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Energy 52 (2013) 37e43

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Energy

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Multi-agent simulation of the time-of-use pricing policy in anurban natural gas pipeline network: A case study of Zhengzhou

Lanlan Li, Chengzhu Gong, Deyun Wang*, Kejun ZhuSchool of Economics and Management, China University of Geosciences, Wuhan 430074, China

a r t i c l e i n f o

Article history:Received 21 March 2012Received in revised form1 February 2013Accepted 2 February 2013Available online 5 March 2013

Keywords:Natural gas pricingTime-of-use pricingMulti-agent simulationUser response

* Corresponding author. Tel.: þ86 2767848527.E-mail addresses: wang.deyun@hotmail.com (D

(K. Zhu).

0360-5442/$ e see front matter Crown Copyright � 2http://dx.doi.org/10.1016/j.energy.2013.02.002

a b s t r a c t

This paper establishes a multi-agent system comprising a government agent, a gas operator agent, and anindustrial and commercial users agent. The system simulates the dynamic change process of demandsand running states in an UGPN (urban gas pipeline network) and explores the optimal TOU (time-of-use)natural gas price to minimize the peakevalley load difference. The government agent plays a monitoringrole of providing the upper and lower limits of natural gas price. The gas operator dynamically setsnatural gas price based on user response, within the bounds established by a government authority.Then, the industrial and commercial users modify their consumption according to the price provided bythe gas operator. This study considers the case of Zhengzhou, China to simulate the hourly gas-usagebehavior of industrial and commercial users under the TOU pricing policy. The results indicate the ex-istence of an optimal peakevalley price difference through which both the gas operator and users cangain benefits. Further, rising peak price also increases the benefits of the end-users, while those of the gasoperator decrease; however, at some threshold value, the gas operator benefits from further increases inthe peak price.

Crown Copyright � 2013 Published by Elsevier Ltd. All rights reserved.

1. Introduction

The use of global energy is at an all-time high, and a range ofsources, including fossil fuels, nuclear power and renewable sour-ces, generate the energy. According to BP (British Petroleum) en-ergy statistics, the primary energy consumption of China in 2011 isequivalent to 2.613 billion tons of oil. Since 2009, China has becomeone of the biggest energy consumers for three years now. Inparticular, natural gas consumption has increased greatly; from the2.6% proportion of natural gas in primary energy in 2005, con-sumption has risen to 4.5% in 2011, with an average annual growthrate of about 9.6% [1,2]. Moreover, the Chinese Government hastried to improve the gas consumption ratio due to its relativecleanliness in recent years. The Outline of the 12th Five-Year Plan ofthe People’s Republic of China for the National Economy and SocialDevelopment stipulates that the country should strengthen theconstruction of the clean energy industry so that the natural gasconsumption ratio can increase to 8.3% by 2015.

However, the combination of this increased demand and thescarcity of natural gas has led to gas shortage in some cities in

. Wang), kxt428@163.com

013 Published by Elsevier Ltd. All

China. Moreover, issues concerning the rigidity of the natural gasprice system exacerbate the problem. In China, the current naturalgas pricing method is based on the cost-plus policy, where thegovernment directly controls the price; such method separates thenatural gas price from its commodity value, and does not reflect thescarcity of the natural gas. Another problem stems from the lack ofpeak shaving and stability capabilities in an UGPN (urban gas pipenetwork) in China. The excessive demand in the peak period leadsto low pressure in the UGPN, and as a result, several gas users areunable to use natural gas. Conversely, the low gas demand in thevalley period leads to high pressure in the gas pipeline, causing thenetwork to runwith low efficiency and introducing safety concerns.

TOU (Time-of-use) pricing, which is commonly utilized in theelectric power market, is the practice of implementing differentprices for different times of use. Power companies determine peakand valley times, and then set higher and lower prices during thepeak and valley periods, respectively, to motivate consumers toadjust their consumption, thereby easing the strain on the networkduring peak periods [3e5]. The TOUprogram is awell-known time-based DR (demand response) program, and has the following ad-vantages: reducing operation cost, increasing profit, shifting andreducing peak loads [6e11].

