Dynamic Pricing Model and Algorithm
in
Energy Intensive Enterprise Microgrid
CONCLUDING REPORT
Systems Engineering Institute
Xi’an Jiaotong University
Dec 9 2011
2
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4
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Abstract
The dynamic pricing problem in microgrid for energy intensive enterprise (EIE) is
studied in this project. We focus on a microgrid which has distributed energy
resources, energy storage devices and utility electricity. It has particular power
consumption characteristic: surge-type load caused by batch production, complicated
time-coupling and space-coupling constraints of end users.
The scope of work is as following:
1) Analysis of elastic power demand and rigid power demand in EIE microgrid,
time coupling relationship analysis among production units;
2) Analysis of how real-time power cost is affected by change of electrical load of
production units;
3) Dynamic pricing models considering enterprise power purchase cost,
enterprise generating cost, effect of production units on real-time power cost
and other factor;
4) By typical case study, put forward some reference ideas about management of
electrical utilization and generation for EIE microgrid.
Base on the research, practical models for describing influence of price maker and
price taker to real-time power cost are built. We also establish three dynamic pricing
mechanism considering different types of production units’ electrical utilization, unit
output, energy storages and time coupling relationship among production units. And a
systematic guiding ideology about management of electrical utilization and generation
for EIE microgrid is given.
I
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
II
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
CONTENTS
1
2
3
4
5
6
7
Abstract .................................................................................................................. I
Background ............................................................................................................ 1
1.1 Background ................................................................................................. 1
1.2 Dynamic Pricing Problem in Industrial Microgrid...................................... 3
1.3 Target ........................................................................................................... 3
1.4 Method Introduction .................................................................................... 4
Symbol Description ............................................................................................... 4
The Analysis of Dynamic Pricing Problem ........................................................... 6
3.1 The Participants of Dynamic Pricing Mechanism ....................................... 6
3.2 Some Issues Involved .................................................................................. 6
The Solution ........................................................................................................... 7
4.1 The Operational Mode of Dynamic Pricing Mechanism ............................ 7
4.2 The Analysis of Dynamic Pricing Mechanism ............................................ 8
4.3 Principles to follow in solution ................................................................... 8
4.4 Problem Decomposition and Analysis ........................................................ 8
Response Analysis of Power Consumption and Generation .................................. 9
5.1 Classification of Electricity Consumption Equipments and Storage Devices
..................................................................................................................... 9
5.1.1 Classification of Batch Production Equipment ................................. 9
5.1.2 Classification of Continuous Production Equipment...................... 10
5.1.3 Classification of Storage Equipments ............................................. 10
5.2 Power Consumption Optimization Model ................................................. 11
5.2.1 Batch Load Curve Analysis ............................................................ 11
5.2.2 The Load Management Model ........................................................ 12
5.3 Power Generation Optimization Model .................................................... 13
5.4 Use Case .................................................................................................... 14
The Electricity Pricing Formation Mechanism .................................................... 17
6.1 The Brief Introduction of Real-time Cost Analysis................................... 17
6.2 Optimal Power Generation Strategy.......................................................... 17
6.2.1 The Cost Analysis of Generation Strategies ................................... 17
6.2.2 The Formulation of Optimal Power Generation Strategy ............... 18
6.3 Pricing Formation Mechanism for Energy Intensive Enterprise Microgrid ..
................................................................................................................... 20
6.3.1 Real-time Cost Based Price Formation Mechanism ....................... 20
6.3.2 Gradient Information Based Price Formation Mechanism ............. 22
6.3.3 Heuristic Method Based Price Formation Mechanism ................... 24
Test Result of Typical Cases and the Analysis ..................................................... 27
7.1 Cases Introduction ..................................................................................... 27
7.2 Pricing Formation Mechanism Based on Real-time Cost ......................... 29
7.3 Pricing Formation Mechanism Based on Gradient Information ............... 31
III
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
7.4
7.5
Pricing Formation Mechanism Based on Heuristic Information ............... 33
Expended Test and the Analysis ................................................................ 36
7.5.1 Change the Batch Number: ............................................................. 36
7.5.2 Analysis of Cost-saving .................................................................. 40
7.5.3 Change the Range of Units Output ................................................. 42
8 Conclusion ........................................................................................................... 53
9 The Description of General Dynamic Pricing Mechanism in Microgrid ............ 55
Reference .................................................................................................................... 58
Equation Chapter 1 Section 1
IV
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
1 Background
1.1 Background
Generally, dynamic pricing refers to a type offer or contract by a provider of a
service or supplier of a commodity, in which the price depends on the time when the
service is provided or the commodity is delivered. In electricity market, dynamic
pricing, as a demand response, provides customers with time-varying prices that reflect
wholesale market costs. Dynamic pricing rate fluctuations follow the real time cost of
electricity. The objective of these programs is to flatten the demand curve by offering a
high price during peak periods and lower prices during off-peak periods. Most
common rates are Time of Use (TOU), Critical Peak Pricing (CPP), and Real Time
Pricing (RTP).[1]
The power supply pattern of industries without self generation power plant is
shown in Figure 1-1. Use less energy during peak hours, or move the time of energy
use to off-peak times under a specified electricity tariff like TOU implemented by the
utilities do help industries reduce their electricity costs.
The
Utility
Demand Side
Energy
management
section
User 1
Figure 1-1
User
M
User 2
without self generation power plant
Electricity distribution
1
0.9
0.8
Price/￥ /kwh
0.7
0.6
0.5
0.4
0.3
0.2
Price of buying electricity
Price of selling electricity
0.1
0
0
20
40
Figure 1-2
60
80
Time/10min
100
120
140
the TOU tariff given by utility
Most energy intensive enterprises (EIEs) have self generation power plant. Based
1
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
on satisfying production related objectives, reducing electricity costs becomes an
important objective for production scheduling in EIEs. Such an EIE integrates power
generation, power consumption and energy storage into a unified whole, and become
an enterprise microgrid in Figure 1-3. Also, the structure is highly coupled with a
multi-energy system which is formed by production processes and other energy
medium.
The
Utility
Microgird
Generator
1
Generator
Generator
…
N
2
Energy
management
section
User 1
Figure 1-3
User 2
User
M
…
the power supply pattern of microgrid
For such an EIE microgrid, electricity cost is concerned with prices of buy/sell
electricity from/to the utility, generating cost and load demand in production progress.
The total cost dynamically changes the power demand and the power generation, and is
inconsistent with tariff implemented by the utility shown in Figure 1-4. In order to
achieve the purpose of saving energy costs, the EIE can establish a price mechanism to
guide the production scheduling. Through dynamic pricing (DP) mechanism, energy
management section uses an internal electricity pricing strategy to release price and to
guide the behaviors of production units to reduce energy cost.
4
7.5
The Cost Curve
x 10
7
6.5
Cost/￥
6
5.5
Gas addition
50KNm3/h
Gas addition
100KNm3/h
5
Gas addition
150KNm3/h
4.5
4
3.5
Fixed price
TOU
0
Figure 1-4
2
10
20
30
40
Time/h
50
60
70
80
the electricity consumption cost curve under different gas addition
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Dynamic pricing has not applied practically in industrial microgrid. At present, the
analysis of demand response behavior and the analysis of relationship between power
consumption and production schedule are still vacancies. A rational price signal which
can guide the demand response is expected. And a dynamic pricing mechanism in
industrial microgrid is needed.
1.2 Dynamic Pricing Problem in Industrial Microgrid
The dynamic pricing problem in microgrid for EIE is studied in this project. We
focus on a microgrid which has distributed energy resources, energy storage devices
and utility electricity. It has particular power consumption characteristic: surge-type
load caused by batch production, complicated time-coupling and space-coupling
constraints of end users. The focus of the problem is shown in Figure 1-5
Figure 1-5
focus of dynamic pricing problem in microgrid for EIE
There are several requirements for a rational dynamic pricing in microgrid for EIE.
The dynamic price should bring cost benefit for both enterprise and each production
unit. For the energy management section, the break even is needed. And the dynamic
price should have usability for manufacture management and frontline workers.
Compare to the utility, the dynamic pricing problem in EIE microgrid has some
unique features:
a) Self generation power plant is connected to the microgrid. Surge-type loads caused
by batch production are common seen in EIE. And the EIE microgird cannot island
from the grid;
b) Some EIE has by-product storage devices like gas holder. The by-products like
blast-furnace gas is used for power generation. By-product scheduling is coupled
with power generation scheduling and production scheduling;
c) Production units have to be rational and obey the short term scheduling of
manufacture management. And the load scheduling of production units should
satisfy production related limitations.
d) Power demand of production units are usually time coupling and space coupling.
Each unit’s fine-tuning range of power demand is limited.
1.3 Target
3
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
The target of this project is forming a dynamic pricing mechanism in enterprise
microgrid which including:
a) Dynamic pricing mechanism;
b) Real-time or lead-ahead price signals for demands response in microgrid;
c) Possible energy cost reduction with the proposed pricing mechanism and rational
demand response;
1.4 Method Introduction
In this project, there are two method play important roles. The power
consumption optimization model are built and the mixed integer linear programming
(MILP) is used for finding the optimal solution. And the linear programming (LP) is
used for the power generation optimization model. Iterative method, heuristic method
and gradient method are also been used in project.
LP is a mathematical method for determining a way to achieve the best outcome
(such as lowest cost) in a given mathematical model for some list of requirements
represented as linear relationships. Linear programming is a specific case of
mathematical programming. More formally, linear programming is a technique for
the optimization of a linear objective function, subject to linear equality and linear
inequality constraints. [2]
If only some of the unknown variables are required to be integers, then the
problem is called a MILP problem.[3] Equation Chapter (Next) Section 1
2 Symbol Description
Indices:
m
n
index of batch production equipments, m  1, 2,
index of power generators, n  1, 2, , N .
k
index of time periods, k  1, 2,
j
index of batch equipment number, j  1, 2,
i
index of iteration number, i  1, 2,
length of each time period.

