Thermal Economy Analysis Model with Matrix Method for the Secondary Loop of PWR Nuclear Power Station

Transcription

1 The 2nd Internatonal Conerence on Computer Applcaton and Sytem Modelng (22) Thermal Economy Analy Model wth Matrx Method or the Secondary Loop o PWR Nuclear Power Staton L Yonglng Huang Yu, Ma Jn,Wang Bnhu North Chna Electrc Power Unverty, North Chna Electrc Power Unverty, Baodng, Hebe, Chna North Chna Baodng Electrc Power Voc. & Tech. College Baodng, Hebe, Chna Abtract-Accordng to charactertc o Preurzed Water Reactor PWR nuclear power taton, the two-tage moture eparator reheater (MSR) model wa propoed wth thermal eulbrum euaton and ma conervaton euaton, nally the thermo-economy analy model wth matrx euaton or econdary loop wa put up. Baed on the model, the thermal economy nluence value o the auxlary teamwater are calculated and compared wth thoe o habtual thermal balance method (HTBM). The reult ndcate that the model preented n the artcle wa correct; t avalable and convenent or computer codng and onlne calculatng. The matrx analy method can provde theoretcal ba or mulatng o the econdary loop thermal ytem or PWR nuclear power taton. Keyword-Preurzed water reactor, econdary thermal economy, tate euaton, Mechanm modelng I. loop, INTROUCTION At preent the man type o nuclear power taton PWR, t occupe about over percent o the total ntalled capacty []. The economy o econdary loop drectly aect the ecency o the whole unt. It tructure n the unt more complex compared wth the coal red one, whch ued the regeneratve cycle wth team reheat. So t dcult or reearcher to analyze the economy o econdary loop n PWR nuclear power taton. There are everal thermal ytem analy method, uch a HTBM, the cycle uncton method, euvalent heat drop method and matrx method and o on [2-4]. HTBM the ba method. Euvalent heat drop analy method can carry out local uanttatve analy concely and convenently, whch ha been wdely appled n thermal ytem analy reearch o nuclear power taton [9].When the local parameter or tructure changng, n order to avod calculatng the comprehenve thermodynamc ytem t neceary or u to nd a clear, convenent, and mple uanttatve economy analy method. The theoretcal tudy o th ueton comparatvely le. Thereore, the thermo-economy analy model wth matrx method n PWR nuclear power taton propoed. II. A. THERMAL ECONOMY ANALYSIS MOEL WITH MATRIX METHO Sytem Introducton Compared wth the coal red power plant, the econdary loop n nuclear power taton adopt the aturated team crcle, o the hgh-preure (HP) cylnder exhaut team hould eparate rom the moture eparator beore enterng the reheater. And the ntermedate reheat team alway the man team []. Thereore, eparatordegned to gather mall water droplet rom team and eparate thoe rom the ppe low. There alo the moture eparator reheater (MSR) n ome nuclear power taton. Accordngly, the dranage o MSR mut enter nto the hgh preure heater (HPH) and low preure heater (LPH) n regeneratve ytem. A hown n Fgure., the aturated water rom the moture eparator low nto the deaerator; the aturated team enter nto lower-preure cylnder ater reheatng by reheat team, ome man team and part o the rt-tage team extracton ; the dranage enter nto the HPH. h rh hrh rh rh 2 hrh rh h hdrhdrh hdrh hdrh 2 h h ohph HPHand andmsr MSRn necondary econdaryloop loop Fgure. Fgure.The Theytem ytemo B. MSR model The ualty euaton or two-tage MSR are expreed n ormula ()(2). rh = drh + rh rh = m = rh rh 2 n = 2 The Thermal eulbrum euaton can be preented by below ormula, h rh rh + (h h drh ) rh + (h h drh 2 ) rh 2 drh h drh = h rh rh 4