Previous studies have considered different TOU pricing methodsand models [12e16]. A multi-objective non-linear optimizationmodel of TOU price has been established on the power demand

rights reserved.

L. Li et al. / Energy 52 (2013) 37e4338

side, and has been solved by maximum satisfaction method infuzzy optimization theory [13]. Nikzad et al. proposed a two-stageSMILP (stochastic mixed-integer linear programming) model todetermine the optimum TOU rates based on grid reliability index,and solved it using CPLEX as a powerful solver for MILP (mixed-integer linear program) [14]. He et al. presented a method toquantify residential DR based on both survey results and Monte-Carlo simulation of TOU rates [15].

Several studies have considered the optimal contract capacityproblems of TOU rate users [17e19]. A multi-pass dynamic pro-gramming technique has been proposed to decide the optimaloperation scheme of a battery energy storage system for a TOU rateuser in Ref. [18]; this study sought to optimize the contract ca-pacities of a TOU rate user. Lee and Chen presented an IPSO (iter-ative particle swarm optimization) algorithm for solving theoptimal contract capacities of a TOU rate industrial user [19].

Few studies have investigated the relationship between TOUtariffs and energy consumption [20e23]. In particular, Torriti hasassessed the impact of TOU tariffs in terms of changes in electricitydemand, price savings, peak load shifting and peak electricity de-mand at the sub-station level [23].

Although the gas pipeline network and the electricity networkare both in the business of energy supply, they differ in their pricingmechanisms and the methods they use for peak shaving. At pre-sent, the natural gas TOU pricing research is limited. Ou et al. haveestablished a TOU pricing decision model for natural gas bycombining the grey relationship with a Monte-Carlo simulation[24]. However, Ou et al. only proposed a static simulation modelwithout considering the dynamic relationship between govern-ment, gas operator, and end-users. A TOU variation of natural gasprice is known to result in a dynamically changing demand, whichaffects the operational state of the UGPN. This variation can resultin the emergence of complex phenomena and characteristics. TheABMS (Agent-Based Modeling and Simulation) method is aneffective tool for capturing and studying complex phenomena andsystems, thus allowing the realization of complex adaptive calcu-lations. The ABMS method has been gradually applied in studyingTOU pricing in the power market [25,26].

This paper develops a simulation model to explore the possi-bility of TOU pricing in Zhengzhou, China. We first introduced theTOU pricing policy for natural gas market, which is implementedfor industrial and commercial users. Then, a TOU price multi-agentsystem, involving the government, gas operator and users agents, isdesigned to simulate the running state of the UGPN in Zhengzhou.Using the multi-agent simulation model, we obtained an optimal

natural gas cost, market value

external environmental factors etc.

GovernmentAgent

Gas OperatorAgent

the

uplim

itofprice

man-machineinterface

re

p

lower

limitof

price

Fig. 1. TOU price multi-agent sim

peakevalley price relationship and achieve two goals. First, boththe gas operator and industrial and commercial users can benefitfrom this peakevalley price. Second, the peakevalley load differ-ence can be reduced effectively to lower the risk of UGPN operation.

2. Problem formulation

The UGPN has a mixture of residential, industrial, and businessusers. For residential users, their relatively fixed patterns ofbehavior result in a small price elasticity of demand compared withother user types [27,28]. Given that their gas consumption is mainlyfor heating, cooling and cooking, modifying their consumptionbehaviors by varying the natural gas price is difficult.

However, for industrial and commercial users, natural gas ismainly used as a raw material or as fuel. Consequently, such userscan more readily modify their consumption to achieve savings bytargeting the valley periods. The price elasticity of demand for in-dustrial and commercial users is relatively large. This characteristicsuggests that the TOU pricing policy would be effective for indus-trial and commercial users. On this basis, this study only considersthe industrial and commercial users in the UGPN.

