Comparison of Theoretical and Simulation Analysis of Electricity Market
for Integrative Evaluation of Renewable Energy Policy
Masaaki Suzuki, Mari Ito and Ryuta Takashima
Department of Industrial Administration, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, Japan
Keywords:
Renewable Energy Policy, FIT, RPS, Social Welfare, Equilibrium Analysis, Multi-agent Simulation.
Abstract:
Governments have introduced various policies for promoting renewable energy technologies. In particular,
feed-in tariff (FIT) and renewable portfolio standard (RPS) have been introduced in various countries. In
this work, multi-agent simulations of electricity markets with FIT/RPS have been conducted for integrative
analysis and rational design of renewable energy policies. We analyze the effects of the FIT price and RPS
level on social welfare. By comparing the results obtained from the simulation and the equilibrium analysis,
we have examined the policies from both bottom-up and top-down viewpoints comprehensively.
1 INTRODUCTION
In recent years, emissions of greenhouse gases such
as carbon dioxide and methane have been implicated
in the worldwide problem of global warming. One
of the solutions being implemented to solve the pro-
blem is to increase th e adoption of renewable energy
(RE) to in turn reduce emissions of greenhouse ga-
ses. However, the cost of RE production is high. Go-
vernments have introduced various policies for pro-
moting RE technolo gies. In particular, feed-in tariff
(FIT) and renewable portfolio standard (RPS) have
been introduced in various countries. FIT is a scheme
that requires non-renewable energy (NRE) produce rs
to purchase RE at fixed FIT prices. RPS requires that
a certain percentage of NRE producers’ electric ge-
neration capacity come from RE. RE producers issue
and sell renewable energy ce rtificates (REC) to NRE
producers in REC mar kets to comply with the RPS
requirement percentage.
There have been few studies discussing whether
FIT or RPS is preferable from the aspect of social wel-
fare. (H ibiki and Kurakawa, 2013) explored how FIT
and RPS affect so c ia l welfare in th e case of o nly one
NRE producer and one RE producer in an electricity
market by theoretical analysis. Their findings indi-
cated that governments should introduce RPS when
marginal damage cost is relatively high. They did not
eva luate the effect of the number of NRE and RE pro-
ducers or market structure. (Siddiqui et al., 2016)
studied how RPS requirement percentage and mar-
ket structure affect social welfare under RPS. They
determined the optima l RPS requirement percentage
and suggested the importance of considering market
structure for setting the optimal RPS requirement per-
centage to maximize social welfare. (Nishino and
Kikkawa, 20 13) studied the inter depend ent effects o f
multiple en ergy policies by theoretical analysis and
multi-agent simulation. However, they did not dis-
cuss the results from the aspect of social welfare.
Our purpose is to clarify how the relationships
among policy, market power, and number of produ-
cers impact so cial welfare. In this work, multi-agent
simulations of FIT and RPS are conducted for integra-
tive analysis and rational design of ren ewable energy
policies. Multi-agent simulations enable u s to eva-
luate more realistic market an d to observe emergent
processes of equilibrium states. By com paring the
results obtaine d from the simula tion and the equili-
brium analysis, we com prehensively examine the po-
licies from both bottom-up and top-down viewpoints.
2 METHODS
For simplicity, in this manuscript, we show the case
of only one NRE producer and one RE producer in a n
electricity market.
2.1 Equilibrium Analysis
The single-level model for determining maximum so-
cial welfare is called Central planning (CP). In CP, a
Suzuki M., Ito M. and Takashima R.
Comparison of Theoretical and Simulation Analysis of Electricity Market for Integrative Evaluation of Renewable Energy Policy.
DOI: 10.5220/0006249304550459
In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems (ICORES 2017), pages 455-459
ISBN: 978-989-758-218-9
Copyright
c
 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
455

central plann e r decides all power pla nts’ capacity so
as to maximize social welfare. Ma rkets with FIT or
RPS are analyzed within the bi-level model. At the
lower level, NRE and RE producers decide gen eration
capacity to maximize their own profits. At the upper
level, policymaker decides the optimal FIT price or
RPS requirement percentage to max imize social wel-
fare.
