Abstract- In this paper, multiple of Flexible AC Transmission System ( FACTS ) devices viz. : Inactive Var Compensator ( SVC ) and Distributed Generation ( DG ) are optimally allocated in a power web for bettering the public presentation of the power system web. A new discrepancy of Genetic Algorithm ( GA ) specialized in multi-objective optimisations job known as Non-dominated Sorting Genetic Algorithm II ( NSGA-II ) have been used for carry throughing the same. To help the determination shaper taking the best via media solutions from the Pareto forepart, the fuzzy-based mechanism is employed for this undertaking. NSGA-II is used to happen the optimum location and scene of multiple SVC in every burden coach system and DG in each low electromotive force ( LV ) of the system. Three nonsubjective maps are considered as the indexes of the system public presentation: maximization of system loadability in system security and stableness border ( voltage bound, line bound and eigen value ) , minimisation of the entire installing costs of multiple FACTS devices and DG, and minimisation of the existent power loss of the transmittal lines. Simulation surveies were carried out on modified IEEE 14-bus system. Consequences showed that the steady province public presentation of the power system can be efficaciously enhanced by the optimum allotment, puting and sizing of multiple SVC and DG.
Index Terms-Power System security border, SVC, Distributed Generation, System loadability, Multiobjective optimisation, NSGA-II.
IN the last few old ages, with the deregulating of the electricity market, the traditional constructs and patterns of power systems have been changed. Better use of the bing power system to increase system capacities, minimising the losingss and thereby cut downing the terminal user runing cost can be achieved by suited installing of FACTS devices and DG into the grid [ 10 ] , [ 23 ] .
The parametric quantity and variables of the transmittal line, i.e. line electric resistance, terminal electromotive forces, and electromotive force angles can be controlled by FACTS devices in a fast and effectual manner [ 3 ] . The benefit brought approximately by FACTS devices includes betterment of system dynamic behaviour and therefore sweetening of system dependability. However, their major function is in commanding power flows [ 9 ] , [ 10 ] . Optimal location of FACTS devices besides improves system loadability [ 9 ] , [ 12 ] and [ 13 ] . These facets are playing an increasing and major function in the operation and control of competitory power systems.
Taking advantages of the FACTS devices depends greatly on how these devices are placed in the power system, viz. their location and size [ 8 ] , [ 19 ] . The scope of FACTS devices include:
Inactive Var compensators ( SVC ) ;
Thyristor Controlled Series Capacitors ( TCSC ) ;
Unified Power Flow Controllers ( UPFC ) ;
Inactive Compensators ( STATCOM ) ;
High Voltage Direct Current Transmission ( HVDC ) .
On the other manus, in recent old ages, integrating of a broad assortment of Distributed Generation ( DG ) engineering in distribution webs has become one of the major direction concerns for professional applied scientists. The chief ground of utilizing DG units in power system is proficient and economic benefits. Some of the major proficient benefits are reduced line losingss, electromotive force profile betterment, increased overall energy efficiency [ 7 ] , [ 23 ] , enhanced system dependability and security, improved power quality, relieved transmittal, and distribution congestion. And some of the major economic benefits are deferred investings for ascents of installations, reduced operation and care costs of some DG engineerings, reduced fuel costs due to increased overall efficiency, reduced modesty demands and the associated costs, lower operating costs due to top out shave and increased security for critical tonss [ 23 ] .
Many researches were made on the optimum location of FACTS devices. Optimal location of different types of FACTS devices in the power system has been attempted utilizing different techniques such as Familial Algorithm ( GA ) [ 19 ] , intercrossed taboo attack and simulated tempering ( SA ) [ 8 ] . Optimal location of multi-type FACTS devices in power system by agencies of GA was proposed to increased loadability of the system [ 19 ] . Optimum allotment of FACTS devices in order to maximise of system loadability in system security border and minimisation to entire coevals fuel cost was reported [ 12 ] . A intercrossed taboo hunt ( TS ) and simulated tempering was proposed to minimise the generator fuel cost in optimum power flow control with multi-type FACTS devices [ 18 ] . Optimal pick an allotment of FACTS devices to minimise the coevals cost map and the investing cost on the FACTS devices was found utilizing GA [ 10 ] . Optimal location and parametric quantity scenes of multiple TCSCs for increasing power system loadability based on GA and PSO techniques has been formulated and solved [ 19 ] . Application of PSO technique for optimum location of multiple FACTS devices sing cost of installing and system loadability was reported [ 13 ] . However, the investing cost of FACTS and their impact on the transmittal loss algorithm with DG arrangement are non entirely considered yet for maximising system loadability.