The UGPN is a complex economic system with non-linearinteraction mechanisms, and the different modules comprising thegovernment, gas operators, and multiple types of users form asupply and demand network. This system can be transformed into amulti-agent system, wherein each module is regarded as an inde-pendent agent, while the various interactions among people, or-ganizations, and machines can be described as independentactivities between agents. An illustration of the TOU price multi-agent simulation model of the UGPN is shown in Fig. 1.

In a multi-agent system, agents are generally categorized intoone of three different types according to their structures andfunctions, namely, cognitive, reaction, and hybrid. Each type ofagent can be described using a set of elements, i.e., Agent ¼ {ID,objective, knowledge base, rule set, internal state, external envi-ronment, attribute, parameter}. This set of elements defines thebehavior rules and interaction mechanisms of the agent at amicroscopic level.

In Fig. 1, there are four categories of agents, i.e., the government,gas operator, user, and real-time monitoring agent; the first threecategories are hybrid type agents, while the last category is a re-action type agent. Their functions are described in detail below.

(1) Government agent: This agent determines the upper and lowerlimits of the natural gas TOU price by considering natural gas

Industrial andCommercial Customer

Agent

Resident CustomerAgent

total energy consumption

real-time

load

Real-time MonitoringAgent

al-time load

price information

rice information

price information

ulation model of the UGPN.

L. Li et al. / Energy 52 (2013) 37e43 39

production cost, transportation cost, market value, externalenvironmental factors, and the total energy consumption in theUGPN, and it provides the limits to the gas operator agent.

(2) Gas operator agent: Under the supervision of the government,the gas operator agent guides user consumption behavior byadjusting the natural gas price to reduce the network peakevalley load difference and to maximize their benefit. Theseprices are passed in real-time to both industrial and commer-cial users as well as to real-time monitoring agent.

(3) User agent: Based on the price information obtained from thegas operator agent, the industrial and commercial users adjusttheir behavior by consuming more gas during valley periods,and reducing consumption during peak periods, therebyreducing their expenditures. In comparison, the residentialuser agent has no response behavior, as the natural gas price forresidential customers is constant.

(4) Real-time monitoring agent: The real-time monitoring agentgathers the peak price, valley price, and the total energy con-sumption of the users in real time, and passes the informationto the government agent for its consideration.

The system should also be able to accept the external parame-ters and allow intervention in order to maintain or recover to a“normal” running state upon detection of an abnormal condition.

3. Behavioral rules of the hybrid type agents

In this work, we assumed that 24 h in a day are divided intothree intervals, namely, peak, flat and valley periods as denoted byp, f and v, respectively. Let i represent i-th hour in a day withi ¼ 1,2,.,24. The three kinds of hybrid type agents (i.e., govern-ment, gas operator, industrial and commercial user agents) havetheir own goals and behavior rules described below.

3.1. Behavioral rules of the government agent

To a certain extent, natural gas price must be supervised andcontrolled by the government to maintain the gas market order.The gas price of end-users is affected by both government regula-tion andmarket demand. The government sets the upper and lowerlimits of the gas price according to the gas production cost, trans-portation cost, service charge, etc. Furthermore, after implement-ing the TOU price policy, the peak, flat, and valley prices mustsatisfy the following constraints:

p0 � pp � pup; plow � pv � p0; pv � pf � pp;

where pp, pf and pv denote the peak, flat, and valley prices,respectively. p0 represents the natural gas price before imple-menting the TOU price, and p0 ¼ pf. pup and plow respectivelyrepresent the upper and lower limits of nature gas TOU price set bythe government.

3.2. Behavioral rules of the gas user agent

3.2.1. Responsive load economic modelUser demand response is formally described as a change in the

natural gas usage by the users from their normal consumptionpatterns, in response to the changes of the prices over time or toavoid jeopardizing the reliability of the UGPN. This paper developsan economic model of natural gas price responsive loads based onthe model originally built by Schweppe et al. [29] and subsequentlyrenovated by Alami et al. [10] and Moghaddam et al. [11]. Themodel is described below.

