Probabilistic Fuzzy Approach to Assess RDS Vulnerability and Plan Corrective Action Using Feeder Reconfiguration ()
1. Introduction
Power distribution systems, especially in developing countries, are steadily approaching towards its maximum operating limits and voltage stability is a major concern. Voltage instability makes the system unreliable and results in system collapse and blackout. Around 30% to 40% of total investments in the electrical sector go to distribution systems, but same have not received the technological impact as generation and transmission systems.
The voltage instability can be addressed using the various techniques. One of the control options for managing RDS is feeder reconfiguration. Reconfiguration is opening and closing the sectionalizing and tie-switches in a RDS. It modifies the network structure and thus reduces the real power losses, and improves voltage stability. However reconfiguration is effective only when tieswitches are planned at optimum location and the best combinations are selected for the same.
Distribution systems have combinations of loads like industrial, commercial, domestic, lighting etc. and each of them peak at different times of the day and need to be effectively captured, while planning reconfiguration or locating tie switches for an existing RDS expansion system.
There are methods proposed by various authors on various methods for reconfiguration. B. Venkatesh and Rakesh Ranjan propose a method that uses fuzzy adaptation of Evolutionary Programming (FEP) as a solution technique [1]. Takanobu proposed distribution network expansion planning method by network reconfiguration and generation of construction plans [2]. Dong-Joon Shin represents an approach for service restoration and optimal reconfiguration of distribution network using genetic and Tabusearch method [3]. B. Venkatesh, Rakesh Ranjan, H. B. Gooi developed a new method for optimal reconfiguration of radial distribution systems which maximizes a fuzzy index developed using a maximum load ability index [4]. R. Ranjan, B. Venkatesh, D. Das proposed novel method for selecting an optimal branch conductor for radial distribution networks based on fuzzy adaption of evolutionary programming [5]. P. V. V. Rama Rao and S. Sivanagaraju proposes plant growth simulation algorithm to enhance speed and robustness and does not require external parameters for loss minimization and load balancing [6].
This paper discusses the plan of optimizing the Radial distribution system via feeder reconfiguration using probabilistic fuzzy modeled solution. The proposed solution calculates node vulnerability index and use the same for reconfiguration. The solution is based on concept of probabilistic fuzzy rules and is suitable for modeling real world systems, where we have both statistical and non-statistical uncertainties. Probabilistic part of the model uses Monte Carlo simulation (MCS) and considers input parameters as random variables with predefined probability distribution shape. Further for calculating vulnerability index, paper uses fuzzy based algorithm, and uses fuzzified node voltage and node voltage stability index as inputs. Based on vulnerability index of nodes, a scheme for planning tie and sectionalizing switches to achieve loss reduction is presented. While the scope of the feeder reconfiguration problem discussed here is limited to the discussion of losses, the results developed provide significant insight into useful characteristics associated with the modeling and properties of related feeder reconfiguration problems. The above technique can be used for long term distribution network expansion planning purposes also.
The paper is organized as follows. In Section 2, the methodology & steps used are discussed. Section 3 defines formulas and calculation algorithm used. Section 4 describes nodal vulnerability index computations, Section 5 elaborates the reconfiguration planning & calculations showing reduction in losses and Section 6 concludes the paper.
2. Methodology
Paper presents RDS reconfiguration planning using following steps:
• Define the load flow & stability index formulas & calculation algorithm;
• Infuse randomness in input variables in line with real time scenario by modeling input data as random variables with predefined distribution to address combination of loads;
• Use Monte Carlo simulation and generate output distribution for nodal voltages & voltage stability index and calculate node vulnerability index;
• Use Node vulnerability index as basis for RDS reconfiguration planning;
• Recalculate the losses after applying proposed reconfiguration.
3. Formulas & Calculation Algorithm
3.1. Load Flow & Stability Index Calculation Formula’s & Algorithm
For simulation purpose this paper uses a load flow algorithm, based on concept described by R. Raina, M. Thomas, R. Ranjan [7] and modified to suite the probabilistic model (for Monte Carlo simulation). The algorithm calculates the total real and reactive system power loss, nodal voltages and stability index.
The load flow calculation algorithm uses the basic systems analysis method and circuit theory and requires only the recursive algebraic equations to get the voltage magnitudes, currents & power losses at all the nodes.
This load flow methodology also evaluates the total real and reactive power fed through any node. Using concept of simple circuit theory, the relation between the bus voltages and the branch currents in Figure 1 can be expressed as:
(1)
where;
= Voltage of phase a at node i with respect to ground;
= Voltage drop between two phases a and b at node I;
= Voltage Drop between nodes i and j in phase a;
= Current through phase a between nodes i and j;
= Selfimpedance between nodes i and j in phase a;
= Mutual impedance between phase a and b between nodes i and j;
= Real, reactive and complex power loads at phase a at ith bus;
= Complex power at phase (a, b and c) between nodes i and j;
= Real power loss in the line between node i and j;
= Reactive power loss in the line between node i and j;
= PLijphase + jQLijphase.
Rewriting (1)
Following equations gives the branch currents between the nodes i and j:
Figure 1. Three phase four wire line model.
The real and reactive power losses in the line between buses i and j are written as;
This algorithm computes the real & reactive power and uses the formula given in Equation (2). Receiving end power at any phase, say phase A, of line between the nodes i and j is expressed as:
(2)
K = index of all nodes fed through the line between nodes i & j.
mn = index of all line connected between nodes m and n through the line between nodes i and j.
The simulation also calculates the voltage stability index (SI) for all the nodes of the radial distribution system using the load flow results. There are several methods to estimate or predict the voltage stability condition of a power system. The simulation utilizes the voltage stability index defined by N. C. Sahoo, K. Prasad [8] to indicate the voltage stability condition at each bus of the system. Stability index (SI) for the bus j, for atypical branch as shown in Figure 2 is defined as:
(3)
The value of SI varies from 0 to 1. For stable operation of the RDS, Stability Index (SI) should be nearing one.
3.2. Infusing Randomness in Inputs & Monte Carlo Simulation to Address Combination of Loads
Monte Carlo simulation principle is described in Figure 3. The principle is based on considering input parameters as random variables and with predefined distribution shape. Probability distribution shape describes the likelihood of same future events. Uncertain input parameter is considered as a random variable P and numbers of realizations Pi of P are generated and load flow algorithm is run for each of them producing an output Ri. Set of outputs Ri represents the set of realizations of the random variable R.
Figure 2. Electrical equivalent of one branch.
For simulation purpose connected load is assumed to be varying based on Table 1 probability distribution shape. This simulation is run on a typical 19 bus distribution system from the D. Thukram, H. M. W. Banda, and J. Jerome [9] for 500 trails and distribution of output results are used as input for calculating node vulnerability index and input data are given in Appendix of this paper.
3.3. Mote Carlo Simulation Results
The simulation is run for 500 trails and distribution of results is tabulated as frequency distribution. Table 2 provides the Real, Reactive power loss values corresponding
Figure 3. Sketch for monte carlo simulation method.
Table 1. Probability distribution for connected load.
to 90% (0.9) cumulative probability. The value of 90% (0.9) cumulative probability signifies that for a simulation run of 500 trails, 90% time values were less than 138.4 kW/66.9 KVAr.
Table 3 shows the simulation distribution results for selected nodal voltages based on 500 trails including minimum nodal voltage corresponding to 90% cumulative probability.