,M .
,K .
, Jm .
,I
Parameters:
d kbase
base load at time period k
kbuy , ksell
electricity price of buy/sell from/to the utility at time period k,
buy ,k  sell ,k  0
4
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
kgene
electricity price of self generation power plant at time period k.
sm, j , sm, j
fine-tuning range of start time sm , j
pn
maximum allowable ramp rate of
power output rate of power
generator n.
pn , pn
maximum and minimum allowable power output rate of power
MD
generator n
maximum demand
V ,V
maximum and minimum allowable fuel-storage level at time period k
Jm
total batch number of batch production equipment m in K time periods
Tm
batch time of batch production equipment m
dcm  d m ,k 
load characteristic value of batch production equipment m, where
d m,,k  0,1, 2,
, Tm .
Variables:
pn ,k
i
average power output of power generator n at time period k in i-th
iteration
d mi,k
average load of batch production equipment m at time period k in i-th
iteration
ki 
internal electricity price for production units in i-th iteration
vk
fuel storage quantity at time period k
vk
available fuel amount for power generation flow into the storage
device at time period k
vk
fuel consumption for power generation at time period k
ve , k
emission amount of gas holder at time period k
sm , j , em , j
start/stop time of j-th batch of batch production equipment m.
Equation Chapter (Next) Section 1
5
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
3 The Analysis of Dynamic Pricing Problem
3.1 The Participants of Dynamic Pricing Mechanism
In the dynamic pricing problem, there are five important participants, including
production units, self generation power plant, the utility, energy management section.
All those participants can be classified into 3 classes: power demander, power
supplier and energy management section.
The production units can be regarded as the power demander. They need to finish
their daily task of production, and also can do some scheduling for production
processes. The purpose of production scheduling is to minimize the production time
and costs, by telling a production facility when to make, with which staff, and on which
equipment. The production units aim to guarantee the production, maximize the
efficiency of the operation and reduce costs, including energy consumption cost.
Self generation power plant and the utility are the power suppliers. Self generation
power plant is those power plants which operate independent of wheeling to the utility.
The EIE microgrid needs to buy electricity from the utility under a certain tariff while
self generation cannot meet its requirement. Thus, one of the responsibilities for self
generation power plant is minimizing the total electricity cost of enterprise.
The energy management section is the core participant of this mechanism. In
position of the entire enterprise, the energy management section needs to use the
price signal or scheduling method for minimizing energy cost, including generation
cost, net electricity cost, penalty fees for gas emission, and energy storage fees, et al.
The Utility
Self Generation
Power Plant
Power
message
Tariff
Price signal/
direct control
Energy Management Section
(Dynamic Pricing Mechanism)
Price
Load
message signal
Production
unit
Production
unit
……
Production
unit
Production units organize production considering
electricity cost information
Figure 3-1
the participants of dynamic pricing mechanism
3.2 Some Issues Involved
6
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
In a general context, the key points need to be focused on in dynamic pricing
problem of industrial microgird are as follows:
a) Production processes; the analysis of production processes helps us definite
the time coupling and space coupling among processes and the load
characteristics.
b) Division of departments responsibilities; the division of department
responsibility definite the role of various departments and the they need to
offer.
c) Production scheduling; when the dynamic pricing is used, the production
scheduling helps to find out what kind of production plan can help the
process unit minimize its cost.
d) Generation scheduling; when the dynamic pricing is used, the generation
scheduling helps to find out what kind of generation plan can help the whole
enterprise minimize the total cost.
e) Dynamic pricing method; the research on dynamic pricing method help us to
make a reasonable internal tariff. And this tariff is suitable for a price signal
and convenient for internal accounting.Equation Chapter (Next) Section 1
4 The Solution
4.1 The Operational Mode of Dynamic Pricing Mechanism
In order to realize the dynamic pricing in industrial microgrid, a dynamic
pricing mechanism is proposed. The operational mode of proposed dynamic
pricing mechanism is shown in Figure 4-1.
Energy Intensive Industrial Microgrid
Production Management
Department
Initial feasible region
for production scheduling
Price
Production
Unit 1
Production
Unit 2
Figure 4-1
……
Load
Message
Production
Unit M
The Utility
Energy Management
Section
Price or
Power
Direct Control Message
Price
Load/Power
Message
Autonomous
Power Plant
the operational mode of dynamic pricing mechanism
According to the initial feasible region of production scheduling provided by the
production management section the energy, the energy management can formulate a
dynamic price based on the price formation mechanism, though the analysis of the
real-time electricity cost and the utility tariff, et al.
7
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Then the energy management section releases the dynamic electricity price signal
to all users, so that users can perceive the current electricity costs and predict the
influence of its electricity variation on their own real-time electricity cost. Based on
the guidance of dynamic price, the mechanism encourages users to do power
management spontaneously. And it lets the users to organize their production schedule
according to the quantity, the rigidity of tasks and the electricity cost. And
corresponding load messages are sent to energy management section. It helps the
section give a price or direct control to the self generation power plant based on a
certain generation strategy.
The energy management section can get the power consumption of each user. A
user m should pay its electricity fee according to the internal settlement cost, which is
K
computed
by
SCm    k  d m ,k  .
So
the
payment
of
all
users
is
k 1
M
K
SC    k  d m ,k  , which is equal to the total electricity cost of enterprise.
m 1 k 1
In this way, every user is trying to reduce their cost. As a combination of
individual users and generators, EIE can reduce the total electricity costs.
4.2 The Analysis of Dynamic Pricing Mechanism
4.3 Principles to follow in solution
There are two principles to follow: cost-benefit for enterprise and usability for
operators.
The cost-benefit principle means to reduce electricity costs of energy intensive
industrial micro grid by encouraging production units use less energy during peak
hours, or move the time of energy use to off-peak times under a specified electricity
tariff like TOU. And the real-time electricity cost analysis provides assessment
criteria.
The usability principle stands for the internal dynamic price mechanism should be
easy to implement, and be simple for operators. That includes two aspects: TOU tariff
is more suitable for giving industrial users a relatively stable price to rescheduling their
production under a limited fine-tuning range; and by modeling customer behavior in
price mechanism, the internal competition and optimization can be realized and set a
final price for users as an internal price which is not a actual competition among
production units. It releases the burden of production units in dynamic pricing
mechanism.
4.4 Problem Decomposition and Analysis
The dynamic pricing problem in industrial microgrid can be decomposed into
8
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
three parts: real-time analysis, electricity characteristic of equipments, and the price
formation mechanism.
In order to minimize the cost of the enterprise, the real-time cost should be
analyzed to find out the composition and proportion of the cost. At the same time, the
classification and analysis of equipments electricity characteristics are carried on.
Based on the two steps above, the power consumption optimization model can be
given which try to find out the optimal solution of minimizing the process units cost.
By the power generation optimization model, we can get the optimal generator units
output curve for minimal cost of enterprise. The optimal power consumption/
generation strategy is also needed which decide the generation strategy in different
utility tariff and power consumption situation. At last, forming a useable dynamic
price is the final goal, so the price formation mechanism should be designed.
The relationship among all parts of the dynamic pricing problem is shown as
follow:Equation Chapter (Next) Section 1
Dynamic pricing
problem
Real-time cost
analysis
Analysis and classification of
equipment power consumption
Power consumption
optimization model
Figure 4-2
Power generation
optimization model
Price formation
mechanism
Optimal power consumption/
generation strategy
all parts of the dynamic pricing problem and their relationship
5 Response Analysis of Power Consumption and
Generation
5.1 Classification of Electricity Consumption Equipments and
Storage Devices
5.1.1 Classification of Batch Production Equipment
Batch production equipments are related to the start time, the end time, the energy
consumption per unit of time or the batch time. So batch production equipments can
be divided into several types. But in these types, there are only 2 types existing.
TABLE 5-1
classification of batch production equipment
9
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Batch time
Energy
consumption
per unit of time
adjustable
nonadjustable
adjustable
Type 1 ()
()
nonadjustable
()
Type 2 ()
Type 1: The start time of each batch, the batch time, and the energy consumption
per unit of time are adjustable. For example, the electric furnace.
Type 2: The start time of each batch is adjustable; the batch time and the energy
consumption per unit of time are nonadjustable. For example, hot rolling and cold
rolling.
5.1.2 Classification of Continuous Production Equipment
Continuous production equipments are related to the start time, the end time, and
energy consumption per unit of time. Then continuous production equipments can be
divided into several types. But in these types, there are only 2 types existing.
TABLE 5-2
classification of continuous production equipment
Energy consumption
per unit of time
Begin time
adjustable
nonadjustable
()
Type 4 ()
Type 3 ()
()
and end time
adjustable
nonadjustable
Type 3: The start time and the end time are nonadjustable; the energy
consumption per unit of time is adjustable. For example, the hot rolling and cold
rolling. For example, the generator units.
Type 4: The start time and the end time are adjustable; the energy consumption
per unit of time is nonadjustable. For example, the blast furnace blowing.
5.1.3 Classification of Storage Equipments
Storage cost is related to storage time and inventory level. And storage time and
inventory level are functions of inflow, outflow and existing inventory.
Then storage equipments can be divided into 4 types. But there are only 2 types
existing.
TABLE 5-3
Classification of intermediate storage devices due to composition of storage cost
Inventory level
Storage time
related
10
related
unrelated
Type 1 ()
()
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
unrelated
Type 2 ()
()
Type 1: Storage cost is related to storage time and inventory level. For example,
soaking pit.
Type 2: Storage cost is only related to inventory level. For example, gasholder.
5.2 Power Consumption Optimization Model
Participant of dynamic price mechanism is achieved by the optimization of
equipment electricity program and the optimization of self generation power plant.
5.2.1 Batch Load Curve Analysis
The load curve is directly related to production process. Production equipments
can be divided into two types: batch production type, continuous production type.
Unlike the quasi-periodicity and slow-variations load characteristics of main grid, the
power consumption curve of EIE has the characteristics of serious surge. And the
surge characteristic is caused by start/stop operation of large batch type production
equipments which consumes a lot of electric energy. Thus, the total load of EIE can
be decomposed into two parts including base load and batch load of large batch type
production equipments.
M
Dk   d m,k d kbase
(5-1)
m 1
Operating parameters and sequences of the batch process are shown in.
Batch time
1
2
em , j
sm , j
sm , j
em , j
sm , j
T
em , j
Time fine-tuning range
Power demand
Figure 5-1
operating parameters and sequences of the batch process
The energy consumption of batch production equipments can be simulated by
variable load factor. The load factor is the ratio between real load and rated load.
Then the energy consumption of batch production equipments can be described as
bellow:
11
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Energy consumption
k-2
k-1
k
k+1
k+2
Time
It is possible that some batch production equipments may have several load
curves. Then these equipments can be divided into several virtual equipments. These
several virtual equipments have these own load curves.
5.2.2 The Load Management Model
Objective Function
The purpose of the load management is that by adjusting the production plan
minimize the electricity cost of production.
The objective is minimizing the electricity cost of production, formulated as
bellow:
 Tm , j
 K
min Cm     dcm  d m, j    com  sm, j  d m, j   CRm, j    kcom  d kbase (5-2)

