뗚27뻭 뗚8웚 뗧 췸 벼 쫵 Vol. 27 No. 8 2003쓪8퓂 Power System Technology Aug. 2003 컄헂뇠뫅ꎺ1000-3673ꎨ2003ꎩ08-0010-06 훐춼럖샠뫅ꎺ 컄쿗뇪쪶싫ꎺA 뗧솦쫐뎡죽훖맑춷뺺헹쒣탍뗄쫐뎡솦럖컶뇈뷏 쯎틀좺1,2ꎬ뫮횾볳1ꎬ컄뢣쮩2ꎬ쓟틔탅2ꎬ컢뢴솢2 ꎨ1ꎮ짏몣붻춨듳톧뗧웸릤돌쾵ꎬ짏몣 200240ꎻ2ꎮ쿣룛듳톧뗧믺뗧ퟓ릤돌쾵ꎬ쿣룛ꎩ COMPARISON OF MARKET POWER IN THREE OLIGOPOLY MODELS OF ELECETRICITY MARKET SONG Yi-qun1,2, HOU Zhi-jian1, WEN Fu-shuan2, NI Yi-xin2, WU Fu2-li ꎨ1. Electrical Engineering Dept., Shanghai Jiao Tong University, Shanghai 200240, China; 2. The University of Hong Kong, the Hong Kong Special Administrative Region, Chinaꎩ ABSTRACT: In economics, market power indicates the ability 1 틽퇔 of a firm to raise market price. In the oligopolistic electricity market, market power measures the ability of a generation firm 쫀뷧랶캧뗄뗧솦릤튵헽쏦쇙ퟅ듓뒫춳뗄벯훐to raise the clearing price of electricity market. Based on game 맜훆쳥훆쿲뺺헹뗄뗧솦쫐뎡맽뛉뗄듳뇤룯ꆣ뗧솦쫐theory, market power in the oligopolistic electricity market is 뎡훐뗄쫐뎡솦ꎨMarket Powerꎩ뗄듦퓚늻샻폚쫐뎡analyzed. After the market clearing price of perfect competition 뗄ퟔ평뺺헹뫍쫐뎡킧싊뗄쳡룟ꎬ틲듋틽웰룷맺뗧솦is calculated as base price, the percentage mark-ups of market 탐튵퓋탐죋풱ꆢ퇐뺿죋풱틔벰뺭볃쇬폲퇐뺿죋풱뗄prices w. r. t. perfect competition in Cournot, Stackelberg (. Leader-Follower) or Forchheimer (. Lea훘쫓ꆣ쫐뎡솦쫇쫐뎡닎폫헟쓜릻펰쿬쫐뎡훐닺욷볛der-priceTaker) models are evaluated analytically, which acts as an index of the 룱뗄쓜솦ꆣ쫐뎡솦폫쫐뎡뷡릹뷴쏜쿠맘ꆣ췪좫뺺헹market power in the corresponding electricity market. The 쫐뎡훐ꎬ쯹폐뗄쫐뎡닎폫헟뻹캪쫐뎡볛룱뗄뷓쫜impacts of cost function coefficients, elasticity of demand, the 헟ꎬ늻쓜펰쿬쫐뎡볛룱ꎬ틲뛸늻듦퓚쫐뎡솦ꆣ뛸퓚number of generation firms as leaders and capacity constraints 맑춷뺺헹쫐뎡훐ꎬ평폚떥룶짺닺뎧짌ꎨfirmꎩ쏦쇙on market power are also discussed. The results of this research show that among the three models the Cournot model possesses 뗄탨쟳쟺쿟쫇튻쳵뗝복쟺쿟ꎬ룷짺닺뎧짌췹췹캪쇋the highest market power, the Forchheimer model has the least. ힷ쟳ퟔ짭뗄ퟮ듳샻죳뛸쿞훆닺솿ꎬ쪹쫐뎡볛룱룟폚KEY WORDS: O췪좫뺺헹쫐뎡뗄볛룱ꎬ듓뛸믱뗃뎬뛮샻죳ꆣ헢쫇평ligopolistic electricity market; Electricity market; Market power; Cournot model; Stackelberg model;폚쫐뎡닎폫헟펵폐늢탐쪹쇋쫐뎡솦뗄풵맊[1]ꆣ뫢솿 Game theory; Power system. 튻룶쫐뎡뗄쫐뎡솦튻냣닉폃샕쓉횸쫽ꎨLerner 햪튪ꎺ쫐뎡퓚뺭볃톧훐뇭쿖캪쫐뎡닎폫헟쓜릻첧룟쫐뎡볛룱IndexꎬLIꎩꆢ볛룱돉놾횸쫽ꎨPrice Cost Margin Indexꎬ뗄쓜솦ꎬ퓚맑춷뺺헹뗧솦쫐뎡훐퓲뇭헷쫐뎡쓚뗧솦릫쮾펰쿬PCMIꎩꆢ벯훐뛈횸쫽 ꎨConcentration RatioꎬCRꎩ쫐뎡뷡쟥뗧볛뗄쓜솦ꆣ펦폃늩?싛럖컶퇐뺿쇋맑춷뺺헹뗧솦틔벰HHI횸쫽ꎨHirschman-Herfindall IndexꎬHHIꎩ쫐뎡뗄쫐뎡솦ꆣ틔췪좫뺺헹쫐뎡쿂뗄뻹뫢랢뗧솿뫍뻹뫢뗧볛[2]ꆣ뗧솦쫐뎡평폚듦퓚ퟅ쫐뎡뷸죫뇚생ꎨ죧룟춶캪믹ힼꎬ럖뇰뇈뷏쇋내Cournot쒣탍ꆢStackelberg쒣탍ꎨ쇬떼헟룺쯦헟쒣탍ꎩ뫍Forchheimer쒣탍ꎨ쇬떼헟볛룱뷓쫜돉놾ꎩ뗈풭틲ꎬ틲뛸췹췹쫇튻룶뷼쯆폚맑춷뺺헹뗄쫐뎡[3]헟쒣탍ꎩ쒣쓢맑춷뺺헹뗧솦쫐뎡쟩뿶쿂뗄뗧솦릫쮾쯹펵폐뗄ꎬ뛔웤뷸탐쫐뎡솦뗄퇐뺿뿉틔쪶뇰뫍쿞훆쫐쫐뎡솦ꎬ늢쟒럖컶짺닺돉놾ꆢ쫐뎡훐뗄뗧솦탨쟳떯탔ꆢ쫐뎡뎡솦ꎬ듙뷸룟킧ꆢ릫욽뗄쫐뎡퓋펪ꎬ늢캪헾뢮볠맜훐ퟷ캪쇬떼헟뗄뗧솦릫쮾쫽솿틔벰죝솿쿞훆뛔쫐뎡솦뗄펰늿쏅훆뚨헾닟쳡릩샭싛틀뻝ꎬ틲뛸쫇폐뫜듳쪵볊틢쿬ꆣ퇐뺿뇭쏷ꎬ퓚3훖쒣탍쫐뎡훐ꎬCournot쒣탍쫐뎡펵폐뗄틥뗄ꆣ 