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A Load Management Method to Reduce the Power Energy Cost for Glass Industry

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A Load Management Method to Reduce the Power Energy Cost for Glass Industry

Jong-Ching Hwang

1

, Jung-Chin Chen

1

, J.S. Pan

1 Department of Electrical Engineering National Kaohsiung University of Applied Sciences

Kaohsiung, Taiwan [email protected]

Yi-Chao Huang

2

Department of Industrial Management

National Pingtung University of Science and Technology Pingtung, Taiwan

[email protected]

Abstract—The aim of this research is to study the power cost reduction of glass manufacturing process for industrial customers and to relieve the crisis of electricity shortage during summer peak time period through load management (LM). This research can also provide decision makers and managers with useful LM strategies to use as guidance. The results indicate that local glass industry is highly willing to participate in the development of LM strategies. As the running time of a ball mill is adjusted to the preferential rates of time of use (TOU), industry customers can save a certain amount of electricity cost.

Index Terms--Load management (LM), Time of Use (TOU), power consumption characteristics, Optimal demand contract, Load demand control, and Demand-side management.

I. INTRODUCTION

ITH the rapid growth of industry and commerce as well as the rise of the living standards, the energy sales of Taiwan Power Company (TPC) have been increasing every year, resulting in the insufficiency of reserved power supply.

Accordingly, power-rationing crisis could occur during summer peak loading hours. This will definitely cause inconvenience to industrial and commercial sectors, affecting the lives of the general public and further leading to doubts and complaints regarding the procedures implemented by TPC.

Therefore, it is an urgent task to alleviate power-rationing pressure through load management (LM) to reduce demand for power during peak hours. If the study on manufacturing process, equipment and power consumption characteristics of the industries with huge power consumption is conducted, the load management methods and the potentiality of power saving or the shifting of peak hours can be achieved. Along with appropriate management and electricity rate incentive package, it can be expected that peak loading can be effectively reduced, power-rationing crisis minimized, and electricity cost lowered [1]. In the face of power shortage caused by deferred construction of power plants and establishment of power transmission and power distribution systems, TPC worked out a preferential electricity rate policy to decrease the demand during peak hours on customers' side.

Efficient use of energy is of critical concern, especially to those industries with huge power consumption such as iron and steel, petrochemical, cement and paper-making, all of

which are required to adopt energy-saving plans to boost their competitiveness [1], [2]. Analysis of the power consumption by commercial customers shows that the operations of air- conditioning equipments are of the highest power efficiency.

Those energy-saving systems that could aid TPC and customers in various LM schemes and load distribution strategies such as demand control, cycling control and timer control to solve the problems of power shortage and energy spending in summer season have become popular subjects of studies [3]-[6].

Foreign load research places emphasis on load forecast and demand-side management mainly as the standing policy of power supply industry [7]. There are very few studies on the power consumption characteristics of individual industry that can provide effective LM measures to assist industry in saving power costs. Yet, domestic power supply industry centers on the feasibility of interruptible load rates in which customers can participate. Besides the focus is placed on the automatic load procedures to control the power consumption during peak hours, the manufacturing process and power consumption characteristics of each industry are rarely analyzed. The best measures to save power costs are also seldom provided. Based on local and foreign experiences, this research analyzes the manufacturing process, equipment operation and power consumption characteristics of the ceramics industry in Taiwan. Through the management on demand side, it is hoped that effective LM strategies can be implemented to reduce power energy costs and ultimately boost the competitiveness [8], [9].

II. THE ANALYSIS ON EQUIPMENT CHARACTERISTICS OF GLASS INDUSTRY

This research requires the visit of glass manufacturers, one of which produces particle materials for tile and the rest are the integration plants from raw materials to finished products.

Their products include floor bricks, wall bricks, quartz bricks and glass tiles. This section depicts the equipment characteristics of glass production procedures. The main production equipments are as follows: ball mills, spray drying furnaces, glazing machines and sintering furnaces. Fig. 1 illustrates the manufacturing procedures of a certain tile factory.

Jung-Chin Chen is with Electrical Engineering Department, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan, R.O.C. (e- mail: [email protected], voice: +886-7-7659990, fax: +886-7- 3804939, Address: No. 245, Shinle St., Fengshan City, Kaohsiung , Taiwan ).