From the old plants, we can reason that most of the job of optimum location of FACTS devices is by and large formulated as a mono-objective optimisation job. Unfortunately, the preparation of FACTS location job as a mono-objective optimisation is non rather practical. While, planners the power systems aim to take advantage of FACTS devices and DG sing several aims at the same clip.
In contrary to the old cited plants, Benadid et Al. [ 1 ] and [ 2 ] formulates the optimum location terminal scenes of SVC and TCSC as a existent assorted whole number uninterrupted multi-objective optimisation job. Where, the job is formulated as a bi-objective and a three-objective optimisation job. The FACTS devices are optimized in order to optimise the electromotive force stableness, existent power losingss and load electromotive force divergence of power system. However, the investing cost of FACTS devices and their impact on arrangement and size of DG beginnings in the web are non entirely considered yet.
In this paper, an algorithm of the optimum arrangement of multiple of FACTS devices and multiple of DG is developed as a multiobjective job to maximise system loadability within system security border. By agencies of FACTS and DG optimum arrangement, the investing costs of FACTS and DG and the existent power loss of the transmittal lines is minimized. In recognizing the proposed aim, the multiple of FACTS devices and DG, their location and their rated values must be determined at the same time. In making so, the NSGA-II is used.
The paper is organized as follows: subdivision 2 presents the job preparation which includes the definition of nonsubjective maps and job restraints. The mold of SVC and DG are presented in subdivision 3. The subdivision 4 is a brief debut of multiobjective jobs utilizing NSGA-II algorithm. In subdivision 5, some interesting consequences are presented along with a elaborate treatment. Finally, major parts and decisions are summarized in subdivision 6.
Facts and DG Modeling
Model of SVC
The SVC is defined as a shunt connected inactive Var generator or consumer whose end product is adjusted to interchange capacitive or inductive so as to keep or command specific parametric quantities of electrical power system, typically a coach electromotive force [ 10 ] . Like the TCSC, the SVC combines a series capacitance bank shunted by thyristor controlled reactor. In this paper, the SVC is modeled as a variable shunt reactance. The reactive power provided is limited as:
( 1 )
Model of Distributed Generation
So far, there are several engineerings of DG from traditional to renewable power coevals. The traditional engineerings are internal burning engines, combined rhythms, burning turbines and micro-turbines. The renewable engineerings are solar, photovoltaic, air current, geothermic, ocean, etc. DG units are modeled as synchronal generators for little hydro power, geothermic power, combined rhythms and burning turbines. They are treated as initiation generators for air current and micro hydro power. DG units are considered as power electronic inverter generators such as micro gas turbines, solar power, photovoltaic power and fuel cells [ 7 ] , [ 23 ] . In general, DG can be classified into four types:
Type 1: DG capable of shooting changeless P merely ( PV )
Type 2: DG capable of shooting both P and modulate coach electromotive force ( Gas Turbine )
Type 3: DG capable of shooting changeless P but consumes Q ( Wind Turbine )
Type 4: DG capable of presenting Q merely ( Synchronous capacitor ) .
As indicated, the end of the stated optimisation job is the optimum arrangements of multi-type of FACTS devices and DG into power web in order to maximise the loadability, security border, minimise the investing costs of FACTS devices and DG and minimise the existent power loss in transmittal lines. The optimum location and scenes of multiple FACTS devices and DG are formulated as a existent constrained assorted distinct uninterrupted multi-objective optimisation job.