Suppose that the users change their gas demand fromd0(i)(initial value) to d(i) during i-th hour in response to the TOUprice. If the income of the users during the i-th hour by consumingd(i) m3 of the natural gas is represented by B(d(i)), then the in-dustrial and commercial user benefit S(d(i)) during the i-th hour isas follows:

SðdðiÞÞ ¼ BðdðiÞÞ � dðiÞ � pðiÞ (1)

The traditional benefit calculation method is described by thefollowing quadratic benefit function [29]:

BðdðiÞÞ ¼ B0ðiÞ þ p0ðiÞ½dðiÞ � d0ðiÞ��1þ dðiÞ � d0ðiÞ

2Eði; iÞd0ðiÞ�: (2)

Where E(i,i) represents own-price elasticity of natural gas, andE(i,i) < 0. Substituting Eq. (2) into Eq. (1), we have the followingequation:

SðdðiÞÞ ¼ B0ðiÞ þ p0ðiÞ½dðiÞ � d0ðiÞ��1þ dðiÞ � d0ðiÞ

2Eði; iÞd0ðiÞ�� dðiÞ � pðiÞ:

(3)

Given that S(d(i)) is a function of d(i), the second derivative ofS(d(i)) for d(i) can be expressed as follows:

v2Svd2ðiÞ ¼ p0ðiÞ

Eði; iÞd0ðiÞ< 0: (4)

Eq. (4) indicates that the user benefit function S(d(i)) has amaximum value, and the maximum benefit can be reached bysetting vS/vd(i) ¼ 0. Therefore, user consumption can be repre-sented as follows:

dðiÞ ¼ d0ðiÞ�1þ Eði; iÞpðiÞ � p0ðiÞ

p0ðiÞ�: (5)

3.2.2. Goals and constraints of the user agentThe goal of the user agent in responding to the peakevalley

price is to reduce his own natural gas consumption expenditure.In other words, the benefit of the user after implementing the TOUprice becomes larger than that before implementing the TOUpricing policy. Suppose that the total energy consumption of theuser in a day is a constant, and then the load can only transfer todifferent times in the day. Further, we assume that the users cannotsatisfy their gas needs from other sources, such as electricity.

Before implementing the TOU price, the user benefit during thei-th hour can be represented by S0(i) ¼ B0(i) � d0(i) � p0. Thus, thetotal benefit of the user in a day is given as follows:

S0 ¼X24i¼1

S0ðiÞ ¼X24i¼1

B0ðiÞ � d0ðiÞ � p0: (6)

After implementing the TOU price, the user benefit during the i-th hour can be expressed by S1(i) ¼ B(d(i)) � d(i) � p(i). Bysubstituting Eq. (2) and Eq. (5) in this formula, we arrive at thefollowing equation:

S1ðiÞ ¼ B0ðiÞ � d0ðiÞ$Eði; iÞ½pðiÞ � p0ðiÞ�2

2p0ðiÞ� pðiÞ$d0ðiÞ (7)

Therefore, the total benefit of the user in a day can be denoted asfollows:

L. Li et al. / Energy 52 (2013) 37e4340

X24 X24 " �pp � p0

�2 #

S1 ¼

i¼1

S1ðiÞ ¼i¼1

B0ðiÞ � Eði; iÞ2p0

þ pp

$d0p �"Eði; iÞ

�pf � p0

�22p0

þ pf

#

$d0f �"Eði; iÞ ðpv � p0Þ2

2p0þ pv

#$d0v; ð8Þ

s:t:X24i¼1

d0ðiÞ ¼ dp þ df þ dv; (9)

S1 � S0; (10)

where d0p, d0f and dov denote initial total demand of industrial andcommercial user in peak period, flat period, valley period, respec-tively. dp, df and dv respectively represent the total demand of in-dustrial and commercial user in peak period, flat period, valleyperiod after implementing the TOU price. Eq. (9) shows the totalenergy consumption of the user as a daily constant before and afterTOU price. Eq. (10) shows that the user benefit after TOU price islarger than the value before the TOU price.

3.3. Behavioral rules of the gas operator agent

The goal of the gas operator agent, when adjusting the peak andvalley prices, is to reduce the peakevalley load difference and loadshifting as well as increase his earnings.

