A Performance Review of Lagrangian Relaxation Method For Unit Commitment in Korean Electricity Market

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A Performance Review of Lagrangian Relaxation Method for Unit Commitment in Korean Electricity Market Don Hur, Member, IEEE , Hae Seong Jeong, and Heung Jae Lee, Member, IEEE  


In 2001, AREVA’s optimization solution, Resource Scheduling and Commitment (RSC), was launched to solve the unit commitment problem in Korean electricity market. At this stage we are making a full review of it, tacking benefits of the recent advances in the operational resear research ch field. To begin with, the features of Korean electricity market are briefly described and then many of the inherent problems associated with Lagrangian Relaxation (LR) algorithms are ferreted out through stark contrast with the robust and flexible Mixed Integer Programming (MIP) formulation.  Index Terms —Economic

dispatch, Korean electricity market,

Lagrangian relaxation, Mixed integer programming, Unit commitment.



HE major purpose of the present study is to gauge the general applicability of Lagrangian Relaxation (LR) method to the unit commitment problem of Cost-Based Pool (CBP) in Korea and to test the essential validity of different integer programming methods, particularly, Mixed Integer Programming (MIP) formulation. Also, this paper primarily sets out to investigate many of inherent problems associated with LR solutions and presents a serious concern about the unit commitment program’s future direction applied in a course of Korean electricity market. Since 2001, the Korean electricity market has been using Resource Scheduling and Commitment (shortly, RSC) which was AREVA’s unit commitment application for a typical day-ahead security constrained unit commitment execution. The RSC, as discussed in [1], makes use of the fundamental Lagrangian Relaxation concepts, but seeks to overcome some convergence problems by Single Unit Dynamic Programming (SUDP) [2]. Unfortunately, this procedure does not explicitly deal with the problem of unit commitment for generating units with the same fuel costs. The RSC includes the sequential  bidding algorithm [3] that complements the problem as ob  D. Hur is with the Department of Electrical Engineering, Kwangwoon University, Seoul, 139-701 Republic of Korea (phone: +82-2-940-5473; fax: +82-2-940-5141;; e-mail: [email protected] ). +82-2-940-5141 H. S. Jeong was with Korea Electrotechnology Research Institute, Uiwang-city, Gyeonggi-province, 437-808 Republic of Korea (e-mail: [email protected] [email protected]). ). H. J. Lee is with the Department of Electrical Engineering, Kwangwoon University, Seoul, 139-701 Republic of Korea (e-mail: [email protected] ))..

served earlier. In this paper, we present some comparisons  between Lagrangian Relaxation in RSC and Mixed Integer Programming in the MOSEK solver. The results are illustrated illustrated from 2006 Korean electric power system consisting of 247 units over a week study horizon from April 13, 1 3, 2006 to April 19, 2006. Finally, to provide improved scheduling and coordination of multiple resources while recognizing the numerous operational and system constraints, some particulars are addressed. OREAN ELECTRICITY MARKET  II.  K OREAN

 A.   Restructuring Plan [4] 

It used to be assumed that electricity generation, transmission, distribution and supply enjoyed significant vertical economies that would be lost if the functions were placed under the control of different companies. Such long-held belief made it possible that the Korea Electric Power Corporation (KEPCO) had monopoly power – supported by legal protection. Since the 1997 financial crisis, economic policy in Korea has aimed to remove barriers to trade and competition. Network industries like electricity and natural gas, which were historically sheltered from competition and operated within national or regional boundaries, have made rapid progress as a consequence. National pressure to liberalize electricity markets reflected the perceived benefits of introducing market forces into the electricity industry previously viewed as a natural monopoly with substantial vertical economies. In the meantime, the generation sector was split up into six subsidiaries which will  be privatized each, after all. all. Still, the KEPC KEPCO O is being engaged in monopolistic business activities of the transmission and distribution systems alike. In an attempt to help mitigate potential negative prospects about which the hasty reform drive could bring, a new transitional electricity market, dubbed ‘Cost-Based Pool (CBP)’, was set up in 2001. In 2004, tripartite commi committee ttee of business, labor, and government decided to delay the two-way bidding pool (TWBP) in which the market clearing price would be determined from the bids of customers and the offers of generation companies in the unconstrained dispatch, to suspend the un bundling and privatization plan in the distribution and sales sector, and to further intensify internal competition among several independent business divisions within KEPCO.