2 The 2nd Internatonal Conerence on Computer Applcaton and Sytem Modelng (22) Where, rh HP cylnder exhaut team low; h rh HP cylnder exhaut team enthalpy; drh aturated water low rom the MSR; hdrh aturated water enthalpy rom the MSR; hrh aturated team enthalpy rom the MSR; h man team enthalpy; h the rt-tage extracton team enthalpy; rh rt-tage reheat team low; rh2 the econd-tage reheat team low; drh the rt-tage reheat dran low; drh2 the econd-tage reheat dran low; hdrh the rt-tage reheat dran enthalpy; hdrh2 the econdtage reheat dran enthalpy; drh, drh2 and drh can be condered a auxlary water low. The thermal eulbrum euaton, takng HPH a an example, etablhed n ormula (4). dk k = γ + ( + drh ) ( + )γ + = c τ rh rh 2 drh ( k = k + k ) C. The team-water dtrbuton matrx euaton In the analy o thermal ytem, the matrx analy method ha been wdely appled becaue o t charactertc o conce expreon and eay converon nto mathematc problem [-]. Accordng to thermal eulbrum euaton and ualty euaton o heater n econdary loop thermodynamc ytem, the matrx euaton o thermal eulbrum obtaned n (6). [A][]+ [A][] +[Q]=[Qτ] 6 Where, [A] the team-water dtrbuton matrx o man ytem, whch nclude the team extracton, dranage, eed water, and the auxlary team-water ytem nclude the team leakage, rt-tage reheat team, econd-tage reheat team, the dranage o MSR and eed water pump enthalpy re. [A] matrx can be expreed a lower trangular matrx. [] hown a a column o team extracton low, [] alo hown a a column, the element mean the um o auxlary team-water low o heater. The matrx [Q] mean the energy change matrx a a reult o the auxlary team-water low o the heater ytem. The matrx [Qτ] mean the correpondng eed water energy change o heater, whch can be expreed by the product o eed-water enthalpy re τ and outlet low w. = k = Where, the expreon h+σ-hc repreent the enthalpy drop o all man team low. and mean the power hortage o the team extracton low and p h σ = h σ = k hkσ auxlary team low. repreent the power hortage o other team leakage low. h mean the energy change o k = σ = + c = = 7 I the eral number o LPH, the nearet collecton type heater eral number, the euaton are hown n (). Where,, τ and γ mean team extracton heat, dranage heat, eed-water enthalpy re. p N = (h +σ hc ) hσ hσ + k hkσ 4 + drh ( h drh h ) ( h h ) = wτ Generally, economc perormance o thermodynamc ytem are calculated on the ba o the man team low. For the econdary loop thermal ytem o PWR nuclear power taton, the man team enthalpy h, turbne exhaut team enthalpy hc, the power euaton expreed n (7), when team extracton o heater and gland leakage team low let the team path o turbne. mall team low, when t let rom HP cylnder, σ h = h + σ hc, and t departed rom IP and LP cylnder, σ h = h hc. σ repreent the team heat n reheater. Compared wth the coal-red power plant, the reheat team come rom man team, and dd not aborb the external heat, o the crculaton heat doe not contan the tem σ (reheater heat) or the econdary loop thermal ytem. The Factor nluencng the workng medum heat are the man eed water and SG blow down low. Accordng to energy balance, the heat euaton expreed, Q = ( h h w ) + bl ( h bl h w ) 8 Euaton (6), (), (2) are known a the thermal economc tate euaton o the econdary loop o PWR nuclear power taton. The euaton are ba euaton, whch relect the heater type and dranage connecton.. Local uanttatve analy model The cycle ecency one o the thermal economy analy ndcator. Accordng to the thermal economy local uanttatve analy method baed