Comparison of Contracts in Vehicle-to-Load to
Benefit Both Retailers and Electric Bus Operators
Masahiro Mae, Keisuke Abe, Ryuji Matsuhashi
Department of Electrical Engineering and Information Systems
The University of Tokyo
Tokyo, Japan
mae@enesys.t.u-tokyo.ac.jp

Abstract—Price fluctuations in the electricity market arebecoming a major risk for retailers, and appropriate retailcontracts with customers who have controllable demand-side
equipment are becoming increasingly important. The aim of
this paper is to identify a suitable contract that benefits both
the retailer and the electric bus operator to promote Vehicle-toLoad as demand response. The electric bus operator optimizes
the charging/discharging operations in various retail contracts,
and the characteristics of the revenue for the retailer and thecost of the electric bus operator are analyzed in each case. By
optimizing the charging/discharging operations of the electric buswith various retail prices in mixed-integer programming, it ispossible to benefit both the retailer and the electric bus operator.
The result shows that the two-step price for stimulating demandis found to be the best in terms of appropriate risk allocation
between the retailer and the electric bus operator.
Index Terms—Electricity Market, Electric Bus, Vehicle-toLoad, Demand Response, Retail Contract

I. I NTRODUCTION
The electricity market provides a risk for retailers withprice fluctuations [1]. The appropriate retail contracts withcustomers who have controllable demand-side equipment arebecoming increasingly important. As demand-side equipment,
electric vehicles that are used as Vehicle-to-Grid is getting
attention. In particular, electric buses are expected to be easier
to make the charging/discharging operations than other typesof electric vehicles, since they have fixed routes and schedules.
More than 20 % of all global carbon dioxide emissions in
2021 were from the transportation sector [2] and the introduction of electric buses can help to use more renewable energies
in the transportation sector [3]. The use of Vehicle-to-Grid isexpected to enter the electricity market for grid stabilizationsuch as demand response and frequency regulation [4], [5], andbe used as an emergency power source in case of disaster [6].
To promote demand response of the consumers using electricvehicles, the real-time retail price that follows the market priceis introduced in several studies [3], [7]–[9]. Though the realtime retail price can promote demand response at the most, it
can make the risk of the cost of the consumers larger becauseof the difficulty of following the price fluctuation completely.
To make the risk of the cost of the consumers smaller, timeof use pricing in that the electricity cost of charging anddischarging changes gradually depending on the time of day
is also introduced [10].

Although several approaches have been developed to utilize
electric vehicles as Vehicle-to-Load for demand response,
the retail price design to benefit both the retailer and theelectric bus operator has been overlooked in pre-existing
approaches. The aim of this paper is to identify a suitable
contract to promote Vehicle-to-Load as demand response that
benefits both the retailer and the electric bus operator withthe optimizing charging/discharging operations of the electricbuses. The contributions of this paper areC1) to optimize the charging/discharging operations with consideration of the electric bus schedule, andC2) to compare several types of retail contracts to benefit both
the retailer and the electric bus operator.
Through the retail price setting and the strategic charging/discharging operation of the electric bus, positive outcomes are
anticipated for both of them. In this paper, the characteristicsof the revenue for the retailer and the cost of the electric bus
operator are analyzed when they enter into retail contracts
in various patterns, and the electric bus operator optimizes
charging/discharging operations in each case. As patterns ofretail contracts, the following cases are considered: (a) fixedprice, (b) two-step price for stimulating demand, (c) two-stepprice for suppressing demand, (d) three-step price, (e) realtime price.
The outline is as follows. In Section II, the problem thatis considered in this paper is formulated. In Section III, theoptimization method of charging/discharging operations considering bus schedule is developed. In Section IV, the modelof the retail prices to promote Vehicle-to-Load is presented.
In Section V, the portfolio analysis of retail prices to benefit
both the retailer and the electric bus operator is conducted. In
Section VI, conclusions are presented.
II. P ROBLEM FORMULATION
Fig. 1 shows the model of electricity procurement andretail in this paper. The retailer buys the electricity fromthe electricity market, and the electric bus operator buys theelectricity from the retailer according to the retail price. Notethat all power flow is used for bus charging and the electric bus
operator office demand, and there is no reverse flow to the grid.
The electric bus operator optimizes the charging/discharging
operations to minimize the electricity cost. However, thetiming of the charging/discharging is affected by the electricTABLE IS YMBOLS OF OPTIMIZATION MODEL .