 k 1
j 1  d m , j 1

Jm
Constraint Condition
The start of the j-th batch should be after the stop of the (j-1)-th batch for the mth
equipment.
sm, j 1  Tm  sm , j
(5-3)
The last batch of the mth equipment should be stop previous to the end of one
day.
sm , j  K  ( J m  j  1)  Tm
(5-4)
The start of the jth batch of the mth equipment should be t time periods after the
start of the jth batch of the mth equipment.
sm ', j '  Tm '  tm ' j ',mj  sm, j
(5-5)
where, tm ' j ', mj reflect factors like logistics speed between upstream and
downstream equipments or timing constraints among batch production tasks of
virtual equipments.
12
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Start time sm , j of batch j of production equipment m should be under fine-tuning
time range:
sm, j  sm, j  sm, j
(5-6)
where, sm, j , sm, j can also be used to describe timing constraints among batch
production tasks of virtual equipments.
Model solution
The mixed integer linear programming (MILP) is used for model solution.
5.3 Power Generation Optimization Model
The purpose of the power generation model is minimizing the electricity cost at one
load curve.
Objective Function
The real-time variable electricity cost at time period k is represented by Ck , and is
composed of fuel cost for self generation Gk and net electricity cost of buy/sell
electricity from/ to the utility Bk , formulate as bellow:
 Gk  Bk
(5-7)
Gk   f n  pn ,k 
(5-8)
kbuyQk , if Qk  0

Bk   0, if Qk  0
 sellQ , if Q  0
k
 k k
(5-9)
min Ck
N
n 1
Qk  Lk  Pk
(5-10)
where, Qk represent the net amount of power flow buy from utility at time
period k, Lk represents the average total load of enterprise during time period k , Pk
represent the average total power output of power generator during time period k,
f n  pn ,k  represent the fuel cost function of power generator n during time period k.
Constraint Condition
Minimum/maximum generation output constraints:
13
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
pn  pn , k  pn
(5-11)
pn ,k 1  pn ,k  pn
(5-12)
Ramp rate of generation output:
Initial and terminal generation output:
pn,0  pn*,0 , pn, K  pn*, K
(5-13)
Balance between fuel supply and fuel demand for generator:
vk  vk 1  vk  vk  ve,k

(5-14)






