。如果神經(jīng)網(wǎng)絡太?。ㄝ斎攵松倩蚴请[含單元少），就不夠靈活來捕獲電力系統(tǒng)的

10、動態(tài)需求變化。這就是我們所知的“欠擬合”現(xiàn)象。相反地，如果神經(jīng)網(wǎng)絡太大，它不僅可以容納基本信號，還可以容納訓練時的噪聲，這就是我們所知的“過擬合”現(xiàn)象?！斑^擬合”模型可能在訓練時顯示較低的錯誤率，但不能以偏概全，可能在實際預測時會有較高的錯誤率。非線性模型可以產(chǎn)生比線性規(guī)劃更高的準確度，但是要更長的訓練時間。較大的神經(jīng)網(wǎng)絡容易出現(xiàn)“過擬合”，預測需要簡約模型的一般化概括。非線性神經(jīng)網(wǎng)絡的大小可以通過檢查相關(guān)性系數(shù)或是通過遺傳算法來選擇最優(yōu)的輸入變量來減小。線性模型相對于非線性模型來說是一個令人滿意的模型，而非線性模型是用來決定輸入?yún)?shù)的。用反向傳播來訓練大型的人工神經(jīng)網(wǎng)絡是很耗費時間的，很多用

11、來減少訓練時間的方法已經(jīng)通過評估，已經(jīng)找到一個減少訓練時間的方法來取代使用最小二乘法來修改網(wǎng)絡權(quán)重而達到速下降搜索的技術(shù)。每一步的計算量大了，但是迭代次數(shù)卻大大減少。減少訓練時間是我們希望達到的，不僅可以通過減少計算消耗，也可以通過研究考慮更多的可取的輸入變量來達到，從而達到優(yōu)化預測的精度。4 神經(jīng)網(wǎng)絡結(jié)構(gòu)的確定4.1 自動校正一階線性自動校正就是校正負荷在兩個不同時間之間的校正系數(shù)，可以用下式表示：其中：是在時的自動校正系數(shù) 是期望值 是在時刻的電力負荷值圖4.1顯示了滯后于某個特殊電力用戶的電力需求自動校正系數(shù)的每小時負荷變化。這個圖證實了常識經(jīng)驗，就是在任何時候的負荷與前幾天同一時刻的負

12、荷有高度相關(guān)性。這很有趣，并且對負荷預測很多幫助，另外，滯后的自動校正在24小時中比前整個一周都高出許多。除了前4天，負荷的相關(guān)峰值下降到0.88外，第7天又上升了。圖4.1電力負荷自動校正系數(shù)與滯后時間的比較我們也分析了樣本負荷在時間序列上的偏自相關(guān)函數(shù)（pacf）。這衡量去除了干擾變量后和之間的依賴關(guān)系。圖4.2顯示了負荷序列的pacf?？梢杂^測到，負荷變化與之前的負荷有很大影響，這就表明一個小時后的負荷預測將會變得簡單。圖4.2 上午1點負荷的pacf4.2 遺傳算法在時間序列模型中重要系數(shù)可以通過遺傳算法自動鑒定出，不像反向傳播模型的最小平方誤差那樣，遺傳算法可以直接將mape減到最小

13、。mape就是平均絕對誤差百分比，它廣泛用于衡量負荷預測的準確度。為了描述遺傳算法里的負荷預測模型，要定義一根曲線，它包括滯后值和每個滯后的系數(shù)或是，那么這根曲線可以表示為：常數(shù)項 第一個滯后， 系數(shù)第二個滯后， 系數(shù)滯后， 系數(shù)第一個獨立變量的滯后，系數(shù)第二個獨立變量的滯后，系數(shù) 獨立變量的滯后，系數(shù)這樣一種曲線是隨機產(chǎn)生的。然后兩根曲線被隨機選擇（與它們的mapes的概率成反比）。兩根曲線的交叉點被隨機選擇，而兩條母曲線通過交叉點復制兩條新的曲線。這個過程中產(chǎn)生了新一代的曲線。將會計算出每一條曲線的適應值（通過一組負荷數(shù)據(jù)訓練而產(chǎn)生的預測mape的逆值）。這些低適應能力的將會被丟棄，高適應