3.3.1. Price adjustment ruleBy assuming that the price adjustment rule of the gas operator

agent is such that at each time, the peak price can be increased by1% over the flat price, we can then deduce the variation rules of thevalley price. According to Eq. (5), we have the following:

dp ¼ d0p

�1þ Eði; iÞ$pp � p0

p0

�: (11)

Simplifying Eq. (11), the load variation of peak period is obtainedby Ddp ¼ dp � d0p ¼ d0$E(i,i)$pp � p0/p0]. Based on the suppositionthat the total energy consumption of the user in a day is constant,the decreasing load in the peak period equals the increasing load inthe valley period. Thus, we have the following equation:

Ddv ¼ �Ddp ¼ �d0p$Eði; iÞ$pp � p0

p0

�: (12)

Furthermore, according to Eq. (5), we have the following:

dv ¼ d0v

�1þ Eði; iÞ$pv � p0

p0

�: (13)

Table 1The daily load data in Zhengzhou city.

Hour Gas consumption (m3) Hour Gas consumption (m3)

0 18,460 6 48,7801 24,040 7 48,8802 21,140 8 54,0203 25,660 9 51,6604 29,020 10 53,5005 28,780 11 59,640

Note: “0” means 0:00e1:00, “1” means 1:00e2:00,.., “23” means 23:00e24:00.

Simplifying Eq. (13) and substituting Eq. (12), the valley price isobtained using the following equation:

pv ¼ p0 �d0p �

�pp � p0

�d0v

�: (14)

3.3.2. Goals and constraints of the gas operator agent

(1) Minimum peak load:

Lp ¼ minpp;pf ;pv

�max1�i�24

Li�pp; pf ;pv; i

��; (15)

(2) Maximum valley load:

Lp ¼ maxpp;pf ;pv

�min

1�i�24Li�pp; pf ;pv; i

��; (16)

(3) Minimum peakevalley load difference:

Lp�v ¼ minpp;pf ;pv

�max1�i�24

Li�pp;pf ; pv; i

�� min

1�i�24Li�pp; pf ; pv; i

��

(17)

where Li denotes the total loads of the residential, industrial andcommercial user.

Before implementing the TOUprice, the gas operator benefit in aday can be expressed as follows:

R0 ¼ ðp0 � CÞX24i¼1

d0ðiÞ: (18)

After implementing the TOU price, the gas operator benefit in aday can be represented as follows:

R1 ¼�pp � C

�dp þ

�pf � C

�df þ ðpv � CÞdv: (19)

Where C denotes nature gas cost of gas operator. The followingconstraint should be satisfied to ensure that the benefit of the gasoperators increases:

R1 � R0: (20)

4. Case study

Zhengzhou, the capital of Henan Province located in the nationalgeographic center of China, is an important central city and acomprehensive transportation center. The total area of Zhengzhouis 7446.2 square kilometers, and has a population of 9.1 millionpeople. End-users here mainly consume energy in the followingforms: coal, electricity, natural gas, oil, and heat. According to sta-tistics, natural gas consumption rate achieved 13% in the energy-consuming enterprise of Zhengzhou in 2011, higher than the na-tional average of 4.5% [30]. In 2011, the average daily natural gas

Hour Gas consumption (m3) Hour Gas consumption (m3)

12 48,420 18 51,16013 47,700 19 42,68014 48,780 20 38,98015 50,020 21 41,68016 57,800 22 21,66017 63,580 23 23,960

Fig. 2. Relationships between peak, flat and valley prices and increased ratio of peak price.

Fig. 3. Maximum peak loads.

Fig. 5. Gas operator benefits.

L. Li et al. / Energy 52 (2013) 37e43 41

consumption of Zhengzhou was approximately 1 million m3, whilethe peakevalley load ratio was close to ten times in the UGPN.