v  vk 1  vk  V , if vk  vk 1  vk  V  0
ve,k   k
0, else


(5-15)
Capacity of fuel storage device:
V  vk  V
(5-16)
v0  v0* , vK  vK*
(5-17)
Initial and terminal fuel storage:
Model solution
The linear programming (LP) method is used for model solution.
5.4 Use Case
To illustrate the model, a case study for an iron and steel plant is conducted.
For iron and steel industries, the electricity costs about 30% of the total
production costs. In the context of increasing electricity prices and the introduction of
time varying electricity rates by utilities, iron and steel plant can fine-tune their
production operations schedule and schedule self generator units to reduce their
electricity costs.
The iron and steel enterprise being studied include three main factors that
influence the real-time electricity costs: self gas-steam combination circulation
generating unit (CCPP) with COREX furnace gas, time-of-use (TOU) tariff,
production electricity loads.
The production-gas-power correlation structure is shown as Fig. 1, where, the
white arrow indicate the production processes, red arrows indicate electricity flow,
and green arrows indicate gas flow; LF furnaces for steel making and rolling mills for
medium plant production belong to the most highly energy intensive batch type
production equipments; And self CCPP generator using COREX furnace gas provides
14
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
electricity for production process together with grid, power exchange between grid
and enterprise is inevitable, electricity costs saving become a problem need to be
considered under TOU tariff.
Diffusion
Other Use
Gas
Holder
Oxygen
Making
COREX
Furnace
CCPP
Steelmaking
(LF Furnace)
Production Process
Medium Plate
Production
Electricity Flow
Grid
Gas Flow
Fig. 1 production-gas-power correlation structure
Parameter Setting and Related Data for Simulation
We consider power generation, power consumption and power-related storage
device in our use case study. Equipments and there parameters are list in Tab. I.
TABLE I.
No.
Equipments
EQUIPMENTS LIST AND PARAMETERS
Type
Parameters
1
LF furnace
Batch production
Power rating: 3000 (KW)
2
blooming mill
Batch production
Power rating: 3000(KW)
3
Finishing mill
Batch production
Power rating:5000 (KW)
4
CCPP generator
Continuous generation
Maximum output: 16945(KW)
Minimum output:8500(KW)
5
Gas holder
Storage device
Storage capacity: 500000(Nm3);
Lower limit: 160000(Nm3);
Gas price:0.5(￥/ Nm3)
Penalty of diffusion: 1(￥/ Nm3)
The average power demands over every 10-min interval are noted and their
variation is shown figure 2 for the batch time of LF furnace, blooming mill and
finishing mill.
15
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Load curve
18
Active power
Base load
17
16
Load/10000KW
15
14
13
12
11
10
9
8
0
50
100
150
Time/10min
Figure 5-2
Load cycles of batch load and base load
The power consumption optimization model can get the result as follow:
Load curve
18
After optimization
Before optimization
17
16
Load/10000KW
15
14
13
12
11
10
9
8
0
50
100
150
Time/10min
Figure 5-3
the load cycles before and after power consumption optimization
The power generation optimization model can get the result as follow:
After optimization generator output and load
18
Generators out
After optimization load
17
16
Load/10000KW
15
14
13
12
11
10
9
8
0
50
100
150
Time/10min
Figure 5-4
16
load cycles and power generation output curve after optimization
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Equation Chapter (Next) Section 1
6 The Electricity Pricing Formation Mechanism
6.1 The Brief Introduction of Real-time Cost Analysis
As we know, reducing the cost of whole EIE is one of the most important purposes
of our electricity pricing mechanism. When forming the dynamic electricity price, the
real-time cost must be fully used. And that makes the mechanism work at the
direction of decreasing power consumption cost for the whole EIE during iteration.
So analyzing the real-time cost of all kinds of equipments and the whole enterprise is
required.
Generally, power supply and demand are integrated in EIE microgrid. There are
generator units, electricity consumption equipments and energy storage devices in the
enterprise at the same time. The real-time costs in EIEs are related to the purchase/sale
price from the utility, the real-time output of self generation power units and the
internal real-time electricity load. Therefore, the electricity costs of EIEs are
time-varying.
The variable part of real-time electricity cost in EIE is variable cost, which includes
generation fuel cost and electric energy exchange cost. For iron and steel enterprises,
further influence factors of these variable costs are: output of generators, mixed
burning proportion of generators, electricity load, gas price, electricity purchasing
price, etc. These should be considered into the mathematical model.
We also investigate the influence of a factor’s variance on cost in EIEs. More
details about real-time electricity cost problem analysis, including the mathematical
model, are described in document:” Real-time electricity cost problem analysis in EIE
microgrid”.
6.2 Optimal Power Generation Strategy
According to the analysis above, power supply and demand are integrated in EIE
microgrid. That means there is an optimal power generation strategy for the power
generation. The strategy determines the power proportion of generation and buying
from utility, which attempts to minimize the power consumption cost. So the pricing
formation mechanism needs to contain this strategy.
6.2.1 The Cost Analysis of Generation Strategies
Considering the relationship between the load and units output, in a period k, the
generation has three strategies:
17
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Case A: pk  d k   k
Case B: pk  d k
(6-1)
Case C: pk  d k   k
Case A means the output is larger than the load at the k-th period. Case B shows
that the output match the equipments load well at the k-th period. And case C means
the units output is lower than the load. The three cases are shown in Figure 7-1.
Electrical
Quantity(KWh)
A
dk  k
B
dk
C
dk  k
Time Period(h)
Figure 6-1 the three cases of relationship between output and load
At a same time k, there are three kind of price: price for buying, price for selling
and the price for generation. The price for generation is denoted as kbuy , ksell and kgene .
The real-time cost function under three cases can be described as:
CkA  kgene  d k   kgene  ksell   k
CkB  kgene  d k
(6-2)
CkC  kgene  d k   kbuy  kgene   k
When the microgrid is in case A, generator output more power than need. The
real-time cost of the enterprise is the cost of generation, plus the profit of selling
electricity. When in case B, the real-time cost is only the cost of generation. And in
case C, the real-time is the cost of generation, plus the cost of buying electricity from
utility. Then we can formulate the strategy after the cost analysis under different price
level.
6.2.2 The Formulation of Optimal Power Generation Strategy
Based on the cost analysis of different generation strategies, we can get the cost
curve shown in Figure 6-2.
18
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Ck
CkC  kgene  d k   kbuy  kgene   k
CkA  kgene  d k   kgene  ksell   k
CkB  kgene  d k
k
Figure 6-2
cost curve in different strategies
Consider the relationship among the 3 kinds of price, kbuy , ksell and kgene , three
possible cases may happened, shown in Figure 6-3.
kgene
ksell
Case 1
kgene
kbuy
Case 2
Figure 6-3
kgene
k
Case 3
the relationship of three kinds of price
Then we can judge the minimal cost function, by the two figures above:
In case 1: kbuy  kgene , ksell  kgene , then min CkA , CkB , CkC   CkA .
In case 2: kbuy  kgene  ksell , then min CkA , CkB , CkC   CkB
In case 3: kgene  kbuy , kgene  ksell , then min CkA , CkB , CkC   CkC
In electricity market, time of use (TOU) tariff is a kind of most common tariff.
There are three general levels of TOU: peak price, valley price and flat price. Base on
the analysis above, in order to minimize the cost of entire enterprise, we can
formulate the optimal power generation strategy.
There are three situations, shown in Figure 6-4:
Situation 1: koff  peak  kgene , kgene  ksell , kpeak  kgene
The optimal strategy: power generation follows power load while peak time; less
power generation and buy more electricity from the utility while valley time.
Situation 2: koff  peak  kgene , kgene  ksell , kpeak  kgene
The optimal strategy: power generation follows power load all the time.
Situation 3: koff  peak  kgene , kgene  ksell , kpeak  kgene
The optimal strategy: power generation at full capacity.
So the generator needs to follow this strategy to get minimal total cost. And this
should be manifested in pricing formation mechanism.
19
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Situation
three
Situation
two
kgene
Situation
one
 peak
0
 sell
Figure 6-4
the 3 kinds of situation among TOU tariff and generation price
 off-peak
Price (￥)
6.3 Pricing Formation Mechanism for Energy Intensive Enterprise
Microgrid
In order to obtain appropriate internal price, we need to design a price formation
mechanism. The formed internal price can be treated as a signal to guide the user
adjusted their production plan for reducing the total cost of the enterprise.
6.3.1 Real-time Cost Based Price Formation Mechanism
As we know, reducing the cost of whole EIE is one of the most important purposes
of our electricity pricing mechanism. So the real-time cost can be used directly to
form a price. Based on the real-time cost analysis mentioned before, a real-time cost
based price formation mechanism has been designed. We also call it the basic
mechanism.
The basic mechanism has the iteration base on real-time electricity cost and
centralized power optimization of end users.
The steps of the price formation mechanism are as follows:
Step 1: the energy management section offers a initial price as an internal price at
will,

(0)
k
k  1, 2,
, K  , set i=1;
Step 2: under the i-th internal price, all production units optimize their electricity
consumption, to minimize their total power consumption cost, and get the d m ,k ,
i
M
K
d mi,k  arg min  C m i,k
m 1 k 1
 k i 1
(6-3)
Step 3: the self generation power plant does the centralized power generation
optimization, and get the optimal units output,
K
pm i,k  arg min  Cki   d mi,k ;
(6-4)
k 1
Step 4: using the generation cost, the cost of buying electricity and the total load,
compute the real-time energy consumption cost price k  , and
i
20
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
M
ki   Cki  /  d mi,k ;
(6-5)
m 1
Step 5: if the total cost and price in this iteration doesn’t satisfy the condition of
convergence:
 K i  K i 1  K i 
  Ck   Ck  /  Ck   C
k 1
 k 1
 k 1
,

i 
 i 1
max k  k
/
i 
k
(6-6)
 
then i=i+1, go to step 2.
Step 6: output and release the internal price k  as a dynamic price signal in
i
microgrid.
And the flow chart of this real-time cost based price formation mechanism is
shown in Figure 6-5.
Energy management section offers a initial
price k(0) k  1, 2, , K  set i=1
i  i 1
Electricity consumption optimization of
production units under internal price
M
K
d m ,k  arg min  C m ,k  k
i
i
i 1
m 1 k 1
Power generation optimization
of self generation power plant
K
pmi ,k  arg min  Cki   d mi,k ,
No
k 1
Compute the real time energy consumption
cost price
M
ki   Cki  /  d mi,k
m 1
Convergence?
Yes
Output the final
price
Figure 6-5
the flow chart of real-time cost based price formation mechanism
This mechanism has several advantages:
a) It manifests the important point of decreasing the total energy consumption cost
of the whole enterprise intuitively;
b) It doesn’t have special requirements to meet for initial price. The initial price can
be given at will.
21
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
And it also has several disadvantages:
a) Without using the historical , the iteration process of internal price is concussive,
and hard to reach convergence;
b) The final internal price is too weak to be used as a price signal;
c) The final internal price has rapid fluctuation during 24 hours, so that it’s hard for
practical use.
And all the features mentioned above will be analyzed and explained in case
study shown in next chapter.
6.3.2 Gradient Information Based Price Formation Mechanism
Because basic price formation mechanism has several obvious drawbacks, such as
the internal price is concussive and it’s difficult to use as a dynamic price. So this
RTP tariff mechanism 1 has been designed.
RTP tariff mechanism 1 is a kind of gradient information based price formation
mechanism. And it has the iteration base on predefined price periods and centralized
power optimization of end users. During iteration, the mechanism gives an increment
to the price of the last iteration based on gradient information.
The iteration direction needs to be the same as the gradient direction of the daily
total cost, which can ensure reducing the cost of whole EIE. The gradient of the daily
total cost is unknown. So considering the real-time cost analysis mentioned above,
here we use the gradient of the k-th period cost instead. The increment function is
chosen as follow:
 
f Qki 
kbuy , if Qki   0
 buy
sell
   k
 k
, if Qki   0
2

ksell , if Qki   0

(6-7)
Where Qk  means the in reception electricity in k-th period of i-th iteration.
i
The steps of the price formation mechanism are as follows:
Step 1: the energy management section offers a initial price as an internal price at
will,
   k  1, 2,
0
k

