Optimal Energy Management of a Retailer with Smart Metering and Plug-in Hybrid Electric Vehicle Meysam Doostizadeh1,2, Mojtaba Khanabadi1,2, Ahad Esmaeilian1, Mohsen Mohseninezhad1 1* University of Tehran 2* NegarAndish Consulting Engineers Tehran, Iran Abstract— A smart grid will integrate extensive distributed resources such as local generation sources, Plug-in Hybrid Electric Vehicles (PHEVs) and demand response (DR) programs. By using smart metering, advanced metering infrastructure (AMI) facilitates consumer participation in DR programs and changes the consumption pattern of residential user via tariff schemes for electrical energy. 1In addition, the smart grid will play an important role in controlling and coordinating of PHEVs charging or discharging activities. In this paper, an optimization technique is used, in order to minimizing a retailer energy cost. The retailer controls charging or discharging of PHEVs during a day and considers the impact of time variant tariff schemes on customer behavior. The behavior of customer is modeled by means of economic demand models. Keywords- Smart grid; Plug-in Hybrid Electric Vehicles; Smart Metering; Retailer;
I.
INTRODUCTION
There are several interpretations of smart grid concept among researchers. A smart grid is defined as using digital information and control technologies to improve the reliability, security, and efficiency of the electric grid. A smart grid allows deployment and integration of distributed and renewable resources, smart consumer devices, automated systems, electricity storage and peak shaving technologies [1]. One of the greatest challenges for future electricity grids relates to demand side response and creating a system that can shift peak demand and being socially acceptable at the same time. Different tariff schemes such as real time pricing (RTP), day ahead pricing, time of use (TOU) pricing and critical peak pricing have been proposed to change the behavior of electricity consumers [2]. In spite of several advantages of RTP such as economic advantages [3,4], environmental effects [5] and energy efficiency improvement, recent studies have shown that lack of knowledge among consumers and lack of home automation systems are main barriers for completely practically use the benefit of RTP program. By using smart infrastructure such obstacles will be eliminated. A linear programming algorithm is described in [6] that can be easily integrated in the energy management system of a household or a small business. The hardware and software structure of smart controller that is installed on the electric plug of electric appliance is proposed in [7]. In addition, high penetrations of PHEVs into distribution system, which can potentially increase demand, have further 1
2-
[email protected] ww.negarandish.ir
need to new method for demand side management. Also, PHEVs could act as distributed storages. PHEV batteries are charged when the energy price is low and discharged during peak periods when the price is high. Many studies have been accomplished to evaluate the benefit of PHEVs. In [8] potential environmental impacts of wide integration of PHEVs are investigated in the context of Alberta’s system. The provision of grid support in terms of voltage control, peak load control, regulation services and reserve services via PHEVs is studied by [9-11]. The integration of PHEVs as reactive power capable devices to provide voltage support to the grid is investigated in [12]. Related to this work, an optimization framework for an aggregator to manage charging and discharging of PHEVs is presented in [13] and the aggregator has a responsibility to buy and sell electricity energy from and to the spot market on behalf of a number of electric vehicles owners. In this paper, mathematical models are developed to represent the operational aspects of retailer in the smart grid environment and its interaction with the spot market. Time variant tariff schemes and integration of PHEVs into distribution system as important features of smart distribution system are considered in the operational aspects of retailer. However, in this study competition amongst retailers is neglected and the retailer is assumed a price taker and has not any market power. The remaining of this paper organized as follows: Section II describes time-variant tariff and PHEV charging and discharging models. Section III presents the scheduling and operation method. Section IV represents the result of applying the proposed method in four scenarios. Finally, Section V concludes the paper. II.
PROBLEM DISCRIPTION
Retailers are entities that purchase energy from wholesale electricity market or from bilateral contracts with generation companies and sells it to customers. With implementation of smart meter, retailers could offer different time-variant tariff schemes to consumers and the customers can choose one these tariffs. Also, with high penetration of PHEVs into distribution grid, the retailer will have to carefully know the impact of these subjects on consumption patterns to reduce its unpredictability risk of spot market price. A. Time-variant tarriff model TOU pricing: In TOU pricing a day is divided to fixed number of periods. The electricity price for each period is determined based on the production cost in the same period.