쫐뎡솦캪ퟮ듳ꎬStackelberg 쒣탍쫐뎡듎횮ꎬForehheimer 쒣쒿잰뛔뗧솦쫐뎡쫐뎡솦뗄퇐뺿뿉틔맩쓉캪3탍쫐뎡캪ퟮ킡ꆣ 샠ꎺꋙ쫐뎡솦횸쫽램[4~6]ꎬ룹뻝룷뗧솦릫쮾쯹펵폐맘볼듊ꎺ맑춷뺺헹뗧솦쫐뎡ꎻ뗧솦쫐뎡ꎻ쫐뎡솦ꎻCournot뗄뗧솦죝솿볆쯣룷뗧솦릫쮾뗄쫐뎡럝뛮듓뛸뗃떽쒣탍ꎻStackelberg쒣탍ꎻ늩?싛ꎻ뗧솦쾵춳?쫐뎡뺲첬횸쫽ꎨHHIꎩꎬ틲듋뿉좷뚨룃뗧솦쫐뎡쫇럱
뗚27뻭 뗚8웚 뗧 췸 벼 쫵 11 룟뛈벯훐ꆣ평폚뗧솦쫐뎡뢺뫉뇤뮯뷏듳ꎬ룷뗧솦릫쓚횻폐믰뗧믺ퟩꎩꎬ랢뗧릫쮾i뗄돉놾몯쫽캪 쮾뗄쪵볊랢뗧솿늢늻뫍죝솿퇏룱돉뇈샽ꎬ쟒뮹뫍뗧C1(q)=a+bq+q2c뎧샠탍ꎨ믰뗧ꆢ쮮뗧ꆢ뫋뗧뗈ꎩꆢ좼쇏샠탍ꎨ좼쎺ꆢ (i=1,2,L,N) (1) iiiiiii2웸ꆢ쪯폍ꎩꆢ뮷놣뫍짺닺돉놾뗈폐맘ꎬ틲듋뺲첬HHI쪽훐 aiꎬbi뫍ci캪돉놾쾵쫽ꎬqi캪뗧솦릫쮾i뗄랢컞램헽좷뗘랴펳뗧솦쫐뎡훐쫐뎡솦뗄닙ퟝ탐캪ꎬ뗧솿ꆣ Bialek쳡돶쇋횻볆벰뗷뛈췢쫐뎡뗄룷뗧솦릫쮾뗄쫐죴쫐뎡훐뗧솦쓦탨쟳몯쫽캪쿟탔몯쫽ꎬ퓲볇ퟷ 뎡럝뛮뗄HHIꎬ뾼싇쇋뢺뫉뗄뇤뮯뛔쫐뎡솦뗄펰쿬Np=e−fD=e−f∑q (2) i[5]ꎬ뷏뺲첬HHI룼럻뫏뗧솦쫐뎡뗄튪쟳ꆣAlvaradoi=1쳡돶쇋쇭튻훖뚯첬HHI틔뫢솿뻖폲쫐뎡솦ꎬ볆벰쇋쪽훐 p캪쫐뎡뗧볛ꎬD캪쫐뎡뗧솿ퟜ탨쟳ꎻe뫍f쫤뗧쿟슷뛔룷뗧솦릫쮾쯹펵폐뗄쫐뎡솦뗄펰쿬[6]ꆣ캪뗧솦쓦탨쟳쟺쿟뗄뷘뻠뫍킱싊ꆣ ꋚ펦폃뗧솦쫐뎡럂헦웷뷸탐쫐뎡쒣쓢ꆣ헢훖럂헦웷퓚췪좫뺺헹쫐뎡훐ꎬ뗧솦릫쮾i뗄쒿뇪쫇ힷ쟳뿉틔쒣쓢뢴퓓뗄뗧솦쫐뎡퓋펪뫍뗧솦쾵춳퓋탐ꎬ폐ퟔ짭뗄샻죳piퟮ듳뮯ꆣ벴 훺폚통솷쫐뎡뮷뺳쿂뗄붻틗맜샭죋풱뫍쾵춳퓋탐maxp=pq−C(q) (i=1,L,N) (3) iiii죋풱ꎬ떫쓑틔쒣쓢룷닎폫헟뗄춶뇪닟싔벰웤쿠뮥펰qi쿬[7]ꆣꋛ믹폚늩?뻹뫢샭싛뗄쫐뎡솦럖컶램[8-12]ꆣ평dpi=0뿉볆쯣qi뗄ퟮ폅뷢ꎬ붫웤듺죫쪽(2)뿉뗃dq폃듋랽램퇐뺿뗧솦쫐뎡훐룷닎폫헟뗄럖즢뻶닟벰i췪좫뺺헹쫐뎡ꎨ쿂뇪캪pcꎩퟮ훕뗄뻹뫢뗣뗧볛p∗쿠뮥ퟷ폃ꎬ웤쒿뗄쫇ퟮ듳뮯닎폫헟뗄ퟔ짭샻틦ꆣ헢pc뫍샠랽램춨맽볆쯣뗧솦쫐뎡뗄Cournot뻹뫢믲릩룸몯쿠펦ퟜ랢뗧솿q∗∑pc캪 쫽뻹뫢ꎨNNSupply Function Equilibriaꎩꎬ럖컶룷훖쟩뿶∗fbf쿂뗧솦쫐뎡훐뿉쓜돶쿖뗄쫐뎡솦ꆣ폐킩컄쿗뮹횸ppc=(e+∑i)/(1+∑) (4) cci=1ii=1i돶ꎬ퓚뗧솦쫐뎡훐믡평폚쫤뗧죝솿쿞훆뗄듦퓚뛸떼N∗−Nebf훂돶쿖쒳킩뗧솦릫쮾닙ퟝ쫐뎡ꆢ첧룟뗧볛뗄쿖쿳qi∑pc=(∑)/(1+∑) (5) =1c=1ciiii[8,9,11]ꆣ 평캢맛뺭볃톧샭싛뿉횪ꎬ룃뻹뫢뗣뗧볛뫍쫐뎡폃늩?