Therefore, in order to test the validity of the proposed modeland calculation method, we considered the UGPN in Zhengzhou asa case study to simulate the dynamic operation of the gas pipelinenetwork. Table 1 presents the daily load data. We divided 24 h in aday into three period types, i.e., peak, flat, and valley periods. Thepeak period refers to the time period between 08:00 and 12:00,andbetween 16:00 and 19:00. The flat period refers to the time periodbetween 06:00 and 08:00, between 12:00 and 16:00, and between19:00 and 22:00. The valley period refers to the time period be-tween 22:00 and 06:00.

Fig. 4. Maximum peakevalley load difference.

Net Logo software [31] was used to simulate this multi-agentsystem. Details of the input and output variables are listed below.

Input variables are as follows: total natural gas consumption:Q¼ 1million m3; natural gas price before implementing TOU price:p0(i) ¼ 2 Yuan/m3; natural gas costs of the gas operator:C ¼ 1.4 Yuan/m3; upper and lower limits of the natural gas price:pup ¼ 3 Yuan/m3, plow ¼ 1 Yuan/m3; elasticity coefficient:E(i,i) ¼ �0.581 (see Ref. [32]); residential users consumption ratio

Fig. 6. Industrial and commercial user benefits.

Fig. 7. Comparison of daily load curves before and after implementing TOU price in Zhengzhou.

L. Li et al. / Energy 52 (2013) 37e4342

of total consumption: [20%, 30%]; and increased ratio of the peakprice over the flat price: [0, 50%].

Output variables are as follows: peak price, valley price,maximum peak load, maximum peakevalley load difference, thebenefit of the gas operator, and the benefit of the gas users.

4.1. Simulation results of the peakevalley prices

Fig. 2 shows the changes in peak, flat, and valley prices afterimplementing the TOU price; when the peak price increases 24%over the flat price, the peak and valley prices are 2.48 and0.95 Yuan/m3, respectively. At this time, the monitoring agent de-tects that the valley price is beyond the lower limit (the govern-ment sets the range of peak and valley price as pup¼ 3 Yuan/m3 andplow ¼ 1 Yuan/m3). When the peak price increases 23% over the flatprice, the peak and valley prices are 2.46 and 1.00 Yuan/m3,respectively. The valley price equals the lower limit exactly, whichmeans that the peak price can be increased at a maximum of 23%over the flat price.

4.2. Simulation results of maximum peak load and peakevalleyload difference

Figs. 3 and 4 show the variation trends of the maximum peakload and maximum peakevalley load difference, respectively. Wecan see that when the residential user consumption ratio is aconstant, both the maximum peak load and the maximum peakevalley load differences decrease along with the increase of thepeak price. Moreover, when the increased ratio of the peak price is aconstant, both the maximum peak load and the maximum peakevalley load differences decrease in response to the decrease in theresidential user consumption (i.e., the increase of the industrial andcommercial user consumption).

The above results indicate that the natural gas TOU price forindustrial and commercial users effectively reduces the peakevalley load difference and load shifting in the UGPN.

4.3. Simulation results for the benefits of the gas operator andindustrial and commercial users

Fig. 5 shows the variation trend of the gas operator benefits. Wecan see that when residential user consumption ratio is a constant,the gas operator benefit decreases at first, and then increases alongwith the increase of the peak price. Furthermore, if the increasedratio of the peak price is less than 15%, then the gas operator incurslosses. In other words, the gas operator begins to benefit only whenthe increased ratio reaches a threshold value. In comparison, whenthe increased ratio of the peak price is a constant, the gas operatorbenefit decreases in response to the increase of the residential userconsumption (i.e., the decrease of the industrial and commercialuser consumption). If the consumption ratio of residential users ismore than 28%, the gas operator incurs losses, indicating that the

industrial and commercial users are the main sources of the gasoperator benefits.

Fig. 6 indicates that when the residential user consumption ratiois a constant, the industrial and commercial user benefits increasefaster according to the increase in the peak price. Hence, imple-menting the natural gas TOU price policy for industrial and com-mercial users can effectively increase their benefits.