W

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Fig. 1. The production equipment and power capacity of Tile Maker.

A. The Characteristics Analysis of Ball Mill

This equipment is to mill stone of large grain size into particles or powder. 35% of water is added to form slurry and prepare for spray drying later. The equipment functions are divided into two categories: stone milling and glaze milling.

The power capacity of the former is bigger than that of the latter. Electric power is the only energy source for the equipment. Generally speaking, its power capacity accounts for 44%-56% of the whole production line. Its power consumption is rather huge with a running time of approximately 13-16 hours. The running time depends on the particle size. This equipment runs once a day. Feeding and unloading makes up the remaining time. The milling cycle of a ball mill consists of one hour of feeding, 13-16 hours of milling and half an hour of unloading. After milling, the slurry is stored in the sink and the ball mill is not classified as continuous production type. During the 15-hour milling time, the first ball mill starts to feed at 8:00am, begins to mill at around 10:0am and stops at 1:00am the next day. The second ball mill starts to feed at 10:00am, begins to mill at 12:00pm and stops at 3:00am the next day.

Since the milled slurry can be stored in the sink, this equipment can stop operating after milling. Accordingly this equipment can coordinate with the LM implementation of the interruptible rate and TOU rate. However there are no concrete energy-saving measures. The power capacity of this equipment is approximately 600kW-1150kW. Its running greatly influences daily load curve of glass manufacturing process.

Therefore, this equipment should be seen as the center target of LM in the glass manufacturing process.

B. The Characteristics Analysis of Spray Drying

This equipment injects the milled slurry into tower and blows into tower the hot air produced by burning heavy oil.

The slurry is instantly dried into particles, which fall down to the bottom of tower in a natural way.

The thermal source of this equipment is the burning of heavy oil and the tower's working temperatures from bottom to top range from 100°C to 600°C. There is a ventilator at the lower part of the tower to exhaust waste heat into the atmospheric layer as the waste heat cannot be reused. The energy source of this equipment comes from electricity and heavy oil. The power capacity of this equipment is approximately 1109kW-260kW. The operation of this equipment is classified as continuous production mode and cannot be singly stopped to coordinate with LM of the interruptible rate. This equipment cannot be run during off- peak hours. There are no concrete energy-saving measures.

C. The Characteristics Analysis of Forming Machine

Through high temperatures and oil or an air compressor, this equipment forms the dried particles for sintering in the next step. The power capacity of electricity equipment in the

forming machine is approximately 200kW. The cooling machine is served as the cooling of forming machine to avoid the damage of the mold. In general the cooling machine comes in ice water pump, and the power capacity is 35kW-50kW.

The running of this equipment is in continuous production mode and can not be individually stopped for load management strategy. There’s also no concrete measures for energy saving.

D. The Characteristics Analysis of Glazing Machine

This equipment is to glaze the formed particles. Based on the color classification, this process is divided into a few steps:

screening, glazing and printing. Its power capacity is approximately 4kW-11kW. The operation of the equipment is in continuous mode and cannot be singly halted for the LM of the interruptible rate scheme.

E. The Characteristics Analysis of Sintering Furnace This equipment is to sinter the glazed compact into finished product with high temperature. The product quality completely depends on this equipment's operation. According to the product classification, this machine can be divided into two parts, one of which is an open tunnel kiln of 70-90 meters in length. The thermal source is natural gas. The glazed compact is put on a cart to slowly enter the tunnel from front end. In the sintering process, it takes 30-40 hours for the compact to go through the tunnel on a cart at a computer-controlled speed and become finished product. This tunnel can process bricks and glass tiles. The electric equipments of the kiln include ventilator, exhauster and drag motor with a total power capacity of 55kW. The other is roller hearth which is quite different from the former one in the operation method. The glazed compact directly enters the hearth from the front and goes through the whole hearth by the underneath bearing, which is full of rollers. The thermal source is also natural gas at high working temperature of 1150°C. It takes 40-50 minutes to go through the whole hearth of 80 meters in length and becomes the finished product.