14、能力的將會繁殖下一代。突變也用來隨機修改下一代中獨特的。結(jié)果就是經(jīng)過多代的繁殖過程，曲線具有高度的適應性（低mape值），這就是用電力負荷通過訓練后最好的預測值。5 短期負荷預測系統(tǒng)本文的短期負荷預測系統(tǒng)是一個線性神經(jīng)網(wǎng)絡（arma模型）和非線性神經(jīng)網(wǎng)絡的組合。整個系統(tǒng)的結(jié)構(gòu)如圖5.1示。圖5.1 短期負荷預測系統(tǒng)的結(jié)構(gòu)圖在這個系統(tǒng)中，線性系統(tǒng)和非線性系統(tǒng)兩者都有第二部分中提到的影響負荷預測的幾種或全部因素作為歷史數(shù)據(jù)的輸入。數(shù)據(jù)處理器的數(shù)據(jù)是從線性和非線性神經(jīng)網(wǎng)絡的歷史數(shù)據(jù)中提取出來的，分別地，線性神經(jīng)網(wǎng)絡的輸出作為反饋，輸入到非線性神經(jīng)網(wǎng)絡中。有歷史數(shù)據(jù)和線性神經(jīng)網(wǎng)絡的輸出作為輸入，非線性

15、神經(jīng)網(wǎng)絡就會預測出一天或者一周的負荷值。這兩個網(wǎng)絡組成的最初的網(wǎng)絡結(jié)構(gòu)是基于統(tǒng)計分析和遺傳算法。如圖4.2所示，時刻的負荷值很大程度上取決于時刻的歷史負荷值。所以，準確地預測1小時后負荷的會提高短期負荷預測準確度。但是，一天（24小時）后或在一個星期（168小時）后的預測，在之前的幾個小時的負荷值仍然是預測值。例如，我們要預測明天上午10點的負荷值，顯然，我們擁有的明天上午9點的負荷值不是實際值，我們只有明天上午9點的預測值。因為在9點的負荷對10點的負荷的影響較密切，準確的預測9點的負荷會提高預測10點負荷的準確度。在我們這個系統(tǒng)中，線性神經(jīng)網(wǎng)絡（arma模型）是用來預測一個小時后的負荷值的

16、。對于非線性神經(jīng)網(wǎng)絡來說，輸入層包括不同時間滯后的變量。雖然時刻的負荷受到時刻的顯著影響，但是時刻的負荷本身的準確度不足夠以至影響預測時刻負荷的準確度。這主要受長期負荷變化的影響（見圖4.1）6 仿真結(jié)果我們可以通過公共事業(yè)公司獲得歷史數(shù)據(jù)和各種天氣數(shù)據(jù)。我們用來仿真的數(shù)據(jù)是1898，1990和1991年的每小時歷史負荷數(shù)據(jù)和當年的每小時的溫度數(shù)據(jù)。非線性神經(jīng)網(wǎng)絡由24個子網(wǎng)組成，沒一個代表一天中一個特定的時間。相似的，線性神經(jīng)網(wǎng)絡也有24個子網(wǎng)。全部48個子網(wǎng)有很多個輸入節(jié)點，但是只有一個輸出節(jié)點。在任何時候，只有一個非線性子網(wǎng)和一個線性子網(wǎng)在工作（總共只有2個網(wǎng)）。這種獨一無二的結(jié)構(gòu)具有以

17、下優(yōu)點：（1） 預測速度快（2） 重新訓練系統(tǒng)快（3） 模塊化。可以在特定時間根據(jù)預測精度更新系統(tǒng)（4） 預測精度高可以得出系統(tǒng)的這些優(yōu)點對于商業(yè)應用來說是很重要的。根據(jù)每小時或每天預測的原則來說，預測速度很精度對于公共事業(yè)來說是非常需要的我們用1898和1990年的歷史負荷數(shù)據(jù)和溫度數(shù)據(jù)來訓練；1991年的負荷和溫度來作驗證。在訓練和驗證期間，用到了未來的實際溫度。圖6.1顯示了利用1991年第一季度的數(shù)據(jù)驗證我們的系統(tǒng)預測24小時后的mape值曲線。圖6.1 1991第一季度mape的驗證結(jié)果7 優(yōu)化處理 由經(jīng)驗可知，我們發(fā)現(xiàn)只有一個傳統(tǒng)神經(jīng)網(wǎng)絡的系統(tǒng)不足夠處理我們往往遇到的那些具有多種變

