電力負(fù)荷預(yù)測(cè)畢業(yè)論文中英文資料外文翻譯文獻(xiàn)

中英文資料PAGE29中英文資料外文翻譯文獻(xiàn)基于改進(jìn)的灰色預(yù)測(cè)模型的電力負(fù)荷預(yù)測(cè)[摘要]盡管灰色預(yù)測(cè)模型已經(jīng)被成功地運(yùn)用在很多領(lǐng)域，但是文獻(xiàn)顯示其性能仍能被提高。為此，本文為短期負(fù)荷預(yù)測(cè)提出了一個(gè)GM（1，1）—關(guān)于改進(jìn)的遺傳算法（GM（1，1）-IGA）。由于傳統(tǒng)的GM（1，1）預(yù)測(cè)模型是不準(zhǔn)確的而且參數(shù)的值是恒定的，為了解決這個(gè)問題并提高短期負(fù)荷預(yù)測(cè)的準(zhǔn)確性，改進(jìn)的十進(jìn)制編碼遺傳算法（GA）適用于探求灰色模型GM（1，1）的最佳值。并且，本文還提出了單點(diǎn)線性算術(shù)交叉法，它能極大地改善交叉和變異的速度。最后，用一個(gè)日負(fù)荷預(yù)測(cè)的例子來比較GM（1，1）-IGA模型和傳統(tǒng)的GM（1，1）模型，結(jié)果顯示GM(1，1)-IGA擁有更好地準(zhǔn)確性和實(shí)用性。關(guān)鍵詞：短期的負(fù)荷預(yù)測(cè)，灰色系統(tǒng)，遺傳算法，單點(diǎn)線性算術(shù)交叉法第一章緒論日峰值負(fù)荷預(yù)測(cè)對(duì)電力系統(tǒng)的經(jīng)濟(jì)，可靠和安全戰(zhàn)略都起著非常重要的作用。特別是用于每日用電量的短期負(fù)荷預(yù)測(cè)（STLF）決定著發(fā)動(dòng)機(jī)運(yùn)行，維修，功率互換和發(fā)電和配電任務(wù)的調(diào)度。短期負(fù)荷預(yù)測(cè)（STLF）旨在預(yù)測(cè)數(shù)分鐘，數(shù)小時(shí)，數(shù)天或者數(shù)周時(shí)期內(nèi)的電力負(fù)荷。從一個(gè)小時(shí)到數(shù)天以上不等時(shí)間范圍的短期負(fù)荷預(yù)測(cè)的準(zhǔn)確性對(duì)每一個(gè)電力單位的運(yùn)行效率有著重要的影響，因?yàn)樵S多運(yùn)行決策，比如：合理的發(fā)電量計(jì)劃，發(fā)動(dòng)機(jī)運(yùn)行，燃料采購計(jì)劃表，還有系統(tǒng)安全評(píng)估，都是依據(jù)這些預(yù)測(cè)。傳統(tǒng)的負(fù)荷預(yù)測(cè)模型被分為時(shí)間序列模型和回歸模型。通常，這些模型對(duì)于日常的短期負(fù)荷預(yù)測(cè)是有效的，但是對(duì)于那些特別的日子就會(huì)產(chǎn)生不準(zhǔn)確的結(jié)果。此外，由于它們的復(fù)雜性，為了獲得比較滿意的結(jié)果需要大量的計(jì)算工作?；疑到y(tǒng)理論最早是由鄧聚龍?zhí)岢鰜淼模饕悄Ｐ偷牟淮_定性和信息不完整的分析，對(duì)系統(tǒng)研究條件的分析，預(yù)測(cè)以及決策?；疑到y(tǒng)讓每一個(gè)隨機(jī)變量作為一個(gè)在某一特定范圍內(nèi)變化的灰色量。它不依賴于統(tǒng)計(jì)學(xué)方法來處理灰色量。它直接處理原始數(shù)據(jù)，來尋找數(shù)據(jù)內(nèi)在的規(guī)律?；疑A(yù)測(cè)模型運(yùn)用灰色系統(tǒng)理論的基本部分。此外，灰色預(yù)測(cè)可以說是利用介于白色系統(tǒng)和黑色系統(tǒng)之間的灰色系統(tǒng)來進(jìn)行估計(jì)。信息完全已知的系統(tǒng)稱為白色系統(tǒng)；相反地，信息完全未知的系統(tǒng)稱為黑色系統(tǒng)?；疑Ｐ虶M（1，1）（即一階單變量灰色模型）是灰色理論預(yù)測(cè)中主要的模型，由少量數(shù)據(jù)（4個(gè)或更多）建立，仍然可以得到很好地預(yù)測(cè)結(jié)果?；疑A(yù)測(cè)模型組成部分是灰色微分方程組——特性參數(shù)變化的非常態(tài)微分方程組，或者灰色差分方程組——結(jié)構(gòu)變化的非常態(tài)差分方程組，而不是一階微分方程組或者常規(guī)情況下的差分方程組?；疑Ｐ虶M（1，1）有一個(gè)參數(shù)，它在很多文章里經(jīng)常被設(shè)為0.5，這個(gè)常數(shù)可能不是最理想的，因?yàn)椴煌膯栴}可能需要不同的值，否則可能產(chǎn)生錯(cuò)誤的結(jié)果。為了修正前面提到的錯(cuò)誤，本文嘗試用遺傳算法來估算值。JohnHolland首先描述了遺傳算法（GA），以一個(gè)抽象的生物進(jìn)化來提出它們，并且給出了一個(gè)理論的數(shù)學(xué)框架作為歸化。一個(gè)遺傳算法相對(duì)于其他函數(shù)優(yōu)化方法的顯著特征是尋找一個(gè)最佳的解決方案來著手，此方案不是以一個(gè)單一逐次改變的結(jié)構(gòu)，而是給出一組使用遺傳算子來建立新結(jié)構(gòu)的解決措施。通常，二進(jìn)制表示法應(yīng)用于許多優(yōu)化問題，但是本文的遺傳算法（GA）采用改進(jìn)的十進(jìn)制編碼表示方案。本文打算用改進(jìn)的遺傳算法（GM(1,1)-IGA）來解決電力系統(tǒng)中短期負(fù)荷預(yù)測(cè)（STLF）中遇到的問題。傳統(tǒng)的GM（1，1）預(yù)測(cè)模型經(jīng)常設(shè)定參數(shù)為0.5，因此背景值可能不準(zhǔn)確。為了克服以上弊端，用改進(jìn)的十進(jìn)制編碼的遺傳算法來獲得理想的參數(shù)值，從而得到較準(zhǔn)確的背景值。而且，提出了單點(diǎn)線性算術(shù)交叉法。它能極大地改善交叉和變異的速度，使提出的GM（1，1）-IGA能更準(zhǔn)確地預(yù)測(cè)短期日負(fù)荷。本文結(jié)構(gòu)如下：第二章介紹灰色預(yù)測(cè)模型GM（1，1）；第三章用改進(jìn)的遺傳算法來估算；第四章提出了GM（1，1）-IGA來實(shí)現(xiàn)短期日負(fù)荷預(yù)測(cè)；最后，第五章得出結(jié)論。第二章灰色預(yù)測(cè)模型GM（1，1）本章重點(diǎn)介紹灰色預(yù)測(cè)的機(jī)理?；疑Ｐ虶M(1,1)是時(shí)間序列預(yù)測(cè)模型，它有3個(gè)基本步驟：（1）累加生成，（2）累減生成，（3）灰色建模。灰色預(yù)測(cè)模型利用累加的原理來創(chuàng)建微分方程。本質(zhì)上講，它的特點(diǎn)是需要很少的數(shù)據(jù)。灰色模型GM（1，1），例如：?jiǎn)巫兞恳浑A灰色模型，總結(jié)如下：第一步：記原始數(shù)列：=是n階離散序列。是m次時(shí)間序列，但m必須大于等于4。在原始序列的基礎(chǔ)上，通過累加的過程形成了一個(gè)新的序列。而累加的目的是提供構(gòu)建模型的中間數(shù)據(jù)和減弱變化趨勢(shì)。定義如下：有，則是r次累加序列。第二步：設(shè)定值來預(yù)測(cè)通過GM（1，1），我們可以建立下面的一階灰色微分方程：它的差分方程是。