C ONCLUSIONES

The power system state estimation problem was introduced by Schweppe [6] [7] [8] for transmission systems. However, research and development on SE for distribution systems is an emerging area. Most previous research considered distribution networks as unidirectional power flow passive networks.

Ghosh et al. applied a probabilistic approach for the distribution circuit state estimation based on forward and backward sweeps [9]. The algorithm takes into account the limitation of real measurements in distribution systems. The estimator performs effectively on a small system. Hoffman in [10] applied a similar load flow based estimation technique that is referred to as a ladder algorithm. The algorithm converts all measurements into current measurements. The current magnitude is considered as the primary state and the algorithm aims to match the feeder current magnitude measurements. Application of the proposed

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method could be infeasible as a consequence of the following two assumptions that have been made in the presented research; 1) a number of the real measurements have zero variance, and 2) the magnitudes of the real power flow measurements on a radial feeder should always be monotonically decreasing the further it is located from the feeder source. It is important to note that both assumptions are not practical for active distribution systems. The current measurements data are extensively studied by Baran and Kelley [11]. These authors adopt a Weighted Least Squares (WLS) approach to develop a 3-phase DSSE tool. The DSSE tool considers the availability of only a few real measurements and large numbers of pseudo-measurements. The authors observe through a few case studies that power flow measurements are more effective in bad data identification than current measurements. The case studies demonstrate an important fact with regard to the power distribution system SE problem, which is, the improvement of the estimation quality largely depends on the accuracy of pseudo-measurements in presence of limited real measurements [11]. The same authors later have developed a branch-current based 3-phase DSSE tool in order to achieve more computational efficiencies and less sensitivity to line parameters than the conventional node voltage based tools [12]. Similar to reference [10], the authors convert all real power flow and pseudo load measurements into current measurements [12]. References [11][12] have successfully applied their proposed algorithms to obtain good quality of estimated values, however without considering the presence of distributed generators that may cause bidirectional power flows. Reference [13] also applies a 3-phase estimator that uses a current magnitude based formulation. Here the estimation problem is solved using WLS optimization criteria. Test cases imply the necessity of real measurement data for greater quality of estimated values. The proposed methodologies are successfully applied with limited real measurement data. A revised version of a branch current based estimation tool is developed by Wang and Schulz using current magnitude and phase angle as the primary states [14]. The algorithm undergoes additional computation to define the initial states but also decouples the three phases to improve computational efficiency. Significant improvement in estimation quality is observed by reducing real measurement errors from 5% to 3% and pseudo- measurement errors from 50% to 30% [14]. Reference [10]-[14] have applied branch-current magnitude as the key measurement element as well as the state variable to estimate. The outcomes are impressively correct in the presented case studies. However, there is high possibility of bidirectional power flow in future active networks; it will be then highly important to consider the direction of current flow along with its magnitude. The state estimation

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algorithms based on current magnitudes may not work very effectively for future distribution systems.

New generation DMS issues like the impact of DG penetration, ill-conditioning problems resulting from normal equation based optimization, heavy computational burden arising from large distribution networks and the impact of smart grids have been addressed in some relatively recent works. Due to the presence of diverse confidence levels of multi- source measurements and various branch sizes, the normal-equation based state estimator is prone to matrix ill-conditioning. Many papers have considered the virtual measurements as equality constraints, which reduces this problem to some extent [15] [16] [17] [18] [19].