978-1-4244-8782-0/11/$26.00 ©2011 IEEE
These tariffs can change in each day, week or in different season. RTP: In RTP program, market settlements for energy consumption are calculated based on hourly real time market prices. The customers change their consumption based on realtime or day-ahead market prices [14]. Consumers are provided with real time market prices and therefore they are able to respond to the prices, effectively. Demand elasticity is defined as the demand sensitivity with respect to price changes [15]: 1 where E is elasticity of the demand; D represents demand (MWh); ρ is electricity energy price ($/MWh); ρ0 is initial electricity energy price ($/MWh); and D0 is initial demand (MWh). In response to changes in energy prices, the demand would typically respond as follows: Some of the loads are not able to move from one period to another and they could be only “on” or “off” (e.g. illuminating loads). So, such loads have a sensitivity just in a single period and it is called “self elasticity” [15], which is a negative value. Some of the consumption could be transferred from the peak period to another period. Such behavior is called multi period sensitivity and it is evaluated by “cross elasticity”, which is always positive. Thus, self elasticity (ξii) and cross elasticity (ξij) can be written as: ∆ ∆
∆ ∆
0,
0
2
where ∆ is demand changes in time interval ; ∆ are price changes in intervals and , and ∆ respectively. So, the elasticity coefficients can be arranged in a 24 by 24 matrix E [16]: ,
,
,
,
,
,
,
,
3
,
,
,
,
,
,
,
,
The detailed process of modeling and formulating how the RTP program affects electricity demand and how the maximum benefit of customers is achieved are discussed in [17]. The final responsive economic model in time interval is given by: 1
,
4
The above equation shows how much the customer's demand should be, in order to achieve maximum benefit in a 24 hour interval. Time varying loads for 24 hours within one day are considered for estimating the amount of demand in the next day.
In order to estimate real time demand behavior the matrix given by (3) should be modified in the following manner: A new matrix is built from elimination of rows and columns of the original matrix that their index is smaller than the real time. B. PHEV charging and discharging model Charging the PHEV batteries can occur through specific electrical outlets of a household or through specific charging station designed for personal or public use such as shopping malls and work offices. However, in the presence of smart grid technologies electricity flow to the vehicle could be controlled at the most economically possible time. Therefore, charging of PHEV batteries are not allowed during peak period when the electricity price is very high. In this work, three scenarios are considered for PHEV charging and they are summarized below: •
Non-peak charging: vehicle owners charge their vehicles at home; however the initial charge is controlled by the retailer and it occurs at the most optimal time.
•
Uncontrolled charging: vehicle owners charge their vehicles at home in an uncontrolled way. This scenario is designed for vehicle owner that want to charge their vehicle when it is plugged in.
•
Continuous charging: vehicle owners charge their vehicles whenever parked at charging station. In this scenario PHEVs are available during specific periods.
In the third case, vehicle owner could have a contract with the retailer to operate PHEV batteries when they are plugged in charging station. Therefore, the retailer sends signals to control charging and discharging of PHEVs to minimize its energy cost. There are many constraints that the retailer has to consider during operation of PHEVs at charging station. These constraints are as follows: batteries capacity ( ), ramp , ), charging and up and ramp down of batteries ( ), available periods, initial discharging efficiencies (ŋ , ŋ charging level and final charging level that must be higher than the desired level determined by the vehicle owner. III.
PROPOSED FRAMEWORK
In this section, a day-ahead scheduling model and real time operation model of the retailer in competitive electricity market are presented. In day-ahead market, the retailer submits its offers to the market based on its prediction of demand, electricity price and PHEVs’ characteristics in the next day. Additionally, the retailer participates in real time market in order to adjust the difference between day-ahead scheduled grid purchase and its actual demand. A. Optimal day-ahead scheduling The objective function of the retailer in day-ahead market is formulated in (5) which minimize retailer’s energy cost while meet its demand:
IV. 5
. Subject to: .
ŋ
1
ŋ
6
.
7
0
8
0
9 10
is the scheduled grid purchase, is the where is total demand in time day-ahead electricity price and interval h. NPHEVs is the number of PHEVs in time interval h. is the power charged to PHEV, is the power discharged from PHEV and is PHEV battery level at the end of time interval h that must higher than the specific level when PHEV leaves the station. , , and when PHEV is not at charging station. B. Optimal real time operation In this stage, the retailer adjusts the imported power to meet its actual load in the spot electricity market. The objective function for this stage is: . .
11
Subject to: ŋ
.
and (7) – (10). The first component of (11) represents a penalty that the retailer has to pay for deviation of its real time imported power decisions from the day decisions in time interval k. Also, the second component represents the summation of penalties for the following period k+1 to N. The real time optimization problem implements as follows: Step1) acquire the real time ( the current interval k.
) load and price (
In order to analyze the operational issues as mentioned before, we have selected September 1, 2010 NYISO’s (LONGIL) load and price curves [18]. In this case, the demand is divided by 100 of the actual load in [18]. The day-ahead and real time market prices are shown in Fig. 1. The optimization problem described in section III is modeled as a linear programming (LP) problem. A code in GAMS environment [19] is developed, and the BARON solver is used to solve the LP problem. The following scenarios are simulated to examine the retailer operation in both day-ahead scheduling periods and real time operation periods: Scenario 1: This scenario is the base case with initial load curve, where no time-variant tariff programs and no PHEVs are taken into account. Scenario 2: In this scenario, consumers are equipped with smart meter. Also, TOU pricing and RTP programs are implemented for each customer. We assumed that 30 percent of customers have chosen RTP program and rest of them have chosen TOU pricing to pay their energy cost. The TOU pricing consists of three different time periods with different energy prices, low-peak interval (1 to 9), off-peak interval (10 to 13 and 19 to 24) and peak interval (14 to 18). Also, 12 ¢/KWh, 16.5 ¢/KWh and 25 ¢/KWh are considered as the energy price for low-peak, off-peak and peak intervals, respectively. 16.65 ¢/KWh was the average New York retail price of electricity to ultimate customers ( ) in September 2010 [20]. Self and cross elasticity coefficients are defined in Table I (For both RTP and TOU programs). It is worth mentioning that in RTP program each period is an hour. Scenario 3: non-peak charging of PHEVs is simulated in this scenario. This scenario incorporates 3000 PHEVs (PHEV-20 Mid-Sized Sedan), using a 120V/15A circuit [21]. The technical parameters of PHEV-20 Mid-Sized Sedan are summarized in Table II.