Both electricity and natural gas are the energy source of this equipment. The electricity equipments include ventilator, exhauster and drag motor and its power capacity is 110kW.

Since this equipment is working in continuous production mode and it can't be individually stopped to cope with the LM of interruptible rate.

III. THE RESEARCH METHOD

This research is conducted using questionnaire, field visit and the collection of relevant materials to analyze power consumption characteristics. According to the power consumption characteristics of different manufacturing processes, the greatest potentiality of LM can be achieved.

The research flow chart is show in Fig. 2, and the methods and the steps are listed as below.

1. Survey the current status and future development of glass industry; Visit glass manufacturers to have a further understanding of the issues on environment, raw materials, power strategy and the expansion investment.

2. Survey the manufacturing process, equipments and the power consumption of glass industry.

3. The power consumption characteristics of different processing equipments in the sampled industry can be summarized through a rigid survey and analysis of the

Formula Ball Milll Spray Dry Tower Formula Ball Mill

Forming Furnace Glazing

Kiln Finished

2kW 600kW 600kW

110kW 195kW 110kW 90kW

110kW 2kW

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equipments and power consumption characteristics. In the meantime, it can be understood whether the equipment can be flexibly regulated or be put on duty cycling control in line with LM procedure.

4. The data collected from a multi-function digital power meter, the power consumption ratio of each process and power consumption of the major equipments can be analyzed to cope with LM procedure.

5. Through the gathering of monthly power consumption data and peak and off-peak load of the manufacturing industry, the potentiality of the introduction of LM can be evaluated for the preferential electricity rate package.

6. Determine the LM strategy for the sampled industry.

According to the power consumption characteristics of different manufacturing processes, the greatest potentiality of interruptible load rate in each plant can be achieved.

7. It is hoped that the proposed suggestion will be adopted by the manufacturing industry to implement LM to achieve the benefit of reduced power costs.

Fig. 2. The research flow charts.

IV. THE LOAD MANAGEMENT AND RATE ANALYSIS This section studies and analyzes the rate policy of TPC.

The power consumption of customers is observed through daily load curve. In the meantime, the electricity rates are used to evaluate its potentiality in LM participation.

A. The Analysis of the TOU Rate

The load curve Fig. 3 and 4 of two tile makers are used for the understanding of the power consumption of a few tile makers with large production value. Their manufacturing processes and equipments are similar; however the power consumption status is different due to their manufacturing

process arrangements. This will affect the electricity expenditure of the customers. Fig. 3 remarkably indicates that before 3:00am, the power consumption during off-peak hours is larger than 8:00am peak power consumption. Yet Fig. 4 shows the power consumption during peak hours is larger than that of off-peak hours. The former indicates that TOU rate concept is deeply rooted in the management level and the manufacturing process designs. However Fig. 4 shows that the customer leaves much to be desired in the implementation of the LM of TOU rate.

Plant visits reveal that the two customers have the same problems, i.e. their ball mills of large power consumption starts running in peak hours (after 1:00pm) for 14-15 hours and stop operation at 3:00am, leading to a period of four and a half hours during off-peak hours, when the power cannot be used.

This causes a loss to both TPC and the manufacturers. Fig. 4 indicates that customers B can serve as an example for the analysis of the effect of power consumption status when the ball mill changes its running time.

This customer has four sets of ball mills with total power capacity of 2400kW. The running is arranged in this way: The first ball mill starts running at around 12:00pm during the lunch break to reduce high instant consumption for one hour.

After that, the rest of three ball mills take turns to run at an interval of an hour. The daily peak hours normally fall at 4:00pm. After 1:00am, the ball mills shuts down one after another. The result during the off-peak hours (from the shutdown of machines until 7:00am) cannot be used as clearly shown on Fig. 4.

Customer B's demand contract capacity is 3500kW with total power capacity of 3985kW for major production equipments. While the power capacity of ball mill makes up 56% of major production equipments. If customer B can postpone the running of the four ball mills until four hours later, it can decrease its peak power consumption by 9600kWh (2400kWx4 hour). Although the off-peak power consumption will accordingly increase, it can still save NT$11,328 (9600xNT$1.89-9600xNT$0.71) in electricity fee without affecting its manufacturing process.