싛살럖컶뗧솦쫐뎡벰웤쫐뎡솦ꎬ훷튪폐ퟜ랢뗧솿뿉틔ퟷ캪에뛏맑춷뺺헹뗧솦쫐뎡쫐뎡솦3훖쒣탍ꎬ벴틔닺솿뺺뇪뗄Cournot쒣탍ꆢ틔볛룱뗄믹ힼꆣ 뺺뇪뗄Bertrand쒣탍벰춬쪱틔닺솿ꆢ볛룱뺺뇪뗄릩룸몯쫽쒣탍ꎨ3 뗧솦쫐뎡뗄맑춷뺺헹쒣탍 SFEꎩꆣ웤훐틔릩룸몯쫽쒣탍뇈뷏럻뫏쪵볊뗧솦쫐뎡뗄퓋탐쟩뿶ꎬ떫쫇웤뻹뫢뗣뗄뛠뷢탔쪵볊뗧솦쫐뎡춨뎣쫇튻맑춷뺺헹쫐뎡ꆣ럖컶듋쪹뗃럖컶뗧솦쫐뎡쳘탔뇈뷏삧쓑ꆣ평폚놾컄뗄쒿뗄훖뺺헹쫐뎡폐3훖뗤탍뗄쫐뎡쒣탍ꎺCournot쒣탍ꆢ퓚폚뚨솿쏨쫶뗧솦쫐뎡훐뗄쫐뎡솦틔벰퇐뺿펰쿬Stackelberg쒣탍벰Forchheimer쒣탍[13]ꆣ죧맻쫐뎡쫐뎡솦뗄룷훖틲쯘ꎬ틲듋틔Cournot쒣탍ꆢ훐횻폐짙솿벸룶뗧솦릫쮾ꎬ룷릫쮾햼쫐뎡럝뛮뷏Stackelberg쒣탍벰Forchheimer쒣탍캪믹뒡ꎬ췆떼듳ꎬ웤랢뗧솿붫횱뷓펰쿬쫐뎡뷡쟥뗧볛ꎬ룷릫쮾뛀쇋룼쳹뷼폚뗧솦쫐뎡뗄뛠쇬떼헟쟩뿶쿂뗄쿠펦쒣솢훆뚨랢뗧닟싔ꎨ랢뗧솿ꎩꎬ듋쪱뗄쫐뎡퓲뿉폃탍늢뛔뻹뫢뗣쟳뷢컶뷢ꎬퟅ훘럖컶짺닺돉놾ꆢ쫐뎡Cournot쫐뎡쒣탍뷸탐쒣쓢ꆣ뛸쪵볊뗄뗧솦쫐뎡튻훐뗄뗧솦탨쟳떯탔ꆢ쫐뎡훐ퟷ캪쇬떼헟뗄뗧솦릫쮾냣폐죴룉듳탍뗧솦릫쮾벰튻엺킡탍뗧솦릫쮾ꎬ듳탍쫽솿틔벰죝솿풼쫸뛔쫐뎡솦뗄펰쿬ꆣ뗧솦릫쮾퓚뗧솦쫐뎡훐쇬떼쫐뎡뗧볛ꎨ돆캪뗧볛뗄 쇬떼헟ꎨleaderꎩꎩꎬ킡탍뗧솦릫쮾룹뻝늻춬뗄닟싔2 췪좫뺺헹쫐뎡뗄뻹뫢뗣 돉캪룺쯦헟ꎨfollowerꎩ믲헟볛룱뷓쫜헟췪좫뺺헹쫐뎡훐ꎬ쯹폐뗄쫐뎡닎폫헟뗄닺솿늻ꎨprice-takerꎩꎬ듋훖쟩뿶쿂뗄쫐뎡럖뇰뛔펦폚ퟣ틔틽웰닺욷쫐뎡볛룱뗄뇤뮯ꎬ쫇쫐뎡볛룱뗄뷓쫜Stackelberg뫍Forchheimer쒣탍쫐뎡ꆣ틔췹뗄컄쿗헟ꆣ죴폃췪좫뺺헹쫐뎡쒣쓢뗧솦쫐뎡쪱ꎬ퓲룷뗧솦훐춨뎣횻뾼싇1룶쇬떼헟ꎨStackelberg쒣탍뫍릫쮾룹뻝쫐뎡뗧볛좷뚨ퟔ벺뗄ퟮ폅닺솿틔믱뗃ퟔForchhei-mer쒣탍ꎩ믲2룶뺺헹헟ꎨCournot쒣탍ꎩꆣ 짭뗄ퟮ듳샻죳ꆣ?ꎨ1ꎩCournot쫐뎡쒣탍 볙짨튻뗧솦쫐뎡쓚폐N룶뗧솦릫쮾ꎨ볙뚨쫐뎡퓚Cournot늩?훐룷뗧솦릫쮾훆뚨랢뗧닟싔
12 Power System Technology Vol. 27 No. 8 쒿뇪몯쫽캪 늻쓑떼돶짏쫶M쇬떼헟–ꎨN−Mꎩ룺쯦헟샠탍maxð=p(Q)q−C(q) (i=1,L,N) (6) 뗄맑춷뺺헹뗧솦쫐뎡ꎨ쿂뇪볇ퟷLFꎩ뗄뻹뫢뗣 iiiiqiN뗧볛p*LFꆢ쿠펦뗄ퟜ랢뗧솿q*ΣLF벰룷뗧솦릫쮾뗄랢쪽훐 Q=∑qꆣ i뗧솿럖뇰캪 i=1MM폫쪽fb(3)쿠쯆ꎬ평쪽(6)뿉떼돶뗧솦릫쮾i퓚웤 =jfp*LF(e′+∑)/(1+∑′) (14) 쯻릫쮾랢뗧솿럖뇰캪q(j≠i)쪱뗄ퟮ폅랢뗧닟싔=1f′+c=1f′+cjjjj