18、化情況的公共事業(yè)公司。例如，當天氣突然變化時，利用常規(guī)的數(shù)據(jù)來訓練系統(tǒng)不能得到較好的預測效果。當系統(tǒng)的歷史數(shù)據(jù)點不足夠系統(tǒng)來學習時，可以通過簡單地增加相似的歷史負荷點到訓練數(shù)據(jù)中來解決上述問題。我們將增加兩個附加的子系統(tǒng)到我們的短期負荷預測系統(tǒng)中，給它取名為：基于規(guī)則的系統(tǒng)和模式識別系統(tǒng)。這兩個字子系統(tǒng)在遇到上述的一些情況下會起不同的作用和完成不同的任務。7.1 基于規(guī)則系統(tǒng)模式識別，遺傳算法和人工神經(jīng)網(wǎng)絡的時間序列模型所構(gòu)成的神經(jīng)網(wǎng)絡都可用作短期負荷預測。但是，為了獲得最小的預測誤差，且在可接受的復雜程度和訓練時間，需要知道使用這個網(wǎng)絡的特殊公共事業(yè)的使用范圍。特別是對于區(qū)域的負荷預測，這些

19、特殊地理區(qū)域和服務場所或多或少受到諸如溫度和假期的影響，取決于這個區(qū)域的負荷是工業(yè)負荷占重要部分，還是商業(yè)負荷，或是民用負荷，或取決于負荷是在夏季達到峰值還是冬季達到峰值等。為了使公共事業(yè)單位或其他沒背景的公司能夠成功使用人工智能的短期負荷預測系統(tǒng)，當它達到最佳性能的時候，有必要提供根據(jù)當?shù)貤l件來設置變化參數(shù)的規(guī)則。7.2 模式識別系統(tǒng)這個系統(tǒng)被很多公共事業(yè)單位所用來作日常負荷預測的一種方法，它給出了一個小時為單位的負荷的大型數(shù)據(jù)庫，只要找出與預測日相似的負荷記錄，將它所在那天的數(shù)據(jù)作為預測的依據(jù)。這個系統(tǒng)的問題就是如何在歷史負荷數(shù)據(jù)記錄中找出相似的記錄。有很多種可行的方式來定義相似，我們所用

20、的其中一種就是比較平均絕對誤差百分比，我們概括為：（1） 神經(jīng)網(wǎng)絡可以用來識別模式或評估相似匹配程度。（2） 這些神經(jīng)網(wǎng)絡應該組合起來，如用時間序列法(利用延遲線) 那樣單獨來預測，就存在每一種方法矛盾錯誤的權(quán)重。結(jié) 論在本文中，我們介紹了以用線性和非線性網(wǎng)絡組成的負荷預測系統(tǒng)為基礎的混合神經(jīng)網(wǎng)絡。我們已經(jīng)論證了這個系統(tǒng)是理想的，可為公共事業(yè)或是商業(yè)應用服務的。另外本文也描述兩個子系統(tǒng)，它們作為優(yōu)化處理我們現(xiàn)有的系統(tǒng)來處理各種不平常的情況。外文文獻原文artificial neural networks in short term load forecastingk.f. reinschmid

21、t, president b. lingstone h webster advanced systems development services, inc. 245 summer street boston, u 0221 0phone: 617-589-1 84 1abstract：we discuss the use of artificial neural networks to the short term forecasting of loads. in this system, there are two types of neural networks: non-linear

22、and linear neural networks. the nonlinear neural network is used to capture the highly non-linear relation between the load and various input parameters. a neural networkbased arma model is mainly used to capture the load variation over a very short time period. our system can achieve a good accurac

