Electricity Markets by Sayyad Nojavan & Kazem Zare

Author:Sayyad Nojavan & Kazem Zare
Language: eng
Format: epub
ISBN: 9783030369798
Publisher: Springer International Publishing

6.2 Uncertainty Modeling

In this chapter, uncertain sources are split into two categories: electricity prices and renewable production. The price of electricity in various markets is the most substantial factor affecting the offering strategy problem, which is entirely faced with many uncertainties. On the other hand, the output of the PV site is proportional to the solar irradiance, which is an uncertain parameter. Despite the almost zero irradiance during night-long, it is not even possible to consider a specified value for this parameter throughout the daylight. A variety of factors, including season and climatic conditions have the potential to affect the solar irradiance. For example, during certain hours of the daylight, solar radiation may be at the highest level, but due to specific weather conditions, such as cloudy weather, this potential can be significantly reduced. In the present chapter, normal and beta distributions are utilized to characterize the market prices and solar irradiance, respectively [17].

After modeling the probabilistic behavior of uncertain parameters with proper distribution functions, the roulette wheel technique (RWT) will be applied for scenario generation [18]. To this end, first, the continuous probability density functions (PDF) of each parameter are divided into 20 levels with their relevant normalized probabilities as depicted in Fig. 6.1a for the normal PDF. It is noteworthy to say that the number of levels for each parameter is selected in such a way that it does not reduce the precision of the proposed method and not raise the intricacy of the problem [18]. Next, as shown in Fig. 6.1, the interval [0, 1] is occupied by the different levels of discretized probability density function concerning their normalized probabilities. Then, a random number in the range of [0, 1] pertaining to each uncertain parameter is generated. This random number will be allocated to a specified level of the roulette wheel, which will represent the corresponding realization of the uncertain parameter in each scenario. This procedure will be reiterated till the required number of scenarios is attained. It is undeniable that considering a large number of scenarios will lead to an intractable problem. To this end, fast forward reduction technique is employed to reduce the initially generated scenarios [19]. Consequently, by applying this method, the initial scenarios pertaining to the electricity market prices (DA and imbalance prices) and solar irradiance are reduced to ten scenarios for each separate parameter. Eventually, the final set of scenarios for the proposed offering strategy problem will contain 1000 scenarios (103). It is worth highlighting that the current chapter does not cope with the correlation between electricity prices and renewable power production. A survey on the correlation between all uncertain parameters entails a new topic which is outside the scope of this chapter.

Fig. 6.1A typical PDF and its relevant roulette wheel technique. (a) PDF of electricity prices. (b) Roulette wheel technique

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