Based on the analysis of the above mentioned simulation re-sults, within the range of the prices set by the government, thegreater peakevalley price difference and smaller residential userconsumption ratio result in the smallermaximumpeakevalley loaddifference as well as greater benefits for both the gas operator andthe industrial and commercial users. In Zhengzhou, when the peakprice increases by 23%, and the residential users consumption ratiois 20%, the maximum peakevalley load difference is the smallest,and the benefits of the gas operator and the industrial and com-mercial users are the highest, thereby leading to the following re-sults: peak price pp ¼ 2.46 Yuan/m3, valley price pv ¼ 1 Yuan/m3;maximum peak load Lp ¼ 57,983.82 m3, minimum valley loadLv ¼ 22,790.77 m3; and maximum peakevalley load differenceLp�v ¼ 35,193.05 m3.

Fig. 7 compares the daily load curves before and after imple-menting the natural gas TOU price in Zhengzhou. The load duringthe period of 17:00e18:00 is the maximum, whereas that during0:00e01:00 is the minimum. The maximum peak load reduced by5596.18 m3, while the minimum valley load improves by4330.77 m3. The maximum peakevalley load difference decreasesby 9926.95 m3 (i.e., 22%). Finally, the benefits of the gas operatorand the industrial and commercial users increase by more than5932.11 and 58,530.87 Yuan, respectively.

5. Conclusions

We examined the natural gas TOU price for the industrial andcommercial users in the UGPN using a multi-agent simulationmethod. We analyzed the UGPN in Zhengzhou, China as a casestudy for our simulation experiment to test the efficiency of theproposed model and simulation method. The results are summa-rized below.

(1) Implementing TOU price effectively reduces the peakevalleyload difference, increases the benefits of the gas operatorsand users, and provides a basis for decisions pertaining to theimplementation of the natural gas TOU pricing policy in otherregions.

(2) After implementing the TOU price, the gas operators suffer aloss in the following two cases: when the natural gas con-sumption of the industrial and commercial users falls below agiven threshold, and when the peakevalley price differencefalls below a given threshold. Therefore, the gas operatorstend to increase the peak price and supply more natural gasto the industrial and commercial users to maximize their

L. Li et al. / Energy 52 (2013) 37e43 43

own benefits. In comparison, the industrial and commercialusers benefit from the TOU pricing policy, and the greaterpeakevalley price difference results in more earnings forthem.

(3) The natural gas TOU pricing mechanism is a complex system,because the natural gas consumption structure and character-istics vary across different regions. The customer response tothe price change can also vary. To provide more empirical datafor implementing the natural gas TOU price, further study isneeded in applying the technique to more representative citiesin other regions.

Acknowledgement

This research was supported by the National Natural ScienceFoundation of China, Grant No. 71173202. The authors would like tothank the reviewers for their helpful comments.

References

[1] BPstatisticalreviewofworldenergy,www.bp.com/statisticalreview;June2012.[2] Yu SW, Zhu KJ. A hybrid procedure for energy demand forecasting in China.

Energy 2012;37(1):396e404.[3] Tishler A. A model of industrial demand for electricity under time-of-use

pricing and three labor shifts. Resources and Energy 1984;6(2):107e27.[4] Atkinson SE. Reshaping residential electricity load curves through time-of-use

pricing. Resources and Energy 1981;3(2):175e94.[5] Tishler A. The industrial and commercial demand for electricity under time-

of-use pricing. Journal of Econometrics 1983;23(3):369e84.[6] Aazami R, Aflaki K, Haghifam MR. A demand response based solution for LMP

management in power markets. International Journal of Electrical Power &Energy Systems 2011;33(5):1125e32.

[7] Wang JH, Bloyd CN, Hu ZG, Tan ZF. Demand response in China. Energy 2010;35(4):1592e7.

[8] Cappers P, Goldman C, Kathan D. Demand response in U.S. electricity markets:empirical evidence. Energy 2010;35(4):1526e35.

[9] Faria P, Vale Z. Demand response in electrical energy supply: an optimal realtime pricing approach. Energy 2011;36(8):5374e84.

[10] Aalami HA, Moghaddam MP, Yousefi GR. Demand response modelingconsidering interruptible/curtailable loads and capacity market programs.Applied Energy 2010;87(1):243e50.

