Abstract
Operational and planning studies of high-wind penetrated power systems have well come to the light as a major concern of future energy systems. This paper focuses on the procedure of determining required static reserve of the high-wind penetrated power systems which has not been well accompanied by comprehensive analysis and proper modeling tools. To reach this goal, first, a probabilistic algorithm has been proposed to effectively model the variations in output generation of wind turbines. In this algorithm, the fuzzy c-means clustering method (FCM) is exploited as an efficient as well as robust clustering method to find the multi-state model of wind turbines output generation. Based on this probabilistic analytical model, a stochastic framework is developed to investigate the roles of two important factors, i.e. wind power penetration rate and installed capacity of wind farms on the required static reserve of the system. In this regard, different wind power penetration rates have been defined for generation sector of the IEEE-RTS and the adequacy studies of this test system is performed to show that how variations in wind power penetration rate can affect the required static reserve of the system. In addition, a sensitivity analysis based on an exhaustive search algorithm is conducted on the capacity of installed wind farms to examine the effects of this important factor on the reliability level of power systems. This studies not only emphasize on the necessities of employing stochastic approach to determine the require reserve of a high-wind penetrated power system, but also, proves the applicability of proposed analytical approach.
Keywords
Introduction
Wind energy is a viable alternative to fossil energy because of its low cost, mild environmental impact and interminable attributes. Recently, different supportive policies have been employed in many countries all around the world to increase the share of wind power in generation sector of power systems. Based on the reports addressed in [1], the installed global capacity of wind power has been reached to 318.1 GW in 2013 [1].
Unpredictability and intermittency of this green energy, however, impose many new challenges on operational and planning studies of power system such as security, stability, and reliability studies. In response, there have been significant activities in the literature addressing these various issues with the main goal of maximizing the presence of wind power in power systems [2–9]. Among these issues, reliability assessment of power systems in presence of the wind farms has widely been studied (see [10, 11] as someexamples).
A few works in the literature focus on the required static reserve of high-wind penetrated power systems based on reliability indices. Once the contribution of wind energy in generation sector of power system increases, many new factors needs to be considered in the static reserve determination procedure of high-wind penetrated power systems. These factors are wind power penetration level, the installed capacity of wind farms, the correlation between output generation of wind farms with each other and also load and wind farms output generation coincidence. This paper focuses on the impacts of wind power penetration level and the installed capacity of wind farms as two effective factors in reliability studies of power systems with the main goal of determining the required reserve of power systems.
In this regard, at first, an appropriate model for wind farms output generation needs to be developed. This model, then, should be involved in the adequacy studies. Sequential Monte Carlo simulation (SMCS) approach has been usually applied to model wind farms output generation in adequacy studies of wind-penetrated power systems [11]. This method is the most accurate one to evaluate adequacy studies of power systems incorporating wind energy. The computational burden of this method and a long wind speed historical data requirement, however, threaten its practicality, specially, when applied to large-scale systems [12]. To cover these deficiencies, the authors in [10] tried to present an analytical model for wind farm output generation. These models can easily be involved in the available evaluation procedure of the reliability indices. Moreover, the analytic approach can easily overcome the computational burden and large data requirements of simulation-based methods. Based on these discussions, a multi-state analytical method proposed in past works of the authors has been used in this paper to efficiently model the variations in output generation of wind farms [13].
Once the multi-state model of wind farms output is extracted, the roles of mentioned factors in the procedure of determining required static reserve of power systems can be put under investigation. Wind power penetration level, as one of the most important factors, has a significant impact on reliability and security of the power systems. Based on the studies addressed in [14], the authors came to this point that the 45 and 90 MW wind farms respectively have the same capacity values compared with two conventional units with capacities of 5- and 10-MW. Therefore, they conclude that with increasing the share of wind power, it becomes hard to maintain the reliability level of power systems. In addition, they emphasize that employing conventional criterion in determining the required static reserve of power systems, i.e., the largest capacity of generating unit, will put security of power systems under risk. Thus, to guarantee reliability level of the power delivered to consumers in high-wind penetrated power systems, a proper probabilistic approach to determine static reserve needs to be developed.
The installed capacity of wind farms is the other effective factor which strongly affects the reliability level of power systems [15]. Therefore, proposing any probabilistic algorithm to determine the required amount of reserve of a power system without modeling this factor would be impractical. To cover both of these effective factors in procedure of determining the required static reserve of high-wind penetrated power systems, this paper introduces a probabilistic framework. In this regard, first, a probabilistic multi-state model is borrowed to properly model wind farms output generation in reliability assessment of power systems. This model employs the fuzzy c-means clustering method (FCM) to find the optimal states associated with the probabilistic model of a wind farm. This multi-state model then can easily be used in analytical approach of adequacy studies for power systems. Based on this analytical approach, the roles of these two factors, i.e. wind power penetration rate and installed capacity of wind farms in reliability level of power systems are scrutinized.
