Abstract-This paper presents a novel methodologyfor optimal placement of Distributed Generation (DG) inan Optimal Power Flow (OPF) based wholesale electricitymarket. DG is placed in real time wholesale electricitymarket. The problem of optimal placement including sizeis formulated for two different objectives, namely, fuelcost reduction and to provide voltage stability atdistribution level. DG reduces the cost of electricity to thecostumer, relieve network congestion and provideenvironmental friendly energy close to load centers. Thecandidate locations for DG placement are identified on thebasis of locational marginal price (LMP). OPF is widelyused for both the operation and planning of a powersystem. The key feature of standardization of restructuredpower market like Standard Market Design (SMD) is theLMP scheme. OPF problem by placing DG in DeregulatedEnvironment is solved using Genetic Algorithm (GA). Theproposed methodology is tested with IEEE 30 bus testsystem.
Keywords: Distributed Generation, LocationalMarginal Pricing, Standard Market Design, OptimalPower Flow and Genetic Algorithm.
TABLE 1: INDEX FOR ABBREVIATIONS
NomenclatureOPF Optimal Power FlowDG Distributed GenerationLMP Locational Marginal PriceSMD Standard Market DesignGA Genetic AlgorithmLMpenergy Marginal cost ofproviding EnergyLMPicong ith Node that accounts for the costs of
congestionLMPiloss ith Node that accounts for the marginal real
power lossesPgi,Qgi calculated real , reactive power generations
forPQ bus iPLi ,QLi calculated real and reactive power loads for
PQbus iP(V,D), Q(V,D) Injected real and reactive powersa, basic cost coefficient of the ith generatorb, linear cost coefficient of the ith generatorCi Quadratic cost coefficient of the ith
generatorNg number of generators including the slack
bus generatorPG vector of real power outputs of all
generator units
M.V. RameshDepartment ofElectrical and
Electronics Engineering,P. V'P. Siddhartha Institute ofTechnology,
Pr: ,Qgimax upper real and reactive power generationlimits of generator at bus i
Pgirnin ,Qgirnin lower real and reactive power generationlimits of generator at bus i
vr: ,Virnin upper and lower limits of voltage at bus isijmax '~imax complex power flow limit for line ij and
linejiSij,~i complex power transfer from bus ito busj,
and bus j to bus ipop size population sizepop vn population countergen max Maximum generations
I. INTRODUCTION
The electricity market has experienced enormoussetbacks in delivering on the promise of deregulation.In theory, deregulating the electricity market wouldincrease the efficiency of the industry by producingelectricity at lower costs and passing those cost savingson to customers. For the electric industry, deregulationmeans the generation portion of electricity service willbe open to competition. However, the transmission anddistribution of the electricity will remain regulated andour local utility company will continue to distributeelectricity to us and provide customer services to us.The generation of electricity is being deregulated,which means we will have the opportunity to shoparound for the electricity power generation supplier ofchoice [1].The restructured power markets haveevolved around scale of economy making the smallergenerating units viable and feasible.
DGs are considered as small power generators(typically 1 kW - 50 MW) that complement centralpower stations by providing incremental capacity topower system. Penetration and viability of DG at aparticular location is influenced by technical as well aseconomic factors. The technical merits of DGimplementation include voltage support, energy lossreduction, and release of system capacity and improveutility system reliability [2]. Economical meritencompasses hedge against high electricity price. Thisincentive is enhanced with vertical unbundling ofutilities and market mechanisms such as real timepricing. By supplying loads during peak load periods,where the cost of electricity is high, DG can best serveas a price hedging mechanism. DG can have a great
Optimal DG placement under Standard Market Design using GA
value in a highly congested area where LMPs are higher.In such situation, it can serve the local load andeffectively reduce the load. The placement of DGshould be carried out with due consideration to its sizeand location. The placement should be optimal in orderfor the maximum benefit of DG implemented in thenetwork. Improper placement in some situations canreduce benefits and even jeopardize the systemoperation. Numerous techniques are proposed so far toaddress the viability of DGs in power system. Capacityinvestment planning of distributed generation undercompetitive electricity market from the perspective of adistribution company is proposed [3]. An approach foroptimal design of grid connected DG systems inrelation to its size and type to satisfy onsite reliabilityand environmental requirements is presented in Ref.Besides, several optimization tools, including artificialintelligence techniques, such as GA, tabu search, etc.,are also proposed for achieving the optimal placementof DG. An optimization approach GA has been used toobtain penetration level of DG for minimizing the totalcost of operation including fixed and variable cost andlosses for a defined planning horizon are presented [4].
Distributed generators include synchronousgenerators, induction generators, reciprocating engines,micro turbines, combustion gas turbines, fuel cells,solar photovoltaic, and wind turbines. The planningstudies include penetration level and placementevaluation, which are influenced by the type of DG.