Therefore, the presented job becomes a multi-objective optimisation job that has three nonsubjective maps to be optimized at the same time, which can be denoted as:
( 2 )
( 3 )
Where F is known as the nonsubjective vector, F1, F2, and F3, are the three nonsubjective maps to be optimized, x is the vector of dependent variables, and U is the vector of control variables.
In all optimisation jobs several instances in footings of usage of
FACTS devices and DG are considered viz.
Base instance without DG and SVC.
Case 1: DG merely.
Case 2: multiple SVC merely
Case 3: coordinated DG and multiple SVC.
The nonsubjective maps considered in this paper are presented in item as given below.
The FACTS devices and DG cost map minimisation.
The investing cost of DG unit I is assumed to be relative with the maximal evaluation of DG, which can be expressed as:
( 4 )
where the relative changeless KIi is in $ /MVA. The value of KIi is different for different type of bring forthing units. For the Biomass type of DG the changeless unit of KIi can be change to US $ /KW utilizing factor 1464. The sum of investing cost is transferred to hard currency value in the beginning of be aftering period by utilizing economical looks ( i.e. one-year cost based on certain involvement rate and life span ) as expressed in ( 5 ) . fci is the scaling factor associated with the installing cost ( one-year cost based on certain involvement rate ‘i ‘ and life span ‘T ‘ )
( 5 )
The preparation to minimise the cost of installing of FACTS devices as the aim has been mathematically formulated and is given by [ 13 ] , [ 23 ] .
( 6 )
Where C1 ( degree Fahrenheit ) and C2 ( degree Fahrenheit ) is the optimum installing cost of DG and FACTS devices severally in US $ , C ( degree Fahrenheit ) is the cost of installing of FACTS devices in US $ /kVar and degree Fahrenheit is vector that represent the variable of FACTS devices and DG.
Based on the Siemens AG Database, the cost maps for SVC, TCSC and UPFC are developed: The cost map for SVC is [ 10 ] , [ 13 ] :
( 7 )
where CSVC is in US $ /kVar and S is the operating scope of the FACTS devices in MVar.
( 8 )
where Q2 is the reactive power flow in the line after put ining FACTS devices in MVAR and Q1 is the reactive power flow in the line before put ining FACTS device in MVAR.
The unit for DG cost and FACTS devices are in US $ /year. The sum of investing cost of FACTS devices is transferred to hard currency value in the beginning of be aftering period by utilizing economical looks as DG utilizing equation ( 5 ) .
Maximize the system loadability within security border
( 9 )
( 10 )
where VL is the thermic and bus misdemeanor bound factor, OLLi and BVVj represent the overladen line factor and subdivision the coach electromotive force misdemeanor factor severally and will be expatiated on subsequently ; NL and NE are the entire Numberss of transmittal lines and burden coachs severally ; and I»1 is a load parametric quantity of the system, which aims to happen the maximal sum of power that the web is able to provide within system security border.
The burden parametric quantity I»1 in ( 9 ) is defined as a map of a burden factor I»f [ 12 ] :
( 11 )
where I? is the coefficient to set the incline of the map, and is the maximum bound of I»f. The burden factor I»f reflects the fluctuation of power demands PDi and QDi, which are defined as:
( 12 )
( 13 )
where I = 1, aˆ¦ . , ND and ND is the entire figure of power demand coachs. I»f = 1 indicates the base burden instance.
The index of system security province contains two parts. The first portion, OLLi, relates to the subdivision burden and penalizes overloads in the lines. The value of OLLi peers to 1 if the jth subdivision burden is less than its evaluation. OLLi increases logarithmly ( existent logarithm ) with the overload and it can be calculated from:
( 14 )
where Pij and are the existent power flow between coachs Is and J and the thermic bound for the line between coachs Is and J severally. is the coefficient which is used to set the incline of the exponential map.
The 2nd portion BVVj in ( 10 ) concerns the electromotive force degrees for each coach of the power web. The value of BVVj is defined as:
( 15 )
where BVVj is the coach electromotive force misdemeanor factor at coach J and represents the coefficient used to set the incline of the exponential map in the above equation. The equation indicates that appropriate electromotive force magnitudes are close to 1 p.u. Similar to OLLi, The value of BVVj peers to 1 if the electromotive force degree falls between the electromotive force minimum and maximum bounds. Outside the scope, BVVj increases exponentially with the electromotive force divergence.