2.1.1 Central Planning
Social we lfare SW is defin e d and max imized as fol-
lows:
SW ≡ A(q
n
+ q
r
) −
1
2
Z(q
n
+ q
r
)
2
−C
n
(q
n
) −C
r
(q
r
) − D
n
(q
n
),
(1)
max
q
n
≥0,q
r
≥0
A(q
n
+ q
r
) −
1
2
Z(q
n
+ q
r
)
2
−C
n
(q
n
) −C
r
(q
r
) − D
n
(q
n
)
(2)
where e le ctricity price p shows linear inverse de -
mand function (i.e., p = A − Z(q
n
+ q
r
)) (in US dol-
lars (USD)), A is the intercept of linear inverse de-
mand functio n, Z is the slope of linear inverse de-
mand function, q
n
is NRE productio n (in MWh),
and q
r
is RE production (in MWh). The third,
fourth and fifth terms in Eq.(1) are co st functio ns.
Here, C
n
(q
n
) =
1
2
c
n
q
2
n
is the cost function for NRE
production, C
r
(q
r
) =
1
2
c
r
q
2
r
is the cost function f or
RE production, D
n
(q
n
) =
1
2
kq
2
n
is the damage cost
function for NRE production, and c
n
,c
r
,k > 0 are
constants (in USD/MWh
2
). The optimal solution of
CP is obtained by solving Eq.(2) and is as follows:
¯q
n
=
Ac
r
c
r
(Z + c
n
+ k) + Z(c
n
+ k)
(3)
¯q
r
=
A(c
n
+ k)
c
r
(Z + c
n
+ k) + Z(c
n
+ k)
(4)
¯p =
A{c
r
(Z + c
n
+ k) + Z(c
n
+ k)} − ZA{(c
n
+ k) + c
r
}
c
r
(Z + c
n
+ k) + Z(c
n
+ k)
(5)
¯
α =
c
n
+ k
c
n
+ k + c
r
(6)
where ¯q
n
and ¯q
r
are optimal NRE and RE production,
respectively, ¯p is optimal electricity price, and
¯
α is
optimal proportion of RE.
2.1.2 FIT
At the lower level, we now c onsider payoff function s
for the NRE producer and RE producer:
π
n
= p(q
n
+ q
r
) −C
n
(q
n
) − p
FIT
q
r
(7)
π
r
= p
FIT
q
r
−C
r
(q
r
) (8)
where p
FIT
is FIT price. When the NRE producer is
dominant and behaves `a la Cournot, optimal solution
is as follows:
˜q
n
=
Ac
r
− 2Z p
FIT
c
r
(2Z + c
n
)
(9)
˜q
r
=
p
FIT
c
r
(10)
˜p =
Ac
r
(Z + c
n
) − Zc
n
p
FIT
c
r
(2Z + c
n
)
(11)
˜
α =
(2Z + c
n
)p
FIT
Ac
r
+ c
n
p
FIT
(12)
At the u pper level, we maximize social welfare
about p
FIT
:
max
p
FIT
A( ˜q
n
+ ˜q
r
) −
1
2
Z( ˜q
n
+ ˜q
r
)
2
−C
n
( ˜q
n
) −C
r
( ˜q
r
) − D
n
( ˜q
n
)
(13)
As a result, we ob ta in the following op timal FIT price
˜p
FIT
:
˜p
FIT
=
Ac
r
(3c
n
Z + 2Zk + c
2
n
)
4Z
2
(k + c
n
) + c
2
n
Z + c
r
(2Z + c
n
)
2
(14)
2.1.3 RPS
At the lower level, we now consider payoff functions
for the NRE producer and RE producer:
π
n
= pq
n
−C
n
(q
n
) − αp
REC
q
n
(15)
π
r
= pq
r
−C
r
(q
r
) + (1 − α)p
REC
q
r
(16)
where p
REC
is REC price, α is RPS requirement per-
centage. When the NRE produc er is dominant and
behaves `a la Cournot, optimal solution is as follows:
q
∗
n
=
A(1 − α)
(2Z + c
n
+ c
r
)α
2
− 2(Z + c
n
)α+ (2Z + c
n
)
(17)
q
∗
r
=
Aα
(2Z + c
n
+ c
r
)α
2
− 2(Z + c
n
)α+ (2Z + c
n
)
(18)
p
∗
=
A{(2Z + c
n
+ c
r
)α
2
− 2(Z + c
n
)α+ (Z + c
n
)}
(2Z + c
n
+ c
r
)α
2
− 2(Z + c
n
)α+ (2Z + c
n
)
(19)
p
∗ REC
=
A{(2Z + c
n
+ c
r
)α− (Z + c
n
)}
(2Z + c
n
+ c
r
)α
2
− 2(Z + c
n
)α+ (2Z + c
n
)
(20)
At the u pper level, we maximize social welfare
about α:
max
α
A(q
∗
n
+ q
∗
r
) −
1
2
Z(q
∗
n
+ q
∗
r
)
2
−C
n
(q
∗
n
) −C
r
(q
∗
r
) − D
n
(q
∗
n
)
(21)
We solve the above equation numerically to find the
optimal RPS requirement percentage α
∗
.
ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems
456

2.2 Multi-agent Simulation Analysis
In this work, the deregula ted electricity mar ket con-
sists of NRE produ cer agents, RE producer agents
and consumers expressed as the linear inverse demand
function, and is modeled as the blind and single-price
call auction with reference to (Nishino and Kikkawa,
2013). In this auction, each energy producer agent
offers its asking p rice and production. A ll order s are
aggregated into the market schedules of supply and
demand , and their intersection determines a single,
market-clearing price for all feasible quantities (Fi-
gure 1).
Figure 1: Trading mechanism of multi-agent simulation.
Each agen t learns the optimal pricing strategies
based on the Q-learning method (Watkins and Dayan,
1992) in order to maximize its profit. The Q-learning
proced ure used in this work is described below:
1. Decide action based on Q-value by sof tmax se-
lection with Boltzmann distribution:
Prob(a|s) =
exp{Q(s,a)/T }
Σ
a
′
exp{Q(s,a
′
)/T }
(22)
where s = s(p
ask
n
, p
ask
r
) is the state o f the market,
p
ask
n
and p
ask
r
are the asking-price of NRE and RE
producer agents respectively, a ∈ {p
ask
+1 , p
ask
±
0, p
ask
− 1} is the action of each producer agent,
Q(s,a) is Q-value, T > 0 is the ”temp erature”.
2. Calculate the asking-quantity of production of
each producer age nt as the optimal response for
each upda te d p
ask
.
3. Decide transactio n pric e and actual quantity of
production of each produc er agent.
4. Calculate profit of each producer agent an d social
welfare.
5. Up date Q-value of each producer agent using th e
following equation:
Q(s
t
,a) ← (1 − β)Q(s
t
,a)
+ β{r
t
/100 + γ max
a
Q(s
t+1
,a)}
(23)
where s
t
is the state at th e t learnin g step, β is le-
arning rate, r
t
≡ (π
t
− π
t−1
) is the reward of each
producer agent at the t learning step, π
t
is the pro-
fit of ea ch produce r agent at the t learning step,
and γ is the discount rate .
6. End search if the ma ximum number of learnin g
steps is reach e d.
We now c onsider a electricity market with no re-
newable energy policy and then obtain the following
payoff functions:
π
n
= pq
n
−C
n
(q
n
) (24)
π
r
= pq
r
−C
r
(q
r
) (25)
Optimal asking-quan tity of production q
ask
for an
asking-price p
ask
is:
q
ask
n
=
p
ask
n
c
n
(26)
q
ask
r
=
p
ask
r
c
r
(27)
3 RESULTS AND DISCUSSION
We evaluate the effect of the renewable e nergy po-
licy from the aspect of social welfare. Table 1 shows
the evaluation conditions. The parameter values were
set by reference to (Hibiki and Kurakawa, 2013) and
(Nishino and Kikkawa, 20 13).
Figure 2 shows le arning history abou t pric ing of
each producer agent. Asking-prices of both produ-
cer agents converge to specific values. Consequently,
transaction price , actual su pply q uantity of ea ch pro-
ducer agent and social welfare also converge to spe-
cific values (Figure 3 and Figure 4 (top)). Figure 4
(bottom) and Table 2 show comparison of social wel-
fare, energy production, propor tion of RE and elec-
tricity price between equilibrium analysis and multi-
agent simulation. Compa red with CP, FIT leads to
Comparison of Theoretical and Simulation Analysis of Electricity Market for Integrative Evaluation of Renewable Energy Policy
457

Table 1: Evaluation conditions.