a稱為發(fā)展系數(shù)，b稱為控制變量。以微分的形式表示導(dǎo)數(shù)項(xiàng)，我們可以得到：在一個(gè)灰色GM（1，1）模型建立前，一個(gè)適當(dāng)?shù)闹敌枰o出以得到一個(gè)好的背景值。背景值序列定義如下：其中，為方便起見，值一般被設(shè)為0.5，推導(dǎo)如下：然而，這個(gè)常量可能不是最理想的，因?yàn)椴煌膱?chǎng)合可能需要不同的值。而且，不管是發(fā)展系數(shù)a還是控制變量b都由值確定。由于系數(shù)是常量，原始灰色信息的白化過程可能被抑制。因此，GM（1，1）模型中預(yù)測(cè)值的準(zhǔn)確性將會(huì)嚴(yán)重的降低。為了修正以上不足，系數(shù)必須是基于問題特征的變量，因此我們用遺傳算法來估算值。第三步：構(gòu)建累加矩陣B和系數(shù)向量。應(yīng)用普通最小二乘法（OLS）來獲得發(fā)展系數(shù)a，b。如下：于是有第四步：獲得一階灰色微分方程的離散形式，如下：解得為為第三章運(yùn)用改進(jìn)GA估算值為了預(yù)測(cè)出準(zhǔn)確的灰色模型GM（1，1），殘差校驗(yàn)是必不可少的。因此，本文中所提出的目標(biāo)函數(shù)的方法可以確保預(yù)測(cè)值誤差是最小。目標(biāo)函數(shù)定義為最小平均絕對(duì)百分比誤差，如下：且，為原始數(shù)據(jù)，為預(yù)測(cè)值，n是該數(shù)列的維數(shù)。從上面描述構(gòu)建的GM（1，1），我們可以得到：在GM（1，1）中參數(shù)的值能夠決定的值；不管是發(fā)展系數(shù)a還是控制變量b都由值確定。更重要的是，的結(jié)果由a，b決定，因此整個(gè)模型選擇過程最重要的部分就是的值。在和殘差之間有著某些復(fù)雜的非線性關(guān)系，這些非線性是很難通過解析來解決的，因此選擇最理想的值是GM(1,1)的難點(diǎn)。遺傳算法是一個(gè)隨機(jī)搜索算法，模擬自然選擇與演化。它能廣泛應(yīng)用正是基于后面兩個(gè)基本方面：計(jì)算代碼非常簡(jiǎn)單并且還提供了一個(gè)強(qiáng)大的搜索機(jī)制。它們函數(shù)相對(duì)獨(dú)立，意味著它們不會(huì)被函數(shù)的屬性所限制，例如:連續(xù)性,導(dǎo)數(shù)的存在，等等。盡管二進(jìn)制法經(jīng)常應(yīng)用于許多優(yōu)化問題，但是在本文我們采用改進(jìn)十進(jìn)制編碼法方案來解決。在數(shù)值函數(shù)優(yōu)化方面，改進(jìn)的十進(jìn)制編碼法相對(duì)于二進(jìn)制編碼法擁有很大的優(yōu)勢(shì)。這些優(yōu)勢(shì)簡(jiǎn)要的敘述如下：第一步：GA的效率提高了，因此，沒有必要將染色體轉(zhuǎn)換為二進(jìn)制類型。第二步：由于有效的內(nèi)部電腦浮點(diǎn)表示，需要較少的內(nèi)存。第三步：甄別二進(jìn)制或其它值不會(huì)使精度降低，并且有更大的自由來使用不同的遺傳算子。我們利用改進(jìn)的十進(jìn)制碼代表性方法來尋找在灰色GM（1，1）模型中最佳系數(shù)的值。本文中，我們提出單點(diǎn)線性算術(shù)交叉法，并且利用它來獲得值；它能極大地提高交叉和變異的速度。改進(jìn)的十進(jìn)制碼代表性方法的步驟如下：（1）編碼：假設(shè)是二進(jìn)制字符串的C位，然后由右至左每隔n位轉(zhuǎn)換為十進(jìn)制。（n<C，n和C的值要確保精度）（2）隨機(jī)化種群：選擇一個(gè)整數(shù)M作為種族的大小，然后隨機(jī)地從集合選擇M點(diǎn)，如，這些點(diǎn)組成個(gè)體的原始種群，該序列被定義為：（3）評(píng)估適應(yīng)度：在選擇的過程中，個(gè)體被選擇參與新個(gè)體的繁殖。擁有高度地適應(yīng)度F（）的個(gè)體逐代衍化和發(fā)展。適應(yīng)度函數(shù)是是從個(gè)體獲得的預(yù)測(cè)值。是迭代最小二乘總和的最大值。第四步：選擇：在本文中，我們根據(jù)它們的適應(yīng)度函數(shù)分別地計(jì)算出個(gè)體選定的概率，然后我們通過輪盤選擇法，使繁殖的各自概率是，最后我們拿原始的個(gè)體來生成下一代的。第五步：交叉和變異：編碼和交叉是相關(guān)的；我們利用了十進(jìn)制碼表示法，因此我們提出了一種新的交叉算子“單點(diǎn)線性算術(shù)交叉”。1）選擇合適的兩個(gè)有交叉概率的個(gè)體。2）為這兩個(gè)選擇的個(gè)體，我們?nèi)匀徊捎秒S機(jī)抽樣方法以得到交叉算子。例如：3）交叉①互相交換它們的正確的字符串。②位在左側(cè)的交叉可以通過以下計(jì)算算法：a：基因分析：b：交換后基因：稱為交叉系數(shù)，每次根據(jù)隨機(jī)的交叉系統(tǒng)來選擇。4）變異：下面是一個(gè)新的變異方案：當(dāng)變異算子被選擇，新的基因值是一個(gè)在域權(quán)重的隨機(jī)數(shù)，它是用原始基因值得到的加權(quán)總和。如果變異算子的值是，變異值是：是變異系數(shù)，。r是一個(gè)隨機(jī)數(shù)，。每當(dāng)進(jìn)行變異操作時(shí)，r會(huì)被隨機(jī)的挑選。因此，新的后代可以通過交叉和變異操作來創(chuàng)建。第六步：推出原則：選擇當(dāng)前的一代個(gè)體來繁殖下一代個(gè)體，然后求出適應(yīng)度值并判斷算法是否符合退出條件。如果符合條件，這個(gè)值就是最佳的，否則回到第四步，直到種群內(nèi)所有個(gè)體達(dá)到統(tǒng)一標(biāo)準(zhǔn)或幾代個(gè)體的數(shù)量超過最大值100。第四章．負(fù)荷預(yù)測(cè)案例在本章，我們?cè)囍鴮?duì)GM（1，1）-關(guān)于改進(jìn)的遺傳算法進(jìn)行性能評(píng)估。第一步：m天的日負(fù)荷數(shù)據(jù)序列定義為，我們測(cè)量了每個(gè)小時(shí)的電力負(fù)荷，于是負(fù)荷序列向量就是一個(gè)24維數(shù)據(jù)。1點(diǎn)：2點(diǎn)：j點(diǎn)：24點(diǎn)：式中m是所建模型的天數(shù)，是日負(fù)荷數(shù)據(jù)序列的第j點(diǎn)。圖1.原始數(shù)據(jù)和預(yù)測(cè)值第二步：我們利用改進(jìn)的遺傳算法為各自的負(fù)荷數(shù)據(jù)序列來選擇值。接著，我們可以算出a和b，然后我們利用GM（1，1）-IGA來預(yù)測(cè)第m+1天中的第j點(diǎn)的負(fù)荷，于是我們可以得到，最后第m+1天地24個(gè)預(yù)測(cè)值構(gòu)成了這個(gè)負(fù)荷數(shù)據(jù)序列。這有一個(gè)GM（1，1）-關(guān)于改進(jìn)的遺傳算法（GM（1，1）-IGA）的例子，兩種預(yù)測(cè)日負(fù)荷數(shù)據(jù)曲線（7月26號(hào)）和原始的日負(fù)荷曲線同時(shí)在圖1中畫出。第三步：我們可以利用GM（1,1）-遺傳算法的四個(gè)指標(biāo)來檢驗(yàn)精度，包括相對(duì)誤差，均方差率，小誤差概率和關(guān)聯(lián)度誤差。