The cost of the electricity available from the grid isgiven by the nodal LMP while the cost of electricity ofthe DG depends upon its type, capacity, etc. The firstobjective is to locate DG at economically viablelocations (siting problem) [5]. The penetration level ofthe DG has to be computed incrementally by OPF.Capacity addition by DG will affect the economicdispatch and hence LMP costs. Hence, the problembecomes nonlinear and iterative. The study is useful fordetermination of viable DG capacity in a typicaldistribution system.
The paper is organized as follows. Section-2describes the role of DG in the deregulated environment.SMD market and LMP calculation are discussed insection 3. DG planning under SMD is considered insection-4.GA and GA based OPF explained in section-5.Results are presented in section- 6. Section -7 concludesthe paper.
II. DISTRIBUTED GENERATION IN DEREGULATEDENVIRONMENT
In addition to meet future energy needs, DG willhave vital role in a deregulated environment. It canprovide independence and flexibility to the consumersin planning and developing the installation as per thecriticality of the load. It can minimize the investmentmade over Transmission and Distribution (T&D) [6].
infrastructure by locating it near the load. It haspotential to serve as an ancillary service. Many new DGmodels are commercialized in United States and Europe.The liberalization of wholesale and retail electricmarkets is giving rise to customer choice and newofferings by unregulated energy retailers. Due to thecontinuous improvements in DG technologies, it ispossible to provide cost effective electricity to thecustomers. In wholesale power markets, customerowned DGs can respond to the extreme price swings soas to reduce the volatility in prices. During peak hoursand emergencies, a part of the total load can betransferred to an isolated generator, relieving theutility's burden to some extent. Furthermore, theparallel operation of DG with the utility is much moreflexible than that of the standalone system.
In competitive electricity markets, DG can competewith the centralized power generation and hence marketregulations should ensure that there should be standardoperational practices and reliability requirements so asto have fair competitive environment for DG. Variouselectricity market models like pool model, SMD are inoperation in different parts of the world. Since the costof electricity from the grid is dependent upon themarket model, the model will influence the DGplanning.
III. STANDARD MARKET DESIGN
LMP provides market participants a clear andaccurate signal of the price of electricity at everylocation on the grid. These prices, in tum, reveal thevalue of locating new generation of upgradingtransmission systems. Under SMD, the term 'multisettlement market' implies that the energy marketconsists of day ahead and real time markets, eachproducing its own separate and unique financialsettlements[7]. The day ahead market producesgeneration and load schedules one day ahead beforeoperating day. The real time market reconciles anydifferences between the amounts of scheduled dayahead and real time conditions. The DGs can participatein the real time market.
In this work market operates under SMDframework. Hence, the knowledge of LMP at everynode is used to take a decision for the placement ofaDG.
A Locational Marginal Pricing
LMP is the lagrangian multipliers associated withthe active power flow equations for each bus in thesystem. LMP at any node in the system is the dualvariable for the equality constraint at that node [8].LMP is generally composed of three components, amarginal energy component, a marginal loss componentand a congestion component. Considering the case ofreal power spot price at bus i, higher LMP implies a
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greater effect of active power flow equations of thenode on total social welfare of the system. It thusprovides indication that for the objective of socialwelfare maximization, injection of active power at thatnode will improve the net social welfare. As the DG isassumed to inject real power at a node, the node withhighest LMP will have first priority for DG placement.
The determination of LMPs is similar, but notidentical, in the day ahead and real time markets. Dayahead LMPs are output from the day ahead marketclearing process. Generation, demand, externalcontracts and increment/decrement positions that are inthe day ahead market settle at prices determined by dayahead LMPs. The real time market balances supply anddemand as the system operates. Real time LMPs arebased on current power system operating data.Deviations between day ahead and actual real timepositions settle at prices determined by real time LMPs.
LMPi=LMpenergY+LMPicong+LMPilossWhere,LMpenergy-The component of the LMP that reflects
the marginal cost of providing Energyfrom a designated reference location.
LMPicong-The component ofLMP at a ith Node thataccounts for the costs of congestion, asmeasured between that Node and aReference Bus.
LMPiloss_The component of LMP at a ith Node thataccounts for the marginal real powerlosses as measured between that Nodeand a Reference Bus.
B OPF Formulation
The heart of the above algorithm is OPF program.The OPF schedules the MW generations throughout thesystem to minimize cost of generation or social welfarecost. In particular we consider the objective function tobe the total cost of real power generation. The problemis formulated as follows.
1) Proposed OPF problem formulation
In any optimization problem, the OPF problem isformulated as a minimization or maximization to acertain objective function in which it is subjected to avariety of equality and inequality constraints. Theproposed objective function is the Minimization ofGeneration Fuel Cost [9]. The main objective is tominimize the fuel cost of thermal units. OPF generationfuel cost function can be expressed by a quadraticfunction as follows.