jMNe−bN*je−bqk∑LF=(∑+∑)/e−b−*fqi∑j=1f′+c=+1f+cjjkMkq*=j=1,j≠i (i=1,L,N) 쪱 (7) MM if′f2f+ci [(1+∑)(1+∑)] (15)떱Cournot맑춷뺺헹뗧솦쫐뎡ꎨ쿂뇪캪ccꎩ=1f′+c=+1f+cjjkMk 듯떽Nash뻹뫢쪱ꎬ뻹뫢뗣뗧볛p*cc뫍쿠펦뗄ퟜ랢뗧p*−b*LFjq= (j=1,L,M) (16) j솿q*f′+cj∑cc럖뇰캪 NN**fbf*pLF−bp=e+∑iq=kk ( k=M+1,L,N) (17) cc()/(1+) (8) 1f+∑=cf′+cki=1f+ciiiNN∑e−bꎨ3ꎩForchheimer쫐뎡쒣탍 fq*i∑cc=()/(1+) (9) 1f+∑짨잰M룶뗧솦릫쮾캪쇬떼헟ꎬ웤쯻N−M룶릫=c=f+ciii1iꎨ2ꎩStackelberg쫐뎡쒣탍쮾쫴폚킡탍뗧솦릫쮾ꆣ떱뷓쫜쫐뎡뗧볛캪pꎬ킡탍 볙짨쫐뎡훐잰M룶뗧솦릫쮾캪쇬떼헟ꎬ웤쯻뗧솦릫쮾kퟮ듳뮯샻죳쪱뗄랢뗧솿캪 N−M룶릫쮾쫴폚킡탍뗧솦릫쮾ꆣ*p−b q=kk (k=M+1,L,N) (18) ퟷ캪룺쯦헟뗄킡탍뗧솦릫쮾kꎬ캪쇋ퟮ듳뮯ퟔck짭샻죳ꎬ펦쪹듋쪱M룶쇬떼헟쯹쏦쇙뗄쪣폠쫐뎡쓦탨쟳쟺쿟뿉 maxð틔룄킴캪 k=p(Q)qk−ck(qk) (k=M+1,L,N) (10) qNMiMNp=e−f쪽훐∑qk−f∑q=jp틾몬쇋쇬떼헟뗄펰쿬ꎬQ=∑q+∑qjkꆣ k=M+1j=1j=1j=M+1NNfbf평쪽 (e+(10)ꎬ뗧솦릫쮾k닉좡뗄ퟮ폅랢뗧닟싔캪 ∑k)/(1+∑)− k=M+1f+ckk=M+1f+ckMNMNMq*fk=e−bk−f∑q−f∑q (k=M+1,L,N) jl f∑q∆e′′/(1+−f′′q ( 19) jj=∑∑j=1l=M+1,l≠kj=1k=M+1ckj=1(11) 뻝듋ꎬ뿉틔뗃돶쯹폐룺쯦헟뗄ퟮ폅랢뗧솿ퟜ뫍캪?닎헕쪽(6)ꎬM룶쇬떼헟쯹닉좡뗄ퟮ폅닟싔캪 MNN∑∑e−bNfq*=e′′−b−f′′∑q)/(2f′′+c)jjijq*=kk()/(1+∑)−i=1,i≠ (20) jk=M+1k=M+1f+ckk=M+1f+ckNNM? (j=1,L,M)∑ff [()/(1+∑)]∑q (12)j룃M쇬떼헟–ꎨN−Mꎩ볛룱뷓쫜헟Forchheimer k=M+1f+ckk=M+1f+ckj=1뛸M룶쇬떼헟쯹쏦쇙뗄쪣폠쫐뎡쓦탨쟳몯쫽뿉붫쫐뎡ꎨ쿂뇪캪LTꎩ뗄뻹뫢뗣뗧볛p*LTꆢ쿠펦ퟜ랢뗧쪽솿q*(12)듺죫쪽(2)뗃떽∑LT틔벰룷뗧솦릫쮾뗄랢뗧솿럖뇰캪 NMMM p=e−f∑qk−f∑q= ∑f′′*bf′′p=jLF(′′+)q*e∑LT/(1+∑) (21) j=1f′′+cjjj=1f′′+cjk=M+1j=1MNNe−bNfbf*jebki q (e+∑)/(1+)− ΣLF=(∑∑−+)/ =1f′′+c1cjjk=M+kk=M+1f+∑ckk=M+1f+ciNMMMMff′′f [f/(1+∑)]∑q∆e′−f′q) ij=∑ (13) [(1+∑)(1+∑)] (22)=f′′k=M+1f+c1+ck=M+1cjjkii=1j=1