To cover this goal, the IEEE-RTS has been considered as the test system and the generation sector of this system is modified by replacing some conventional units by the wind farms. Different wind penetration rates are defined for this test system and the reliability indices of power system at Hierarchical Level I (HLI) are evaluated. Based on this analysis, it has been shown that how the required reserve of power system will vary while the penetration rate of wind power increases. Then, a novel algorithm based on the concept of exhaustive search algorithm is proposed to show the effects of wind farms installed capacities on the reliability level of the system. Applying this algorithm, a predefined penetration rate of wind power can wisely distribute between different windy sites. Running this algorithm on the modified IEEE-RTS, the reliability indices of this test system are reported. The results show that utilization of the proposed method makes the adequacy studies of wind-penetrated power systems more accurate. Furthermore, this method can efficiently be utilized in future power system planning studies with less computational burden and data requirement.
The following sections are organized as follows. Wind farms generation output modeling procedure is introduced in Section 2. Section 3 presents impacts of wind power generation on the required static reserve of power systems. Then, the installed capacity of wind farms is discussed and simulated in Section 4. Relevant discussions and conclusions finally come in Section 5.
Wind farm generation output modeling procedure
The wind farms output generation at each time is a nonlinear function of wind speed. As a result, extracting an accurate model for variation in output generation of wind farms is dependent on the changes of wind speed. This section briefly explains wind farm output modeling procedure.
Wind speed characteristics
The historical data of Manjil, Loutak, Kish and Chabahar, respectively in the North, South, and Southeast part of Iran, measured and recorded by Renewable Energy Organization of Iran, are used in wind farm modeling procedure of this paper [16]. The hourly wind speed data of one year (2008) in these four windy regions are utilized for reliability studies. It is assumed that wind speed is constant within an hour. The measured historical wind speed data should be transformed to the height where the generators hubs of wind turbines are usually placed. Thus, a relation which represents the nonlinear relation of wind speed with the height needs to be employed as shown in (1).
Here, it is assumed that all the under studied wind farms are comprised of a number of 2 MW V90 turbines type manufactured by “Vestas Wind Systems”. The height of hub for these turbines is 105 m [18]. The Hellman exponent of Manjil, Loutak, Kish and Chabahar site was respectively assessed equal to 0.12, 0.16, 0.17 and 0.16 [17]. Since the historical data associated with wind speed of these four windy regions were measured at height of 40 m, these data are transformed to the desired height, i.e. 105 m using (1). The variations of hourly wind speed in Manjil at height of 105 m are illustrated at Fig. 1.
As stated previously, at each time, the wind turbine output generation is a nonlinear function of the wind speed as shown in (2).
Based on the input–output relation of a wind turbine presented in (2), the output power of a Vestas wind turbine in Manjil site for a given year are extracted and shown in Fig. 2. Tracing the rapid changes in output generation of the wind turbine in Fig. 2 proves this fact that only a stochastic model can represent the random behaviors of such units.
The available wind farms output modeling procedures proposed in the past works can be classified into simulation and analytical approaches [20, 21]. Amongst, the ARMA time-series model has been widely utilized to model the variations in wind speed [21]. A large volume of historical wind speed data for the wind site under study is the main deficiency of this method which overshadows its practicality.
Here, an analytical method based on the previous works of the authors presented in [13] is borrowed to model the variations of wind farms output generation as a multi-state model. The main steps of this algorithm are as follows: The historical hourly wind speed data of the site under study is collected. Based on the input–output relation of the wind turbine expressed in (2), the output generation of a wind turbine at each time needs to be calculated. At this step, the output generation of the wind farm at each time is considered to be equal to the sum of each wind turbine generation. Running the optimization of the FCM presented in (3) on the extracted data in step 2, the optimal clusters would be attained.
Based on the optimal clusters attained in step 3, the power level and probability of each state are calculated.
Interested readers are referred to [13] for more information about modeling procedure of this method. Running the proposed multistate analytical model for these four sites, the 5-states probabilistic wind turbines output generation model in Manjil, Loutak, Kish and Chabahar can be found which are respectively shown in Tables 1–4.
As discussed earlier, being unable to accurately predict the wind speed at different times together with intermittency in wind farms output power are of the most key factors which affect the security of generation sector in power systems. To determine the optimal amount of static reserve in high-wind penetrated power systems, a probabilistic approach needs to be applied. In this approach, the commonly used reliability indices, i.e. Expected Energy Not Served (EENS) and Loss of Load Expectation (LOLE) are usually exploited as factors of decision making. To put an investigation on the role of wind power penetration as an effective criterion in determining the required reserve of a power system,a detailed study is run on the IEEE-RTS. The load duration curve (LDC) of this test system is depicted in Fig. 3. In this regard, various wind penetration rates in the range of 5% –40% are assumed for this test system. To modify generation sector of the IEEE-RTS, some of the conventional generating units in the original system are replaced by the wind farms. These modifications are itemized in Table 5.
