Fotovoltaik sistemlerin stokastik metodlarla modellenip en düşük maliyet için tasarımı

ÖZET FOTOVOLTAİK SİSTEMLERİN STOKASTİK METODLARLA MODELLENİP EN DÜŞÜK MALİYET İÇİN TASARIMI ERGÖNÜL, Aral Hüseyin Doktora Tezi, Güneş Enerjisi Enstitüsü Tez Yöneticisi: Prof.Dr.Metin ÇOLAK Şubat 2000, 73 sayfa Fotovoltaik bir sistemin literatürde bulunanlara göre daha iyileştirilmiş üç farklı matematiksel modeli geliştirildi. Bütün modellerde, günlük veya saatlik ölçekte bataryada birikmiş enerjinin zaman ile değişimi sonlu durumlu bir Markov zincir ile ifâde edilip, durağan haldeki durum olasılıklarının çözülmesiyle verilen bir yük ve batarya kapasitesi ile çalıştığında sistemin devre dışı kalma olasılığını hesaplama metodu geliştirildi. Durum geçiş olasılıkları ışıma verilerinden elde edilen sistemin enerji çıktısına ait ortalama, standart sapma, üçüncü moment değerleri, bir ve iki günlük korelasyon katsayıları île verilen yüke bağlı olarak hesaplandı. Belirli bir devre dışı kalma olasılığı ile çalışması öngörülen bir sistemde olması gereken minimum batarya kapasitesinin ortalama sistem enerji çıktısına göre değişim grafikleri elde edilip, panel alam ve batarya kapasitesi maliyetlerim en aza indiren sistem tasarımı gerçekleştirildi. Gerçekleşen devre dışı kalma olasılıkları ile bu tezde ve literatürde bulunan modellerin tahminleri karşılaştırıldı. Anahtar Sözcükler: Fotovoltaik sistemler, güç kaybı olasılığı, ışımanın stokastik modellenmesi

vn ABSTRACT STOCHASTIC MODELLING and COST-OPTIMIZED DESIGN of PHOTOVOLTAIC SYSTEMS ERGÖNÜL, Anıl Hüseyin Ph.D. Thesis, Solar Energy Institute, Ege University Thesis Supervisor: Prof.Dr.Metin ÇOLAK February 2000, 73 pages Three different mathematical models, more improved than the existing ones, are developed for a photovoltaic system. In all models, the temporal change of the net energy entering the battery on daily or hourly time scales is expressed as a 3-state Markov chain X[n], the stationary state probabilities of which have been determined as functions of the mean, the variance and the third moment of the system's energy input, and the load. In the first model the energy accumulated in the battery is expressed as an N-state Markov chain S[n], and the stationary state probabilities are solved, giving the loss of load probability when the system is operated with a given load and battery capacity. Since the state transition probabilities of S[n] only depend on the dairy or hourly data statistics, the correlation information inherent within the insolation data is not effectively used. Therefore, a 2N-state Markov chain W[n] is defined to model the day-to-day correlation of the insolation data, W[n] designates two bits of information: the accumulated battery energy by the end ofvm the n* day or hour and the net energy input into the battery during the day. In this way, the chain contains information as to whether the state of energy has been reached by an increase, or a decrease in energy, or stayed the same with respect to the previous day-end. In the second model, the transition probabilities of W[n] is determined from the knowledge of one-day correlation coefficient, as a result of simplifying assumptions. In the third model, the transition probabilities are determined as functions of both the one-day and the two-day correlation coefficients, requiring fewer assumptions. In both cases, the stationary states of W[n] are analytically solved, and an analytical expression for the loss of load probability is derived as a function of the panel area, the load, and the battery capacity. Additionally, graphics showing the minimum battery capacity required at a given value of the average input energy are obtained for a system to meet a given loss of load probability requirement. The loss of load probabilities are computed by counting and the model predictions are compared to determine which model gives the best prediction. Using the best model, the constant-cost curves are obtained, and an optimum-cost system design is carried out determining the optimum panel area and battery capacity. Finally, the results are compared with those of the existing models in the literature. Keywords: Stochastic modelling of photovoltaic systems, loss of load probability.