development of optimization methods for operating...

加藤研究室・大岡研究室・菊本研究室Kato Lab., Ooka Lab., and Kikumoto Lab.

Keywords: Batteries, Thermal energy storage, Heat source machine, Optimal control, Artificial intelligence, Annual optimisation, District heating and cooling, Heat-sharing network

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It is hard to be used in complex systems2

Research objectives

Development of optimization methods for operating energy systems in buildings and districts

What is “operating optimization”?

It is to decide following issues:

1) Which machines should be worked?

2) When start and stop the machines?

3) How much heat should be generated?

1

It is not difficult to be applied to a simple system though,…

Building energy system District heating and cooling

What should we do?

1) Development of optimization methods for complex system

2) Incorporation of the methods in practical use

3

Development of optimization methods4

• Significant functions of the methods

1) Rapid calculation for real-time controls

2) High accuracy of a given result

3) Adaptability

i. Un-limitation of machine’s configurations

ii. User friendly to set some parameters

iii. Incorporation of unsteady calculations

Key technology: Artificial intelligence

Artificial intelligence, especially metaheuristic

optimization methods and neural networks, has

required characteristics mentioned above.

We focused on 𝜀DE-RJ(epsilon constrained differential

evolution with random jumping) in this study.

5Boiler

Boiler

CR

CR

AR

ART

E

S

BoilerT

E

S

CR

CR

AR

AR

T

E

S CHP

CHP

*TES: Thermal energy storage

*CR: Centrifugal refrigerator

*AR: Absorption refrigerator *CHP: Combined power and heat

Cooling

Heating

Hot water

Electricity

ex)



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Optimization method

What is 𝜀DE-RJ (Epsilon differential evolution with random jumping)?

Decis

ion v

ariable

1

Decision variable 2

Feasibledomain

1) Initialization of 𝜀(=1)

2) Calculation of constraint violation

(𝜑) and objective function (𝑓)

3) Replacement of individuals by

comparison of 𝜑 or 𝑓 as follows:

i) Comparison of 𝑓𝑖𝑔

and 𝑓𝑖𝑔+1

when 𝜑 < 𝜀.

ii) Comparison of 𝜑𝑖𝑔

and 𝜑𝑖𝑔+1

when 𝜑 ≥ 𝜀.

6) 𝜀 decreases exponentially

7) Return to 1) Conceptual diagram of ε constraint method

Differential evolution (DE)

Epsilon (𝜀) constraint method

+

Random jumping (RJ)

+Individual

-100 -100 0 100 100 150 150 400 200 370

0 -100 -100 50 150 100 300 500 350 250

Schedule of TES Schedule of machine No.1

Time (h)

Output

(kW)

Charge

Discharge

1 2 3 4 5 1 2 3 4 5

TES

100

200

Demand

-100Machine No.1

Machine No.2

400

1. Initialization: Individuals (𝑁𝑝𝑜𝑝 = 100) is randomly generated

2. Evaluation of each individual

3. Create new individuals by mutation and crossover methods

1) Iteration of individuals, 𝑥𝑖(𝑖 = 1,… ,𝑁𝑝𝑜𝑝)

2) Selection of two individuals (𝑥𝑚, 𝑥𝑛(𝑚 ≠ 𝑛 ≠ 𝑖))

3) Donor individual: 𝑣𝑖𝑔+1

= 𝑥𝑖𝑔+𝑀 𝑥𝑚

𝑔− 𝑥𝑛

𝑔, 𝑀: mutation rate(=0.5)

4) Crossover:

𝑥𝑖𝑔

𝑅𝑎𝑛𝑑 0.23 0.87

0.78 0.23

𝑣𝑖𝑔+1 0.82 0.23

Crossover rate=0.7

𝑥𝑖𝑔+1 0.82 0.87

The same values

Replace by

uniformly

random number First

variable

Second variable

0

𝑥𝑚𝑡

𝑥𝑛𝑡 𝑥𝑖

𝑔

𝑣𝑖𝑔+1

×𝑀

(Donor)

Search a solution

Solve constraints

Avoid local optimum

Applied random jumping

Algorithm of DE and RJ

Problem formulation

Algorithm of 𝜀 constrained method




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Optimal operation of complex energy system

Objective function: daily operating costs

Energy system configuration

Hot waterdemandWater

Boiler

GAS

DC/DCElectricitydemand

GridPV

Secondarysystem

Lowerside (80)

Higherside (85)

83

75

Battery

DC/AC

DC/DC

Power conditioner

CGSCoolingTower

CoolingTower

500 m2

12

12

12

127

7

7

7

88

88

83

20

12

Secondarysystem

7

CoolingTower

Lower side (7) Higher side (12)

127

HRAR

AR

AHP1

AHP2

TR

-10

0

10

20

30

40

50

-200

0

200

400

600

800

1,000

0 2 4 6 8 10 12 14 16 18 20 22

(yen

/kW

h)

(kW

h)

Time (h)

The price of purchased elec.

