1
Optimum Allocation of Parking Lots in Distribution Systems for Loss Reduction Mahnaz Moradijoz, Student Member, IEEE, Mohsen Parsa Moghaddam, Member, IEEE Abstract— Plug-in-hybrid electric vehicles (PHEVs), are becoming more popular. The batteries of these plug-in-hybrid electric vehicles can act as storage and participate in various electricity markets. In this paper, optimal allocation of parking lots providing vehicle-to-grid (V2G) power for loss reduction is studied. The objective function containing active and reactive power indices is minimized using genetic algorithm. Power flow is done utilizing backward-forward sweep method. Finally, simulation is carried out on a 30 bus test system. Also, the effect of variation both in the number of vehicles in parking lot and the battery charge rate on the simulation results is investigated. Index Terms— Distribution system, genetic algorithm (GA), loss reduction, parking lot allocation, vehicle-to-grid (V2G)
I
I. INTRODUCTION
N recent years, high efficiency of PHEVs, environmental issues and the need for decreasing dependency on fossil fuels have offered electric vehicles to transportation system. With higher gasoline prices resulted from the limited crude oil resources, PHEVs will be more attractive because the electricity prices are not sensitive to the supply of crude oil [1]. Following the emergence of electric vehicles, vehicle-togrid (V2G) concept has also been offered. V2G concept is based on the fact that vehicles are parked for about 93-96 percent time during a day. As a result, they are available for other purposes. V2G concept applies the EVs (electric vehicles) as a resource for the support of electrical grid, where power can be absorbed or sourced by the vehicle energy storage system. However, there are many intermediary steps that have to be achieved, before this vision comes to fruition [2]. It is not usual to have storages in power systems however, since storages can provide ancillary services for the network, they are valuable for power system [3]. CO2 limits, air quality, and price will shift more generation to non-dispatchable resources (i.e. renewable energy). Thus much greater need is to dispatchable storages [3]. The additional volatility introduced by renewable energy source to the grid can be compensated by energy storage systems [4]. Having batteries that can be connected to the network, PHEVs can act as storages when they are parked. A case study to assess how far large scale EV penetration may lead to increasing the potential for the use of renewable electricity is analyzed in [5], where Authors are with the Faculty of Electrical and Computer Engineering of Tarbiat Modares University, Tehran, Iran (e-mails: m.moradijoz@modares. ac.ir,
[email protected],).
978-1-4673-2729-9/12/$31.00 ©2012 IEEE
the possible revenues for EV owners from providing vehicle to grid power is discussed. Participation of electric vehicles in frequency regulation market [6], [7], providing peak power [5] and economic benefits stemming from electric vehicles participation in these markets [8], [9] have been investigated through a number of studies. Optimal participation of PHEVs in various electricity markets depends on various factors. One of the factors is V2G scheduling in constrained parking lots for the success of the V2G research. Parking lot is a player whose role is to collect the electric vehicles in order to reach high storage capacity from small battery capacity of multi electric vehicles that can affect the grid beneficially. If gridable vehicles are charged from the grid at off peak load times and discharge to the grid at peak load times, generation cost can be decreased. V2G scheduling in constrained parking lots is investigated in various studies [5], [10]-[12]. Allocation of parking lots is another important issue. Highpenetrations of distribution-connected storage devices or plugin vehicles can have adverse grid impacts due to their charging loads, randomly-located or unmanaged additions [10]. Incorrect allocation of parking lots which may be used as V2G power sources, may increase losses or have bad effect on voltage profile. On the contrary, optimal parking lot allocation can reduce the losses. To illustrate this fact, in this paper parking lot placement is carried out, using genetic algorithm in presence of time varying loads. In so doing, it is presumed that batteries of vehicles in parking lot are charged in light load times and discharged in peak load times and consequently contribute to peak power market. The remainder of the paper is organized as follows: Section II presents the problem formulation. In section III genetic algorithm (GA) is discussed. In section IV placement algorithm is discussed. Case study and results analysis are driven in section V and VI, respectively. Finally, section VII concludes the paper. II. PROBLEM FORMULATION A. Objective Function For placement of parking lot, it is necessary to define objective function. The objective function can be selected for various purposes. In this paper the objective function is selected for reducing power losses. Active and reactive power loss indices are stated as below:
2 P LPI = LV 2G PL LQI =
(1)
Q LV 2G QL
(2)
2) Backward sweep to sum up line section current The current in line section l is computed as
J l (k ) = −i n (k ) +
∑ J m (k )
m∈M
(7)
In (1) and (2) PLV2G and QLV2G are the total active and reactive power losses of the distribution system in the presence of V2G, PL and QL are the total active and reactive system power losses without V2G in the distribution system. The objective function in order to find the optimal location of parking lot is a combination of active and reactive power indices.