It has been assumed that these wind farms have been installed in the windy site of Manjil region. The same procedure explained in the previous section is implemented on the historical wind speed data of Manjil and multi-state probabilistic model of the wind turbine is extracted. The 5-state model of a 2 MW wind turbine is presented in Table 1. Based on this analytical model of wind turbines output generation, the multi-state model of wind farm output generation can be attained. A simple two-state reliability model (as shown in Fig. 4) has been considered as reliability model of conventional units. Convolving the multi-state model of wind farms output generation and the Markov model of conventional units [22], different reliability indices for the defined scenarios would be evaluated as shown in Figs. 5 and 6.
As can be traced in these figures (Figs. 5 and 6), once the penetration of wind power in generation sector of the IEEE-RTS increases, the amount of LOLE and EENS associated with the system would be aggravated which can be translated to a lower level of reliability for the test system. These conditions become worse as the penetration rate of wind power in the system goes beyond 30% . Therefore, one can come to this important point that the penetration rate of wind power is an essential factor which has to be considered in determining the required static reserve of a high-wind penetrated power system. Moreover, this factor can shade a light for power system decision makers in optimally and practically develop supportive rules associated with the wind power.
Installed capacity of wind farms and static reserve of the power systems
Up to this section, it has been discussed that how the penetration rate of wind power in a high-wind penetrated power system can affect the required static reserve of the system. In this section, another effective factor in procedure of static reserve determination will be introduced, i.e. installed capacity of wind farms. To properly investigate the effects of this factor, a sensitivity analysis will be run on the installed capacities of wind farms. There are many factors which usually determine the size of a new wind farm in a windy site. However, share of this new generating unit in reliability level of the power system is of great consequence.
In this paper, a new algorithm based on exhaustive search method has been proposed to find the optimal size of wind farms in different windy sites. Main concept and implementation procedure of this algorithm can be found in [23, 24]. The main idea behind employing this algorithm is to examine different combinations of wind farms with various sizes aimed to find a state with the most improvement in the reliability indices. In other words, taking into account all the windy sites of a power system, this algorithm determines the size of wind farm for each site and evaluates different reliability indices of the power system. It finally searches among different states to find the optimal one in viewpoint of reliability indices. The flowchart of this algorithm is depicted in Fig. 7.
It should be notified that for each state of the proposed algorithm the constraint presented in (4) needs to be checked. This constraint ensures us that the cumulative capacity of each windy site is equal to the amount determined by the decision makers of power system under study.
To run the exhaustive search algorithm, four different windy regions in Iran including Manjil, Loutak, kish and Chabehar are considered. The multi-state models of a 2 MW wind turbine in these regions are shown in Tables 1–4.
To investigate the applicability of the proposed search method, it has been implemented on the modified IEEE-RTS. This test system has been modified by considering 10% wind power penetration rate which can be translated to replacing a 350 MW wind farms to this system (see Table 5). Based on these assumptions, the exhaustive search algorithm tries to allocate the wind farms in these four windy regions, i.e. Manjil, Loutak, kish and Chabehar with the main goal of improving reliability level of the system. The predefined maximum amount of installed capacity of wind farms which needs to be met in this algorithm is
Two widely-used indices (EENS and LOLE) have been considered as the reliability indices in the search algorithm. In other words, the search algorithm has been run twice. In the first run, the EENS has been considered as the reliability criterion and in the second one, the optimal capacity of wind farms in different regions have been found regarding the value of LOLE. The load duration curve (LDC) presented in Fig. 8 has been used to evaluate different reliability indices.
Running the exhaustive algorithm for different peak loads of the systems considering the mentioned assumptions, the optimal capacity of wind farms in different regions have been attained as shown in Tables 6–9. As can be traced in the obtained results, as long as the static reserve, which is the difference between installed capacity and peak load, of system has been considered lower (Tables 6 and 7), there is a remarkable difference between the optimal results obtained in the first run (the EENS criterion) and the second run (the LOLE criterion). In contrast, in the conditions that the static reserve of the system increases (see Tables 8 and 9), the difference between the obtained results via the first and second run would be negligible. Although all the reported states in Tables 6–9 are optimal in reliability point of view, the EENS can be introduced as a more effective index in determining the required static reserve of power system.
Unpredictability and intermittency in output power of renewable generating units such as wind farms impose many new challenges on operational and planning studies of power system such as security, stability, and reliability studies. These conditions become worse as the penetration rate of wind power increases. This paper tries to show the necessities of employing a stochastic framework to determine the required static reserve of high-wind penetrated power systems. In this regard, the effects of two new factors (the wind power penetration rate and installed capacity of wind farms) have been well put under investigation. Employing the FCM is acknowledged to properly model the variations in output generation of wind farms. Taking into account the probabilistic model of wind farms output generation, it has been tried to reach a stochastic framework to investigate the roles of mentioned factors. The Modified IEEE-RTS network was taken under consideration as the case study. Different wind power penetration rates were defined for this test system and the effects of this factor were evaluated by calculating the reliability indices for these scenarios. Also, an exhaustive search algorithm has been proposed to examine the effects of installed capacity of wind farms on the required static reserve of the system. Having implemented this stochastic framework on the modified IEEE-RTS, it well confirms the fact that many new important factors should be considered in determining the required static reserve of the high-wind penetrated power systems.