The price ofsold elec.

CGS to ED

G to ED

Charging elec. B to EDPV to ED

Remaining B ED

-30

-10

10

30

50

70

90

-3,000

-1,000

1,000

3,000

5,000

7,000

9,000

0 2 4 6 8 10 12 14 16 18 20 22

(yen

/kW

h)

or

(yen

/m3

)

Time (h)

Remaining TES

CD

Charging thermal energy

TR

AR

HRAR

AHP1

AHP2

(kWh)

-20

0

20

40

60

80

100

120

-200

0

200

400

600

800

1,000

1,200

0 2 4 6 8 10 12 14 16 18 20 22

(yen

/kW

h)

or

(yen

/m3

)

(kW

h)

Time (h)

The priceof gas

RemainingTESh

HWD

Charging thermal energyDischarging thermal energy

CGS to HWD

BB

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 2 4 6 8 10 12 14 16 18 20 22

Part

ial l

oad

rat

e (-

)

Time (h)

AHP2

AHP1

❖ Although the number of decision variables was 336 with nonlinear

configuration, computation costs was just 6 min on an ordinal PC.

❖ Powerful advantage: computational complexity of 𝜀DE does not

depend on the number of decision variables.

❖ 𝜀DE could incorporate variations of water temperature.

❖ CHP worked during daytime because of high electricity costs.

❖ Partial load rate of AHP1 and AHP2 were almost the same.

❖ Above result was optimal solution based on the mathematical

theorem such as Lagrange multiplier method.

Optimal operation: Electricity system Cooling system Hot water system CHP Partial load rate of AHPs

Benefits: rapid calculation of 𝜀DE1

Optimal operating schedules2



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3

4

5

6

7

8

9

3 4 5 6 7 8 9

MLRR2=0.927

3

4

5

6

7

8

9

3 4 5 6 7 8 9

m-PSOR2=0.981

3

4

5

6

7

8

9

3 4 5 6 7 8 9

CFR2=0.995

3

4

5

6

7

8

9

3 4 5 6 7 8 9

ANNR2=0.997

モデル温度 (ºC) モデル温度 (ºC)

モデル温度 (ºC) モデル温度 (ºC)

予測温度

(ºC

)予測温度

(ºC

)

予測温度

(ºC

)予測温度

(ºC

)


Optimization of a district cooling system using ANN and 𝜀DE-RJ

PlantOffice 1

Office 2 Hospital

HotelCommercial 1

Commercial 2

Pipe 1

Pipe 2 Pipe 5

Pipe 3

Pipe 4

Pipe 6

50

m Pipe 7

50m

Modeling

Office 1

Office 2

Commercial 1

Commercial 2

Hospital

Hotel

Conceptual diagram of a district

Location of buildings

CR1

AR1

ASHP2

GHP1

GHP2

CR2

CR3

ASHP1

Pipe 1

AR2

Pipe 1

Thermal energy

storage

Energy system configuration

4 °C4 °C

4 °C

14 °C

4 °C～6 °C

Comparison of results of each regression model

TES operations

• Neural network is used to predict bottom temperature, the same meaning as outlet temperature of TES, to reduce computation costs instead of physical model of stratified TES. 19

蓄放熱なし

Maximum stored

energy, 𝐻𝑀(kWh)

Stored energy at

time step t, 𝐻𝑅𝑡 (kWh)

Bottom temperature, 𝑇20𝑡 [°C]

Input data No1.

Input data No.2

Output data

00.30.60.91.21.51.82.12.42.73

0 4 8 12 16 20 24

CR1 CR2 CR3 AR1 AR2

ASHP1 ASHP2 GHP1 GHP2

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0 4 8 12 16 20 24

Time (h)

Prim

ary

energ

y b

ased C

OP

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0 4 8 12 16 20 24

Time (h)

(a) Case 1 (b) Case 2

Comparison of COP in two cases

Conventional operation Optimal operation

Target [°C] Target [°C]

Target [°C] Target [°C]

Pre

dic

ted [°C

]

Pre

dic

ted [°C

]

Pre

dic

ted [°C

]

Pre

dic

ted [°C

]

Sto

red e

nerg

y [

kW

h]

Time [h]

development of optimization methods for operating...

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