[11] Moghaddam MP, Abdollahi A, Rashidinejad M. Flexible demand responseprograms modeling in competitive electricity markets. Applied Energy 2011;88(9):3257e69.

[12] Lou SXC, Keng CWK, Jiang J, Cheng F. Time of use (TOU) rate effect using thepattern clustering method. Energy 1992;17(11):1093e104.

[13] Tan ZF, Wang MB, Qi JX, Hou JC, Li X. Time-of-use price optimizing model andfuzzy solving method. Systems Engineering e Theory & Practice 2008;28(9):145e51.

[14] Nikzad M, Mozafari B, Bashirvand M, Solaymani S, Ranjbar AM. Designingtime-of-use program based on stochastic security constrained unit commit-ment considering reliability index. Energy 2012;41(1):541e8.

[15] He YX, Wang B, Wang JH, Xiong W, Xia T. Residential demand responsebehavior analysis based on Monte Carlo simulation: the case of Yinchuan inChina. Energy 2012;47(1):230e6.

[16] Doostizadeh M, Ghasemi H. A day-ahead electricity pricing model basedon smart metering and demand-side management. Energy 2012;46(1):221e30.

[17] Chen C, Liao C. A linear programming approach to the electricity contractcapacity problem. Applied Mathematical Modeling 2011;35(8):4077e82.

[18] Lee T, Chen N. Determination of optimal contract capacities and optimal sizesof battery energy storage systems for time-of-use rates industrial customers.IEEE Transactions Energy Conversion 1995;10(3):562e8.

[19] Lee T, Chen C. Iteration particle swarm optimization for contract capacitiesselection of time-of-use rates industrial customers. Energy Conversion andManagement 2007;48(4):1120e31.

[20] Bernard J, Bolduc D, Yameogo N. A pseudo-panel data model of householdelectricity demand. Resource and Energy Economics 2011;33(1):315e25.

[21] Olmos L, Ruester S, Liong SJ, Glachant JM. Energy efficiency actions related tothe rollout of smart meters for small consumers, application to the Austriansystem. Energy 2011;36(7):4396e409.

[22] Walawalkar R, Fernands S, Thakur N, Chevva KR. Evolution and current statusof demand response (DR) in electricity markets: Insights from PJM and NYISO.Energy 2010;35(4):1553e60.

[23] Torriti J. Price-based demand side management: assessing the impacts oftime-of-use tariffs on residential electricity demand and peak shifting innorthern Italy. Energy 2012;44(1):576e83.

[24] Ou CQ, Xie C, Xu JX, Liu FH. Time-of-use price decision model of natural gasbased on simulation and grey relationships. In: 2010 3rd International Con-ference on Information Management, Innovation Management and IndustrialEngineering; 2010.

[25] Valenzuela J, Thimmapuram PR, Kim J. Modeling and simulation of consumerresponse to dynamic pricing with enabled technologies. Applied Energy 2012;96:122e32.

[26] Yousefi S, Moghaddam MP, Majd VJ. Optimal real time pricing in an agent-based retail market using a comprehensive demand response model. Energy2011;36(9):5716e27.

[27] Meier H, Rehdanz K. Determinants of residential space heating expendituresin Great Britain. EnergyEconomics 2010;32(5):949e59.

[28] Nilsen OB, Asche F, Tveteras R. Natural gas demand in the European house-hold sector. The Energy Journal 2008;29(3):27e46.

[29] Schweppe FC, Caramanis MC, Tabors RD, Bohn RE. Spot pricing of electricity.Kluwer Academic Publishers; 1989. Appendix E.

[30] http://www.zzjnw.com/news_show.asp?id¼4072&BigClassID¼75; 2012.[31] Wilensky U. NetLogo [M]. Evanston, IL: Northwestern University, Center for

Connected Learning and Computer-based Modeling; 1999.[32] Feng L, Zhang D, Wang XQ. Demand model construction and measurement

analysis for Shanghai gas market. Natural Gas Industry 2009;2:120e2. 147. [InChinese].