 B.  Structure of Korean Electricity Market

systems (all figures are approximate, as of the end of 2006):

In April 2001, Korea’s generation sector was split into six  power generation subsidiaries including one big hydro and nuclear power company (Korea Hydro & Nuclear Power com pany, KHNP) and five thermal power companies (Korea East-West Power Co., LTD., Korea South-East Power Co., LTD., Korea Midland Power Co., LTD., Korea Southern Power Co., LTD., Korea Western Power Co., LTD.) on an equal basis in terms of commercial and technical aspects. Most

- Population: 48.8 [million] - Generating capacity: 65,514 [MW] - Peak demand: 58,994 [MW] - Annual generation output in market: 354,858 [GWh] - Transmission lines: 29,276 [C-km] - Annual trading amount: USD 20.3 [million]

of all, KHNP as a public entitysupply in consideration of nuclear safety,will the remain characteristics of power and demand, nuclear power development, and the capability of building new  plants, while the other five power generation companies, consisting of fossil and pumped storage power plants, will be privatized in the near future. As a neutral and independent organization, Korea Power Exchange (KPX) plays a pivotal role in Korea's electric power industry. The tasks to be performed by Korea Power Exchange are organized in Fig. 1.

Mission < Market Operation > ⋅ Competitive market management ⋅ Market monitoring

< System Operation > ⋅ System planning ⋅ Restoration planning ⋅ Demand forecast

< Real-time Dispatch > ⋅ Power balancing ⋅ Quality management

< Statistics and Interconnection > ⋅ Statistics analysis ⋅ Overseas interconnection

Fig. 1. Korea Power Exchange’s mission

Below are the scopes of KPX operations in Korean power

C.  Key Features of Korean Electricity Market

The Korean Cost-Based Pool (CBP) is shortly summarized as follows: 1) All generators should offer their available capacities daily to the pool. 2) KEPCO is the only purchaser in the market. 3) Eligible customers have been allowed to buy electricity from the pool since January 2003. 4) The dispatch schedule is naturally made based on the predetermined costs of each generating unit. In fact, the Generation Cost Evaluation Committee assesses the variable costs of generating units once a month. 5) Two marginal prices (short-term marginal price and  base-load marginal price) and capacity payment (CP) are paid to generation companies. 6) Both short-term marginal price (SMP) and base-load marginal price (BLMP) cover actual production costs, which are made up of start-up, no-load, incremental costs, of the last generating unit involved in the price-setting schedule. As such, there is no locational signal. 7) The capacity payment is paid to all generating units that can  produce electricity whether they are dispatched or not. Plus, it ensures the recovery of capital costs and thus underpins further investment of generating facilities. The trading process in Korean electricity market is sketched in Fig. 2. Generators

KPX Prod. Cost Evaluation Demand Forecast

CP: Yearly

Construction Cost


Fuel Cost

Day ahead Offer

< Scheduling >

Available Capacity

⋅  SMP / BL BLMP MP ⋅  Commitment

Historical Data Weather Data

Trading day

Dispatch Instruction Gen. Operation

Real-time Dispatch After 26 days Settlement

Fig. 2. Trading process

Gen. Ready

Invoice  Notification Payment




Metropol Me tropol itan Region

6 1 4




Legend 765 kV Route 345 kV Route DC 180 kV Submarine Cable 765 kV Substation 345 kV Substation Power Plant Fig. 3. Schematic of major transmission facilities in Korean power system