on the matrx euaton, a long a we ll n related matrx by the rule, the ecency change o the ytem can be calculated dependng on ettng the correpondng parameter n the matrx o the eect actor we analyzed to. I the cycle ecency or actual ytem η, t can be ued the ormula expree n (9). The cycle ecency whch gnored one or everal auxlary team-water dturbance expreed a η. A a reult the nluence relatve value o thee auxlary team-water low are calculated by the ormula. The overall ecency o nuclear power taton can be expreed n (). η=n/q 9 Δη = η η /η % ηa=ηr ηg ηp η ηm ηg Thereore, the nuclear reactor uel conumpton ba(g/(kw h)) can be repreented a, The change o nuclear reactor uel conumpton can be determned by the ormula () a the cycle thermal ecency alter. 42

3 The 2nd Internatonal Conerence on Computer Applcaton and Sytem Modelng (22) Δ b a.4 = =.4 η η η ηa ηrη gη P.4 m g Δη (2) b = = δη η η η ηη η η = a ba ba b () a R g P m g Thereore, the relatve value δη can be avalable to ndcate the thermal economc nluence o thee auxlary team-water dturbance. III. RESULTS OF ONE EXAMPLE ON MATRIX EQUATION In order to very the correctne and accuracy o the model, a numercal example o a PWR nuclear power taton calculated, a hown n Fgure.2 (ome parameter are lted n tab.and tab.2). There are ome tructural eature, uch a ngle-ax, our-cylnder, extuple-low, double-tage reheat. Some parameter o the econdary loop thermal ytem lted ollowng: the preure and temperature o man team are 6.4 Mp a and 279.9, reheated team preure and temperature are.978 Mp a and 26.2, the reheat heat rom man team and HP cylnder exhaut team to MSR are σ zr, =7. kj/kg and σ zr,2 =67 kj/kg. Fll n the matrxe dependng on the rule o tate euaton or the econdary loop thermal ytem o PWR nuclear power taton etablhed n th paper. The man matrxe, power euaton and heat euaton are lted below. drh rh2 γ2 2 2 drh2 γ γ drh A= γ 4 γ4 γ4 = 4 = 4 τ τ τ τ τ 6 γ6 6 6 τ 7 γ7 γ ( h h ) u( h u h ) ( ) τ 2 ( h2 h) u v 2 ( 2 rh( hdrhh ) ( h h ) + ( ) τp ( [ Q ] [ Qτ ] = ( 4 ( ( ) τ 6 7N( N hwc) + 7 T( T ) + 7 B( B )}) ( + bl 7 Q = ( h h w ) + bl ( h bl h ) w N = ( h + σ h c ) ( h + σ h c ) ( h + σ h c ) 2 2 ( h + σ h c ) ( h h c ) ( h h c ) 4 4 ( h h c ) ( h h c ) ( h + σ h c ) A A ( h + σ h c ) ( h + σ h c ) ( h + σ h c ) B B H H E E + ( h + σ h c ) + ( h + σ h c ) ( h + σ h c ) A A H H W W ( h + σ h c ) 2 ( h + σ h c ) M M 2 ( h + σ h c ) N N + ( )( h + σ h c ) drh + ( h h c ) ( h h c ) T T Accordng to above matrxe, we can determned the man team low and team extracton low,,, 2,, 4,, 6, 7. ependng on the ualty euaton o MSR, the reheat team low can be conrmed. Accordng to the calculaton reult o the power and heat euaton, we can calculate the ecency η. ependng on ettng the correpondng parameter we analyzed n the matrx to, the changed ecency η can be calculate. A a reult the thermal economy nluence relatve value Δη calculated. Calculaton reult are hown n tab. 4. The reult how that the matrx reult are n good agreement wth thoe o HTBM, whch prove that the matrx method preented n th dertaton correct and avalable. The matrx ully relect the thermal economy nluence o man ytem and auxlary ytem. Each ubmatrx ha explct phycal meanng and trong regularty, o that t can make the overall computaton and local analy clear and mple, and utable or computer programmng. IV. CONCLUSIONS Accordng to charactertc o PWR nuclear power taton, the econdary loop thermal ytem ung the twotage MSR wa manly analyzed. The thermal eulbrum euaton and ma conervaton euaton on heater o the econdary