Parameter Value Unit
Demand Intercept of inverse demand function A 100 USD
Slope of inverse demand function Z 0.01 USD/MWh
Cost Coefficient of NRE production cost c
n
0.025 USD/MWh
2
Coefficient of RE production cost c
r
0.25 USD/MWh
2
Coefficient of damage cost k 0.025 USD/MWh
2
Q-learning Maximum number of learning step t
max
200,000 -
Temperature T
t
50 × (0.99995)
t
-
Learning rate β 0.5 -
Discount rate γ 0.5 -
higher NRE production cost and damage cost w hile
RPS leads to higher RE production cost. We can see
that multi-agent simulation (MAS) with no renewable
energy policy yields higher produc er surplus, lower
proportion of RE, higher dama ge c ost, and as a result,
social welfare indicates the smallest value.
0 0.5 1 1.5 2 2.5
# of learning step
10
5
0
20
40
60
80
100
Price (USD)
Non-renewable
Renewable
0 0.5 1 1.5 2 2.5
# of learning step
10
5
0
1000
2000
3000
4000
Quantity (MWh)
Non-renewable
Renewable
Figure 2: Asking electricity price (top) and quantity
(bottom) of each producer agent.
4 CONCLUSIONS
We modeled the deregulated elec tricity market as the
blind and sing le -price call auction, and constructed
multi-agent system in order to clarify how the relati-
onships among renewable energy policy, market p o-
wer, and number of produce rs impact social welfare.
Under the conditions of this evaluation, RPS achieved
superior social welfare value to FIT and MAS (with
no renewable energy policy). Additional numer ic al
experiments a nd assessments of the market dynamics
that spe c ifica lly take into account realistic diversity
of age nts’ characteristics an d various uncertainties are
important topics for futu re researc h.
0 0.5 1 1.5 2 2.5
# of learning step
10
5
0
20
40
60
80
100
Price (USD)
Transaction price
0 0.5 1 1.5 2 2.5
# of learning step
10
5
0
500
1000
1500
2000
2500
3000
Quantity (MWh)
Non-renewable
Renewable
Figure 3: Transaction price (top) and actual supply quantity
of each producer agent (bottom).
0 0.5 1 1.5 2 2.5
# of learning step
10
5
0
2
4
6
8
10
12
(USD)
10
4
NRE cost
RE cost
Damage cost
Producer surplus
Consumer surplus
Social welfare
1 2 3 4
-1
-0.5
0
0.5
1
1.5
(USD)
10
5
NRE cost
RE cost
Damage cost
Producer surplus
Consumer surplus
Social welfare
CP FIT RPS MAS
Figure 4: Breakdown of social welfare: (top) Convergence
history of multi-agent simulation, (bottom) Comparison be-
tween equilibrium analysis and multi-agent simulation.
ACKNOWLEDGEMENTS
This work was supported by JSPS KAKE N H I Grant
Numbers JP15H02975, JP16H07226.
ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems
458

Table 2: Comparison between equilibrium analysis and multi-agent simulati on.
CP FIT RPS MAS
NRE production cost (U SD) -32,522 -53,354 -44,557 -56,180
RE production cost (USD) -13,041 -15,488 -27,730 -9,800
Damage cost (USD) -32,522 -53,354 -44,557 -56,180
Producer surplus (USD) 110,478 114,442 107,941 116,420
Consumer surplus (USD) 18,740 29,234 27,824 28,800
Social welfare (USD) 96,697 90,321 91,208 89,040
NRE production (MWh) 1,613 2,066 1,888 2,120
RE production (MWh) 323 352 471 280
Total production (MWh) 1,936 2,418 2,359 2,400
Proportion of RE (-) 0.17 0.15 0.20 0.12
Electricity price (USD/MWh) 80.6 75.8 76.4 76
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Comparison of Theoretical and Simulation Analysis of Electricity Market for Integrative Evaluation of Renewable Energy Policy
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