 D.  Structures of transmission facilities in Korea

More than 40% of system load is in the metropolitan region, while the majority of generation is in the non-metropolitan regions. Further, most base-load generating units with low generation costs are scattered all over the non-metropolitan regions. For the purpose of economic benefits, therefore, real  power generation in non-metropolitan regions increases in  parallel with the consumption level, resulting in the power transfer from the south and central parts of the Korean electric  power system to the northwestern part through one of the most critical corridors ofmetropolitan the grid. Fig.regions 3 is a schematic showing six routes connecting and others, including major power plants in Korean electric power system. Due to the trend of heavier real power flows into the metropolitan region, the constraint of the interface flows will be vital to our national-interest transm transmission ission bottlenecks, leading to establishment of new market rule that will correctly deal with this significant problem. It is needless to say that a new unit commitment and economic dispatch program is prepared to suggest possible solution of transmission congestion that decreases reliability, restricts competition, enhances opportunities for suppliers to exploit market power, increases prices to customers, and increases infrastructure vulnerabilities. III.  OPTIMIZATION METHODS FOR U NIT COMMITMENT  The unit commitment is utilized to determine the minimum  production cost schedule for thermal generating units. Operating fuel costs, maintenance costs and start up costs are ac-

counted for in the calculations. An extensive set of constraints may be imposed on the schedule. In terms of time scales involved, unit commitment scheduling copes with the scope of hourly power system operation decisions with a one-day to one-week horizon. Chaining of schedules to provide longer time horizons is possible. A typical day-ahead security constrained unit commitment execution in the PJM market has to schedule upwards of 1000 generating units to meet over 100GW demand in a system of 10,000+ buses [5]. A Mixed Integer Programming (MIP) not only has to perform reliably over a wide range of bidding  patterns to produce optimized solutions that withstand challenges from the market participants, it is also subject to rigorous audits by the market monitoring staff, which demands a high level of transparency and repeatability. The MIP formulation allows for more sophisticated modeling and flexibility of complex resources such as combined cycle plants and pumped storage facilities. In recent deployments, other complex constraints such as transmission congestion have been directly incorporated into the problem formulation, resulting in low-cost reliable commitment solutions. More, the MIP formulation allows the inter-temporal constraints, such as energy constraints, to be directly modeled within the mathematical problem. This avoids getting sub-optimal unit commitment solution, as it may occur when using the traditional Lagrangian Relaxation (LR) or Dynamic Programming (DP) methodologies. In [6], several approaches for solving the unit commitment  problem were detailed starting from the oldest and most  primitive method, method, the priority li list. st. Different major procedures in LR problem formulation, search for a feasible solution through the minimization of the duality gap, updating the multiplier, and formation of single-unit relaxed problems were discussed for the unit commitment problem of large-scale  power systems. IV.  FUTURE EXTENSIONS IN U NIT COMMITMENT PROGRAM Given the extraordinary nature of CBP in Korea, the im plementation with the LR formulation to solve the unit commitment problem is now being faced with the challenges of coming up with new schemes to deal directly with a number of constraints and models. These include modeling of combined cycle plants, pumped storage plants, several types of regional reserve constraints, and conditional constraints, e.g., hot, intermediate, and cold startup model. To put it more concretely, a new generation scheduling program will have to co-optimize the costs of energy and reserve as well as to maximize social welfare of market participants. Moreover, it should reflect water constraints of hydroelectric plants, heat constraints of co-generation, and fuel constraints (LNG or bituminous coal). Apparently, it necessarily follows that essential features of each generating unit should be satisfied: minimum up and down time, ramp rate, maximum and minimum available ca pacity, start up and shut down constraints, forced and unforced outage schedules, must-run or fixed generation as well as fixed




amount of reserves, and the ratio of steam turbine and gas turbine in combined cycle power plants. A new unit commitment program should be able to handle various constraints in an efficient way: generation, transmission, reserve, emission, and security constraints.  A.  Generation constraints

1) Water constraints of hydroelectric power plants 2) Pumping and generation constraints of pumped storage  power plants 3) Heating constraints of co-generation 4) Fuel constraints in case of LNG or bituminous coal 5) Must-run or fixed generation output 6) Constraints of 1), 2), 3), and 4) should be applied to a single generating unit as well as in group. 7) Energy and fuel constraints should be modeled in a particularly specified period. 8) Hydraulic, thermal, and fuel constraints are expressed in lower limit, upper limit, or alternatively fixed one.  B.  Transmission constraints

A new unit commitment program should take into account transmission network constraints. More specially, transmission constraint between Jeju Island and the southwestern inland area of Korea should be formulated in the following: Min(Installed capacity of HVDC, 60 % of load-demand in Jeju Island) (1) C.   Reserve constraints

