Journal of Power and Energy Engineering, 2015, 3, 274-281
Published Online April 2015 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2015.34037
How to cite this paper: Nomoto, S. and Kumano, T. (2015) Improved Optimal Operation Planning Method Based on Tabu
Search for Residential PEFC-CGS Considering Ramping Rate. Journal of Power and Energy Engineering, 3, 274-281.
http://dx.doi.org/10.4236/jpee.2015.34037
Improved Optimal Operation Planning
Method Based on Tabu Search for
Residential PEFC-CGS Considering
Ramping Rate
Satoshi Nomoto, Teruhisa Kumano
Depart ment of Electrical Engineering, Meiji University, Kawasaki, Japan
Email: ce41079@meiji.ac.jp
Received February 2015
Abstract
This paper proposes an improved optimal operation planning method for residential PEFC-CGS
(Polymer Electrolyte Fuel CellCo-Generation System). Residential PEFC-CGS has recently been ga-
thering attention as one of the distributed power sources with high efficiency and low environ-
mental impacts. Previous research pointed out that the output variations of PEFC adversely affect
the durability. It can be surmised that smaller output variations will be desired to extend durabil-
ity years. However, in this field, ramping rate have not been sufficiently considered. For local
search and tabu search, ramping rate constraint makes our operation planning difficult because it
restricts the search for feasible neighborhood solutions. Therefore, the auth o rs proposed a me-
thod to deal with typical an d harsher ramping rate constraints in comparison with conventional
methods. There are two key points for the improvement. One is the reinforcement of the search
along the output power axis; the other is to make use of the strategy of tabu search which avoids
the local optimal solutions. The simulation results show the effectiveness of the proposed method
in the daily operation planning. Furth erm ore , in the case using typical ramping rate parameter, it
is confirmed that tabu search doesnt contribute the reduction of daily operational cost due to the
above stated restriction of the search area.
Keywords
Distributed Generation, PEF C-CGS, Local Search, Tabu Search, Operation Planning, Ramping Rate
1. Introduction
Residential PEFC-CGS has been on sale in Japan since 2009 as one of the distributed power supplies with high
efficiency and low environmental impact. According to [1], in 2013 the shipment volume of PEFC-CGS ap-
proximately reached 250,000 [kW] in Japan, a nd in 2014 [2 ] shows that it started to be on sale in Germany. It
can be estimated that PEFC-CGS will be spreading out other countries in the future. For these reasons, the oper-
S. Nomoto, T. Kumano
275
ation planning for residential PEFC-CGS becomes more important in order to maximize the introduction effects.
The operation planning method for fuel cell CGS has been already researched in the existing studies such as
[3]-[5]. However, they disregarded ramping rate constraint in the operation planning. In addition, [6] pointed out
that the output variations of PEFC adversely affect the durability. Accordingly, it can be considered that smaller
output variations will be desired to extend durability years. Consequently, it is essential for the optimal opera-
tion planning to consider and discuss the ramping rate constraint.
For easily considering the ramping rate constraint and the efficacy of tabu search, in this paper, we apply tabu
search to the operation planning considering ramping rate for residential PEFC-CGS, and improve it for avoid-
ing the trap into local optimal solutions. Moreover, we studied how ramping rate constraint affects the operation
planning with the 2 simulation cases; harsh ramping rate and the standard ramping rate are applied in the respec-
tive cases.
2. Problem Formulation
2.1. Assumed Model
Assumed PEFC-CGS model and its specifications are shown in Figure 1 and Ta ble 1. The output of PEFC non-
linearly affects its electrical and heat efficiencies. Therefore, we introduce the electricity and heat efficiency
shown in Figure 2. The efficiency and the specifications are assumed based on [7]. According to [7], they are
not the best ones in Japanese top-runner program, but reasonably selected considering aged deterioration. In ad-
dition, the adequacy of the specifications is calculated and evaluated in [8]. Table 2 describes electrical power
and gas charge. Table 3 displays the temperature of supply water used in calculation.