Workday

0 200 400 600 800 1000 1200 1400 1600 1800 2000

00:00 01:00

02:00 03:00

04:00 05:00

06:00 07:00

08:00 09:00

10:00 11:00

12:00 13:00

14:00 15:00

16:00 17:00

18:00 19:00

20:00 21:00

22:00 23:00

Time Non-workday kW

Nom-workday

Workday

Fig. 3. The Daily Load Curve on Workday and Non-workday of Customer A The research of power consumption characteristics of sampling industry

to policy on load management

The determination of research plan

Information collection of production & sale, power consumption of equipment in the ceramics industry

Data collection of power

consumption Papers review

Information compilation

Analysis on the power consumption characteristics

To decide power energy management strategy

Conclusions and suggestions

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max

min

Subject to PPoptP

Workday

0 500 1000 1500 2000 2500 3000 3500

00:00 01:00

02:00 03:00

04:00 05:00

06:00 07:00

08:00 09:00

10:00 11:00

12:00 13:00

14:00 15:00

16:00 17:00

18:00 19:00

20:00 21:00

22:00 23:00

Time Non-workday kW

Fig.4. The Daily Load Curve on Workday and Non-workday of Customer B.

B. The Analysis of the Optimal Demand Contract

With the rapid growth of air conditioner load, the peak loading of customers in summer daytime increases dramatically and the condition of peak loading in the 15- minute leading demand contract become more serious.

According to electricity price system of TPC, customers are asked to pay extra cost based on the portion of basic fee in case the peak loading is higher than that stated in demand contract. Although the inappropriate high demand contract can avoid the occurrence of the previous stated problem, it will result in another problem, higher basic electricity fees. The basic idea of an optimal demand contract strategy is to derive a better demand contract so that annual basic electricity cost can be minimized [10], [11]. In other words, the maximum demand is measured by 15-minutes in average. In case customers' actual maximum demand is in excess of that stated in the contract, the demand charge of an excess within 10% of the contracted capacity is twofold of the electricity rate stated in the contract, and an excess of over 10% renders threefold of the stated electricity rate.

For those customers who adopt regular rate under maximum demand contract, the regular contracted demand is set according to the agreement between the customer and the power company based on customers' maximum demand in summer. The non-summer contracted demand is the demand in excess of the regular contracted demand in non-summer time. In case, customers' actual maximum demand is in excess of the contracted capacity, the demand charge of and excess of less than 10% of the contracted capacity is charged twofold of the rate stated in contract, while an excess of over 10% the contracted capacity is charged threefold of the stated rate in the contract.

Fig. 5 shows the schematic diagram of an optimal demand contract derivation. In this figure, 12 one-month time intervals with different monthly peak loading are selected to describe the derivation of the optimal demand contract for high-tension customer. In the months of 1, 2, 3, 11 and 12, the monthly peak loading Pi, max is lower than the demand contract but the customers are still required to paybasic electricity fee stated in the demand contract PDC. The blocks with slash shows the lost cost due to the insufficient peak loading. Besides the peak loading Pi, max in the remaining months are higher than the demand contract, which leads to an extra payment for electricity fees. The blocks filled with slash lines in these months express the penalty cost for basic electric fees. The

smaller the area of the block with slashes, the lower the extra payment for the electricity fees. It indicates that the minimization of the area of those blocks will bring about an optimal demand contract.

The following shows the computation of monthly basic electricity fee under three conditions. Based on (1), the formula of the optimal demand contact with linear programming form is obtained in (2). In (2), the only one inequality constraint is that Popt is within the interval of between Pmin and Pmax. Also the terms of Ci (Popt) and EC (Popt) mean the basic electric fee and extra payment. It is noted that the Popt affects both these two terms. The calculation of monthly electric basic fee is shown as follows:

⎪⎩

⎪⎨

>

×

− +

× +

×

<

×

×

− +

×

×

=

DC max max

max max

max

1 . 1 3

) 1 . 1 ( 2

. 0

1 . 1 2

) (

P P

S P P S P S P

P P

P S P P S P

P P S P CB

i DC i

DC DC

Dc i

DC DC

i DC

DC i DC

(1)

Where

CB: basic monthly electricity fee (demand charge);

PDC: demand contract negotiated with TPC in kW;

S: coefficient in summer (6, 7, 8 and 9 month) is NT$213/ kW in non-summer (1, 2, 3, 4, 5, 10, 11 and 12 month) is NT$159/ kW;

Pi, max: customer monthly peak loading kW.