Reserves should satisfy the inter-regional requirements and types of reserves. For example, some types of reserves with fast response time can replace the one with slow response time. Besides, transmission bottlenecks should be allowed to optimize regional reserves. Accordingly, reserves in the receiving region may be appended to reserves in the sending region.  D.   Extra constraints

Security-constrained economic dispatch is performed by contingency analysis. In addition, transmission losses for the overall network may be appropriately taken into consideration. The constraint on emission of harmful gases should be inde pendently managed apart from the energy constraint, though the former is quite similar to the latter. V.  CASE STUDY  When we carry out the unit commitment to Korean electricity market with LR and MIP formulation, the latter will make further generation cost savings possible and help to facilitate the power system operations in terms of reserve and congestion. The results of our study are expected to provide a useful guideline to improve or replace the existing generation scheduling program for more sophisticated unit commitment  problem, along withpresents recent advances in Korean MIP commercial solvers. This section results from electricity market consisting of 247 units over a week study horizon.


Date Apri Aprill 13, 13, 20 2006 06 Apri Aprill 14, 14, 20 2006 06 Apri Aprill 15, 15, 20 2006 06 Apri Aprill 16, 16, 20 2006 06 Apri Aprill 17, 17, 20 2006 06 Apri Aprill 18, 18, 20 2006 06 Apri Aprill 19, 19, 20 2006 06

LR [×103 won] 25,1 25,133 33,2 ,280 80 23,8 23,897 97,3 ,349 49 20,6 20,645 45,4 ,466 66 13,7 13,796 96,6 ,615 15 22,8 22,816 16,0 ,052 52 24,1 24,141 41,5 ,538 38 24,0 24,045 45,4 ,475 75

MIP [×103 won] 25 25,0 ,087 87,6 ,673 73 23 23,8 ,888 88,1 ,135 35 20 20,6 ,643 43,6 ,631 31 13 13,7 ,743 43,8 ,883 83 22 22,7 ,762 62,5 ,560 60 24 24,0 ,087 87,8 ,877 77 24 24,0 ,015 15,3 ,301 01

Cost savings [%] 0.18 0.18 0.04 0.04 0.01 0.01 0.38 0.38 0.23 0.23 0.22 0.22 0.13 0.13





April 13, 2006 April 14, 2006 April 15, 2006 April 16, 2006 April 17, 2006 April 18, 2006 April 19, 2006 Average

85 83 77 67 83 83 83 80

83 80 74 66 79 80 80 78


Constraints Reserve Transmission  Network Reserve + Tran Transm smis issi sion on


Energy cost [×103 won]


157,411,505 157,320,434 157,722,120 156,877,832 158,849,457 15 158, 8,20 208, 8,59 592 2

CPU times [sec/day] 120 134 120 129 120 157 157

Average reserve [MW/h] 2,496 1,637 1,460 365 2,588 1,64 1,642 2

Table I shows total energy cost for the LR and MIP runs in the unconstrained dispatch. The largest difference between the LR and the MIP is ₩53,661,000 on April 18, 2006. Typically, the MIP are producing more excellent solution for unit commitment problem with similar CPU times, taking approximately 2 minutes minutes in this case. In the other hand, the average number of generating units committed as per hour is described in Table II. In general, the average number of generating units committed in the MIP is obviously less than that in the LR, which results in the remarkable cost savings. In Table III, simulation results of three cases are given for comparative analysis of the total energy costs for a whole week, average cpu times occupied, and average reserves secured in the LR and the MIP. Here, the amount of 1,500 [MW] is imposed on the reserve constraint, while the transmission network constraint is regarded as the limit of northward real  power flows from the non-metropolitan regions to the metropolitan area through six interconnections. From 9:00 AM to 7:00 PM, the amount of 11,300 [MW] is applied and the amount of 10,100 [MW] is assumed from 7:00 PM to 9:00 AM. The final case includes the reserve constraint and transmission network constraint at the same time. As mentioned earlier, the