如果相對(duì)誤差和均方差率較低，或者小誤差概率和關(guān)聯(lián)度誤差較大，GM（1,1）-GA的準(zhǔn)確性檢驗(yàn)是較好的。設(shè)置模擬殘差為，k=1，2，…，n設(shè)置模擬的相對(duì)剩余為k=1，2，…，n設(shè)置平均值為設(shè)置的方差為設(shè)置殘差平均值為設(shè)置殘差方差為因此，GM（1，1）-IGA的校驗(yàn)值如下：1).平均相對(duì)誤差為2).均方差率為3).小誤差概率為4).關(guān)聯(lián)度為其中，根據(jù)上述公式，GM（1，1）-IGA的指標(biāo)的校驗(yàn)值見表1。表1GM-IGA和GM的四個(gè)指標(biāo)GM-GAGM平均相對(duì)誤差0.0000900.0001均方差率0.00390.0073小誤差概率10.92關(guān)聯(lián)度0.980.90通過表1可以看出，GM-GA所以指標(biāo)的精確度都是一級(jí)的，因此這個(gè)GM（1，1）-IGA可以被用來預(yù)測(cè)短期負(fù)荷。第四步：在圖1中，我們可以得到GM（1，1）-IGA的預(yù)測(cè)負(fù)荷數(shù)據(jù)曲線比GM（1，1）的曲線更接近于原始的日負(fù)荷數(shù)據(jù)曲線。進(jìn)一步分析，本文選擇相對(duì)誤差作為標(biāo)準(zhǔn)來評(píng)價(jià)兩種模式。兩種模型的偏差值如下，GM（1，1）的平均誤差為2.285%，然而，GM（1，1）-IGA的平均誤差為0.914%。第五章．結(jié)論本文提出了GM（1，1）-關(guān)于改進(jìn)的遺傳算法（GM（1，1）-IGA）來進(jìn)行短期負(fù)荷預(yù)測(cè)。采用十進(jìn)制編碼代表性方案，改進(jìn)的遺傳算法用于獲得GM（1，1）模型中的最優(yōu)值。本文也提出了單點(diǎn)線性算術(shù)交叉法，它能極大地提高交叉和變異的速度，因此GM（1，1）-IGA可以準(zhǔn)確地預(yù)測(cè)短期日負(fù)荷。GM（1，1）-IGA的特點(diǎn)是簡(jiǎn)單、易于開發(fā)，因此，它在電力系統(tǒng)中作為一個(gè)輔助工具來解決預(yù)測(cè)問題是適宜的。圖2.GM（1，1）的偏差值圖3.GM（1，1）-IGA的偏差值致謝這項(xiàng)工作是由國家自然科學(xué)基金部分支持。（70671039）參考文獻(xiàn)[1]P.GuptaandK.Yamada,“AdaptiveShort-TermLoadForecastingofHourlyLoadsUsingWeatherInformation,”IEEETr.OnPowerApparatusandSystems.VolPas-91,pp2085-2094,1972.[2]D.W.Bunn,E.D.Farmer,“ComparativeModelsforElectricalLoadForecasting”.JohnWiley&Son,1985,NewYork.[3]AbdolhosienS.Dehdashti,JamesRTudor,MichaelC.Smith,“ForecastingOfHourlyLoadByPatternRecognition-ADeterministicApproach,”IEEETr.OnPowerApparatusandSystems,Vol.AS-101,No.9Sept1982.[4]S.RahrnanandRBhamagar,“AnexpertSystemBasedAlgorithmforShort-TermLoadForecast,”IEEETr.OnPowerSystems,Vol.AS-101,No.9Sept.1982[5]M.T.Hagan,andS.M.Behr,“TimeSeriesApproachtoShort-TermLoadForecasting,”IEEETrans.onPowerSystem,Vol.2,No.3,pp.785-791,1987.[6]XieNaiming,LiuSifeng.“ResearchonDiscreteGreyModelandItsMechanism”.IEEETr.System,ManandCybernetics,Vol1,2005,pp:606-610[7]J.L.Deng,“Controlproblemsofgreysystems,”SystemsandControlLetters,vol.1,no.5,pp.288-294,1982.[8]J.L.Deng,Introductiontogreysystemtheory,J.GreySyst.1(1)(1989)1–24[9]J.L.Deng,PropertiesofmultivariablegreymodelGM(1N),J.GreySyst.1(1)(1989)125–141.[10]J.L.Deng,Controlproblemsofgreysystems,Syst.ControlLett.1(1)(1989)288–294.[11]Y.P.Huang,C.C.Huang,C.H.Hung,Determinationofthepreferredfuzzyvariablesandapplicationstothepredictioncontrolbythegreymodelling,TheSecondNationalConferenceonFuzzyTheoryandApplication,Taiwan,1994,pp.406–409.[12]S0aeroandMRIrving,“AGeneticAlgorithmForGeneratorSchedulingInPowerSystems,”IEEETr.ElectricalPower&EnergySystems,Vol18.No1,pp19-261996.[13]Edmund,T.H.HengDiptiSrinivasanA.C.Liew.“ShortTermLoadForecastingUsingGeneticAlgorithmAndNeuralNetworks”.IEEECatalogueNo:98EX137pp576-581[14]Chew,J.M.,Lin,Y.H.,andChen,J.Y.,"TheGreyPredictorControlinInvertedPendulumSystem",JournalofChinaInstituteofTechnologyandCommerce,Vol.11,pp.17-26,1995[15]J.GreySyst.,“Introductiontogreysystemtheory,”vol.1,no.1,pp.1–24,1989ApplicationofImprovedGreyPredictionModelforPowerLoadForecasting[Abstract]Althoughthegreyforecastingmodelhasbeensuccessfullyutilizedinmanyfields,literaturesshowitsperformancestillcouldbeimproved.Forthispurpose,thispaperputforwardaGM(1,1)-connectionimprovedgeneticalgorithm(GM(1,1)-