# Available Transfer Capability Enhancement Engineering Essay

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Available Transfer Capability is what exactly the allowable power limit to accommodate new users without violating the commitments of the existing users. Thus in the deregulated environment, this transfer capability is of more concern. ATC is a dependent factor on the system thermal, stability and voltage limits.

With the introduction of FACTS devices, the line overloads, bus voltage problems are considerably brought down. Series compensators like Thyristor Controlled Series Capacitors (TCSC) are used for line flow controls. The ATC can be increased by adjusting the settings of the FACTS device (such as reactance, phase angles, reactive power injection) with respect to the system parameters. Particle Swarm Optimization (PSO) is an evolutionary technique that is used to solve multi objective optimization problem. In this paper PSO technique is used to estimate the feasible optimal settings [2] for the TCSC device to enhance the power transfer capability of the system to an appreciable limit.

Key Words: ATC, FACTS, PSO, PTDF, TCSC.

I. INTRODUCTION

Deregulation of the electric industry throughout the world aims at creating competitive markets to trade electricity, which generates a host of new challenges to market participants and power system researchers. One of the major consequences in the transmission network is the adequate demand of available transfer capability (ATC). Secured and satisfactory operation with the existing transmission assets with less congestion will be more profitable for transmission owners and customers will also get improved services at a reduced price [1].

A simple test IEEE 6bus system is considered in which the DC load flow [4] was run and the ATC calculation was done using the power transfer distribution factor (PTDF) method. For studying the effect of FACTS [5] a controller, TCSC a series controller is incorporated in the lines on a random selection and the effect on ATC was observed. The analysis was done on the standard IEEE six bus systems [4]. The study was done by installing a single

TCSC at a line and running the load flow for testing the effect of the variation in the system impedance through TCSC.

The approach analyzed here is without considering the contingency effect. While calculating the ATC, the values of the transmission reliability margin (TRM) and the capacity benefit margin (CBM) were also neglected and only the base case flow was accounted apart from the thermal limit of the lines.

Particle swarm optimization (PSO) is a tool for multi-objective, evolutionary optimization tool that rely on numerical data. PSO is used in estimating the optimal setting of the TCSC to be installed in the lines. The choice for PSO is that it is a very efficient algorithm in converging towards the global solution that optimizes the function. Choice of TCSC among various FACTS device for this problem is that, it can be easily modeled as a reactance to be in series with that of the line reactance in the equivalent circuit.

II. AVAILABLE TRANSFER CAPABILITY (ATC)

ATC calculation is a vital issue in the power system operation under deregulated environment. Utilities therefore need to determine adequately their ATC to ensure that system reliability is maintained The information about the ATC is to be continuously updated and made available to the market participants through the internet based system such as the open access same time information system (OASIS).

According to the NERC report, ATC is a measure of the transfer capability remaining in the physical transmission network for further commercial activity over and above already committed uses. The term capability here refers to the ability of the lines to reliably transfer power from one bus / area to another. Mathematically, ATC is defined as shown.

ATC = TTC - TRM - CBM - ETC.

ATC between two areas gives the upper limit of additional power flow between them for the specified time period under given conditions.

Total transfer capability (TTC) is the amount of electric power that can be transferred over the interconnected transmission network in a reliable manner under a reasonable range of uncertainties and contingencies. It is more or less similar to the first contingency total transfer capacity (FCTTC). While determining the TTC, system conditions, critical contingencies, system limits, parallel path flows and effects of non - simultaneous transfers are to be considered.

Transmission reliability margin (TRM) is defined as the amount of transmission transfer capability necessary to ensure that the interconnected network is secure under a reasonable range of uncertainties in the system conditions.

Capacity benefit margin (CBM) is that amount of transmission transfer capability reserved by the load serving entities to ensure access to generation from the interconnected systems to meet generation reliability requirements. It also helps to reduce the installed capacity of the plant.

The constraints applicable to ATC are,

a) Static constraints:

1) Line thermal limits

2) Bus voltage (magnitude) limits

3) Saddle node bifurcation (SNB)

b) Dynamic constraints:

1) Small signal stability limit

2) Large signal stability limit.

Dynamic ATC refers to the calculation of the ATC considering the dynamic constraints of the system. These problems are usually solved using dynamic constrained optimization techniques. Here as in case of the static ATC calculation the constraints are same yet they differ only by the nature of their time function [6].

III.PARTICLE SWARM OPTIMIZATION

Particle swarm optimization (PSO) is an evolutionary computation technique [9] developed by

Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling.

Similar to genetic algorithms (GA), PSO is a population based optimization tool. The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles are "flown" through the problem space by following the current optimum particles. Compared to GA, the advantages of PSO are that PSO is easy to implement and there are few parameters to adjust. PSO has been successfully applied in many areas: function optimization, artificial neural network training, fuzzy system control, and other areas where genetic algorithm can be applied.

