An efficient probabilistic-chronological matching modeling for DG planning and reliability assessment in power distribution systems


Develop a reduced multi-state method to represent the intermittent nature of wind and PV.

Evaluate different time representation models for renewable resources and load.

Size and allocate DGs considering the reduced state method and different time models.

Assess the supply adequacy for distribution system with renewable resources under different time models.

Validate the results using time series and sequential Monte Carlo simulation.


In recent decades, power distribution systems have encountered a considerable shift toward utilizing renewable resource based distributed generation (DG) systems. This is due to the proven ability of DGs to reduce fossil fuel consumption, which reduces harm done to the environment. In this paper, a new state reduction algorithm is proposed to determine the minimum number of states required to describe or represent the behavior of wind speed and solar irradiance in DG planning problems and reliability analysis. This algorithm could be generalized to incorporate any planning problem where wind or PV power is part of its parameters. Moreover, an adequate time representation that mimics the fluctuation of renewable resource based DGs and chronologically matches the fluctuations in system demand is presented. Three different data clusters are applied (monthly, seasonal and yearly) to investigate the variability of DG power output and electricity demand on both DG planning problems and reliability assessment. These models are evaluated considering DG siting and sizing problems, as well as a supply adequacy-based reliability assessment. The proposed model measures the deviations in annual energy losses (AEL), total DG penetration, loss of load expectation (LOLE), and loss of energy expectation (LOEE).


  • DG planning;
  • DG reliability evaluation;
  • Rounding technique;
  • Wind and PV states;
  • k-means cluster

1. Introduction

The electricity demand worldwide is expected to increase significantly in the next few decades [1]. This anticipated increase reflects the widespread growth of population, infrastructure, industrial sectors, and commercial sectors. From 2011 until the end of 2040, the electricity demand is expected to grow by 28%, growing from 3, 839 billion kWh in 2011 to reach 4, 930 billion kWh in 2040 [2]. During this period, power utilities are responsible to meet this increased demand; the expansion in generation capacities is considered to be one of the duties of planning engineers. Meanwhile, the interest in utilizing renewable resources based distributed generation (DG) systems in the conventional power distribution system networks has dramatically increased [3]. This is due to the cleanness and sustainability of these resources, as well as their ability to support the existing grid with the help of energy storages and other technologies. DG technologies consist of wind turbines, photovoltaic modules, solar-thermal systems, fuel cells, and others. As an instance for the global trend to implement renewable resources, currently, wind power installed generation capacity is almost 10% of Ontario’s installed generation capacity, and it is equivalent to 3504 MW [4]. Indeed, various books, associations, utilities, and papers have given different definitions of the term “Distributed Generation”. These definitions vary, with some taking into account the size of the DGs, while others concentrating on the location of these DGs or their technical effects such as voltage level or power quality. Distributed generation is defined as, “an electric power source connected directly to the distribution network or on the customer site of the meter” [5].

Distribution system planning based on the use of renewable resources can be classified into two categories [6]. The first category is short term planning, which includes unit commitment problems and storage scheduling. Wind speed forecasting and prediction techniques are usually preferred for this category. However, for long term planning problems, analyzing large sets of data to indicate the behavior of these variables (wind speed and solar irradiance) is more desirable. For this second category of long term planning, these data are often fitted to suitable distribution functions for the investigated sites. The uncertainty introduced by the fluctuations in wind and PV output power increases the challenge of modeling these resources, and therefore more effort is required to overcome the technical and economic challenges [7].

Extensive work has been done to model renewable resources in the planning frameworks [8], [9], [10], [11], [12], [13], [14], [15] and [16]. In the investigation of one site in particular, the output power of wind turbines is modeled using time-series data obtained from wind speeds and hourly load variations [8]. The annual duration curve for DG produced power is utilized in Ref. [9] to size the photovoltaic based DGs. In another investigation, the capacity factors for non-dispatchable DGs are applied in the analysis to represent the estimated production of wind turbines [9] and [10]. More detailed probabilistic generation models using the probability distribution functions for the uncertain parameters and Markov matrix simulation are considered in Refs. [10], [11], [15] and [16]. Probability distribution functions PDFs verified their effectiveness in describing the uncertainty in wind speed as well as solar irradiance since PDFs can use a huge number of population for the uncertain parameter [11]. Moreover, PDFs are willing to mimic the pattern of any stochastic parameters using the multi-state representation or what is known as scenarios-based modeling [17].

Indeed, in order to extract the output power from wind and PV based DGs, wind and PV output power should be divided initially into many states or scenarios to be incorporated in the probabilistic model. These states vary and depend on accuracy and the complexity of selected states in power flow, reliability, and optimization calculations. Large number of wind or PV states led to a very large number of overall system states so that the analytical reliability evaluation is almost impossible to perform, and the operation or planning analysis that require fast processing (computational) time will take longer. Furthermore, one of the challenges of reliability and planning analysis is that there are numerous system states which require researchers to utilize simulation techniques rather than analytical methods. These obstacles exist because overall system states are represented by an exponential equation which is a composite of the number of system components and the states of each component as shown in equation (1):



where, m is the number of states for each component, n is the number of system components, and s is the system’s overall states.

This paper proposes a novel algorithm based on a clustering method and rounding technique in order to determine the minimum number of wind and PV states required, as well as an appropriate time representation that can represent the randomness in wind and PV output power for long term planning and analysis. The importance of this method is reflected in its ability to reduce the complexity in stochastic power system planning and reliability analysis such that the number of overall system states will be minimized when the analytical evaluation methods are utilized. Moreover, when the computational time needs to be minimized in power operation or planning problems, the proposed method offers a solution, since it reveals considerable savings in the computational time needed. The main contributions of this paper can be summarized as follows:

It proposes a new method for reducing the number of renewable resource output power states.

It evaluates different time modeling for generating-load chronological matching.

It incorporates the reduced states method and the generating-load chronological matching model in DG planning and reliability analysis.

The remainder of this paper is organized as follows: Section 2 outlines the state representation of wind and PV output power; Section 3 describes the chronological modeling of renewable resources and load; Section 4 presents the multi-state modeling of renewable resources; Section 5 presents the method of selecting the minimum representing states of renewable output power; Section 6 formulates the applications; Section 7 presents the case studies and the results and, finally, Section 8 summarizes the conclusions.

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