, K , set i=1;
Step 2: under the i-th internal price, all production units optimize their electricity
consumption, to minimize their total power consumption cost, and get the d m ,k ,
i
M
K
d mi,k  arg min  C m i,k
m 1 k 1
 k i 1 ;
(6-8)
Step 3: the self generation power plant does the centralized power generation
22
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
K
optimization, and get the optimal units output, pmi,k  arg min  Cki   d mi,k ,
k 1
Step 4: using the internal price generated by the last iteration, and the gradient
function, compute the internal price k  for next iteration, and the price
i
formulation is
ki   1   k  ki 1
k 

i
 
M
N
m 1
n 1
 f Qki  , Qki    d mi,k   pmi,k ;
 
f Qk 
i
(6-9)
kbuy , if Qki   0
 buy
sell
   k
i
 k
, if Qk   0
2

sell
k
, if Qki   0

Step 5: realizing the normalization through k     k  , to make sure that the
i
i
i
total internal settlement cost is consistent before and after the Step 4.
K
 i  
 C 
k 1
i
k
 
M
 a


   1   f Qki   ki 1   d mi,k 
i

k 1  
m 1

K
(6-10)
Step 6: if the total cost and price in this iteration doesn’t satisfy the condition of
convergence:
 K i  K i 1  K i 
  Ck   Ck  /  Ck   C
k 1
 k 1
 k 1
,


(6-11)
max ki   ki 1 / ki    
then i=i+1, go to step 2.
Step 7: output and release the internal price k  as a dynamic price signal in
i
microgrid.
And the flow chart of this gradient information based price formation mechanism
is shown in Figure 6-6.
23
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Energy management section offers initial price and set i=1
   k  1, 2,
0

,K
k
i  i 1
Electricity consumption optimization of production units
M
K
d m ,k  arg min  Cm ,k  k
i
i
i 1
m 1 k 1
1
Power generation optimization of self generation power plant
K
pm ,k  arg min  Ck   d m ,k
i
i
i
k 1
Update price by optimization direction
ki   1   k  ki 1
No
Normalization
ki    i ki 
Convergence?
Yes
Output the final
Price
Figure 6-6
the flow chart of gradient information based price formation mechanism
This mechanism has several advantages:
a) It fully uses the historical information, the iteration process of internal price reach
convergence rapidly;
b) The final internal price is enough strong to be used as a dynamic price signal.
c) The final internal price has the particular of both RTP and TOU tariff. It’s easy for
practical use.
And it also has several disadvantages:
a) It has a little special requirement to meet for initial price.
And all the features mentioned above will be analyzed and explained in case
study shown in next chapter.
6.3.3 Heuristic Method Based Price Formation Mechanism
RTP tariff mechanism 2 is a kind of heuristic method based price formation
mechanism. And it has the iteration base on predefined price periods and centralized
power optimization of end users. During iteration, the mechanism gives an increment
to the price of the last iteration based on predefined price periods, which made by the
prior knowledge.
When the reception electricity is positive, it represents the enterprise is buying
24
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
electricity from utility. Then we give a increment of price like 1  kbuy  kgene  . The
increment encourages users to reduce their electricity consumption, when kbuy  kgene
is positive, and to increase their electricity consumption, when the difference is
negative. The mechanism combines the cost of buying electricity and generation for
comparison ingeniously. It stands for smaller increment that the price for generation
is closed to the price for buying electricity, which conforms to reality.
When the reception electricity is negative, similar conclusion can be gained. The
increment function is chosen as follow:
 
f Qk 
i
1  kbuy  kgene  , if Qki   0


i
  2  kbuy  kgene  , if Qk   0

i 
sell
gene
 3  k  k  , if Qk  0
(6-12)
The steps of the price formation mechanism are as follows:
Step 1: the energy management section offers a initial price as an internal price at
will,
   k  1, 2,
0
k

, K , set i=1;
Step 2: under the i-th internal price, all production units optimize their electricity
consumption, to minimize their total power consumption cost, and get the d m ,k ,
i
M
K
d mi,k  arg min  C m i,k
 k i 1 ; (6-13)
m 1 k 1
Step 3: the self generation power plant does the centralized power generation
optimization, and get the optimal units output,
K
pm i,k  arg min  Cki   d mi,k ,
(6-14)
k 1
Step 4: using the internal price generated by the last iteration, and predefined
price periods, compute the internal price k  for next iteration, and the price
i
formulation is
ki   1   k  ki 1
 
M
N
1
 k   f Qki  , Qki    d mi,k   pmi ,k
i
m 1
n 1
 
f Qki 
(6-15)
1  kbuy  kgene  , if Qki   0


  2  kbuy  kgene  , if Qki   0

i 
sell
gene
 3  k  k  , if Qk  0
25
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Step 5: realizing the normalization through k     k  , to make sure that the
i
i
i
total internal settlement cost is consistent before and after the Step 4.
K
 i  
 C 
i
k
k 1
 
M
 1


   1   f Qki   ki 1   d mi,k 
i

k 1  
m 1

K
(6-16)
Step 6: if the total cost and price in this iteration doesn’t satisfy the condition of
convergence:
 K i  K i 1  K i 
  Ck   Ck  /  Ck   C
k 1
 k 1
 k 1
;

i 
 i 1
max k  k
/
i 
k
(6-17)
 
then i=i+1, go to step 2.
Step 7: output and release the internal price k  as a dynamic price signal in
i
microgrid.
And the flow chart of this gradient information based price formation mechanism
is shown in Figure 6-7.
26
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Energy management section offers initial price and set i=1
   k  1, 2,
0