The formulation of optimal demand contract is expressed as follows:

[ ]

=

+

=

12

1

) ( )

(

i

opt opt

i

P EC P

C Min

CB

(2)

Fig. 5. The schematic diagram of optimal demand contract selection.

In the plant visit, the optimal contract capacity is not well implemented by industry customers. As the customer roughly estimates the optimal demand contract based on the historical information and didn't analyze using mathematical method.

Thus the expenditure of demand charges increase. After explanation and analysis, the customer is willing to implement an optimal contract capacity. The analysis of power consumption characteristics and optimal demand contract is shown in Table I.

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TABLE I

THE ANALYSIS OF OPTIMAL DEMAND CONTRACT

Month kW (Monthly peak

loading) Equipment Capacity: 3985kW The scope of peak loading:

2004kW~3546kW Regular contract capacity:

3500kW

Non-optimal contract fee:

NT$7453596 /year Optimal contract capacity:

3160kW

Optimal contract fee:

NT$7142526 /year Customer sampled saves NT$311070/year January 2148

February 2004 March 2890

April 2953 May 3302 June 3546 July 3458 August 3346 September 3160

October 3043 November 2812 December 2171

Table I indicates the monthly peak load for the sampled customer and the peak load within one-month period is between 2004kW and 3546kW (Pi, min=2004kW and Pi, max

=3546kW). This customer's current regular demand contract capacity is 3500kW with total power capacity of 3985kW.

Consequently, the customer can reduce the contract capacity with TPC from 3500kW to 3160kW.

To sum up, this sampled customer may adjust his contract capacity to save a considerable electricity cost. If this customer select an optimal contract capacity (3160kW), he can save NT$311070 (NT$7453596-NT$7142526) in annual power cost.

C. The Analysis of Interruptible Load

TPC is proactively engaged in power development and implements various LM measures such as interruptible rate, TOU rate and seasonal rate in the hope that the reliability of system power supply can be increased and peak load be reduced. Taking interruptible rate for example, TPC started the implementation in 1987 and expanded it and revised its content every year. Based on the power system, the six different interruptible rates are planned for different industrial customers' selection. Additionally, TPC, according to their interruptible capacities, offers demand charge discounts if the customers sign a contract with TPC.

D. The Load Demand Automatic Control Analysis

In order to implement LM, demand contracts that require an interruptible load are offered to customers at a discount.

The peak load can be reduced during periods of high demand by interrupting loads according to the load control scheduling.

To minimize the inconvenience for customers, to absolutely minimum, the load groups should be shed in sequence according to the schedule of the interruptible load groups [12], [13]. In addition to the critical issue of production quality, cost-effective electric energy management is now being considered by customers [12]-[15]. To save power energy, a load control scheduler is required to assist customers in electricity cost saving with minimal discomfort.

The control method of load consumption is another way to reduce electricity cost. The load consumption in automatic control can prevent customers from the penalty for exceeding contract capacity. It means when the power consumption climbs up to the climax, this method can get rid of unimportant load or the interruptible electricity equipments. The load control device of power consumption aims to prevent the

occurrence of new climax with the hope of avoiding added rates. The customer has to carry out the control management of load consumption, if the purpose of the economical use of electric equipments is required. The monthly power consumption can be reviewed at any time to decrease the electricity cost.

V. THE DETERMINATION OF THE LOAD MANAGEMENT STRATEGIES

After compiling and analyzing the returned questionnaires and the collected information from our plant visits, the research finds (1) that the manufacturing process characteristics of the glass industry are very similar in their production procedures, most of which are nearly the same. (2) The majority of Taiwan's glass manufacturers favor using electricity during peak hours.