MIP is more cost effective than the LR since much less of reserve for each hour is obtained in the MIP while meeting the reserve requirements. VI.  CONCLUSION  In recent years, the yearly production costs in Korea required to meet the nationwide load-demand account for about 10 billion dollars. If we slightly enhance the efficiency of resource scheduling and commitment, we can experience the tremendous generation cost savings in real-life situations. The unit commitment program installed in Korea makes the  best of Lagrangian Relaxation Relaxation algorithm, which seems, seems, in part, to be inefficient and inflexible on uncertain changes of the future electricity market. In this context, we have tried to make a comparative analysis of Lagrangian Relaxation and Mixed Integer Programming suitable for the unit commitment in Korean electricity market. Consequently, it can be concluded that the Mixed Integer Programming offers a number of important advantages over the Lagrangian Relaxation. R EFERENCES EFERENCES  [1]  Resource Scheduling and Commitment (RSC) Software Specification Document (SSD), CEGELEC ESCA Corporation, 1998. [2]  F. Zhuang, F. Galiana, “Towards a More Rigorous and Practical Unit Commitment by Lagrangian Relaxation,” IEEE Transactions on Power Systems, Vol. 3, No. 2, May 1988. [3]  F. Lee, “Thermal Unit Commitment by Sequential Methods,” in Application of Optimization Methods for Economy/Security Functions in Power System Operations, IEEE Tutorial Course 90EH0328-5-PW 90EH0328-5-PWR, R, pp. 47–54. [4]  H. S. Jeong, Y. H. Moon, T. K. Oh, D. Hur, J. K. Park, “Status and Perspective of Transmission Pricing Scheme in Korean Electricity Market,” CIGRE/IEEE PES, 2005. International Symposium, San Antonio, TX, October 5–7, 2005, pp. 36–43. [5]  D. Streiffert, R. Philbrick, and A. Ott, “A Mixed Integer Programming Solution for Market Clearing and Reliability Analysis,” IEEE PES 2005 General Meeting, San Francisco, CA, USA, June 12–16, 2005. [6]  J. A. Momoh, Electric Power System Applications of Optimization.  New York, NY: Marcel Dekker, Inc., 2001, pp. 293–323.

BIOGRAPHIES   Don Hur (M’00) was born in Seoul, Republic of Korea, on January 17, 1974. He received B.S.(1997), M.S.(1999), and Ph.D.(2004) degrees in electrical engineering from Seoul National University, Seoul, Republic of Korea. He was employed as an assistant electrical engineer by Burns&McDonnell Engineering Company, Kansas City, MO, USA from 2001 to 2002. He was also appointed a visiting researcher in Engineering Research Institute at Seoul  National University in 2004. In 2005, he was a visiting scholar at the University of Texas at Austin, Austin, TX, USA. Since September, 2005, he has been working as a full-time lecturer at the Department of Electrical Engineering, Kwangwoon University. He has co-authored more than 30 technical papers  published in international reviews on power system planning, reliability

evaluation, and restructuring issues. He is a member of the Institute of Electrical and Electronics Engineers (IEEE), the Institution of Engineering and Technology (IET), and the Korean Institute of Electrical Engineers (KIEE). Hae Seong Jeong was born in Seoul, Republic of Korea, on December 22, 1969. He received B.S.(1993), M.S.(1996), and Ph.D.(2004) degrees in electrical engineering from Seoul National University, Seoul, Republic of Korea. In 2004-2005, he worked as a senior researcher at Korea Electrotechnology Research Institute, Uiwang city, Gyeonggi province, Republic of Korea. His research interests are in the areas of power system restructuring, power system operation, and risk management in the deregulated electrici ty markets. Heung Jae Lee was born in Seoul, Republic of Korea, on January 28, 1958. He received B.S.(1983), M.S.(1986), and Ph.D.(1990) degrees in electrical engineering from Seoul National University, Seoul, Republic of Korea. He worked as a researcher for Gold Star Central Research Center from 1983 to 1984. He is a professor of the Department of Electrical Engineering at Kwangwoon University, Seoul, Republic of Korea, where he has been working since 1990. He is a member of the Institute of Electrical and Electronics Engineers (IEEE) and the Korean Institute of El ectrical Engineers (KIEE). His research interests are in the areas of artificial intelligence, fuzzy systems, and expert systems for fault location detection and rapid fault restoration as well as reactive power planning.

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