. ŋ
CASE STUDIES
) in
Step2) update load forecast ( ), price forecast ( ) and number of PHEVs for the future intervals (from k+1 to N) Step3) solve the objective function Step4) determine how PHEVs should be operated and the amount of imported power. Step5) update the PHEV batteries level, move to the next interval and repeat the step 1.
Scenario 4: In this case, as the same as scenario 3, the impact of both time-variant programs and charging of PHEVs are considered. In addition, PHEV batteries can be charged and discharged during the day when they are available in the charging station and retailer operates PHEV batteries to minimize its energy cost. For simplicity, the uncertainty of PHEVs availability at any given time is neglected in this study. Also, we assumed that 1000 PHEV-20s Mid-Sized Sedan are available for operation from 8 am to 6 pm in the charging station during the simulation day. The day-ahead and real time imported power for each scenario are shown in Fig. 2 and Fig. 3, respectively. It is observed that by using time variant tariff programs, the amount of loads shift to off-peak hours and lead to smoother load curve. For better specification the impact of such programs on load characteristics, peak reduction, electrical energy consumption, load factor, and peak to valley distance are evaluated for scenario 1 and scenario 2 in Table III. Also, the results illustrate that the non-peak charging of PHEVs occurs at the time that energy price is the lowest (1am to 6am for dayahead scheduling and 2am to 7am for real time operation). As
TABLE I.
60 55 Imported power (MW)
evident from Fig. 2 and Fig. 3, in scenario 4, energy cost is minimized through PHEVs’ charging during the low price periods and discharging in peak period when energy price is high (around 4 pm). The discrepancy of day-ahead scheduled and real time imported power is shown in Fig. 4. The inaccuracy of day-ahead forecasted price and load curve causes this difference. Therefore, the optimal real time energy management does not strongly support that the day-ahead schedule. However, the retailer tries to minimize the balancing cost in the real time electricity market. The difference between day-ahead scheduled grid purchased and actual load causes a penalty of 6078.72 US $. Majority of this penalty comes from spike price at 4 pm.
50 45 40
Peak -0.5 0.008 0.006
Off-peak 0.008 -0.5 0.005
Scenario2
30
Scenario3
25
Scenario4
20 15
SELF AND CROSS ELASTICITY COEFFICIENTS
Peak Off-peak Low-peak
Scenario1
35
1
Low-peak 0.006 0.005 -0.5
4
7
10
13 16 19 Hour Figure 3. Real time imported power
22
60
PHEV-20 MID-SIZED SEDAN BATTERY PARAMETER
Pack Size (kWh)
Rated Pack Size (kWh)
Charging Size (kW)
Charger Rate (kWh/hr)
Time to Charge Empty Pack (hours)
5.9
4.7
1.4
1
4.7
300
50 45 40 35 30
Day-ahead scheduled imported power Real time imported power
25 20 15
250 Price ($/MWh)
Imported power (MW)
55 TABLE II.
Day-ahead market price Real time market price
200
1
4
7
10
150
16
19
22
Figure 4. The comparision of day-ahead scheduled imported power and Real time imported power for scenario
100
TABLE III.
50
COMPARISION OF LOAD CHARACTERISTICS
0 1
4
7
10
13
16
19
22
Time (h) Figure 1. Day-ahead and real time market prices 50 45 Imported power (MW)
13 Hour
40
Scenario1
30
Scenario2
25
Scenario3
20
Scenario4
15 1
4
7
10
13 16 19 Hour Figure 2. Day-ahead scheduled imported power
22
Scenario 2
Peak (MW)
52.512
48.606
Peak reduction (%)
0
7.438
Load factor (%)
76.146
81.821
Electrical energy consumption (MWh) peak to valley distance (MW)
959.654
948.487
26.177
18.92
V.
35
Scenario 1
CONCLUSION
In this paper the mathematical methods are developed to represent the operational aspects of the retailer in the smart grid environment. Also, the impact of time variant tariff programs are modeled by utulizing the economic demand model. The proposed method optimizes the retailer energy cost by controlling charging and discharging of PHEVs. The simulation results indicate that time variant tariffs lead to more flattened load curve. In addition, the retailer energy cost is minimized through discharging of PHEV batteries in peak period and charging in non-peak period.
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