This section describes the information collection, glass industry's willingness to adopt LM options and the LM strategies [16]-[20]. It includes (1) the implementation of TOU rate, (2) the participation of interruptible load rate, (3) the implementation of optimal demand contract, (4) the load demand automatic control and (5) the installation of automatic power factor regulators.

A. The Implementation of TOU Rate (strategy one)

The customers expressed their interest in the daily load curve figure of the power consumption. In line with the power consumption and rate analytical figure of peak & off-peak hours provided by this research, the customer realizes that the TOU rate measures will save its electricity cost in very short period of time. Thus the customers are willing to participate in the load management options. Meanwhile, the customer will consider how to change manufacturing process to various beneficial rate options provided by TPC. Due to the characteristics of manufacturing process and equipment, the sampled industry can further implement the TOU rate options.

B. Participating the Interruptible Rate (Strategy two)

The customer usually operates in the full load production.

Yet under the recession impact, the actual peak loads has already decreased to 75% of the original demand contract or lower than that. It can be realized by introducing between the peak load and the demand contract of daily load curve. It is therefore suggested that the customer should review its actual load capacity to better coordinate with power consumption.

The reduction of demand contract or participation in the interruptible rate package can be the alternatives to decrease demand charge. Besides the customer can arrange the original equipment under condition non-full loaded. Meantime the production procedure and time can be re-planned and arranged to avoid the concurrent operation of heavy load equipment which will result in the very high load demand. Since the customer worries about damaging the semi-product; they will shift the process to nighttime and thus increase the difficulties on management.

The management difficulties mentioned by the customers include: (1) the personnel cost will increase in the night production (2) the key management personnel is unwilling to join the night production (3) the stipulations of Labor Standards Laws.

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C. The Load Demand Automatic Control (Strategy three) The customer expressed willingness to adopt, but the installation of automatic load controller need extra operation cost which therefore reduces the participation willingness from the customer. From the long-term viewpoint, this load management strategy will save electricity cost for the customer.

After the explanation, the customer can accept the concept and will proceed to implement this alternative.

D. Implementation of Optimal Demand Contract (Strategy four)

The optimal contract capacity is not well implemented by the customer. As the customer roughly estimates the optimal demand contract based on the historical information and didn't analyze using a mathematical method the mathematical method. Thus the expenditure of demand charges increase.

After explanation and analysis, the customer willingly proceeds with the implementation of optimal contract capacity.

E. Implementation of Automatic Power Factor Regulator (Strategy five)

As the customer roughly estimates the PF based on the historical information (PF=0.8 to 0.9), the Automatic Power Factor Regulator (APFR) is not well implemented by the customer. Customer’s monthly charge will be decreased (increased) respectively by 0.15% (0.30%) for every 1% of the customer's average power factor that is more (less) than 80%.

VI. CONCLUSIONS AND SUGGESTIONS

1. The product classification and process of the glass industry are fully understood through this research. Besides, the daily load curve of power consumption and rate analysis are considered. Therefore the suggestion is submitted on the adjustment of ball mill running time for the glass industry.

This suggestion is considerably welcome by the glass industry.

2. The sampled industry is more than willing to participate in the interruptible load rate package. Also the sampled customer is willing to install the automatic load demand controller and to decrease power energy cost and boost the competitiveness eventually.

3. It is recommended that the customer should adopt the load demand control to automatically adjust load as long as the load consumption varies so that the peak load won't exceed the one stated in the demand contract.

4. It is suggested that the customer should review the ratio between current capacity and demand contract in order to decrease the demand contract or participate in the interruptible rate package for the reduction of demand charge.

5. It is also advisable that a feasible LM strategy is developed to assist other industry customers in reducing power energy cost and to increase the competitive capability.

REFERENCES

[1] Bureau Energy,Ministry of Economic Affairs of USA, White book, ch.4, 19986.

[2] M. L. Chan, Load Management Master Plan for Taiwan Power Company. Sunnyvale, CA: ML Consulting Group, 1996.

[3] L. Yao, W.-C. Chang, and R.-L. Yen, “An iterative deepening genetic algorithm for scheduling of direct load control,” IEEE Trans. Power Syst., vol. 20, no. 2, pp. 1414–1421, May 2005.