,K
k
i  i 1
Electricity consumption optimization of production units
M
K
d m ,k  arg min  Cm ,k  k
i
i
i 1
m 1 k 1
1
Power generation optimization of self generation power plant
K
pm ,k  arg min  Ck   d m ,k
i
i
i
k 1
Update price by optimization direction
ki   1   k  ki 1
No
Normalization
ki    i ki 
Convergence?
Yes
Output the final
Price
Figure 6-7
a)
b)
c)
d)
the flow chart of heuristic method based price formation mechanism
This mechanism has several advantages:
The increment function intuitively reflect the guidance function of price signals.
And those parameters can be adjusted for changing the strength of function;
It fully uses the historical information, the iteration process of internal price reach
convergence rapidly;
The final internal price is enough strong to be used as a dynamic price signal.
The final internal price has the particular of both RTP and TOU tariff. It’s easy for
practical use.
And it also has several disadvantages:
a) It has a little special requirement to meet for initial price.
And all the features mentioned above will be analyzed and explained in case
study shown in next chapter.Equation Chapter (Next) Section 1
7 Test Result of Typical Cases and the Analysis
7.1 Cases Introduction
27
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
In order to observe and analyze the property of those mechanisms, two typical
cases have been studied.
Case 1 represents a typical small scale iron & steel manufactory enterprise. A
period lasts 10 minutes and there are 144 periods totally. Based on primarily research
results on an iron and steel plant, the case contains 3 kinds of equipments, which is
ladle refining furnace (LF furnace), blooming mill and finishing mill. And also
contain a self generation power plant called combined cycle power plant (CCPP).
Figure 7-1 is the schematic diagram of technological process. The equipments list and
their parameters are shown in TABLE 7-1. There are three preconditions during
optimization time horizon: unlimited fuel supply for power generation; total electricity
consumption keeping constant; Electricity users belonging to typical batch type 2.
Emission
Other Use
Gas
Holder
Oxygen
Making
COREX
Furnace
Production Process
CCPP
Steelmaking
(LF Furnace)
Medium Plate
Production
Electricity Flow
Grid
Gas Flow
Figure 7-1 the schematic diagram of technological process
TABLE 7-1
No.
Equipment
1
LF furnace
2
3
4
5
equipments list and parameters for case 1
Type
Parameters
Batch production
Power rating: 20000 (KW)
(Type 2)
Batch time:50 (min)
Blooming
Batch production
Power rating: 20000(KW)
mill
(Type 2)
Batch time: 60 (min)
Finishing
Batch production
Power rating: 40000 (KW)
mill
(Type 2)
Batch time: 90 (min)
Continuous
Maximum output: 169000 (KW)
production
Minimum output:85000(KW)
(Type 3)
Δ Output :50000(KW/period)
CCPP
Gas holder
Storage (Type 2)
Minimum ：160000 (Nm3)
Maximum ：500000(Nm3)
number
3
3
1
1
1
Tariff:
There are three general levels of TOU: peak price, valley price and flat price. And
the feed-in tariff which happened when enterprise sold electricity to utility is smaller
than the valley price. We use the TOU tariff implemented by utility in Shanghai
28
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
district, shown in TABLE 7-2.
TABLE 7-2
TOU Tariff Implemented by the Utility
Time period (hours)
Tariff (￥/KWh)
Valley
0:00-6:00,22:00-00:00
0.219
Flat
6:00-8:00,11:00-13:00, 15:00-18:00, 21:00-22:00
0.56
Peak
8:00-11:00,13:00-15:00, 18:00-21:00
0.926
Feed-in tariff
0:00-24:00
0.2
7.2 Pricing Formation Mechanism Based on Real-time Cost
The numerical testing result of pricing formation mechanism is shown below.
Figure 7-2 is the figure of the practical daily cost for enterprise during iterations.
Figure 7-3 is the internal price curve and external TOU tariff curve during a day, which
shows the relationship between the internal dynamic price and TOU tariff
implemented by utility. Figure 7-4 is the total load curve and units output curve during
a day, which intuitively shows the effect of this mechanism on production and
generation scheduling.
Case 1:
6
1.124
x 10
1.122
Daily Total Cost (￥ )
1.12
1.118
1.116
1.114
1.112
1.11
1.108
1.106
0
5
Figure 7-2
10
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
29
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
1
Initial Price
Final Price
TOU Tariff
0.9
Internal Price (￥ /KWh)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
Figure 7-3
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-4
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
Base on the result, a brief analysis is given:
a) It almost decreases the total energy consumption cost of the whole enterprise.
Because all the production equipments belong to batch equipment, and their load
level is discrete, the fluctuation during iterations is inevitable;
b) The internal price curve can be divided to three segments, and the time segments
division is same as TOU tariff. In off-peak periods, the better choice is buying
electricity. Because the output is pn at the first segment, the internal price is
30
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
concussive and has the opposite trend with load;
c) At the second segment, the units output follows the total load to avoid buying
electricity in peak period. Therefore the internal cost price is equal to generation
cost price which is constant. And the internal price in the second segment is
higher than the first and third segments definitely
d) The internal price signal is too weak, and the concussive price is hard for practical
use;
e) The multiplicity of problem exists in this pricing formation mechanism. The
practical daily cost for enterprise during iterations presents a severe concussion in
case 2 although finding out the optimal solution.
7.3 Pricing Formation Mechanism Based on Gradient Information
The numerical testing result of pricing formation mechanism is shown below.
Figure 7-5 is the figure of the practical daily cost for enterprise during iterations.
Figure 7-6 is the internal price curve and external TOU tariff curve during a day, which
shows the relationship between the internal dynamic price and TOU tariff
implemented by utility. Figure 7-7 shows the cost price, which compute by the
practical cost and total load. Figure 7-8 is the total load curve and units output curve
during a day, which intuitively shows the effect of this mechanism on production and
generation scheduling.
Case 1:
6
1.124
x 10
1.122
Daily Total Cost (￥ )
1.12
1.118
1.116
1.114
1.112
1.11
1.108
1.106
0
5
Figure 7-5
10
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
31
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
1
Initial Price
Final Price
TOU Tariff
0.9
Internal Price (￥ /KWh)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
Figure 7-6
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
1
Initial Price
Final Price
TOU Tariff
0.9
Cost Price (￥ )
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
Figure 7-7
32
20
40
60
80
Time (10mins)
100
120
140
the cost price curve and external TOU tariff curve during a day
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-8
a)
b)
c)
d)
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
Base on the result, a brief analysis is given:
The mechanism decreases the total energy consumption cost of the whole
enterprise. Because it fully uses the historical information, the iteration process of
internal price reach almost convergence rapidly, and the fluctuation during
iterations is avoided in case 1;
The trend of internal price is the same as external TOU tariff, and also can be
treated as a like TOU tariff, which is a dynamic price changed among days. The
internal price is enough strong to be a signal, and easy for practical use because of
small ripple.
The units output follows the total load to avoid buying electricity in peak period,
which conform to reality. Therefore the internal cost price is equal to generation
cost price which is constant shown in Figure 7-7.
The mechanism realizing the normalization to make sure that the total internal
settlement cost is consistent during iteration. So the cost price curve computed by
the mechanism is the same as the curve computed by real-time cost based price
formation mechanism, which is stand for the optimal solution.
7.4 Pricing Formation Mechanism Based on Heuristic Information
The numerical testing result of pricing formation mechanism is shown below.
Figure 7-9 is the figure of the practical daily cost for enterprise during iterations.
Figure 7-10 is the internal price curve and external TOU tariff curve during a day,
which shows the relationship between the internal dynamic price and TOU tariff
implemented by utility. Figure 7-11 shows the cost price, which compute by the
practical cost and total load. Figure 7-12 is the total load curve and units output curve
33
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
during a day, which intuitively shows the effect of this mechanism on production and
generation scheduling.
Case 1:
6
1.124
x 10
1.122
Daily Total Cost (￥ )
1.12
1.118
1.116
1.114
1.112
1.11
1.108
1.106
0
5
10
Figure 7-9
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
1.4
Initial Price
Final Price
TOU Tariff
1.2
Internal Price (￥ /KWh)
1
0.8
0.6
0.4
0.2
0
0
Figure 7-10
34
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
1
Initial Price
Final Price
TOU Tariff
0.9
Cost Price (￥ )
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
Figure 7-11
20
40
60
80
Time (10mins)
100
120
140
the cost price curve and external TOU tariff curve during a day
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-12
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
Base on the result, a brief analysis is given:
a) The mechanism decreases the total energy consumption cost of the whole
enterprise. Because it fully uses the historical information and heuristic
information, the iteration process of internal price reach convergence rapidly, and
the fluctuation during iterations is avoided;
b) The trend of internal price is the same as external TOU tariff, and also can be
35
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
treated as a like TOU tariff, which is a dynamic price changed among days. The
internal price is enough strong to be a signal, and easy for practical use because of
small ripple.
c) The units output follows the total load to avoid buying electricity in peak period,
which conform to reality. Therefore the internal cost price is equal to generation
cost price which is constant shown in Figure 7-11.
d) The mechanism realizing the normalization to make sure that the total internal
settlement cost is consistent during iteration. So the cost price curve computed by
the mechanism is the same as the curve computed by real-time cost based price
formation mechanism, which is stand for the optimal solution.
The convergence costs of the three price formation mechanism are shown in
TABLE 7-3. In this case, all the three mechanism have found the optimal solution.
The item called net cost means the cost of buying electricity from utility.
TABLE 7-3
the convergence costs of the three price formation mechanism
Cost Item
Cost Method
Gradient Method
Heuristic Method
Net Cost
50071
50071
50071
Generation Cost
1057333
1057333
1057333
Total Cost
1107404
1107404
1107404
7.5 Expended Test and the Analysis
In order to verify the influence of different parameters values, the expended
situations are tested. The expended test includes changing the number of batch,
changing the range of units output, 6 tests totally.
7.5.1 Change the Batch Number:
Numbers of batch represent the density of production. In this expended test, the
work intensity of equipments has been increased for observation. The heuristic
method based price formation mechanism is used for the tests.
a) Based on TABLE 7-1, change the batch number of LF furnace, blooming mill,
and finishing mill from 3, 3, 1 to 5, 5 and 2.
36
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
6
1.175
x 10
Daily Total Cost (￥ )
1.17
1.165
1.16
1.155
1.15
0
5
10
Figure 7-13
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
1.4
Initial Price
Final Price
TOU Tariff
1.2
Internal Price (￥ /KWh)
1
0.8
0.6
0.4
0.2
0
0
Figure 7-14
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
37
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
180
Initial Load
Final Load
Final Output
170
160
Power Level (MW)
150
140
130
120
110
100
90
80
0
20
Figure 7-15
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
Although the daily total cost rises because of the increase of batch number, the
convergence of the mechanism doesn’t change. And the trend of internal price is also
same as external TOU tariff in Figure 7-14. And in Figure 7-15, we can easily find out
the effect of production scheduling. The production activities are allocated to the
off-peak hours as possible, and the units output track the load well to minimize the
total cost.
b) Further, change the batch number of LF furnace, blooming mill, and finishing
mill from 3, 3, 1 to 7, 7 and 3.
38
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
6
1.1513
x 10
Daily Total Cost (￥ )
1.1513
1.1513
1.1513
1.1513
1.1513
0
5
10
Figure 7-16
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
1.4
Initial Price
Final Price
TOU Tariff
1.2
Internal Price (￥ /KWh)
1
0.8
0.6
0.4
0.2
0
0
Figure 7-17
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
39
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-18
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
Although the daily total cost rises because of the increase of batch number, the
convergence of the mechanism doesn’t change. And the trend of internal price is also
same as external TOU tariff in Figure 7-17. And in Figure 7-18, we can easily find out
the effect of production scheduling. The production activities are arranged to the
off-peak hours as possible, and the units output track the load well to minimize the
total cost.
7.5.2 Analysis of Cost-saving
For the proposed mechanism, decrease the cost of the whole enterprise is one of
the most important tasks. In the numerical test, we found the ability of cost-saving is
related to the production intensity. In this section, we discuss the capacity of saving
energy consumption cost in different production intensity.
In this expend test, we have three illustrations.
a) The test shows us the capacity of saving cost, and the capacity is measured by
the different between only power generation optimization and also using the
dynamic price mechanism for power consumption optimization. Without the
power generation optimization, the capacity of saving cost is hard to be
measured. And if the power generation optimization is not used neither, the
index of percentage cost decrease mentioned below would be much larger.
b) To measure the production intensity, we use a index denoted PI, which is
showed as:
40
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
PI 
total time consumption of production
100 0 0
total adjustable time of production
M