Minimization of Real Power Losses of the transmittal lines.
This aim is to minimise the existent power loss ( RPL ) in the transmittal lines and which can be expressed as [ 1 ] :
( 16 )
Where, nl is the figure of transmittal lines ; gk is the conductance of the kth line ; and are the electromotive forces at the terminal buses one and J of the kth line, severally.
Dependent and Control Variables
In the three nonsubjective maps, x is the vector of dependent variables such as slack coach power PG1, burden coach electromotive force VL, generator reactive power end products QG and evident power flow Sk. ten can be expressed as:
( 17 )
Furthermore, u is a set of the control variables such as generator existent power end products PG except at the slack coach PG1, generator electromotive forces VG, the locations of FACTS devices, L, and their scene parametric quantities. U can be expressed as:
( 18 )
Where NF is the entire figure of FACTS devices to be optimally located, and N1 to N3 are the entire Numberss of TCSC, SVC and UPFC severally. The equality and inequality restraints of the NRPF job integrating FACTS devices are given hollas.
These restraints represent the typical burden flow equations as follows:
( 19 )
( 20 )
Where Ni is the figure of coachs next to bus one including coach I, NPQ and N0 are the figure of PQ coachs and entire coachs excepting slack coach, severally.
The inequality restraints h ( x, u ) are bounds of control variables and province variables. Generator active power PG, reactive power QG and electromotive force VG are restricted by their bounds as follows:
( 21 )
The puting parametric quantities of SVC restricted by their bounds as follows:
( 22 )
The restraints of burden electromotive forces at burden coachs VL and transmittal burden PL are represented as:
( 23 )
The burden factor I»f is constrained by its bounds as:
( 24 )
Each generator has a set of nonlinear differential equations depicting the synchronal machine, exciter, and any other control mechanisms. Each generator besides has a set of algebraic equations which couple the generator province variables and the generator ‘s steady province operating point power injection into the system. Finally, there are the power system web equations, i.e. the Kirchhoff ‘s jurisprudence circuit equations that the steady-state operating point must fulfill. The little signal stableness theoretical account of the system with DFIG can be expressed as
where A is the System State Matrix [ 22 ]
( 25 )
where are power flow jacobian matrices
If the complex characteristic root of a square matrixs of the linearized system have negative existent parts, so the power system could able defy little perturbations and is considered stable in the small-signal sense. The Eigen value stableness analysis is incorporated to the restraint by the equation
( 26 )
The Eigen value based stableness assures grid stableness under assorted degrees of system loadability.
Non Dominated Sorting Genetic Algorithm ( Nsga-II ) Method.
NSGA-II Optimization Principle
The capablenesss of multi-objective familial algorithms ( MOGAs ) to research and detect Pareto optimum foreparts on multi-objective optimisation jobs have been good recognized. It has been shown that MOGAs outperform traditional deterministic methods to this type of job due to their capacity to research and unite assorted solutions to happen the Pareto forepart in a individual tally. We will implement a multi-objective optimisation technique called the Non-Dominated Sorting Genetic Algorithm II ( NSGA-II ) , which is described in item by Deb et Al. [ 6 ] . The NSGA-II algorithm may be stated as follows:
Make a random parent population of size N ;
Sort the population based on the nondomination ;
Assign each solution a fittingness ( or rank ) equal to its nondomination degree ( minimisation of fittingness is assumed ) ;
Use the usual binary tourney choice, recombination, and mutant operators to make a new offspring population of size N ;
Unite the progeny and parent population to organize drawn-out population of size 2N ;
Sort the drawn-out population based on nodomination ;
Fill new population of size N with the persons from the screening foreparts get downing from the best ;
Invoke the herding comparing operator to guarantee diverseness if a forepart can merely partly make full the following coevals ( This scheme is called “ niching ” ) ;
Repeat the stairss ( 2 ) to ( 8 ) until the halting standard is met. The halting standard may be a specified figure of coevalss. It is clear from the above description that NSGA-II utilizations ( I ) a fast non-dominated sorting attack, ( two ) an elitist scheme, and ( three ) no niching parametric quantity [ 21 ] .
