Overview of Electric Energy Distribution Networks Expansion Planning <s> H. PROBABILISTIC VS. DETERMINISTIC <s> Proliferation of wind generators (WGs) requires a change in distribution system planning techniques as WGs have intermittent and uncertain output. This paper proposes a Cumulant based stochastic optimal reactive power planning method for distribution systems with high penetration of WGs. Uncertainties in the output of WGs and load forecasts are modeled using probability density functions (PDFs). With a stochastic framework, an optimization challenge is formulated to minimize the total costs of new capacitors and the total annual energy loss. The optimization problem is then solved by using the Logarithmic Barrier Interior Point Method (LBIPM). At the optimal solution, LBIPM provides a linear relationship between the cumulants of independent variables (load and wind power) and the cumulants of the dependent system parameters. The Cumulant method offers a generous advantage in speed, while maintaining acceptable accuracy, as compared to the computationally cumbersome traditional Monte Carlo simulation (MCS) method. The method is tested on 7-bus, 33-bus, and 129-bus systems. The results are reported and discussed. The performance and accuracy are assessed by comparing the results with those from MCS method. <s> BIB001 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> H. PROBABILISTIC VS. DETERMINISTIC <s> Abstract Distributed generators (DGs) are a reliable solution to supply economic and reliable electricity to customers. It is the last stage in delivery of electric power which can be defined as an electric power source connected directly to the distribution network or on the customer site. It is necessary to allocate DGs optimally (size, placement and the type) to obtain commercial, technical, environmental and regulatory advantages of power systems. In this context, a comprehensive literature review of uncertainty modeling methods used for modeling uncertain parameters related to renewable DGs as well as methodologies used for the planning and operation of DGs integration into distribution network. The authors strongly recommend this review to researchers, scientists and engineers who are working in this field of research work. <s> BIB002 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> H. PROBABILISTIC VS. DETERMINISTIC <s> The integration of a massive number of plug-in electric vehicles (PEVs) into current power distribution networks brings direct challenges to network planning, control, and operation. To increase the PEV penetration level with minimal negative impact, the dynamical PEV travel behaviors and charging demand need to be better understood. This paper presents a Markov-based analytical approach for modeling PEV travel behaviors and charging demand. The travel behaviors of individual PEVs are expressed mathematically through Monte Carlo simulation considering two essential factors: temporal travel purposes and state of charge (SoC). Markov model and hidden Markov model (HMM) are adopted to explicitly formulate the probabilistic correlation between multiple PEV states and SoC ranges. This modeling approach provides an efficient and generic tool for analyzing PEV travel behaviors and charging demand based on available PEV statistics. The analytical model is further adopted in the impact assessment of two PEV normal charging scheduling strategies for a range of PEV penetration levels in an IEEE 53-bus test network with field data (network parameters and realistic PEV statistics). The results demonstrate the benefit of the proposed modeling approach in network analysis considering PEV integration. <s> BIB003
As mentioned, the problems with all known or specific input data are considered as a deterministic problem. In real problems, however, uncertain resources substantially impact the quality of the results. Among many methods to handle uncertainties, probabilistic methods enumerate the uncertainty parameter affecting the results by generating scenarios out of probability distribution function (pdf), which is extracted from historical data. In power system studies, we can model the uncertain parameters in wind-turbine power outputs and solar radiations by generating PDFs of these uncertain parameters. Two main well-known methods to generate PDFs are numerical and analytical techniques. Numerical techniques estimate PDFs using Monte Carlo Simulation (MCS), and analytical ones apply arithmetic calculations on PDFs of uncertain parameters. MCS is mainly based on sample generation to mimic the long run of an uncertain parameter. In this regard, different MCS techniques use different sample generation methods such as Latin hypercube sampling and Markov chain BIB003 . However, the main shortcoming of MCS is computational intractability in models with several uncertainty parameters due to generating numerous samples. Thanks to sample reduction methods and chance-constrained optimizations, the computational efficiency of MCS is enhanced BIB002 . On the other hand, analytical techniques utilize several methods to generate efficient samples such as linearization-based and PDF approximation techniques. Popular linearization techniques are convolution, cumulants, expansion of Taylor series, and first-order second-moment methods BIB001 . Well-known PDF approximation methods are also point-estimate and unscented transformation methods.