Jm
 T
m 1 j 1
 J
  em, j  sm , j

m 1  j 1
M

(7-1)
m


Jm 

100
0
0
which means the ratio of time consumption of production and available time
can be used for production.
c) To measure the capacity of saving energy consumption cost, we use a index
denoted PCD, which is showed as:
the cost decrease when using the mechanism
the cost of optimal solution
C  Coptimal
 og
 100 0 0
Coptimal
PCD 
where the Cog means the cost when only use the power generation
optimization. And Coptimal is the cost of optimal solution obtained by the
proposed mechanism.
When we increase the number of batch in different equipments, the PI index will
increase, and the production intensity also increasing. The following table and shows
the capacity of saving energy consumption cost in different production intensity. And
the PI index is an ascending sequence.
TABLE 7-4
the capacity of saving cost in different production intensity
Number of batch in equipments
No.2
1
No.3
1
PI
Cog
Coptimal
PCD
1
No.1
1
9.90%
1.09E+06
1.08E+06
0.65%
2
2
1
1
14.85%
1.10E+06
1.09E+06
1.54%
3
2
2
1
17.33%
1.11E+06
1.09E+06
1.14%
4
3
2
1
22.28%
1.11E+06
1.10E+06
1.28%
5
3
3
1
24.75%
1.12E+06
1.11E+06
1.37%
6
4
3
1
29.70%
1.13E+06
1.12E+06
1.37%
7
4
4
2
34.65%
1.15E+06
1.13E+06
1.35%
8
4
5
2
37.13%
1.16E+06
1.14E+06
2.02%
9
5
5
2
42.08%
1.17E+06
1.15E+06
1.95%
10
5
6
2
44.55%
1.18E+06
1.16E+06
1.61%
11
6
6
2
49.50%
1.18E+06
1.17E+06
0.94%
12
6
7
3
54.46%
1.21E+06
1.19E+06
1.30%
ID
41
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
7
7
Persentage Cost Decrease (PCD)
13
3
59.41%
No solution
0.00%
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00%
Production Intensity (PI)
Figure 7-19
the capacity of saving cost in different production intensity
When the production intensity is low, the mechanism optimizes the production
process and decrease the energy cost. Comparing to the production consumption, the
base load is still large, so the effect of deceasing the cost is not significant, which is
reasonable. For this reason, when the PI is higher, more batches are scheduled, and
the effect of mechanism is pretty good. No more space can be optimization, when the
production intensity is extreme high, so the PCD start to decline.
7.5.3 Change the Range of Units Output
The range of generation units output concern the ability of tracking the total load.
In expended test, the range of unit output is changed for observation. Both heuristic
method and gradient method based price formation mechanism are tested.
TABLE 7-5
parameters and methods in tests
Serial number
Method
Range(KW)
original
Both
85000-169000
a)
Heuristic
105000-169000
b)
Gradient
105000-169000
c)
Heuristic
85000-109000
d)
Gradient
85000-109000
e)
Heuristic
65000-80000
f)
Gradient
65000-80000
a) Heuristic method based price formation mechanism. Based on TABLE 7-1,
change the range of CCPP units output from 85000-169000(KW) to
105000-169000(KW).
42
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
6
1.18
x 10
1.178
Daily Total Cost (￥ )
1.176
1.174
1.172
1.17
1.168
1.166
1.164
0
5
10
Figure 7-20
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
2.5
Initial Price
Final Price
TOU Tariff
Internal Price (￥ /KWh)
2
1.5
1
0.5
0
0
Figure 7-21
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
43
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-22
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
In both Figure 7-20 and Figure 7-21, there are fluctuations at some periods.
Because all the production equipments belong to batch equipment, and their load
level is discrete. Based on the analysis of Figure 7-22, for example, in period 50-100,
units output is larger than the load, that makes the mechanism try to arrange the
production activities here, and sell electricity at off-peak hours. It directly causes the
rising cost. Therefore, at this situation in the mechanism, fluctuations can’t be
avoided, and the mechanism needs to be improved;
b) The gradient method based price formation mechanism. Based on TABLE 7-1,
change the range of CCPP units’ output mill from 85000-169000(KW) to
105000-169000(KW).
44
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
6
1.18
x 10
1.178
Daily Total Cost (￥ )
1.176
1.174
1.172
1.17
1.168
1.166
1.164
0
5
10
Figure 7-23
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
1.2
Initial Price
Final Price
TOU Tariff
1.1
Internal Price (￥ /KWh)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
Figure 7-24
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
45
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-25
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
In both Figure 7-23 and Figure 7-24, there are fluctuations at some periods due to
the same reason. And comparing to the heuristic method, the fluctuations are more
serious. At this situation in the mechanism, fluctuations also can’t be avoided, and the
mechanism needs to be improved;
c) The heuristic method based price formation mechanism. Based on TABLE
7-1, change the range of CCPP units’ output mill from 85000-169000(KW) to
85000-109000(KW).
6
1.155
x 10
1.15
Daily Total Cost (￥ )
1.145
1.14
1.135
1.13
1.125
1.12
1.115
1.11
0
5
Figure 7-26
46
10
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
1.4
Initial Price
Final Price
TOU Tariff
1.2
Internal Price (￥ /KWh)
1
0.8
0.6
0.4
0.2
0
0
Figure 7-27
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-28
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
Figure 7-26 proves that the mechanism is efficient when the upper limit of units
output is lower than the peak load, which can be proved in Figure 7-28. And the
internal price given by Figure 7-27 is proper and rational;
d) The gradient method based price formation mechanism. Based on TABLE 7-1,
change the range of CCPP units’ output mill from 85000-169000(KW) to
85000-109000(KW).
47
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
6
1.155
x 10
1.15
Daily Total Cost (￥ )
1.145
1.14
1.135
1.13
1.125
1.12
1.115
1.11
0
5
10
Figure 7-29
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
1.8
Initial Price
Final Price
TOU Tariff
1.6
Internal Price (￥ /KWh)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
Figure 7-30
48
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
160
Initial Load
Final Load
Final Output
150
Power Level (MW)
140
130
120
110
100
90
80
0
20
Figure 7-31
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
The figures show that the gradient information based mechanism is efficient when
the upper limit of units output is lower than the peak load. The mechanism will be
slightly worth than the heuristic method based mechanism in aspect of convergence.
We also can find there is a pinnacle in Figure 7-29, which will be explained later;
e) The heuristic method based price formation mechanism. Based on TABLE
7-1, change the range of CCPP units’ output mill from 85000-169000(KW) to
65000-80000(KW).
49
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
6
1.23
x 10
Daily Total Cost (￥ )
1.22
1.21
1.2
1.19
1.18
1.17
0
5
10
Figure 7-32
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
1.4
Initial Price
Final Price
TOU Tariff
1.2
Internal Price (￥ /KWh)
1
0.8
0.6
0.4
0.2
0
0
Figure 7-33
50
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
160
Initial Load
Final Load
Final Output
150
140
Power Level (MW)
130
120
110
100
90
80
70
60
0
20
Figure 7-34
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
In this test, the generation units output can’t meet the requirement of the load of
the whole enterprise, which can be proved by Figure 7-34. The test result shows that
the effect in reducing total cost is excellent. And the internal price given by the
mechanism in Figure 7-33 is proper and rational;
The gradient method based price formation mechanism. Based on TABLE 7-1,
change the range of CCPP units’ output mill from 85000-169000(KW) to
65000-80000(KW).
6
1.23
x 10
1.22
Daily Total Cost (￥ )
f)
1.21
1.2
1.19
1.18
1.17
0
5
Figure 7-35
10
15
20
25
30
Number of Iteration
35
40
45
50
the practical daily cost for enterprise during iterations
51
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
1.4
Initial Price
Final Price
TOU Tariff
1.2
Internal Price (￥ /KWh)
1
0.8
0.6
0.4
0.2
0
0
Figure 7-36
20
40
60
80
Time (10mins)
100
120
140
the internal price curve and external TOU tariff curve during a day
160
Initial Load
Final Load
Final Output
150
140
Power Level (MW)
130
120
110
100
90
80
70
60
0
20
Figure 7-37
40
60
80
Time (10mins)
100
120
140
the total load curve and units output curve during a day
The figures show that the gradient information based mechanism is efficient when
the generation units output can’t meet the requirement of the total load. The
mechanism will be slightly worth than the heuristic method based mechanism in
aspect of convergence.
There are pinnacles in Figure 7-29, Figure 7-32, et al. There are two figures below
which show the total load curve under the same parameters, such as the same internal
price. The figure left shows the load curve of the pinnacle during iterations, and the
52
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
right shows the load curve in a single iteration under the same parameters. The test
figure below tells us that the price formation mechanism doesn’t cause pinnacles. The
reason may be the ILOG CPLEX or electricity consumption optimization model of
production units, which still need further research.Equation Chapter (Next) Section 1
15
Load in Iterations
Load in a Single Iteration
14
Power Level (MW)
13
12
11
10
9
8
0
20
Figure 7-38
40
60
80
Time (10mins)
100
120
140
load curve in different iteration situation
8 Conclusion
In this project, the electricity dynamic pricing problem in microgrid has been
researched. Based on the analysis of the problem, an electricity pricing mechanism is
proposed.
The purpose and intent of the price mechanism includes two aspects: for the cost
benefit, the mechanism tries to reduce the total electricity cost of microgrid by
encouraging the end users to use less energy during peak hours, or to move the time of
electricity use to off-peak hours. The optimal power strategy is also considered; at the
same time, considering the usability, the price mechanism should be easy to
implement, and be simple for operators.
There are several key components in the price mechanism:
a) Power consumption models for end users: different end users have different
load control characteristics.
b) Power generation models for self generation power plant: different power
generator units have different output control characteristics and different
generating cost.
c) Iterative or game mechanism for reducing electricity cost: the iterative
mechanism is convergent.
53
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
d) The division of time interval for price mechanism: The division of time
interval is related with tariff implemented by the utility and generating cost.
Though the analysis of real-time cost, the power consumption and generation
optimization model is been built. Then the optimal power generation strategy has
been made and several pricing formation mechanism has been designed. Based on the
analysis of numerical test, the dynamic price mechanism demonstrates following
points:
a) With the optimal power generation strategy, final price is able to lead end user
to shift load from peak hours to off-peak hours. Thus, a cost saving of about 1.5%
is feasible comparing to that of initial load.
b) Total income of energy management section charging to the end users with
final price is equal to the total cost.
c) With the optimal power generation strategy, three dynamic price mechanisms
are able to reduce electricity cost of EIE microgrid.
d) The RTP mechanism with heuristic rule is the best one based on current
research.
e) The ideal dynamic price electricity price curve is dynamic changing according
to tariff implemented by the utility and self generation cost,
f) The dynamic price electricity price is a specific real time pricing.
In addition, we can conclude the applicable scope of the mechanism based on the
analysis. That is the microgrid with adjustable load and self generation power plant,
and the power units have good power generation performance. And the mechanism has
a better performance when the following conditions are satisfied:
a) Microgrid with adjustable load and self generation power plant,
b) Power consumption has a larger adjustment range.
c) Power units have good power generation performance, the installed capacity is
close to the total load and the fuels for power generation are not limited.
d) Relationship among generating cost and tariff implemented by the utility:
Situation one: koff-peak  kgene , kgene  ksell , kpeak  kgene
And, when the situation is as follows, the dynamic price mechanism is no need to
implement:
a) Power outputs have good power generation performance, the installed capacity
is close to the total load, the fuels for power generation are not limited.
b) Relationship among generating cost and tariff implemented by the utility
belong to situations as bellow:
Situation two: koff-peak  kgene  ksell , kpeak  kgene
Situation three: koff-peak  kgene , kgene  ksell , kpeak  kgene
At last, when the power consumption has little adjustment range, the price
mechanism is not applicable to implement.Equation Chapter (Next) Section 1
54
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
9 The Description of General Dynamic Pricing
Mechanism in Microgrid
Base on the analysis of dynamic pricing mechanism in EIE microgrid, we can
give a description of general dynamic pricing in microgrid. In traditional power
supply pattern shown in Figure 1-1, the users hand in the charge of electricity
according to the tariff given by utility. Then the electricity cost of energy management
section (EMS) is zero. It can be expressed as follow:
M
Cm,k  kbuy d m,k , Cktotal   Cm ,k , Ckpay  Cktotal
m 1
gain
k
C
C
pay
k
C
total
k
(9-1)
0
Transition to microgrid is shown in Figure 1-3. Both the utility and self-contained
power supply form the multi-power supply pattern. All users hand in the charge of
electricity to EMS in microgrid according to the internal tariff. And at the same time,
EMS purchases the internal generation according to the internal tariff. The cost is
expressed as follow.
user
gene
gene
Cmuser
, k  m , k d m , k , Cn , k  n , k pn , k
M
N
m 1
n 1
gene
Ckuser   Cmuser
  Cngene
, k , Ck
,k
(9-2)
At this time, the power exchange cost (or benefit) between the utility and
microgrid is undertaken by the EMS. The electricity cost of EMS is expressed as
follow.
Ckgate
kbuyQk , if Qk  0