For each loop k do:
( combine parent and offspring population )
( Application the non-dominated sorting on K Rk )
until ( until the parent population is filled )
Calculate the crowding distance for each atom in Fi
Sort ( Fi ) ( kind in falling order )
( Choose the first elements of Fi )
Qk+1 ( usage choice, crossing over and mutant to make a new population with utilizing Pk+1 )
Best via media solution
Once the Pareto optimum set is obtained, it is practical to take one solution from all solutions that satisfy different ends to some extends. Due to the imprecise nature of the determination shaper ‘s ( DM ) judgement, it is natural to presume that the DM may hold fuzzy or imprecise nature ends of each nonsubjective map [ 5 ] . Hence, the rank maps are introduced to represents the ends of each nonsubjective map ; each rank map is defined by the experiences and intuitive cognition of the determination shaper. In this survey, a simple additive rank map was considered for each of the nonsubjective maps. The rank map is defined as follows [ 1 ] [ 5 ] :
( 27 )
Where and are the lower limit and the maximal value of the ith nonsubjective map among all non-dominated solutions, severally. The rank map i?iˆ iˆ is varied between 0 and 1, where i?iˆ = 0 indicates the mutual exclusiveness of the solution with the set, while i? = 1 agencies full compatibility [ 1 ] .
For each non-dominated solution K, the normalized rank map is calculated as:
( 28 )
where M is the figure of non-dominated solutions and Nobj is the figure of nonsubjective maps. The map K can be considered as a rank map of non-dominated solutions in a fuzzy set, where the solution holding the maximal rank in the fuzzy set is considered as the best via media solution.
The NSGA II algorithm is carried out in the modified IEEE 14-bus trial system [ 14 ] , which consists of two generators, located at coach 1 and 2 ; three synchronal compensators used merely for reactive power support at coachs 3, 6 and 8. The type DG incorporated in this simulation is biomass which injects both active and reactive power. The tonss are typically represented as changeless PQ loads with changeless power factor, and increased harmonizing to ( 18 ) and ( 19 ) .
The determination variables considered are the location and scene of SVC. SVC is modeled as a generator ( or an absorber ) of reactive power which varies continuously between a?’2 plutonium and 2 plutonium. The optimum location of SVC is, besides, considered as a discreet determination variable, where all burden coachs are selected to be the optimum location of SVC. The figure of SVC is specified by user is equal to three SVCs, and it is selected ( on/off ) automatically by control variable. The DG should be formed at low electromotive force side, dwelling of coachs 6, 7, 9, 10, 11, 12, 13, and 14. The figure of DG is specified by user, here as equal one and merely DG type 2 is considered. The parametric quantities of NSGA-II for all optimisation instances are summarized in Table I.
From above status with population size of 100 and after 100 loops, 100 dominated solutions are found by the proposed algorithm.
Case 1: DG merely.
Figure 1 show the Pareto forepart of the optimisation job instance 1, in the nonsubjective infinite: maximizes system loadability ( MSL ) , minimise investing cost of DG ( C1 ) , and minimise existent system power loss ( RPL ) . This set of solutions on the nondominated frontier is used by the determination shaper as the input to choose a concluding via media solution by utilizing the normalized rank map in ( 35 ) . The obtained consequences presented in Table II indicate that the best constellation program of DG arrangement within the system is found at coach 7 with size 44.02 MW and 10.78 MVAR. Besides, the installing of a DG at coach 7 provides the best via media solution of MSL and RPL of 0.4315 plutonium and 3.100 plutoniums severally with 6.47 million US $ /Year on investing cost of DG. The procedure has been repeated for all the three instances and comparison with basal instance as shown in the Table II.