23、y in short term load forecasting.key words: short-term load forecasting, artificial neural network1 introductionshort term (hourly) load forecasting is an essential hction in electric power operations. accurate shoirt term load forecasts are essential for efficient generation dispatch, unit commitme

24、nt, demand side management, short term maintenance scheduling and other purposes. improvements in the accuracy of short term load forecasts can result in significant financial savings for utilities and cogenerators. various teclmiques for power system load forecasting have been reported in literatur

25、e. those include: multiple linear regression, time series, general exponential smoothing, kalman filtering, expert system, and artificial neural networks. due to the highly nonlinear relations between power load and various parameters (whether temperature, humidity, wind speed, etc.), non-linear tec

26、hniques, both for modeling and forecasting, tend to play major roles in the power load forecasting. the artificial neural network (a") represents one of those potential non-linear techniques. however, the neural networks used in load forecasting tend to be large in size due to the complexity of

27、 the system. therefore, training of such a large net becomes a major issue since the end user is expected to run this system at daily or even hourly basis. in this paper, we consider a hybrid neural network based load forecasting system. in this network, there are two types of neural networks: non-l

28、inear and linear neural networks. the nonlinear neural network is used to capture the highly non-linear relation between the load and various input parameters such as historical load values, weather temperature, relative humidity, etc. we use the linear neural network to generate an arma model. this

29、 neural network based arma model will be mainly used to capture the load variation over a very short time period. the final load forecasting system is a combination of both neural networks. to train them, sigxuiicant amount of historical data are used to minimize mape (mean absolute percentage error

30、). a modified back propagation learning algorithm is carried out to train thenon-linear neural network. we use widrow-hoff algorithm to train the linear neural network.since our network structure is simple, the overall system training is very fast. to illustrate the performance of this neural networ

31、k-based load forecasting system in real situations, we apply the system to actual demand data provided by one utility. three years of hourly data (1989, 1990 and 1991) are used to train the neural networks. the hourly demand data for 1992 are used to test the overall system. this paper is organized

32、as follows: section i is the introduction of this paper; section i1 describes the variables sigdicantly affecting short term load forecasting; in section iii, wepresent the hybrid neural network used in our system; in section iv, we describe the way to find the initial network structure; we introduc

33、e our load forecasting system in details in section v; and in section vi, some simulation result is given; finally, we describe the enhancement to our system in section vii.2 variables afferting short-term loadsome of the variables affecting short-term electxical load are:temperaturehumiditywind spe

34、edcloud coverlength of daylightgeographical regionholidayseconomic factorsclearly, the impacts of these variables depend on the type of load: variations in temperature, for example, have a larger effect on residential and commercial loads than on industrial load. regions with relatively high residen

35、tial loads will have higher variations in short-term load due to weather conditions than regions with relatively high industrial loads. industrial regions, however, will have a greater variation due to economic factors, such as holidays.as an example, figure 2.1 shows the loadvariation over one day,

36、 starting at midnight.figure 2.1 example of load variation during one day3 hybrid neurak networksour short-term load forecasting system consists of two types of networks:linear neural network arma model and feedforward .non-linear neural network.the non-linear neural network is used to capture the h

37、ighly non-linear relation between the load and various input parameters.we use the linear neural network to generate an arma model which will be mainly used to capture the load variation over a very short time period(one hour).3.1 linear neutal networksthe general multivariate linear model of order

38、p with independent x,iswhere:-electrical load at time t -independent variable at time t-random disturbance at time t-coefficientslinear neural networks can successfully learn the coefficient and from the historrcal load data,and the independent variables,widrow-hoff has been used to determine the co

39、efficient.this model includes all the previous data up to lag p.as shown above ,these data are not independent ,and have varying degrees of correlation with the load.correlation studies can be used to determine the most significant parameters to be includes in the model,allowing many to be eliminate

40、d.this reduces the size and computer time for a model of given accuracy,or increases the accuracy for a model of given size.3.2 non-linear neural networksfor non-linear forecasting,a nonlinear model analogous to the linear model is:where:f(.) is a nonlinear function determined by the artificial neur