where Jl is the current flow on line section l and M is the set of line sections connected to node n. Line section l connects node s to node n. where n stands for receiving point of line section l and s stands for sending point of line section l.
F = w1 × LPI + w2 × LQI
The voltage at node j is computed as
w1 + w2 = 1
(3)
V j( k ) = Vi( k ) − Z l × J l
w1 and w2 are weight factors. The weight factors are defined based on cost and they are between 0 & 1. In this paper, w1 and w2 are assumed 0.5. B. Constraints The objective function is minimized based on operation constraints. 1) Distribution line capacity limit Power flow of lines should be less than maximum permitted power of line due to line thermal capacity.
S (i, j ) ≤ S (i, j ) max
(4)
where S(i,j) is MVA in the line connecting bus i to bus j, S(i,j)max is MVA capacity of the line between bus i and bus j. 2) Voltage Drop Limit The voltage of bus should be in the range of minimum and maximum voltage. Vmin ≤ V ≤ Vmax
(5)
Vmin and Vmax are minimum and maximum allowable voltage at buses. C. Load Flow To solve the optimal parking lot placement problem for a typical radial distribution network a simpler power flow method known as the backward-forward sweep power flow is used for computing the power loss. 1) Current injection calculation for each node
in ( k ) = (
S n (k ) Vn
3) Forward sweep to update nodal voltage
(k )
)*
(6)
where in is current injection at node n corresponding to constant power load, Sn is scheduled power injection at node n and Vn is the voltage at node n.
(8)
In all of the equations k is the loop counter. Iteration of these steps repeats until the convergence criteria is satisfied ( ΔVik ≤ ε ). ΔVik =| Vik | − | Vik −1 |
(9)
III. PROBLEM OPTIMIZATION USING GA Genetic algorithm is able to reach an optimum solution by finite number of evolution steps performed on a finite set of possible solutions. The objective function stated in (3), is minimized with GA. In this paper, the fitness function is equal to one divided by the objective function because the chromosome with minimum objective function is the fittest chromosome. Each chromosome is copied to the second generation a number of times that is proportional to its fractional fitness function in the reproduction phase. The algorithm stops when acceptable fitness level has been reached for the population. Before using the genetic algorithm to solve the optimization problem, representation of a chromosome must be defined. In this paper, each chromosome represents a binary number related to the bus number at which the parking lot should be connected. Therefore, the number of bits in the chromosomes depends on number of candidate bus for connecting parking lot. In this paper, 6 bits is used in each chromosome because the test system has 30 buses and it is assumed that each bus is candidate to connecting parking lot. Therefore, 6 bits is needed to convert the bus numbers 1 to 30 to their binary equivalent. Other parameters of GA are as following: Population size: 6 Mutation probability: 0.1 Crossover probability: 0.8 IV. PLACEMENT ALGORITHM For placement of parking lot, first charging and discharging
3 program of PHEVs must be determined. The charging and discharging program of PHEVs can be scheduled for participation of parking lot in various power markets. The placement algorithm is shown in Fig. 1.