[4] Lab of load management, Institute of Power Research, TPC, The Technologic Platform of Energy Management and Service for Customers, 2002.

[5] M. S. Kang, C. S. Chen, Y. L. Ke, C. H. Lin, C. W. Huang, “Load Profile Synthesis and Wind -Power-Generation Prediction for An Isolated Power System,” IEEE Trans. on Industry Applications, Vol.

43, No. 6, November/December 2007, pp. 1459-1464.

[6] Karaki, S. H., Chedid R. B., and Ramadan, R., " "Probabilistic Production Costing of Diesel-Wind Energy Conversion Systems, "

IEEE Trans. on Energy Conversion, Vol.15, No. 3, pp. 284-289 (2000).

[7] Yang, H. T., Yang, P. C., and Huang, C. L., "Evolutionary Programming Based Economic Dispatch for Units with Non-smooth Fuel Cost Functions, " IEEE Trans. on Power Systems, Vol. 11, No. 1, pp. 112-118 (1996).

[8] Hsiao, H.C., C.Y. Hsiao, M.C. Lin, Q.F. Wu and T.C. Chan,

"Forecasting the Optimal Contract Capacities in Industrial Distribution Systems," Proceeding of the 11th Symposium on Electrical Power Engineering, pp.215-220, December (1990).

[9] Yang, C.G., R.T. Shu and G.K. Yang, "Load Management, Determination for the Optimal Contract Capacities," Load Management Part II, Taiwan Power Company Internal Report, pp.105- 122, May (1991).

[10] Lee,T.Y. and N.chen,”Optimal Utility Contracts for Time-of-Use Rates Industrial customers”, Journal of the Chinese Institute of Electrical Engineering, Vol.1,No.4, pp.247-257, (1994).

[11] A.I. Cohen, “An Optimization Method For Load Management Scheduling”, IEEE Trans. on Power Systems, Vol.3, No. 2, pp.612- 618, May, 1988.

[12] J.Chen, F.N. Lee, A.M. Breiphl, and R.Adapa, “Scheduling Direct Load Control to Minimize System Operation Cost”, IEEE Trans. on Power Systems, Vol.10, No.4, pp.1994-2000, November, 1995.

[13] D.C. Wei and N. Chen, “Air Conditioner Direct Load Control By Multi-pass Dynamic Programming”, IEEE Trans. on Power Systems, Vol. 10, No. 1,pp.307-313, February, 1995.

[14] Y.Y. Hsu and C.C. Su, “Dispatch of Direct Load Control Using Dynamic Programming”, IEEE Trans. on Power Systems, Vol.6, No.3, pp.1056-1060, August, 1991.

[15] Chu, W.C., Chen, B.K., and Fu, C.K, “Scheduling of direct load control to minimize load reduction for a utility suffering from generation shortage”, IEEE Trans, PWRS-8, (4), pp.1525-1530, 1994.

[16] Lin, W. M., Cheng, F. S., and Tsay, M. T., "An Improved Tabu Search for Economic Dispatch with Multiple Minima, " IEEE Trans.

on Power Systems, Vol. 17, No. 1, pp.108-112, 2002.

[17] Y. C. Chang and H. C. Tu, “An effective method for reducing power consumption-optimal chiller load distribution,” in Proc. IEEE Power Control, 2002, vol. 2, pp. 1169–1172.

[18] K. Y. Huang and Y. C. Huang, “Integrating direct load control with interruptible load management to provide instantaneous reserves for ancillary services,” IEEE Trans. Power Syst., vol. 19, no. 3, pp. 1626–

1634, Aug. 2004.

[19] Lee, T. F., Cho, Y. M., Hsiao, Y. C., Chao, P. J., and Fang, F. M.,

"Optimization and Implementation of a Load Control Scheduler Using Relaxed Dynamic Programming for Large Air Conditioner Loads,"

IEEE Trans. on Power Systems, Vol. 23, No. 2, pp.691-703, 2008.

[20] A. Fernandez, J. Sebastian, P. Villegas, M.M. Hernando, D.G. Lamar,

"Dynamic limits of a power-factor preregulator," IEEE Trans. on Industrial Electronics, vol. 52, no. 1, pp. 77- 87, Jan 2005.

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