41、al network.layered, feed-forward neural networks are used, typically with one hidden layer (although in some cases with two). the layers are fully connected, with one bias unit in each layer (except the output layer). the output of each unit is the slum of the weighted inputs (including the bias), p

42、assed through an exponential activation fiinction.our modiked backpropagation method is applied. the errors are defined to be the sum of the squares of the deviations between the computed values at the output units and the actual or desired values; this definition makes the error function differenti

43、able everywhere.unlike the linear time series model, in which there is one fitted coefficient for each lagged variable, in the nonlinear neural network forecaster tlhe selection of lagged input variables is independent of the number of fitted coefficients, the network weights, the number of which is

44、 determined by the number of layers and the number of hidden units. also, in linear regression models, if an input variable is extraneous, then its regression coefficient is zero (or, more properly, is not significantly different from zero by a t-test). however, in nonlinear neural networks this is

45、not necessarily true; an input variable may be unimportant but still have large weights; the effects of these weights cancel somewhere downstream. the same is true for the hidden units.therefore, in conventional backpropagation for nonlinear neural networks, there is no automatic elimination of extr

46、aneous input nodes or hidden nodes. however, in practical forecasting it is necessary to achieve a parsimonious model, one which is neither too simple nor too complex for the problem at hand. if the neural network is chosen to be too small (to have too few input or hidden units), then it will not be

47、 flexible enough to capture ithe dynamics of the electrical demand system; this is known as underfitting. conversely, if the neural network is too large, then it can fit not only the underlying signal but also the noise in the training set; this is known as overfitting. overfitted models may show lo

48、w error rates on the training set but do not generalize; they may then have high error rates in actual prediction. the nonlinear model can yield greater accuracy than the linear formulation, but takes much longer to train. large nonlinear neural networks are also prone to overfitting. forecasting re

49、quires parsimonious models capable of generalization. the size of the nonlinear neural network can be reduced by examining the correlation coefficients, or by using the genetic algorithm to select the optimum set of input variables. the linear model is a satisfactory approximation to the nonlinear m

50、odel for the purpose of selecting the input terms. large artificial neural networks trained using backpropagation are notoriously time-consuming, and a number of methods to reduce training time have been evaluated. one method that has been found to yield orders of magnitude reductions in training ti

51、me replaces the steepest descent search by techniques that model the network weights using a least-squares approach; the computations in each step are greater but the number of iterations is greatly reduced. reductions in training time are desirable not only to reduce computation costs, but to allow

52、 more alternative input variables to be investigated, and hence to optimize forecast accuracy.4 determination of network structureas we stated above, the neural network used in load forecasting tends to be large in size, which results in longer training time. by carefully choosing network structure

53、(i.e., input nodes, output nodes), one will be able to build a relatively small network. in our system, we apply statistical analysis and genetic algorithm to find the network "optimal" structure which is used as a base for further network turning.4.1 autocorrelation first-order linear aut

54、ocorrelation is the correlation coefficient between the loads at two different times, and is given by: where: is the autocorrelation at lag ze is the expected valuez(f) is the electrical load at time t.figure 4.1 shows the hourly variation in the lagged autocorrelation of electrical demand for a par

55、ticular electric utility. this plot confirms common sense experience, that the load at any hour is very highly correlated with the load at the same hour of previous days. it is interesting, and useful for forecasting, that the autocorrelation for lags at multiples of 24 hours remains high for the en

56、tire preceding week the peak correlation falls to about 0.88 for loads four days apart, but rises again for loads seven days apnpart. figure 4.1 autocorrelation of utility electrical load vs.lag hourswe also analyze the sample partial autocorrelation function (pacf) of the time series of load. this

57、is a measure of the dependence between zt+h and z, after removing the effect of the intervening variables zt+ , z 2, . zt+h-l . figure 4.2 shows the pacf of load series. it can be observed that load variation is largely affected by one at previous hour. this indicates that one-hour ahead forecast wo

58、uld be relatively easy. 4.2 genetic algorithm the most significant coefficients in the time series model can be identified automatically byusing the genetic algorithm. unlike the back propagation method, which minimizes the sum of squares of the errors,the genetic algorithm can minimize the mape directly.