In the particle swarm algorithm, the trajectory of each individual in the search space is adjusted by dynamically altering the velocity of each particle, according to its own flying experience and the flying experience of the other particles in the search space. The position vector and the velocity vector of the ith particle in the d - dimensional search space can be represented as Xi = (xi1, xi2, xi3 â€¦, xid) and Vi = (vi1, vi2, vi3 â€¦, vid) respectively. According to a user defined fitness function, let us say the best position of each particle (which corresponds to the best fitness value obtained by the particle at time t) is Pi = (pi1, pi2, pi3 â€¦, pid), and the fittest particle found so far at time t is

Pg = (pg1, pg2, pg3 â€¦, pgd). The new velocities and the positions of the particles for the next fitness evaluation are calculated using the following equations.

vid = w * vid + c1* rand1 ( ) * (pid - xid) + c1* rand2( ) * (pgd - xid)

xid = xid + vid

w = (w1 - w2) * (1 - current iteration / Maximum iteration) + w2

Constants c1 and c2 are constants known as the acceleration coefficients and rand1 ( ) and rand2 ( ) are two separately generate uniformly distributed rand numbers in the range [0, 1]. Inertia weight is denoted by w, this is to balance the local and global search during the optimization process. By linearly varying the inertia weight over the generations there is a significant improvement in the convergence through PSO technique.

IV. Thyristor Controlled Series Capacitor

TCSC [5] is a capacitive reactance compensator which consists of a series capacitor banks shunted by a thyristor controlled reactor in order to provide a smoothly variable series capacitive reactance.

A variable reactor such as a thyristor controlled reactor (TCR) is connected across a series capacitor. When the TCR firing angle is 1800 the reactor becomes non-conducting and series capacitor has its normal reactance. As the firing angle reduces to less than 1800 the capacitive reactance increases. When TCR firing angle is 900 the reactor becomes fully conducting and the total reactance becomes inductive because the reactor impedance is designed to be much lower than the series capacitor impedance with firing angle 900 to limit the fault current.

The TCSC is employed in the system to adjust the transmission in feed impedance and therefore increase transmission system capacity without increasing the system fault current levels. The capacitor bank is provided with a parallel thyristor controlled inductor that circulates current pulses which add in phase with the line current. This boosts the capacitor voltage.

The TCSC may have one of the two possible characteristics: capacitive or inductive, respectively to decrease or increase the impedance of the branch. It is modeled with variable series reactance. Its value is function of the reactance of the line XL where the device is located It is in the range: -0.8 XL < XTCSC < 0.2XL

- JXC

LINE

T2

T1

JXL

Fig1: Simplified TCSC model

V. METHODOLOGY

A. Introduction to ATC calculation methods

The methods used in static ATC determination can be categorized into the following methods.

(a) Method based on multiple load flow and continuation power flow (CPF)

(b) Method based on optimization power flow

(c) Method based on linear sensitivity factors.

The first method runs AC load flow for each increment of transaction between an interface and checks whether any of the limits are violated. For every increment CPF is run to find out the maximum loadability or voltage instability point. The minimum out of the two critical values is taken as the TTC for the system intact condition. This is repeated for each outage case and the worst case is used to declare the TTC and ATC values.

ATC determination in optimization based methods try to find out the maximum value of the transaction between given interface while satisfying the network power balance (equality constraints) and security constraints such as line flow, voltage limits and voltage instability or SNB conditions.

Static ATC calculation using linear sensitivity method is the method followed in this thesis. This has been discussed below [3].

B. Power transfer distribution factor (PTDF)

PTDF is defined as that fraction of the amount of a transaction from one zone / bus to another that flows over a given transmission line. PTDFij,mn is a fraction of a transaction from zone 'm' to zone 'n' that flows over a transmission line between bus 'i' and 'j'. The used method is called as the DCPTDF method i.e. this method makes use of the DC power flow based formulations and simultaneous determination of ATC. Mathematically,

PTDFij, mn = (Xim - Xin - Xjm + Xjn) / xij

Where, xij is the reactance of the line between bus 'i' and 'j'. Xim are the elements of the X matrix of ith row and mth column. X is called the sensitivity matrix.

Pmn, ijmax = (Pijmax - Pij0) / PTDFij, mn

Where, Pmn, ijmax is the transfer case for the transaction between zone / bus 'm' to 'n'. Pijmax is the line limit of the line between the bus 'i' and 'j'. Pij0 is the base case power flow in line between bus 'i' and 'j'.

ATC = min { Pmn, ijmax }

By running AC power flow using the standard Newton's power flow algorithm, the ACPTDF can be calculated. When the calculation time is of much importance rather than accuracy of calculation, an approximate calculation of ATC using DCPTDF would suffice the need. For analysis that requires consideration of voltage and reactive power constraints, the detailed ACPTDF method can be used.