Fig. 1. Pareto forepart to happen optimum location and size of DG merely
Case 2: multiple SVC merely
The utmost points obtained by NSGA-II, and the optimum solutions of others instances are summarized in Table II. The comparing of the utmost points obtained by NSGA-II and instance 1 optimisation solutions indicates that the research infinite is good explored by the proposed attack. From Table II, it is clear that the installing of SVC at coach 4, 7, and 13 with 0, 0.0017, and 0 plutonium of mention provides the best MSL and RPL 0.475 and 5.526 plutonium severally. The utmost points are slice more addition in MSL but rather larger in RPL as obtained in the old job for instance 1. Furthermore, the installing of SVC at coach 7 with 0.0017 plutonium of mention provides the best via media solution of MSL of 0.475 plutonium and is supply the lowest via media solution of installing cost of 0.05588 million US $ /Year.
Case 3: coordinated DG and multiple SVC.
The utmost points and the optimum solution of the multi nonsubjective optimisation is given in Table II. The comparings of the utmost point and the optimum solution of each aim show that NSGA-II explores good the research infinite. The obtained consequences presented in Table II indicates that the installing of a SVC at coach 5 with 0.2762 plutonium of mention and a DG at coach 7 with 0.5367 plutoniums and 0.0961 plutonium of mention for active and reactive power severally provides the best via media solution MSL of 0.4504 plutoniums and best via media RPL of 2.7794 plutoniums. From Table 7, we conclude that the installing of a SVC and a DG provides the best RPL of 2.7794 plutoniums. From the determination shaper point of position, the best via media solution is the higher obtained for the entire installing cost of 8.5926 million US $ /Year. The Eigen value of the system which indicate the system is stable is presented in Fig. 2.
Fig. 2. Eigen value of the optimum location and size of DG and SVC
NSGA-II Solutions Of all Cases For 3-Objective Optimization.
MSL ( plutonium )
RPL ( plutonium )
( instance 1 )
Location ( coach )
Puting ( P, Q ) in plutonium
0.4402 ; 0.1078
MSL ( plutonium )
C1 ( 106 $ /year )
RPL ( plutonium )
Multiple SVC merely
( instance 2 )
4 ; 7 ; 13
Puting ( plutonium )
0 ; 0.0017 ; 0
MSL ( plutonium )
C2 ( 106 $ /year )
RPL ( plutonium )
Coordinated DG and Multiple SVC
( instance 3 )
Puting DG ( P, Q ) in plutonium
0.5367 ; 0.0961
4 ; 5 ; 13
0 ; 0.2762 ; 0
MSL ( plutonium )
C1 ( 106 $ /year )
C2 ( 106 $ /year )
C1+ C2 ( 106 $ /year )
RPL ( plutonium )
In this work, a fresh attack based on NSGA-II has been presented and applied to optimum location and scene of multiple SVC and individual DG. The job is formulated as a existent assorted uninterrupted whole number multiobjective optimisation job, where three different jobs are considered. At first, three viing aims viz. : maximise system loadability ( MSL ) , minimise installing cost of DG ( C1 ) , and maximise existent power losingss ( RPL ) are considered utilizing DG. In the 2nd job, three aims are besides considered, where we maximise MSL, minimise installing cost of SVC ( C2 ) , and maximise RPL utilizing multiple SVC. Finally by matching the first and 2nd jobs we optimize at the same time the three aims: maximise MSL, minimise entire cost of DG and multiple SVC ( C1+C2 ) , and minimise RPL. In each instance, the optimum location and scene of SVC and DG are performed for several utilizations of multiple SVC and one type of DG. A herding distance technique is used to keep the Pareto front size ; furthermore, a fuzzy based mechanism is employed to pull out the best via media solution from the Pareto forepart. The consequences show that NSGA-II provides good distributed not dominated solutions and good geographic expedition of the research infinite. Furthermore the method does non enforce any restriction on the figure of aims. This work will be farther extended to turn to the job of optimum location of multi-type of FACTS devices with different type of DG to heighten dynamic electromotive force stableness.
The writers would wish to thank Prof. F. Milano for his first-class package bundle PSAT and assorted other utile treatments through the user group.