Input capacity of parking lot & PHEVs charging and discharging time
V. CASE STUDY For placement of parking lot in distribution system some assumption is taken as following: 1. For a typical day, the PHEV owner goes to work in the morning, parks the PHEV, goes back home in the late afternoon and then plugs in the PHEV for charging during the night and thus it is assumed vehicles are in the parking lot from 8 to 20. 2. Number of vehicles in parking lot is constant from 8 in the morning to 20 in the evening. 3. Batteries of vehicles, considering data given in [13], are charged with constant power of 2.5 kW. 4. Loads are time variant. In this paper, load condition is considered in three stages (light, medium and peak load). 5. In the simulation, parking lot is modeled as PQ bus (Q=0). In charging state, P is positive and in discharging, P is negative. The test system for case study is a 30 bus distribution system as shown in Fig. 2.
Initial population generation
Load flow & objective function calculation
Constraints examination
Yes Stop
Termination criteria No Crossover
VI. SIMULATION RESULTS Mutation
A. Scenario 1 In this scenario it is assumed that vehicles charge for 2 hours with maximum charging rate and parking lot deliver electricity to grid for 2 hours in peak time. The number of vehicles in parking lot is 500, on average. Considering losses quantity and problem constraints, optimum location for parking lot is determined by genetic algorithm. The results of this case study are shown in Table I.
Fig. 1. Flowchart of parking lot placement algorithm
B. Scenario 2 In this scenario, it is assumed that vehicles in parking lot charge with half of maximum charging rate and 4 hours instead of charging with maximum charging rate. Number of vehicles is still equal to 500. The results of this case study are shown in Table II. With comparing Tables I and II, it is observed that as batteries charging rate changes, the optimum and the worst location for parking lot varies. With decreasing charging rate and increasing charging time, the network losses are significantly decreased. Fig. 2. IEEE 30-node test feeder.
4 TABLE I RESULTS OF IMPLEMENTING OF SCENARIO 1 Without V2G
With V2G on bus 23
With V2G on bus 27
LPI LQI Average voltage
1 1 0.9488
0.9851 0.9846 0.9489
0.9998 0.9993 0.9488
Objective function
1
0.9848
0.9996
TABLE II RESULTS OF IMPLEMENTING OF SCENARIO 2 Without V2G
With V2G on bus 25
With V2G on bus 1
LPI LQI Average voltage
1 1 0.9488
0.9782 0.9786 0.9489
0.9998 0.9993 0.9488
Objective function
1
0.9784
0.9996
TABLE III RESULTS OF IMPLEMENTING OF SCENARIO 3 Without V2G
With V2G on bus 19
With V2G on bus 27
LPI LQI Average voltage
1 1 0.9488
0.9860 0.9845 0.9489
1.0062 0.9986 0.9488
Objective function
1
0.9853
1.0024
TABLE IV RESULTS OF IMPLEMENTING OF SCENARIO 4 Without V2G
With V2G on bus 23
With V2G on bus 1
LPI LQI Average voltage
1 1 0.9488
0.9704 0.9698 0.9490
0.9998 0.9993 0.9488
Objective function
1
0.9701
0.9996
C. Scenario 3 This scenario is similar to scenario 1; the only difference is that the number of vehicles doubles i.e. 1000. The numerical results are shown in Table III. With comparing Tables I and III, it is observed that as the number of vehicles in parking lot changes, the optimal location for parking lot changes. The results in Table III demonstrate that connecting the parking lot to bus 27 causes an increase in losses compared to lack of V2G. D. Scenario 4 This scenario is the same as scenario 2 but the number of vehicles doubles i.e. 1000. The results are shown in Table IV.
Comparing Tables IV with other Tables, it is observed that as the number of vehicles in parking lot and charging time increases, the network losses are decreased. Thus optimal participation of parking lot providing V2G power for loss reduction depends on number of vehicles and charging rate.