C. Problem Formulation

Based on the DC power flow model, linear ATC calculations typically assumes a lossless system, where changes in the line real power flows are linearly related to changes in the net real power injections [8]. The PTDFs can be determined as linearized sensitivities evaluated at the initial operating point or approximated as constants only network reactance. These PTDFs are essentially current dividers in linear circuit theory [8]. They can be used to predict large change in the line flow (line j-k) due to a transfer (bus s to bus i) as

Î”Pjk = Ïjk,i Î”Ps = -Ïjk,i Î”Pi

Where, Ïjk,i is the PTDF, Î”Ps is the power transferred from bus 's' to bus 'i' and Î”Pi is the power towards 'i' from 's'.

For a given positive line flow limit Pjkmax, which is assumed to be equal to the line MVA rating and an initial positive line flow Pjk0, the size of the transfer that drives the line to its limit is equal to,

Î”Psjk = (Pjkmax - Pjk0) / Ïjk,i, Ïjk,i > 0

ATCsâ†’i = min {Î”Psjk : all lines jk}

The objective of the problem is to maximize the ATC in the considered DC model. To maximize the ATC, TCSC is used to vary the reactance of the line to which it is introduced. The TCSC is introduced into the line with the maximum value of ATC obtained in transaction considered. Here only the bilateral transaction is considered for discussion.

D. Algorithm

The step by step algorithm to solve this problem for ATC calculation is given below.

Step.1 Start

Step.2 Read the system data

Step.3 Formulate the DC power flow solutions

Step.4 Calculate the PTDF values

Step.5 Consider a transaction and solve for the transfer case for all lines

Step.6 Store the minimum of the calculated transfer case value in the ATC list

Step.7 Do from step.4 for all lines

Step.8 Calculate the ATC from the ATC list

Step.9 Using PSO it estimate the TCSC reactance value

Step.10 Run from step 3 to 8 for the new data with the introduction of TCSC

Step.11 Print results

Step.12 Stop

VI. RESULTS AND DISCUSSION

The simulation for the IEEE 6 bus system is studied with single TCSC located to enhance the ATC and simultaneously reduce the line loading to be well far from the line limit. The simulation is carried out in MATLAB version 7.0 for Windows environment. The bus and line data are taken from [4], the system has 11 lines. The calculated ATC without TCSC and the results obtained after including TCSC into the system were compared in the Table3. The objective of introducing TCSC into the line improves the ATC as well as minimizes the loading of the lines operating very close to their line limits.

The TCSC was modeled into the line as a reactance that is solved equivalently with the line reactance. With the introduction of a single TCSC into the line, the ATC was only marginally increased. If the TCSC is connected in the line between the buses 4 and 5 power flow is increased in lines connected between the buses 2 and 4 from 0.32p.u to 0.36p.u, 4 and 5 from 0.04 p.u to 0.08p.u, 5 and 6 from 0.002p.u to 0.01p.u. And in other lines the loading somewhat reduced. And all the transmission lines are carrying power within their thermal rating. And the ATC is improved.

PSO parameters:

Pop size=20

Learning factors C1=2 C2=2

Max velocity Vmax =10

Max iterations =100

TABLE I: BASE CASE POWERS IN P.U

P1-2

0.25

P1-4

0.41

P1-5

0.33

P2-3

0.02

P2-4

032

P2-5

0.16

P2-6

0.24

P3-5

0.17

P3-6

0.44

P4-5

0.04

P5-6

0.003

TABLE II: ATC CALCULATIONS IN P.U

ATC=min {Pmn, ijmax}

P1-2,1-2

0.09944

P1-4,1-2

0.2680

P1-5,1-2

0.3207

P2-3,1-2

-3.23216

P2-4,1-2

-0.23713

P2-5,1-2

-0.404

P2-6,1-2

-0.84740

P3-5,1-2

-0.5014

P3-6,1-2

19.025

P4-5,1-2

46.6285

P5-6,1-2

3.488

TABLE III: ATC IN P.U IN LINES WITH AND WITHOUT TCSC PLACED IN THE LINE BETWEEN THE BUSES 4 AND 5 IN THE 6 BUS SYSTEM

ATC WITH OUT TCSC

ATC WITH TCSC

0.0993

0.1054

VII. CONCLUSION

The optimal location of TCSC for maximizing the ATC and also to maximize the clearance between the operating load and the thermal limit. Simulations were done on the IEEE 6 bus system. Optimizations were performed to find the optimal settings of the device in the line. The ATC was improved by employing the TCSC in the transmission line and reactance is set by using PSO technique in this work. The transfer capability available from loading close towards the thermal limit of the line in enhancing the ATC was brought down by introducing TCSC.

Further extension involves application of modified PSO algorithm for getting better optimization performance. And the use of ACPTDF to calculate ATC with voltage and reactive constraints considered.