Minimize (FT) = r'(!l Fi (PGi)where,Fi(PGi)=~+biPGi + Ci p2Giwhere,PG= [PGh PG2, , PGn]T
2) The constraints
The control variables for OPF include active powerat all generator units, generator bus voltages,transformer tap positions and switchable shunt reactors.OPF constraints are divided into equality and inequalityconstraints. The equality constraints are active/reactivepower equalities. The inequality constraints include busvoltage constraints and generator reactive powerconstraints. Reactive source reactive power capacityconstraints and the transformer tap position constraints,etc. Therefore, the above objective function is subjectedto the below constraints.
3) Equality constraints
The equality constraints of OPF reflect the physicsof the power system. They are enforced through thepower flow equation. The net injection of the real andreactive power at each bus is to be zero as shown.
The power flow equation of the networkPgi-PLi-P(V,8)=O (active power balance equations)Qgi-QLi-Q(V,8)=O(reactive power balance
equations)where,V and 8 are voltage magnitude and phase angles at
different buses.
4) Inequality constraints
The inequality constraints of the OPF reflect thelimits on physical devices in the power system as wellas the limits created to ensure system security. Thetypes of inequality constraints are bus voltage limits atgenerations, maximum line loading limits and limits ontap settings. The inequality constraint on active powergeneration Pgi at each PV bus are,
Real power generation limits:pgimin ::SPgi ::SPgimax .Reactive power generation limits: Qgitmn::SQgi::SQgimax
Bus voltage limit: Vimm::SVisvr:Line flow limit: Sij::S Sijmaxs, S Sjjmax
IV. DG PLANNING UNDER SMD
The placement of DG can be considered on thebasis of nodal LMPs. To start with, the base case OPFof a system is solved. LMPs at system nodes correspondto the price of a unit power received at the node. Thenode with the highest LMP is a clear candidate forlocating the DG since it will yield highest returns. In theformulation, DG is considered as a negative load and itis assumed that it will be paid at the rate of LMP. Thealgorithm is as follows.
Step 1: Initialize the installed DG at each nodefor each DG type to be equal to zero,iteration = 0
Optimal DG placement under Standard Market Design using GA
v. GENETIC ALGORITHM
A simple Genetic Algorithm is an iterativeprocedure, which maintains a constant size population Pof candidate solutions. During each iteration step(generation) three genetic operators (reproduction,crossover, and mutation) are performing to generatenew populations (offspring), and the chromosomes ofthe new populations are evaluated via the value of thefitness which is related to cost function. Based on thesegenetic operators and the evaluations, the better newpopulations of candidate solution are formed
We use genetic algorithm because the features ofGenetic algorithm are different from other searchtechniques in the several aspects. First the algorithm is amultipath that searches many peaks in parallel andhence reducing the possibility of local minimumtrapping. Secondly, GA works with a coding ofparameters instead of the parameters themselves. Thecoding of parameter will help the genetic operator toevolve the current state into the next state withminimum computations. Thirdly, GA evaluates thefitness of each string to guide its search instead of theoptimization function [11]. The genetic algorithm only
Step 2:
Step 3:Step 4:
Step 5:
Step 6:
Step 7:
Run base case security constrained OPFto minimize the total cost of generationor maximize the social benefit function.Consequently, all generation availablefor scheduling is scheduled optimally.Find the node with the highest LMP.If the maximum LMP is lower thanminimum viable DG cost ($ / MWh)option, terminate the algorithm. Elseproceed to step-4.Choose suitable (acceptable) type of DGand locate it at the node with maximumLMP. Initially selection of DG type mayreflect preference of the planner. Alsoonce, a particular type of DG is selectedat a given location, other DG options atthat site may be inhibited.Increment the installed DG at the maxLMP node either by a small value, e.g., 1MW or a value based on the judgment ofplanner.Iteration + 1, run new OPF to obtain newset of LMPs and go to step 2.The processterminates when the cost of energy ($ /MWh) supplied by cheapest availableDG is higher than the maximum LMP($ / MWh) in the system. At this point,no incremental addition of DG in thesystem is economically viable. It shouldbe noted that in step-5, the emphasis isplaced on incremental addition of the DGcapacity.
needs to evaluate objective function (fitness) to guideits search.
Step-by-Step Algorithm for Genetic AlgorithmBased OPF
1. Read the database for the generator data, busdata, capacitor/reactor data, transformer dataand transmission line data [9].
2. Assume suitably population size (pop _size),maximum number of generations orpopulations (gen_max).
3. Set valid number of population counter.pop_vn=O.
4. Randomly generate the chromosomes.5. Run power flow using the Newton-Rapson
method for each set of generating patterns Pgicorresponding to a particular generation andafter that determine, slack bus generation, busvoltage magnitudes and phase angles at all thebuses. Also calculate power flow in eachtransmission line of the system.