2.2. Formulation
In this paper, the operation planning problem for residential PEFC-CGS is formul at ed as follows:
Objective Function:
Figure 1. Assumed model.
Table 1. Specifications of assumed system [7].
Capacity of Storage Tank 200 [L] Electrical Efficiency (Max) 36 [%]
Hot Water Temperature 70 [ ˚C] Heat Efficiency (Max) 45 [%]
Max Power 700 [ W] Heat Efficiency (Gas Boiler) 82 [%]
Minimum Power 250 [W] Start -up Loss (PLoss) 0.5 [kWh]
Initial Storage Water 50 [L]
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276
Figure 2. Electrical and heat efficiency [7].
Table 2. Electrical power and gas charge and conversion factors of CO2 emission.
Electric Power City Gas
Rate 11:00pm ~ 7:00am
1:00pm ~ 4:00pm
Other Times
12 [yen/kWh]
53 [yen/kWh] (Summer)
28 [yen/kWh] 44 [yen/m3]
Conversion Factor of CO2 Emission 0.555 [kg/kWh] [9] 0.689 [kg/kWh] (PE FC) [10]
2.366 [kg/kWh] (Gas Boiler) [11]
Table 3. Temperature of supply water (Tokyo) [ 12] .
Summer (Aug.) Middle Season (Apr.) Winter (Jan.)
Tempera t u r e [˚C] 27.3 13.0 6 .7
( )
( )
{ }
() () ()
{ }
SYSFC FCSYS
00
minCOST COST
TT
tpttGttEtGGt
tt
fPGK PKPKG
α
= =
=⋅+ ⋅+⋅⋅+⋅+⋅
∑∑
(1)
Const rain ts:
1 FCTtTtLtt Gt
WWWW W
=−+ +
(2)
Loss FCSYSDttt
PPPP+=+
(3)
FC
ttGt
GG G= +
(4)
MAX
0Tt T
WW= ≤
(5)
(6)
DOWNFCtFCt 1UP
P PPP
−∆≤−≤ ∆
(7)
where,
f: Daily Operational Cost (DOC) [yen],
α
: Carbon tax (=0.289) [12] [yen/kg *C O2],
T: The number of time frames (48 frames, a day, 24 hours are divided by 0.5 hour),
COST
pt
: Electricitycharge at a time t [ye n/ kW h],
COSTGt
: Gas charge at a time t [yen/m3],
FCt
P
: Electrical energy from PEFC obtaineduntil time t [ kWh] ,
SYSt
P
: Electrical energy from commercial grid obtained until time t [kW h],
Loss
P
: Electrical energy of start-up loss [kWh],
Dt
P
: Electricity demand at a time t [kWh] ,
FC
K
: Conversion factor of CO2 emission (PEFC) [kg*CO2/kW h] ,
S. Nomoto, T. Kumano
277
KE: Conversion factor of CO2 emission (Commercial grid) [kg*CO2/ kW h],
KG: Conversion factor of CO2 emission (gas boiler) [kg*CO2/kWh] ,
Lt
W
: Hot water load at a time t [L] ,
Tt
W
: Amount of hot water in the tank at a time t [ L] ,
FCt
W
: Amount of hot water obtained by PEFC at a time t [L] ,
Gt
W
: Amount of hot water obtained by gas boiler at a time t [L],
t
G
: Amount of used gas at a time t [m3],
FCt
G
: Amount of gas used by PEFC at a time t [m3],
Gt
G
: Amount of gas used by gas boiler at a time t [m3],
UP
P
: Max ramping rate (increase) [kW/0.5h],
DOWN
P
: Max ramping rate (decrease) [kW/0.5h].
Objective function (1) aims to minimize daily operation cost and it takes into account electricity, gas charge,
and carbon tax calculated by the CO2 emission. Equation (2), (3), and (4) represents the equality constraint con-
cerning hot water, electricity and gas. In this problem, hot water supplied from PEFC or ancillary gas boiler.
Moreover, start and stop are assumed once per a day so as to minimize start-up loss. Start-up loss is considered
in Equation (3). Inequality (5) represents tank capacity constraint. Inequality (6) describes max/min output con-
straint for PEFC. Inequality (7) means the ramping rate constraint.