IGA)forshort-termloadforecasting(STLF).WhileTraditionalGM(1,1)forecastingmodelisnotaccurateandthevalueofparameterisconstant,inordertosolvethisproblemandenhancetheaccuracyofshort-termloadforecasting(STLF),theimproveddecimal-codegeneticalgorithm(GA)isappliedtosearchtheoptimalvalueofgreymodelGM(1,1).What’smore,thispaperalsoproposestheone-pointlinearityarithmeticalcrossover,whichcangreatlyimprovethespeedofcrossoverandmutation.Finally,adailyloadforecastingexampleisusedtotesttheGM(1,1)-IGAmodelandtraditionalGM(1,1)model,resultsshowthattheGM(1,1)-IGAhadbetteraccuracyandpracticality.Keywords:Short-termLoadForecasting,GreySystem,GeneticAlgorithm,One-pointLinearityArithmeticalCrossover.IntroductionDailypeakloadforecastingplaysanimportantroleinallaspectsofeconomic,reliable,andsecurestrategiesforpowersystem.Specifically,theshort-termloadforecasting(STLF)ofdailyelectricityusageiscrucialinunitcommitment,maintenance,powerinterchangeandtaskschedulingofbothpowergenerationanddistributionfacilities.Short-termloadforecasting(STLF)aimsatpredictingelectricloadsforaperiodofminutes,hours,daysorweeks.Thequalityoftheshort-termloadforecastswithleadtimesrangingfromonehourtoseveraldaysaheadhasasignificantimpactontheefficiencyofoperationofanypowerutility,becausemanyoperationaldecisions,suchaseconomicdispatchschedulingofthegeneratingcapacity,unitcommitment,schedulingoffuelpurchaseaswellassystemsecurityassessmentarebasedonsuchforecasts[1].Traditionalshort-termloadforecastingmodelscanbeclassifiedastimeseriesmodelsorregressionmodels[2,3,4].Usually,thesetechniquesareeffectivefortheforecastingofshort-termloadonnormaldaysbutfailtoyieldgoodresultsonthosedayswithspecialevents[5,6,7].Furthermore,becauseoftheircomplexities,enormouscomputationaleffortsarerequiredtoproduceacceptableresults.Thegreysystemtheory,originallypresentedbyDeng[8,9,10],focusesonmodeluncertaintyandinformationinsufficiencyinanalyzingandunderstandingsystemsviaresearchonconditionalanalysis,forecastinganddecisionmaking.Thegreysystemputseachstochasticvariableasagreyquantitythatchangeswithinagivenrange.Itdoesnotrelyonstatisticalmethodtodealwiththegreyquantity.Itdealsdirectlywiththeoriginaldata,andsearchestheintrinsicregularityofdata[11].Thegreyforecastingmodelutilisestheessentialpartofthegreysystemtheory.Therewith,greyforecastingcanbesaidtodefinetheestimationdonebytheuseofagreysystem,whichisinbetweenawhitesystemandablack-boxsystem.Asystemisdefinedasawhiteoneiftheinformationinitisknown;otherwise,asystemwillbeablackboxifnothinginitisclear.ThegreymodelGM(1,1)isthemainmodelofgreytheoryofprediction,i.e.asinglevariablefirstordergreymodel,whichiscreatedwithfewdata(fourormore)andstillwecangetfineforecastingresult[12].Thegreyforecastingmodelsaregivenbygreydifferentialequations,whicharegroupsofabnormaldifferentialequationswithvariationsinbehaviorparameters,orgreydifferenceequationswhicharegroupsofabnormaldifferenceequationswithvariationsinstructure,ratherthanthefirst-orderdifferentialequationsorthedifferenceequationsinconventionalcases[13].ThegreymodelGM(1,l)hasparameterwhichwasoftensetto0.5inmanyarticles,andthisconstantmightnotbeoptimal,becausedifferentquestionsmightneeddifferentvalue,whichproduceswrongresults.Inordertocorrecttheabove-mentioneddefect,thispaperattemptstoestimatebygeneticalgorithms.Geneticalgorithms(GA)werefirstlydescribedbyJohnHolland,whopresentedthemasanabstractionofbiologicalevolutionandgaveatheoreticalmathematicalframeworkforadaptation[14].ThedistinguishingfeatureofaGAwithrespecttootherfunctionoptimizationtechniquesisthatthesearchtowardsanoptimumsolutionproceedsnotbyincrementalchangestoasinglestructurebutbymaintainingapopulationofsolutionsfromwhichnewstructuresarecreatedusinggeneticoperators[15].Usually,thebinaryrepresentationwasappliedtomanyoptimizationproblems,butinthispapergeneticalgorithms(GA)adoptedimproveddecimal-coderepresentationscheme.ThispaperproposedGM(1,1)-improvedgeneticalgorithm(GM(1,1)-IGA)tosolveshort-termloadforecasting(STLF)problemsinpowersystem.ThetraditionalGM(1,1)forecastingmodeloftensetsthecoefficientto0.5,whichisthereasonwhythebackgroundvaluez(1)(k)maybeunsuitable.Inordertoovercometheabove-mentioneddrawbacks,theimproveddecimal-codegeneticalgorithmwasusedtoobtaintheoptimalcoefficientvaluetosetproperbackgroundvaluez(1)(k).Whatismore,theone-pointlinearityarithmeticalcrossoverwasputforward,whichcangreatlyimprovethespeedofcrossoverandmutationsothattheproposedGM(1,1)-IGAcanforecasttheshort-termdailyloadsuccessfully.Thepaperisorganizedasfollows:section2proposesthegreyforecastingmodelGM(1,1):section3presentsEstimatewithimprovedgeneticalgorithm:section4putsforwardashort-termdailyloadforecastingrealizedbyGM(1,1)-IGAandfinally,aconclusionisdrawninsection5.2.GreypredictionmodelGM(1,1)Thissectionreviewstheoperationofgreyforecastingindetails.ThegreymodelGM(1,1)isatimeseriesforecastingmodel.Ithasthreebasicoperations:(1)accumulatedgeneration,(2)inverseaccumulatedgeneration,and(3)greymodeling.Thegreyforecastingmodelusestheoperationsofaccumulatedtoconstructdifferentialequations.Intrinsicallyspeaking,ithasthecharacteristicsofrequiringlessdata.ThegreymodelGM(1,1),i.e.,asinglevariablefirst-ordergreymodel,issummarizedasfollows:Step1:Denotetheinitialtimesequenceby=x(0)isthegivendiscreten-th-dimensionalsequence.x(0)(m)isthetimeseriesdataattimem,nmustbeequaltoorlargerthan4.Onthebasisoftheinitialsequencex(0),anewsequencex(1)issetupthroughtheaccumulatedgeneratingoperationinordertoprovidethemiddlemessageofbuildingamodelandtoweakenthevariationtendency,sox(1)isdefinedas:Where，andandisthertimesaccumulatedseries.Step2:Tosetthevaluetofinez(1)(k)AccordingtoGM(1,1),wecanformthefollowingfirst-ordergreydifferentialequation:Anditsdifferenceequationis.WhereawascalledthedevelopingcoefficientofGM,andbwascalledthecontrolvariable.Denotingthedifferentialcoefficientsubentryintheformofdifference,wecanget:BeforeagreyGM(1,1)modelwassetup,apropervalueneededtobeassignedforabetterbackgroundvaluez(1)(k).Thesequenceofbackgroundvalueswasdefinedas:AmongthemForconvenience,thevaluewasoftensetto0.5,thez(1)(k)wasderivedas:However,thisconstantmightnotbeoptimalbecausethedifferentquestionsmightneeddifferentvalue.And,bothdevelopingcoefficientaandcontrolvariablebweredeterminedbythez(1)(k).Theprocessoftheoriginalgreyinformationforwhiteningmaybesuppressedresultedfromthecoefficientwasconstant.Hence,theaccuracyofpredictionvaluex?