Power
Money

PV

PtmarketElectricity

RetailerMarket

PtPV

Ptmarket

Ptmarket · Ctmarket

Bus
Operator

Ptmarket · CtretailFig. 1. Model of electricity procurement and retail.

bus schedule which cannot be changed and the electric bus
can be charged/discharged at the electric bus operator office.
The retailer tries changing the retail price to promote demand
response by the electric bus operator. Although the retail pricethat follows the market price can make the revenue risk of theretailer smaller, the too-dynamic retail price can make the costrisk of the electric bus operator larger. From these discussions,the requirements of the developed approach are
R1) that the charging/discharging operations is optimized withconsideration of the electric bus schedule, andR2) the retail contract is selected to benefit both the retailer
and the electric bus operator.
III. CHARGING / DISCHARGING OPERATIONS OPTIMIZATIONCONSIDERING BUS SCHEDULE

The optimization problem of the charging/discharging operations of the electric bus is formulated from (1) to (12), where
the symbols of the optimization model are listed in TABLE I.
minimizetX
max(Ctretail · Pt · ∆t)

(2)
(3)

i

c
d
Xi,t
, Xi,t∈ {0, 1} (∀i)

(4)

c
d
Xi,t
+ Xi,t≤ 1 (∀i)cdPi,t = Pi,t = 0 (∀i ∈ Bst ∪ Brt )cccd0 ≤ Pi,t≤ Xi,t· Pmax, Pi,t= 0 (∀i ∈ Bct )dddc0 ≤ Pi,t≤ Xi,t· Pmax, Pi,t= 0 (∀i ∈ Bdt )SOCi,t+1 = SOCi,t (∀i ∈ Bst )(5)

δ
SOCi,t+1 = SOCi,t −(∀i ∈ Brt )ηr · Qc
Pi,t∆t
SOCi,t+1 = SOCi,t + ηc(∀i ∈ Bct )Qd∆t
1 Pi,tSOCi,t+1 = SOCi,t −(∀i ∈ Bdt )
ηd Q

unit
–
–
–
hour
kW
kW
kW
kW
kW
kW
kW
kW
–
–
–
kWh
–
km/kWhkm––––

The objective function (1) represents minimizing the electricity
cost of the electric bus operator. (2) represents the power
balance of the electric bus operator office, and note that all
power flow is used for bus charging and the electric bus
operator office demand, and there is no reverse flow to thegrid. (3) represents the total charging power to the battery
considering the charging and discharging of multiple buses.
(4) and (5) are the binary conditions that represent the state ofcharging and discharging. (6), (7), and (8) represent the power
corresponding to the state of the electric buses. (9), (10), (11),and (12) represent the SOC conditions corresponding to thestate of the electric buses.
IV. M ODEL OF RETAIL PRICES TO PROMOTEV EHICLE - TO -L OAD

subject to (∀t ∈ T)i

description
time
end time of optimization period
set of optimization period
time step
demand of bus operator office at time t
power from PV at time t
power from electricity market at time t
total charging power to battery at time tcharging power to battery at time tdischarging power from battery at time t
maximum charging power
maximum discharging powerstate of charge (SOC) of battery at time t
minimum SOC of battery
maximum SOC of battery
capacity of battery
charging/discharging efficiency
running efficiency
running distance per round routeset of bus in staying
set of bus in runningset of bus in charging
set of bus in discharging

(1)

t=1

Dt + Pt = PtPV + Ptmarket
X
X
c
d
Pt =
Pi,t
−
Pi,t

symbol
t
tmax
T
∆t
Dt
PtPV
Ptmarket
Pt
Ptc
Ptd
c
Pmax
d
Pmax
SOCt
SOCminSOCmaxQηc , ηd
ηr
δ
Bst
Brt
Bct
Bdt

(6)
(7)
(8)
(9)
(10)
(11)
(12)

The retail price that follows the market price can promotedemand response of the consumers. In this paper, 5 different
retail price models are investigated to that which retail pricecan benefit both the retailer and the electric bus operator. The
models of the market price and the retail price are shown in
Fig. 2. Fig. 2(a) shows the conventional fixed price model.
It does not change corresponding to the market price andit cannot promote demand response. Fig. 2(b) shows theretail price model with the low price demand response. It
achieves demand response by stimulating demand when themarket price is low. Fig. 2(c) shows the retail price modelwith the high price demand response. It achieves demand
response by suppressing demand when the market price ishigh. Fig. 2(d) shows the retail price model with three-stepprices. It roughly follows the market price and promotes
demand response according to the market price. Fig. 2(e)shows the retail price model according to the real-time market
price. It accurately follows the market price and promotes

retail price(conventional)

price

price

marketpricemarketpricetime(a) fixed

TABLE IIIP RICE VARIABLES TO PROMOTE DEMAND RESPONSE (DR).