Xu et al. [20] developed a WLS optimization problem where the weight of the measurements is termed as 'quality tag'. All measurement data undergo novel bad data detection and processing and the quality tag for the measurement is calculated before they are fed into the WLS optimization tool. The field application shows promising results; however this method does not directly consider the impact of DGs at LV-MV levels [20]. Bignucolo et al. [18] develop a probabilistic voltage state estimation taking into consideration high penetration of DGs. This research proposes discrete step communication support to track down section-wise DG outputs and a load estimation method to reduce pseudo-measurement errors. Incorporation of partial knowledge of the DG in real time has significantly reduced the uncertainty of voltage magnitudes; while indicating suitable communication techniques to adopt and associated costs. The proposed methodology demonstrates its potential for practical applications [18]. Sing et al. [17] investigate compatibility of three different mathematical optimization algorithms (WLS, Weighted Least Absolute Values (WLAV) and Schweppe Huber Generalized M (SHGM) estimators) for DSSE with UK generic distribution networks in presence of DGs. Crucial studies are performed with various levels of measurement error probabilities and redundancy reflecting distribution system scenarios. It is concluded that the classical WLS method performs best when measurement errors are assumed to be Gaussian. The paper also indicates that the most suitable DSSE technique may be different if the measurement error distribution is modelled as other criteria than Gaussian distribution [17]. The authors in [21] have applied generalized three phase state estimation where three phase errors are considered to be correlated. The most significant contributions of the paper are performing three phase unbalanced DSSE and online test on a real distribution network. The algorithm succeeds to correctly identify the areas of the network which were in breach of regulatory

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limits for voltage unbalance, however the paper does not explicitly discuss about the overall improvement of estimation quality applying the proposed method [21]. A two stage distribution substation SE solution to reduce computation burden is proposed in [22] for future smart grids. The paper represents one of few researches regarding network division based DSSE algorithm. The DSSE algorithm improves the convergence property over conventional method. Complete observability of the network is required to achieve by real measurements in this method, making its application to real distribution network limited.

In addition to conventional methods, new and extended concepts are being introduced into the distribution system SE problems. Heuristic methods like particle swarm optimization (PSO) is receiving attention to be applied as DSSE. In [23] [24] [25] [26], different types of PSOs are considered as DSSE solutions. Reference [23] [24] [25] apply a hybrid PSO (HPSO) base SE solution taking into account existence of DGs in the network and limited real measurements; with assumptions of contracted load and estimated power factor values at each node being known. The authors consider that there are impacts on the SE objective function due to the nonlinear characteristics of equipment. Such as the nonlinear characteristics of outputs of static VAr compensators (SVCs), induction generators (output equation expressed by constant impedance, constant current and constant power load) and the discrete tap control function of a transformer. Some improvement with respect to the estimation quality is observed when applying HPSO compare to the application of conventional PSO on a model network. The quality of estimation is compared with respect to the real measurement data; although the estimated values are usually compared with the true values to measure their accuracy for such model network. Chilard et al. [26] has adopted a generalized PSO approach as a meta-heuristic solution of DSSE and compare the performance with a constrained WLS approach. The paper discusses some important issues such as the accuracy of estimation and computation time with respect to the conventional normal equation based approach. The authors conclude that the constrained WLS approach outperforms generalized PSO to solve distribution SE. Formulation of the probabilistic estimation as a multi-objective combinatorial optimization problem is proposed by Hashimoto et al. [27]. The authors treat the objective functions by corresponding to an evaluation of occurrence probability and a proximity evaluation of calculated voltage parameters with values obtained by measurements. The meta-heuristic approach requires to set the occurrence probability to each interval, phase, active and reactive power. It is inferred that the proposed methodology may not need additional investments on

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measurement equipment as the method is designed to consider different supervisory levels of systems developed in the utilities.

Most of the research into distribution state estimation has applied either power flow based algorithms or WLS minimization criteria. It is evident that most research in the past for distribution system estimation is strongly focused on passive distribution networks that considers unidirectional power flow. In recent decades, the development of smart grids is getting more attention and the profound requirements of the DSSE tool have been realized. Wide scale research, taking into account bidirectional load flow and the integration of DG, are being performed. Distribution networks that have been absolutely passive by nature in the past, are now required to undergo extensive infrastructural development to accommodate current and future requirements. Enhanced observability and robust automation control will be major functions of these active distribution networks enabling smart distribution management.