VII. CONCLUSION In this paper, genetic algorithm is used to allocate parking lot in distribution system. Using the proposed algorithm, parking lot placement is able to be carried out so that participation in frequency regulation power market can be implemented. At first, charging and discharging program, considering market in which parking lot participates, is determined and then parking lot placement is designed, using the proposed algorithm. As simulation results demonstrate, any change in charging rate and the number of vehicles in parking lot lead to variation in the optimum location for parking lot. Thus, the precise determining of parking parameters based on the information accessed from previously-built parking lots, in order to allocate parking lots supplying V2G, can be extremely effective. The simulation results indicate that a parking lot incorrect placement can leads to an increase in grid power losses.
REFERENCES [1]
X. Yu, “Impacts Assessment of PHEV Charge Profiles on Generation Expansion Using National Energy Modeling System”, IEEE PES General Meeting, 2008, pp. 1-5. [2] T. Ghanbarzadeh, P. Teimourzadeh Baboli, M. Rostami, M. Parsa Moghaddam, and M. K. Sheikh-El-Eslami, “Wind Farm Power Management by High Penetration of PHEV”, IEEE PES General Meeting, 2011. [3] W. Kempton, “vehicle to grid power”, FERC, 2007. [4] M. Musio, P.Lombardi, A.Damiano, “Vehicles to Grid (V2G) concept applied to a Virtual Power Plant Structure”, XIX International Conference on Electrical Machines (ICEM) , Rome, 2010. [5] P. Kadurek, C. Ioakimidis, P. Ferrao, “Electric Vehicles and their Impact to the Electric Grid in isolated systems,” POWERENG Conf, Portugal, March, 2009, pp. 49-54. [6] W. Kempton, “A Test of Vehicle-to-Grid (V2G) for Energy Storage and Frequency Regulation in the PJM System”, Results from an IndustryUniversity Research Partnership, 2008. [7] S. Han, K. Sezaki, “Development of an optimal vehicle-to-grid aggregator for frequency regulation,” IEEE Trans, Smart Grid, vol. 1, June 2010, pp. 65-72. [8] W. Kempton, J. Tomic, “Vehicle-to-grid power fundamentals: Calculating capacity and net revenue,” Journal of Power Sources, vol. 144, June 2005, pp. 268-279. [9] B. Peterson, J.F. Whitacre, Jay Apt, “The economics of using plug-in hybrid electric vehicle battery packs for grid Storage”, Journal of Power Sources, vol. 195, April 2010, pp. 2377-2384. [10] A.Y. Saber, G.K. Venayagamoorthy, “Optimization of Vehicle-to-Grid Scheduling in Constrained Parking Lots”, IEEE PES General Meeting, 2009. [11] C.Hutson, G.K. Venayagamoorthy, K.A.Corzine, “Intelligent Scheduling of Hybrid and Electric Vehicle Storage Capacity in a Parking Lot for Profit Maximization in Grid Power Transactions”, IEEE ENERGY Conference, 2008. [12] E.Sortomme, M.A. El-Sharkawi, “Optimal Scheduling of Vehicle-toGrid Energy and Ancillary Services”, IEEE Trans, Smart Grid, vol. pp, septamber 2011.
5 [13] K. Clemen, E. Haesen, J. Driesen, “The Impact of Charging Plug-In Hybrid Electric Vehicles on a Residential Distribution Grid,” IEEE Trans, Power Systems, vol. 25, January 2010, pp. 371-380.
BIOGRAPHIES Mahnaz Moradijoz (S’11) was born in Zanjan, Iran, 1988. She received the B.Sc. degree in Electrical engineering from Zanjan University, Zanjan, Iran, in 2009. She is currently pursuing the M.Sc. degree in power engineering at Tarbiat Modares University (TMU). Her research interests include electric vehicle and electricity market. Mohsen Parsa Moghaddam (M’05) was born in Iran, 1956. He received the B.Sc. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1980, the M.Sc. degree from the Toyohashi University of Technology, Japan, in 1985, and the Ph.D. degree from Tohoku University, Japan, in 1988. Currently, he is a Professor in the Faculty of the Electrical and Computer Engineering, Tarbiat Modares University (TMU), Tehran, Iran. His research interests include power system planning & control, energy management, and smart grid.