timemarketpricetime(c) highDR

unit[JPY/kWh][JPY/kWh][JPY/kWh][JPY/kWh][JPY/kWh]

namedescription

retail price Ctretail [JPY/kWh]fixedconventional

lowDR

low priceDR

highDRhigh price
DR

step

step priceDR

rtp

real-time
price DR

Ctretail in TABLE V
if Ctmarket ≤ 1
1 + C wheel
else
Ctretail in TABLE V
if Ctmarket < 20
15 + C wheelelse
31 + C wheel
if Ctmarket < 10
12 + C wheelelse if 10 ≤ Ctmarket < 20
22 + C wheelelse if 20 ≤ Ctmarket
32 + C wheel
Ctmarket + C wheel+ retail revenue (5 JPY/kWh)time(d) step
retail price(real time price)

pricemarketpricetime(e) rtp
Fig. 2. Model of market price and retail price.
TABLE II
C ONDITIONS OF OPTIMIZATION .
condition
objective function
time step ∆t
set of optimization period T

used data

description
market price at time step t
retail price at time step t
average market price in last year
risk premium (= 7 JPY/kWh)wheeling fee (= 5 JPY/kWh)TABLE IVD ETAIL OF RETAIL PRICES .

retail price(step price)

pricemarketprice

optimized variable

symbolCtmarket
Ctretail
C ave
C premiere
C wheel(b) lowDR

retail price(high price DR)

priceretail price(low price DR)

description
minimize electricity cost of bus operator
15 min/1 slot (∆t = 0.25)
96 slot/1 day
tmax = 96, T = {1, 2, 3, ..., 96}
charging/discharging output (Ptc , Ptd )and battery SOC (SOCt )electricity market price and solar radiationfrom April 2017 to March 2022

demand response according to the market price. Although theretail price model according to the real-time market price canpromote demand response at the most, it can make the risk of
the cost of the electric bus operator larger because the electricbus operator cannot follow the price fluctuation completely.
V. P ORTFOLIO ANALYSIS OF RETAIL PRICES TO BENEFIT
BOTH RETAILER AND BUS OPERATORIn this section, the optimization problem of the charging/discharging operations of the electric bus with various
retail prices is conducted in the model based on the actual
bus operator. The portfolio analysis is conducted for the
optimization results to investigate the retail price that benefits
both the retailer and the electric bus operator.
A. Conditions
In this paper, the numerical case study is conducted on
the electric bus route based on the actual bus operator in

TABLE VF IXED RETAIL PRICE [JPY/kWh] BY YEAR .
year
2017
2018
2019
2020
2021
2022

Ctretail
20.29
21.8
20.88
19.17
23.05
26.03

C ave
8.29
9.8
8.88
7.17
11.05
14.03

C premiere

C wheel

7.0

5.0

TABLE VI
S PECIFICATION OF ELECTRIC BUS .
specification
battery capacity Q
cdbattery output Pmax
, Pmaxcharging/discharging efficiency ηc , ηdrunning efficiency ηrrunning distance per round route δvalue
105.6 kWh30 kW
0.91.56 km/kWh
5 km

Hiroshima, Japan, as shown in Fig. 3. Fig. 3(a) shows theelectric bus schedule and the magenta areas are the period
during which the electric bus is running. The two buses
alternatively run the round route as shown in Fig. 3(b). The
electricity demand of the electric bus operator office is also
defined in Fig. 3(c). The specification of PV at the electric bus
operator office is that the power is 30 kW, the azimuth is 0◦
to south, and the tilt angle is 30◦ .
For the optimization calculation, the conditions are shown in
TABLE II. The data of the electricity market is based on Japan
Electric Power eXchange (JEPX) [11]. The price variables arelisted in TABLE III and the retail prices in this paper areprice [JPY/kWh]bus Number

1

MarketRetail

40
30
20
10
00

4

8 12 16 20 0

4

8 12 16 20 0
time [h]4

8 12 16 20

Fig. 4. Market price and retail price in step price.
2

03:00

06:00

09:00

12:00

15:00

18:00

21:00

(a) Bus schedule. (■) denotes periods in that electric buses are running.

power [kW]10050
demand [kW](b) Bus route.

EV charge

Demand25
4

8 12 16 20 0

4

8 12 16 20 0
time [h]4

8 12 16 20(a) Power management.

1.00

10

0.75

6

12
time [h]

18

24

SOC

20
00

market50

30

office(charger)

EV discharge

75

00

40

PV

SOC1

SOC2

0.50
0.25

(c) Electricity demand of bus operator office.