3. Operation Planning Methods
3.1. Local Search (LS)
Local search (LS) method is one of simple optimization methods, and also called hill-climbing method. At
first, LS for daily operation planning creates neighborhood solutions from the initial operation plan. In this
problem, the search can be divided into 2 directions, time axis, and output po we r axis. Therefore, the search
process has two steps as follows:
Step 1: Create neighborhood solutions for start-stop time of PEFC. The types of “neighborhood” are clas-
sified into 9 patterns. The following is the candidate procedures to choose for creating neighborhood solu-
tions concerning start-time and stop-time:
1) Keep start time or stop time
2) Move start time or stop time to the earlier time
3) Move start time or stop time to the later time
Step 2: Create neighborhood solutions along the axis of output from the feasible neighborhood solutions
of Step 1. The types of “neighborhood” here are classified into 2 directions (increase or decrease) at each
time
After 2 steps, the best solution is selected among the feasible neighborhood solutions, and it is regarded as
next initial solution.
3.2. Tabu Search (TS)
Tabu Search (TS) [1 4] [15] is one of metaheuristic algorithms based on local search, and it was proposed by
the analogy to human memory. The algorithm of tabu search introduces a kind of memory called tabu list
into the local searchin order to avoid local optimal solutions. Tabu list has memories of the attribute of the
search, and update serially. The search proceeds to the neighborhood solutions on the way except for the
movements on tabu list, even if it is worse solution. Parameter tuning is one of the complicated problems in
many metaheuristic algorithms. However, tabu search has only one parameter called tabu length, which
means the capacity of memory. For this reason, tabu search has a great advantage which is ease of applica-
tion in comparison to other metaheuristic techniques.
In this problem, the numbers of neighborhood solutions on output axis obviously tend to be created more
than the number on time axis. Thus, local search on output axis is likely to be trapped into the local optimum
solutions. In this paper, we have applied tabu search to the local search on output axis only in order to escape
from local optimum solutions. Therefore, the direction of the search (increase or decrease) and the time are
recorded on tabu list after the determination of the best solution.
S. Nomoto, T. Kumano
278
3.3. Proposed Method (Modified TS, MTS)
For local search and tabu search, it is important to guide the search to the proper direction. In the case of consi-
dering ramping rate, it can be considered that the search on time axis is restricted by ramping rate constraint.
Therefore, we improved local search and tabu search to deal with this problem. The improvement is to restrict
the search on time axis to reinforce the search on output axis. We call it modified tabu search (MTS). Figure 3
describes the flowchart of the proposed method (MTS). As shown in Figure 3, modified tabu search creates
neighborhood solutions on time axis only one per N, which is introduced parameter. In addition, we also used
modified local search (MLS) in the simulation for the purpose of comparison.
4. Simulation Conditions and Results
Table 4 shows the summation of electricity demand and hot water demand in each season, which is determined
based on [7]. The demands are assumed to be known in advance. According to [7], these demands are measured
values. Reference [7] classifies hot water demand into 3 patterns, large, middle, and small on the basis of the
summation. Accordingly, we follow their policy. In this paper, we assumed 2 cases of ramping rate constraint.
One is harsh ramping rate; the other is standard one [7], and they are shown in Table 5. The value of harsh case,
case 1 is selected the half of standard ramping rate.
Table 6 and Table 7 show daily operational cost obtained by each method and contribution rate (CR) of each
method in comparison with local search. Here CR implies the relative cost reduction effect normalized by the
result of LS. We selected the best value of objective function after parameter tuning. Moreover, number of itera-
tion is empirically determined to be 500. It was the value enough to find the best value in all the cases. Figure
4(a), Figure 4(b) shows that the optimal operations obtained by each method in each case. In all the cases, gas
boiler is not used in the best operations, which is attributed to the assumed scenario where hot water demands
don’t have rapid variations. Figure 4(a) shows that the operation planed by proposed method (MTS) avoids lo-
cal optimal solutions; on the other hand, other methods misguide the operations into local optimal solutions.