뗚27뻭 뗚8웚 뗧 췸 벼 쫵 13 p*−b캪쇋뇣폚럖컶룷훖틲쯘뛔쫐뎡솦뗄펰쿬*LTꎬ놾컄j q= (j=1,L,M) (23) jf′′+c퓚쿂쏦럖컶훐볙짨쯹폐뗄뗧솦릫쮾뻟폐쿠춬뗄돉j*놾쾵쫽aꆢbꆢcꎨ볻쪽(1)ꎩꎬ듋쪱쪽(25)~(27)뿉볲뮯*pLT−bq=kk (k=M+1,L,N) (24) c캪 k24 맑춷뺺헹뗧솦쫐뎡뗄쫐뎡솦 MPNf(e−b)cc= (28) [(N+1)f+c](Nfb+ec)놾컄닉폃맑춷뺺헹뗧솦쫐뎡뻹뫢뗣뗧볛폫췪좫뺺헹쫐뎡뻹뫢뗣뗧볛쿠뇈ꎬ늢틔볛룱쿠뛔쳡짽뗄MP1=Nf22LF(e−b){22f+[(N−M)+2]fc+c}/N냙럖뇈살뇭헷쫐뎡솦ꎨMarket PowerꎬMPꎩꎬ퓲짏 {[(N−M+1)f+c](Nfb+ec)⋅쫶3샠쫐뎡쒣탍뗄쫐뎡솦뿉럖뇰뇭쪾캪ꎺ M+22 [(1)f+(N+2)fc+c]} (29)ꎨ1ꎩCournot쫐뎡쒣탍뗄쫐뎡솦 MP=Mf2LTc(e−b)/{[N−M]f+c]⋅MP=p*−p*p* cc(ccpc)/pc= [(N+1)f+c](Nfb+ec)} (30)NNfbfei [(+∑)/(1+∑)−5 쯣샽폫뷡맻럖컶 =1f+c=1f+ciiiiNNNNfbffbf틔IEEE 6믺30쒸쿟쾵춳캪샽럖뇰럖컶짺닺돉ii (e+∑)/(1+∑)]/[(e+∑)/(1+∑)]=1c놾ꆢ뗧솦탨쟳떯탔벰쫐뎡훐ퟷ캪쇬떼헟뗄뗧솦릫쮾=1c=1c=1ciiiiiiii (25) 쫽솿뗈뛔쫐뎡솦뗄펰쿬ꎬ좻뫳퓙럖컶죝솿쿞훆뛔쫐ꎨ2ꎩStackelberg쫐뎡쒣탍뗄쫐뎡솦 뎡솦뗄펰쿬ꆣ MP***LF=(pLF−ppc)/ppc=뇭1캪룷뗧솦릫쮾뗄돉놾쾵쫽ꆣ쫐뎡탨쟳쟺쿟NN캪p=e−fD=50− ($/MWh)ꆣ폃짏쫶3훖뗤탍 [(∑f′bfei′+)/(1)1f′+∑′+−=c=1f′+c쒣탍쒣쓢뗧솦쫐뎡쪱뗄뻹뫢뗣뷡맻볻뇭2ꆣ컞싛쫇럱iiiiNNNN뾼싇랢뗧죝솿쿞훆ꎬ헢3훖쒣탍훐Cournot쫐뎡샠탍+∑fbffbfi (e)/(1+∑)]/[(e+∑i)/(1+∑)]i=1c1c1c1c뗄쫐뎡뗧볛캪ퟮ룟ꎬStackelberg쫐뎡샠탍뗄쫐뎡뗧ii=ii=ii=i (26) 볛듎횮ꎬ뛸Forchheimer쫐뎡샠탍캪ퟮ뗍ꆣ ꎨ3ꎩForchheimer쫐뎡쒣탍뗄쫐뎡솦 뇭1 뗧솦릫쮾뗄돉놾쾵쫽 MP=p*−p*p*LT(=Tab. 1 Cost coefficients of firms LTpc)/pcNN릫쮾 a b c ퟮ킡랢뗧릦싊 ퟮ듳랢뗧릦싊 f′′bf′′1 0 00 0 500 [(e∑i′′+)/(1+∑)−=1f′′+c=1f′′+c2 0 50 0 500 iiiiNNNN3 0 00 0 500 fbffbfii4 0 (e+∑)/(1+∑)]/[(e+∑)/(1+∑)]0 00 0 500 =1c=1c=1c=1c5 0 50 0 500 iiiiiiii6 0 34 0 500 (27) 뇭2 룷샠쫐뎡뗄뻹뫢뗣볆쯣뷡맻 Tab. 2 Results of equilibria in different market structures 늻뾼싇랢뗧죝솿쿞훆 뾼싇랢뗧죝솿쿞훆 췪좫뺺헹?Cournot쒣탍 Stackelberg쒣탍 Forchheimer쒣탍 췪좫뺺헹 Cournot쒣탍 Stackelberg쒣탍 Forchheimer쒣탍 MCP/($/MWh) ퟜ랢뗧솿/MW 2 2 2 2 2 2 2 2 42144 쫐뎡솦/% 0 0 릫쮾랢뗧솿/MW 1* 쫕틦/$/h 1 4 3 1 2 4 4 2 릫쮾랢뗧솿/MW 2* 쫕틦/$/h 2 4 4 2 3 4 4 3 릫쮾랢뗧솿/MW 3 쫕틦/$/h 1 2 2 1 1 3 2 2 릫쮾랢뗧솿/MW 4 쫕틦/$/h 1 2 2 1 1 3 2 2 릫쮾랢뗧솿/MW 5 쫕틦/$/h 1 1 1 1 1 1 릫쮾랢뗧솿/MW 6 쫕틦/$/h 3 5 4 3 3 5 4 3 힢ꎺ* 캪Stackelberg뫍Forchheimer쒣탍쫐뎡훐뗄쇬떼헟ꆣ
14 Power System Technology Vol. 27 No. 8 ꎨ1ꎩ짺닺돉놾ꆢ뗧솦탨쟳떯탔뛔쫐뎡솦뗄펰쿬 MP/%춼151캪폃Cournot쒣탍쒣쓢뗄뗧솦쫐뎡훐쫐뎡솦폫뗧솦쓦탨쟳쟺쿟쾵쫽e뫍fꆢ뗧솦릫쮾돉놾쾵10쫽MPMP~c (*)~b (*3)b뫍c횮볤뗄맘쾵쟺쿟ꆣ듓춼뿉볻ꎬ뗧솦쓦탨쟳MP~f (*)MP~e (*50)쟺쿟킱싊f뫍돉놾쾵쫽cꎨ벴뇟볊돉놾쟺쿟킱싊ꎩ5뛔쫐뎡솦뗄펰쿬뷏듳ꆣf퓶듳뇭쪾쓦탨쟳쟺쿟뇤뚸ꎬ볤뷓뇭쪾쫐뎡쓚뗄탨쟳떯탔뇤킡ꎬ뗧솦탨쟳뛔뗧볛0e, f, b, c/pu0246810 뗄쏴룐돌뛈붵뗍ꎬ룷뗧솦릫쮾뻍풽폐뿉쓜탐쪹쫐뎡춼3 Forchheimer쒣탍뗧솦쫐뎡훐쫐뎡솦폫뗧솦탨쟳쟺쿟솦ꎻ뛸쫐뎡솦폫c뗄맘쾵쟺쿟퓲쿔쪾쇋룷뗧솦릫쮾쾵쫽ꆢ돉놾쾵쫽뗄맘쾵 Fig. 3 Relationships between MP and each coefficient in 죧쓜쳡룟짺닺킧싊ꎬ붵뗍짺닺돉놾쾵쫽cꎬ퓲뿉틔demand curve and cost function in Forchheimer model 쏷쿔뗘쳡룟쫐뎡솦ꎬ첧룟뗧볛ꎬ듓뛸믱뗃룼뛠뗄샻ꎨ2ꎩ쫐뎡훐쇬떼헟쫽솿뛔쫐뎡솦뗄펰쿬 죳ꆣ ퟷ캪쇬떼헟뗄뗧솦릫쮾웤쫽솿뗄뛠짙춬퇹믡MP/ %펰쿬쫐뎡솦ꆣ죧춼4쯹쪾ꎬ짏쫶쯣샽훐Stakelberg400350쒣탍쫐뎡뗄쫐뎡솦쯦M돊U탎뇤뮯ꎬ컞싛쇬떼헟300MP~c (*)쫽쒿뷓뷼폚쇣뮹쫇뷓뷼폚좫쳥닎폫헟ퟜ쫽ꎬ쫐뎡솦250뻹훰붥퓶듳훁Cournot쫐뎡쒣탍훐뗄쫐뎡솦ꎬ틲캪200MP~f (*)쫐뎡쓚쎻폐쇬떼헟믲좫캪쇬떼헟쪱ꎬ쫐뎡틑뺭퇝뇤150캪Cournot쒣탍뗄쫐뎡쇋ꆣ 100MP~MP~b (*3)e (*50)MP50700e, f, b, c/pu024681060 춼1 Cournot쒣탍쫐뎡솦폫뗧솦탨쟳쟺쿟쾵쫽ꆢ 50Stackelberg쒣탍쫐뎡돉놾쾵쫽뗄맘쾵 40Fig. 1 Relationships between MP and each coefficient In demand curve and cost function i30n Cournot model 춼202뫍춼3럖뇰캪Stackelberg쒣탍뫍Forchheimer쒣탍쫐뎡10Forchheimer쒣탍쒣쓢뗄뗧솦쫐뎡훐쫐뎡솦폫뗧솦0M쓦탨쟳쟺쿟쾵쫽0123456?e뫍fꆢ뗧솦릫쮾돉놾쾵쫽b뫍c횮볤뗄맘쾵쟺쿟ꆣ웤훐릫쮾1ꆢ릫쮾2캪쇬떼헟ꆣ춼4 쫐뎡솦폫쇬떼헟쫽맘쾵쟺쿟 Fig. 4 Relationship between MP and number of leaders 퓚춬퇹뗄탨쟳쟺쿟쾵쫽e뫍f쿂ꎬStackelberg쒣탍뛸Forchheimer쫐뎡쒣탍훐뗄쫐뎡솦퓲쯦M돊쫐뎡뗄쫐뎡솦뇈Cournot쒣탍쫐뎡뗄킡ꎬ뛸랴L탎뇤뮯ꎬ쇬떼헟쫽캪쇣쮵쏷쯹폐닎폫헟뚼캪킡Forchheimer쒣탍쫐뎡훐쫐뎡솦ퟮ킡ꆣ 탍뗧솦릫쮾ꎬ벴볛룱뷓쫜헟ꎬ듋쪱뗄쫐뎡뒦폚췪좫MP/%250뺺헹ힴ첬ꎬ틲듋쫐뎡솦캪쇣ꆣ뛸떱쇬떼헟쫽쒿뷓뷼폚좫쳥닎폫헟ퟜ쫽쪱ꎬ쫐뎡솦훰붥퓶듳훁Cournot200MP~c (*)쒣탍쫐뎡훐뗄쫐뎡솦ꎬ풭틲춬Stackelberg쒣탍쫐뎡150MP~f (*)뗄럖컶ꆣ 컞싛쫐뎡훐뗄쇬떼헟쫽쒿폐뛠짙ꎬForchheimer100쒣탍쫐뎡뗄쫐뎡솦쪼훕뇈Stackelberg쒣탍쫐뎡뗄50MP~e (*50)MP~b (*3)쫐뎡솦튪뗍뗄뛠ꆣ틲듋죧뫎틽떼뗧솦쫐뎡ퟟ쿲0e, f, b, c/puForchheimer쒣탍뗧솦쫐뎡퓋펪믺릹뫍볠맜믺릹펦0246810 춼횵뗃훘쫓ꆣ 2 Stackelberg쒣탍뗧솦쫐뎡훐쫐뎡솦폫뗧솦탨쟳 쟺쿟쾵쫽ꆢ돉놾쾵쫽뗄맘쾵ꎨ3ꎩ랢뗧릫쮾죝솿쿞훆뛔쫐뎡솦뗄펰쿬 Fig. 2 Relationships between MP and each coefficient in 쪵볊짏ꎬ쎿룶뗧솦릫쮾뚼폐튻뚨뗄랢뗧죝솿쿞demand curve and cost function in Stackelberg model 훆ꆣ죧맻짏쫶룷뗧솦릫쮾뻹뻟폐ퟮ듳랢뗧죝솿뗄쿞
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