0.000

Fig. 3. Model of bus operator.

4

8 12 16 20 0

4

8 12 16 20 0
time [h]4

8 12 16 20(b) SOC trend.
Fig. 5. Conventional charging operation after bus service.

100
power [kW]defined in TABLE IV that follows the idea of revenue neutral
as far as possible, where the fixed retail price by year is given
by TABLE V. The specifications of electric bus is shownin TABLE VI. The optimization calculation is conducted byusing Python [12] and Gurobi [13].
B. Optimization result

EV dischargemarketEV charge

Demand

75
50
25
00

4

8 12 16 20 0

4

8 12 16 20 0
time [h]4

8 12 16 20(a) Power management.

1.00

SOC1

SOC2

0.75
SOC

The optimization of the charging/discharging operations of
the electric bus is conducted with various retail prices in Fig. 2.
To focus on the behavior of the charging/discharging operations with demand response, the three days from October 1
to 3 in 2021 are analyzed in step price as an example. Fig. 4
shows the market price and the retail price in step price forthese 3 days. In step price, the retail price roughly follows thetrend of the market price.
Fig. 5 shows the power management and the SOC trend
in the conventional charging operation after the electric bus
service. It results in that the electric bus is charged during themarket and the retail prices are high and it is not preferable
for the cost of the electric bus operator.
Fig. 6 shows the power management and the SOC trend instep price with optimizing the charging/discharging operations.
It results that the battery of the electric bus is charged moreduring the retail price is low and is discharged during the retailprice is high. Note that all power flow after the optimization
is used for bus charging and the electric bus operator officedemand, and there is no reverse flow to the grid.

PV

0.50
0.25
0.000

4

8 12 16 20 0

4

8 12 16 20 0
time [h]4

8 12 16 20(b) SOC trend.
Fig. 6. Optimized charging operation in step price.

C. Portfolio analysis in various retail contracts
The key point that is identified in this paper is the retail pricethat can benefit both the retailer and the electric bus operator.
The benefit of the retailer and the electric bus operator canbe analyzed by the portfolio that consists of the average andstandard deviation of the revenue of the retailer and the cost

average of revenue [×104 JPY]

12

VI. C ONCLUSION

10
8
6
4
fixed
rtp
step
lowDR
highDR

2
0

0

2

4

6

8

10

standard deviation of revenue [×104 JPY](a) Revenue portfolio of retailer.

average of cost [×104 JPY]

50

48

46

R EFERENCES

44
fixed
rtp
step
lowDR
highDR

42

40

This paper identifies a suitable contract that benefits both
the retailer and the electric bus operator to promote Vehicle-toLoad as demand response. The electric bus operator optimizes
charging/discharging operations in various retail contracts, andthe characteristics of the revenue for the retailer and the costof the electric bus operator are analyzed in each case. By
optimizing the charging/discharging operations of the electricbus with various retail prices in mixed-integer programming,
it is possible to benefit both the retailer and the electric bus
operator. The results show that two-step price for stimulating
demand is found to be the best in terms of appropriate risk
allocation between the retailer and the electric bus operator.
Cooperation between retailers and electric bus operators will
be important for the practical realization of demand responsewith electric vehicles in the future. Ongoing researches focus on the consideration of the battery degradation becauseof charging/discharging, the faster optimization calculation
method in mixed integer programming, and the experimentand the social implementation with actual bus companies.

0

2

4

6

8

10

12

14

standard deviation of cost [×104 JPY](b) Cost portfolio of electric bus operator.
Fig. 7. Portfolio analysis in various retail contracts. (⃝) denotes conventionalcharging operation after bus service, and (+) denotes optimized charging
operation.

of the electric bus operator. The monthly portfolio analysis invarious retail contracts is shown in Fig. 7.
Fig. 7(a) shows the revenue portfolio of the retailer. It
shows that the standard deviation of the revenue of the retailer
becomes small when the retail price follows to the market
price. In contrast, the average value of revenue does not changemuch corresponding to the retail price. It results in the retailprice that follows the market price benefits the retailer to makethe business risk smaller.
Fig. 7(b) shows the cost portfolio of the electric bus operator. It shows that the average cost of the electric bus operator
is reduced by the optimization of the charging/discharging operations. The standard deviation of the cost of the electric bus
operator can be reduced by lowDR, fixed, and highDR retailprices. Although the real-time price can make the standard
deviation of the revenue of the retailer smaller, it makes thestandard deviation of the cost of the electric bus operator muchlarger, and it cannot be accepted by the business risk of theelectric bus operator. As a result, the lowDR retail contract isthe best because it benefits both the retailer and the electricbus operator.

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