 0
, if Qk  0
 sell
k Qk , if Qk  0
M
N
m 1
n 1
Qk   d m,k   pm ,k
(9-3)
Ckgain  Ckuser  Ckgate  Ckgene
Different tariff in microgrid brings different net income for EMS. There are three
situations shown in TABLE 9-1 and TABLE 9-2. In situation 1, the internal price is
the tariff implemented by the utility which is a single time period. And the internal
power demand/generation will bring income for the EMS. In situation 2 and 3, the
internal price TOU tariff implemented by the utility which has peak hour and
off-peak hour. Different tariff will adjust the power demand/generation, which means
different income for EMS.
55
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
TABLE 9-1
the items value in situation 1
Items
Situation 1
Power demand
1000KWh
Power generation
200KWh
Net power demand
800KWh
Tariff implemented by the utility
1$/KWh
Net electricity cost
800$
Internal power demand price
1$/KWh
Internal power generation price
0.3$/KWh
Internal electricity cost
1000$
Internal generation cost
60$
Net income for EMS
1000-60-800=140 $
TABLE 9-2
Items
the items value in situation 2 and 3
Situation 2
Situation 3
Peak hour
Off-peak hour
Peak hour
Off-peak hour
Buying tariff
1 $/KWh
0.5 $/KWh
1 $/KWh
0.5 $/KWh
Feed in tariff
0.3 $/KWh
0.1 $/KWh
0.3 $/KWh
0.1 $/KWh
Power demand
1000 KWh
1000 KWh
700 KWh
1300 KWh
Power generation
200 KWh
200 KWh
300 KWh
100 KWh
Net electricity cost
800 $
400 $
400 $
600 $
Internal electricity cost
1000 $
500 $
700 $
650 $
Internal generation cost
60 $
20 $
90 $
10 $
Internal cost
940 $
480 $
610 $
640 $
Net income for EMS
140 $
80 $
210 $
40 $
Total net income for EMS
220 $
250 $
In this situation, the users pay the charge according to the internal dynamic
electricity price, and arrange the electricity for reducing electricity cost. Meanwhile,
the generators receive repayment according to the internal dynamic generation price,
and arrange the generation in each period for increasing income.
It brings a problem. That is how to distribute the benefit for win-win, which can
be assigned to game. And a dynamic pricing based solution is proposed. The flow
chart of this generalized game mechanism is shown in Figure 9-1.
56
Dynamic Pricing Model and Algorithm in Energy Intensive Enterprise Microgrid
Initial setting
Power users
K
d   arg min  C
m ,k
user
m ,k
k 1
 muser
,k
No
Power generators
K
 p   arg max  C
n ,k
k 1
gene
n ,k
 d m ,k , ngene
,k
Energy management section

gene
n ,k
,
  arg max  C
K
user
m ,k
k 1
gain
k
 d m,k , pm,k , kbuy , ksell
Equilibrium?
Yes
End
Figure 9-1
the flow chart of generalized game mechanism
Different types of microgrid need different price mechanisms. In view of
classification of price mechanism, the microgrid can be classified according to:
a) Demand response of power users: centralized scheduling or decentralized
decision making;
b) Demand response of power generators: centralized scheduling or decentralized
decision making;
c) Integration degree of power users and power generators;
d) The benefit-based relationships among power generators, power users and
energy management section
57
Dynamic Pricing in Microgrid for Energy Intensive Industrial Enterprises
Reference
[1] Triki Chefi, Violi Antonio. “Dynamic pricing of electricity in retail markets,” A
Quarterly Journal of Operations Research, vol. 7, no. 1 ,pp: 21-36, Mar 2009;
[2] George B. Dantzig and Mukund N. Thapa. Linear programming 1: Introduction.
Springer-Verlag, 1997.
[3] George B. Dantzig and Mukund N. Thapa. Linear Programming 2: Theory and
Extensions. Springer-Verlag, 2003.
58