loop thermal ytem were propoed; nally the thermo-economy ytem tate euaton or t wa put up. The mplct topologcal tructure o matrx relect the heater type and dranage connecton. The accuracy and practcablty o the method wa vered by a calculaton example. The matrx euaton wth the great regularty convenent to ll n and utable or the computer to calculate n partcular wth MATLAB. The matrx analy method can provde theoretcal ba or thermal economy reearch and ytem mulaton o the econdary loop thermal ytem or PWR nuclear power taton. ACKNOWLEGMENTS Proect upported by the Fundamental Reearch Fund or the Central Unverte under Grant MG2,and alo upported by the Young Teacher Fund or Scentc Reearch n North Chna Electrc Power Unverty (28). REFERENCES [] Zhu hua. Automatc energy and nuclear power taton. Hangzhou: Zheang Unverty Pre, 29.:-2. [2] Ln Wanchao.Energy-avng analye method o thermal power plant thermal ytem [M].X an: X an Jaotong Unverty Pre,994:-4(n Chnee). [] Zheng Tkuan. Thermal power plant [M]. Beng: Chna Electrc Power Pre,2:44- (n Chnee). [4] Ma Fangl. Energy-avng analye prncple o thermal power plant thermal ytem [M]. Beng:Chna Electrc Power Pre,992. [] Yan June,Ln Wanchao, eng Shmn. Reearch on thermoeconomc dagnotc method or the econdary-crcut o PWR nuclear cogeneraton plant [J].Proceedng o the CSEE,2,2 (8) :6-6(n Chnee). [6] Yan June, L Yunze. Reearch on thermo-economc analy theory or thermal ytem o the econdary-crcut o PWR nuclear power taton [J].Proceedng o the CSEE,2,2 () :-8(n Chnee). [7] L Yunze, Yan June, Ln Wanchao, et al. A lnear element method or analyzng the econdary loop o a preurzed water reactor (PWR)nuclear power taton[j].journal o Engneerng or Thermal Energy and Power, 2,():44-47(n Chnee). 4

4 The 2nd Internatonal Conerence on Computer Applcaton and Sytem Modelng (22) L Yunze,Yan June,Ln Wanchao,et al.the euvalent heat drop method or the econdary-crcut analy o PWR nuclear power taton ytem[j].turbne Technology,2,42(): -(n Chnee). [9] L Jangang,L Lpng,Yang Xaokun.A tudy o team-water low dtrbuton calculaton or the econdary-crcut thermodynamc ytem o PWR nuclear power taton[j].turbne Technology, 24,46(2):94-96(n Chnee). [] Sterman L S,Terln S A,Sharkow A T.Thermal and Nuclear Power Staton.Mocow: Mr Publher, 986,28. [] Guo Janglong,Zhang Shuang,Song Zhpng,et al.a matrx method or thermal ytem analy n a power plant [J].Proceedng o the CSEE,24,24 () :2-2(n Chnee). [8] [2] Zhang Chuna,Zhang Suxang,Cu Ynghong,et al. Thermo-economy tate euaton o modern power ytem [J]. Journal o engneerng thermophyc,2,22(6):66-667(n Chnee). [] Zhang Chun-a, LI Juan. Quanttatve tudy or the lmtaton o mall dturbance theory on the tep out o hgh-preure heater[j]. Turbne technology. 28, 2(): 4-6. [4] Chen Hapng.Calculaton o thermodynamc ytem n power plant baed on ma unt [].Baodng:North Chna Electrc Power Unverty,22,4 (n Chnee). [] Zhang Chuna, Xe Fe, L Yonglng. Thermal economc tate euaton o MW ar coolng unt [J].Electrc Power Scence and Engneerng, 2, 2: Fgure.2. Fgure 2. Flow chart o a PWR nuclear power taton TABLE I. MAIN ORIGINAL ATUM OF THE MAIN THERMOYNAMIC SYSTEM Heater Number /(kj/kg) γ/(kj/kg) τ/(kj/kg) TABLE II. ATUM OF AUXILIARY STEAM-WATER SYSTEM Auxlary team team-water proporton ① ② ③ ④ ⑤ ⑥ α =.92 αdrh=.424 αdrh2=.44 α 7=.46 αmn=.6 α S = h /(kj/kg) /(kj/kg)

5 The 2nd Internatonal Conerence on Computer Applcaton and Sytem Modelng (22) TABLE IV. THE THERMAL ECONOMY CALCULATING RESULTS (%) Item Matrx method HTBM Actual cycle ecency The nluence on thermal economy wth auxlary team-water low