(0)(k)inGM(1,1)modelwouldseriouslybedecreased.Inordertocorrectthedefect,thecoefficientmustbeavariablebasedonthefeatureofproblems,soweestimatebygeneticalgorithms.Step3:ToconstructaccumulatedmatrixBandcoefficientvectorXn.ApplyingtheOrdinaryLeastSquare(OLS)methodobtainsthedevelopingcoefficienta,bwasasfollows:andSoStep4:Toobtainthediscreteformoffirst-ordergreydifferentialequation,asfollows:Thesolutionofx(1)isAndthesolutionofx(0)is3.EstimatewithimprovedGAInordertoestimatetheaccuracyofgreymodeGM(1,1),theresidualerrortestwasessential.Therefore,theobjectivefunctionoftheproposedmethodinthispaperwastoensurethattheforecastingvalueerrorswereminimum.Theobjectivefunctionwasdefinedasmeanabsolutepercentageerror(MAPE)minimizationasfollows:Where，x(0)(k)isoriginaldata,isforecastingvalue,nisthenumberofsequencedata.However,fromtheabovedescriptionoftheestablishmentofGM(1,1),wecanget:InGM(1,1),thevalueofparametercandeterminez(1),and,bothdevelopingcoefficientaandcontrolvariablebweredeterminedbythez(1)(k).Whatismore,thesolutionofx(0)wasdeterminedbyaandb,sothekeypartofthewholemodelselectingprocesswasthevalueof.Thereiskindofcomplicatednonlinearrelationshipbetweenandresidualerrors,andthisnonlinearitywashardtosolvebyresolution,sotheoptimalselectionofwasthedifficultpointofGM（1,1）.Geneticalgorithmisarandomsearchalgorithmthatsimulatesnaturalselectionandevolution.Itisfindingwidespreadapplicationasaconsequenceoftwofundamentalaspects:thecomputationalcodeisverysimpleandyetprovidesapowerfulsearchmechanism.Theyarefunctionindependentwhichmeanstheyarenotlimitedbythepropertiesofthefunctionsuchascontinuity,existenceofderivatives,etc.Althoughthebinaryrepresentationwasusuallyappliedtomanyoptimizationproblems,inthispaper,weusedtheimproveddecimal-coderepresentationschemeforsolution.Theimproveddecimal-coderepresentationintheGAoffersanumberofadvantagesinnumericalfunctionoptimizationoverbinaryencoding.Theadvantagescanbebrieflydescribedasfollows:Step1:EfficiencyofGAisincreasedasthereisnoneedtoconvertchromosomestothebinarytype,Step2:Lessmemoryisrequiredasefficientfloating-pointinternalcomputerrepresentationscanbeuseddirectly,Step3:Thereisnolossinprecisionbydiscriminationtobinaryorothervalues,andthereisgreaterfreedomtousedifferentgeneticoperators.Weutilizedtheimproveddecimal-coderepresentationschemeforsearchingoptimalcoefficientvalueingreyGM(1,1)model.Inthispaper,weproposedone-pointlinearityarithmeticalcrossoverandutilizedittoselectthevalueof;itcangreatlyimprovethespeedofcrossoverandmutation.Thestepsoftheimproveddecimal-coderepresentationschemeareasfollows:（1）Coding：SupposeisabinarystringofCbits,thenleteverynbitstransformadecimalfromrighttoleft.(n<C,thevaluesofnandCareensuredbyprecision)（2）Randomizepopulation:SelectoneintegerMasthesizeofthepopulation,andthenselectMpointsstochasticallyfromtheset,as,thesepointscomposetheindividualsoftheoriginalpopulation,thesequenceisdefinedas:（3）Evaluatethefitness:Intheselectionstep,individualsarechosentoparticipateinthereproductionofnewindividuals.TheindividualwiththehighestfitnessF（）hasthepriorityandadvancestothenextgeneration.Thefitnessfunctionisandisthevalueofforecastingwhichisgainedbytheindividual.isthemaximumofthesumofiterativesquares.Step4:Selection:Inthispaper,wecalculateindividualselectedprobabilityrespectivelyaccordingtotheirfitnessfunctions,thenweadopttheroulettewheelselectionscheme,sothatthepropagatedprobabilityofrespectiveindividualisp(k),afterthatwetaketheinbornindividualtocomposethenextgenerationp(k+1).Step5:CrossoverandMutation:Codingandcrossoverarecorrelative;weutilizedthedecimal-coderepresentation,soweproposeanewcrossoveroperator“one-pointlinearityarithmeticalcrossover”1)Selectthefittwoindividualswithprobabilityofcrossover.2)Forthetwoselectedindividuals,westilladopttherandomselectionmeanstoensurethecrossoveroperator.Forexample:3)crossover:①Weexchangetheirrightstringseachother.