Figure 3. Flowchart of proposed method (N: Parameter [-], IMAX: Maximum number of iteration).
Table 4. Summation of electricity demand and hot water demand in each season.
Hot Water Demand Large Midd le S ma ll
Seas on Summer Midd le
Seas on Winter Summer Middle Season Winter Summer Middle
Seas on Winter
Electricity Demand [kWh] 36.21 38.36 54.80 29.91 31.34 57.2 33.61 32.92 37.2
Hot Water Demand [L] 12.09 34.72 46.52 9.52 13.71 37.91 0.00 11.28 20.54
S. Nomoto, T. Kumano
279
(a)
(b)
Figure 4 . Optimal operations obtained by each method. (a) Case 1, Summer, (Large); (b) Case 2, Summer, (Middle).
Table 5. As s umed ramping rate constraints in each case.
UP
P
[k W/0.5h]
DOWN
P
[k W/0.5h]
Case 1 (harsh case) 0.1125 0.2250
Case 2 [7] (standard case) 0.2250 0.4500
Table 6. Dail y operational cost (DOC) obtained by each method and contribution rate (CR) of each method (Case 1).
Hot Water Demand Large Midd le S ma ll
Seas on Summer Middle Season Winter Summer Middle Season Winter Summer Middle Season Winter
DOC (LS) [yen] 504.05 532.66 760.89 417.14 430.87 795.29 469.30 455.07 514.08
DOC (TS) [yen] 504.52 524.84 752.44 413.80 427.01 787.32 466.83 450.17 506.43
DOC (MLS) [yen] 504.36 524.58 756.34 414.97 428.24 789.74 468.37 450.49 507.40
DOC (MTS) [yen] 503.78 524.53 752.74 413.76 427.01 787.01 466.88 450.17 506.38
CR (TS) [%]0.09 1.47 1.11 0.80 0.89 1.00 0.53 1.08 1.49
CR (MS) [%] 0.06 1.52 0.60 0.52 0.61 0.70 0.20 1.01 1.30
CR (MTS) [%] 0.05 1.53 1.07 0.81 0.89 1.04 0.52 1.08 1.50
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Table 7. Daily operational Cost (DOC) Obtained by each method and contribution rate (CR) of each method (Case 2).
Hot Water Demand Large Midd le S ma ll
Seas on Summer Middle Season Winter Summer Middle Season Winter Summer Middle Season Winter
DOC (LS) [yen] 503.76 523.60 751.37 412.95 428.15 786.21 466.27 449.16 506.21
DOC (TS) [yen] 503.32 523.72 751.46 413.32 427.48 786.21 466.27 449.16 506.41
DOC (MLS) [yen] 503.76 530.82 752.67 416.10 430.87 786.10 468.83 455.04 506.25
DOC (MTS) [yen] 503.38 523.72 751.46 413.38 427.48 786.21 466.27 449.16 506.41
CR (TS) [%] 0.090.020.010.09 0.16 0.00 0.00 0.000.04
CR (MS) [%] 0.001.380.170.760.63 0.010.551.310.01
CR (MTS) [%] 0.090.020.010.09 0.16 0.00 0.00 0.000.04
5. Conclusions
This paper proposes an optimal operation planning method based on tabu search for residential PEFC-CGS.
From the simulation results of case 1, the efficacy of MTS and tabu search was confirmed about 1 [%]. In addi-
tion, the results of case 2 shows tabu search and MTS don’t contribute to the reduction of daily operational cost
in many conditions. This result attributes to the restriction of the search to avoid the trap into local optimal solu-
tions. In case 2, the search along output power axis proceeds more easily in comparison with case1. Thus, it can
be considered tabu search and proposed method adversely guide the search into local optimal solutions.
In this paper, we disregard hot water for disposal because on only daily operation planning is considered.
However, disposal water is clearly wasteful for the operation. In near future, we plan to study the operation
planning for residential PEFC-CGS considering hot water for disposal to plan more practically.
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