6. Check the constraints, if any of the abovelimits is violated, go to step 4.
7. If all the above constraints are satisfied,increment pop_vn by 1. If pop_vn less than orequal to pop_size, go to step 4, otherwise go tonext step.
8. Calculate and then store the total cost ofgeneration corresponding to each validgeneration pattern of chromosome.
9. Find and store minimum cost among all validindividual parents and correspondinggeneration pattern.
10. Check if random no. ri < Cr (crossover rate) fori=1 to pop_size, select ith chromosome. Applythe crossover operator to that individual.
11. Run power flow using Newton-Raphsonmethod for each set of new generating patternsand hence determine, slack bus generation, busvoltage magnitudes and phase angles at all thebuses. Also calculate power flow in eachtransmission line of the system.
12. Check system constraints as mentioned in 6.13. If all the constraints are satisfied, the
individual of the new population becomesvalid otherwise it becomes invalid.
14. Apply the mutation operator to the calculatedgeneration patterns.
15. Run power flow using the Newton raphson andcheck all the constraints as mentioned in step 6.
16. If all the constraints are satisfied go to nextstep otherwise go to step 4.
17. Calculate the total cost of all valid patterns.18. Find the optimum solution among all
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VI. SIMULATION RESULTS AND DISCUSSION
In this section, we present case study forMATPOWER IEEE 30 bus system [12].The nodal LMPat each bus is calculated by using the standard OPFformulation of MATPOWER package. The costs perunit value are available for the capacity and type of DGin the below table or they should be calculated forparticular sites under consideration. The penetrationlevel can be defined on the base case and peak case.The peaking cost of energy at customer level due tovarious types of DGs along with the DG lifetime and itsinitial cost are tabulated below. The cost of energy iscomputed using a discount factor of 11.1%.
TABLE 2: COSTOFENERGY WITH VARIOUS TYPESOFDGs
DGType Initial % % Life in Cost ofCost Efficie Availa Yrs Energy at($ / ncy bility Customer
Using GA number of values that can be accessedbetween the minimum and maximum limit is decidedby the number of bits selected for that parameter. So theaccuracy of the parameters optimized depends on thenumber of bits selected. In this paper, 12 bits areconsidered for each generator power output i.e. we get212 values. Similarly the adequate numbers of bits areconsidered for the remaining parameters such asvoltages, transformer taps, shunts and DG. Similarly,for each voltage 8 bits, for each transformer tap 5 bits,for each shunt 3 bits and for each DG 8 bits areconsidered [13].
Fig. 1: LMP's for IEEE 30 Bus System by GA without DG andafter Placement of DG
Fig. 3: Fuel Cost without DG and after Placement of DG withGA for IEEE 30 bus Systems
From the above graph we can observe that fuel costhas reduced after placement ofDG.
TABLE3: OPTIMAL LOCATION BASEDONLMP ANDSIZEOFDG BYGA FORIEEE 30 Bus SYSTEMS
Optimal Bus Optimal Size of DGTypeLocation for DG DG by using GA inPlacement Based (p.u.)
onLMP30 0.019765 Mini gas turbine26 0.009647 Reciprocating Engine19 0.009206 Mini gas turbine
From the above table it is observed that the mostsuitable DG types are selected based on data given intable 1.
TABLE4: FUELCOSTFORIEEE 30 BUSSYSTEM BYGA WITHOUT DGANDAFTER PLACEMENT OFDG.
Fuel Cost with GA AfterPlacement of DG in $/hr
789.441332
Fig. 2: Voltages in (p.u.) for IEEE 30 bus System by GA without DGand after Placement of DG
VII. CONCLUSIONS
1. An algorithm is proposed for solving the DGplacement and penetration problem which tellsthat the cost of grid electricity is higher thanthe DG electricity cost.
Optimal DG placement under Standard Market Design using GA
2. LMP is used as an indicator of grid electricitycost at a node as it is sensitive to generationcost, losses and location of the node in thesystem.
3. The optimal placement and penetrationdepends on the cost characteristics of DG aswell as those of central generations. The DGwith incremental cost lower than the centralgeneration have a higher penetration in thesystem, and similarly, the one with higherincremental cost have the lower penetration.Considerable reduction in central generationdispatch is observed with high DG penetration.
4. The base case OPF of a system is solved.LMPs at system nodes correspond to the priceof a unit power received at the node. The nodewith the highest LMP is a clear candidate forlocating the DG since it will yield highestreturns. The optimal location is founded basedon LMP values.
5. The OPF problem by placing DG at exactlocations in deregulated environment is solvedby using GA. It is observed that GA gave bestresults for optimal size of DG, minimum fuelcost, and reduction in losses and improvedvoltage profile.
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