②Thebitontheleftofcrossovercanbecalculatedthroughthefollowingalgorithm:a:Geneanalysis:b:Exchangethebackgene:Theiscalledcrossovercoefficient,itischoseneachtimebyrandomcrossoveroperation.4)Mutation:Thereisanewmutationoperation:whenthemutationoperatorwaschosen,thenewgenevalueisthatarandomnumberwithinthedomainofweight,whichisoperatedintoaweightedsumwithoriginalgenevalue.IfthevalueofmutationoperatorisZi,themutationvalueis:Andisthemutationcoefficient,.risarandomnumber,.Itisselectedrandomlyeverytimewhenmutationoperationishappening.Therefore,thenewoffspringcanbecreatedthroughcrossoverandmutationoperations.Step6:Quitprinciple:Selecttheremainingindividualsinthecurrentgenerationtoreproducetheindividualsinthenextgeneration,thenevaluatethefitnessvalueandjudgewhetherthealgorithmfulfilsthequitcondition.Ifitiscertifiable,inthiscasethevalueisoptimalsolution,elserepeatfromStep4untilallindividualsinpopulationmeettheconvergencecriteriaorthenumberofgenerationsexceedsthemaximumof100.4.LoadpredictionexampleInthissection,wetrytoevaluatetheperformanceofGM(1,1)-connectionimprovedgeneticalgorithm.First:Thedailyloaddatasequencesofmdaysaredefinedas,wemeasuredthepowerloadeachhour,andtheloadsequencevectorisatwenty-four-dimensionaldata.01thetimeofday:02thetimeofday:jthetimeofday:24thetimeofday:Wheremisthenumberofmodelingdays,Xjisthedailyloaddatasequenceofthej-thtimeofday.Fig1.OriginaldataandforecastingvalueSecond:WeutilizeimprovedgeneticalgorithmtoselectthevalueofforrespectiveloaddatasequenceXj.Afterthat,wecancalculateaandb,thenweutilizeGM(1,1)-IGAtopredicttheloadforecastingofthej-thtimeofthe(m+1)-thday,sowecouldgetXj(m+1),andthetwenty-fourforecastingvaluesofthe(m+1)-thdaystructuretheloaddatasequence.TherewasanexampleofGM(1,1)-connectionimprovedgeneticalgorithm(GM(1,1)-IGA),boththetwoforecastingdailyloaddatacurves(July26)andtheoriginaldailyloaddatacurveweredrawnsimultaneouslyonFig1.Thirdly:WecanusefourindexesofthisGM(1,1)-GAtoverifytheprecise,includingoftherelativeerror,theratioofmeansquareerror,themicroerrorprobabilityandtherelevancedegree.TheaccuracyverificationofGM(1,1)-GAisbetteriftherelativeerrorandtheratioofmeansquareerrorislower,orthemicroerrorprobabilityandtherelevancedegreeislarger[16].Setthesimulatedresidualofx(0)(k)isk=1，2，…，nSetthesimulatedrelativeresidualisk=1，2，…，nSetthemeanofx(0)isSetthevarianceofx(0)is1SetthemeansofresidualerrorisSetthevarianceofresidualerrorisSothecheckvalueofthisGM(1,1)-GAisasfollowed:1).themeanrelativeerroris2).theratioofmeansquareerroris3.)themicroerrorprobabilityis4).therelevancedegreeisThereamong,Onthebasisofaboveformula,theindexesofverificationofGM(1,1)-GAandGMisinTable1.Accordingtotable1,theallprecisionindexesofGM-GAarefirstdegree,sothisGM(1,1)-GAcanbeusedtopredicttheshort-termload.Fourth:AtFig1,wecangetthattheforecastingloaddatacurveofGM(1,1)-GAwasmoreclosedtotheoriginaldailyloaddatacurvethanGM(1,1)’s.Forfurtheranalysis,thispaperselectsrelativeerrorsasacriteriontoevaluatethetwomodels.Theerrorfiguresoftwomodelsareasfollows,andtheaverageerrorofGM(1,1)was2.285%,otherwise,theaverageerrorofGM(1,1)-IGAwas0.914%.5.ConclusionThispaperproposesGM(1,1)–connectionimprovedgeneticalgorithm(GM(1,1)-IGA)forshort-termloadforecasting.Adoptingdecimal-coderepresentationscheme,theimprovedgeneticalgorithmisusedtoselecttheoptimizevalueofGM(1,1)model.Thepaperalsoputsforwardtheone-pointlinearityarithmeticalcrossoverwhichcangreatlyimprovethespeedofcrossoverandmutation,sothattheGM(1,1)-IGAcanforecasttheshort-termdailyloadsuccessfully.TheGM(1,1)-IGAischaracteristicofbeingsimpleandeasytodevelop,therefore,itisappropriateasanaidtooltosolvetheforecastingproblemsinpowersystem.Fig2.TheerrorsofGM(1,1)Fig3.TheerrorsofGM(1,1)-IGAAcknowledgementThisworkispartiallysupportedbytheNationalNaturalScienceFoundation(70671039)參考文獻(xiàn)[1]P.GuptaandK.Yamada,“AdaptiveShort-TermLoadForecastingofHourlyLoadsUsingWeatherInformation,”IEEETr.OnPowerApparatusandSystems.VolPas-91,pp2085-2094,1972.[2]D.W.Bunn,E.D.Farmer,“ComparativeModelsforElectricalLoadForecasting”.JohnWiley&Son,1985,NewYork.[3]AbdolhosienS.Dehdashti,JamesRTudor,MichaelC.Smith,“ForecastingOfHourlyLoadByPatternRecognition-ADeterministicApproach,”IEEETr.OnPowerApparatusandSystems,Vol.AS-101,No.9Sept1982.[4]S.RahrnanandRBhamagar,“AnexpertSystemBasedAlgorithmforShort-TermLoadForecast,”IEEETr.OnPowerSystems,Vol.AS-101,No.9Sept.1982[5]M.T.Hagan,andS.M.Behr,“TimeSeriesApproachtoShort-TermLoadForecasting,”IEEETrans.onPowerSystem,Vol.2,No.3,pp.785-791,1987.[6]XieNaiming,LiuSifeng.“ResearchonDiscreteGreyModelandItsMechanism”.IEEETr.System,ManandCybernetics,Vol1,2005,pp:606-610[7]J.L.Deng,“Controlproblemsofgreysystems,”SystemsandControlLetters,vol.1,no.5,pp.288-294,1982.[8]J.L.Deng,Introductiontogreysystemtheory,J.GreySyst.1(1)(1989)1–24[9]J.L.Deng,PropertiesofmultivariablegreymodelGM(1N),J.GreySyst.1(1)(1989)125–141.[10]J.L.Deng,Controlproblemsofgreysystems,Syst.ControlLett.1(1)(1989)288–294.[11]Y.P.Huang,C.C.Huang,C.H.Hung,Determinationofthepreferredfuzzyvariablesandapplicationstothepredictioncontrolbythegreymodelling,TheSecondNationalConferenceonFuzzyTheoryandApplication,Taiwan,1994,pp.406–409.[12]S0aeroandMRIrving,“AGeneticAlgorithmForGeneratorSchedulingInPowerSystems,”IEEETr.ElectricalPower&EnergySystems,Vol18.No1,pp19-261996.[13]Edmund,T.H.HengDiptiSrinivasanA.C.Liew.“ShortTermLoadForecastingUsingGeneticAlgorithmAndNeuralNetworks”.IEEECatalogueNo:98EX137pp576-581[14]Chew,J.M.,Lin,Y.H.,andChen,J.Y.,"TheGreyPredictorControlinInvertedPendulumSystem",JournalofChinaInstituteofTechnologyandCommerce,Vol.11,pp.17-26,1995[15]J.GreySyst.,“Introductiontogreysystemtheory,”vol.1,no.1,pp.1–24,1989基于C8051F單片機(jī)直流電動(dòng)機(jī)反饋控制系統(tǒng)的設(shè)計(jì)與研究基于單片機(jī)的嵌入式Web服務(wù)器的研究MOTOROLA單片機(jī)MC68HC（8）05PV8/A內(nèi)嵌EEPROM的工藝和制程方法及對(duì)良率的影響研究基于模糊控制的電阻釬焊單片機(jī)溫度控制系統(tǒng)的研制基于MCS-51系列單片機(jī)的通用控制模塊的研究基于單片機(jī)實(shí)現(xiàn)的供暖系統(tǒng)最佳啟停自校正（STR）調(diào)節(jié)器單片機(jī)控制的二級(jí)倒立擺系統(tǒng)的研究基于增強(qiáng)型51系列單片機(jī)的TCP/IP協(xié)議棧的實(shí)現(xiàn)基于單片機(jī)的蓄電池自動(dòng)監(jiān)測(cè)系統(tǒng)HYPERLINK"/detail.htm