Optimal dynamic dispatch of surplus gas among buffer boilers in steel plant

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J．Cent．South Univ．(20 1 31 20：2459—2465DoI：10．1007／sl1771．013．1757．7Optimal dynamic dispatch of surplus gas among buSUN Wen—qiang(~IJx文强)，CAI Jiu-ju(蔡九菊)垒Springerr boilers in steel plantInstitute of Thermal and Environmental Engineering，SEP Key Laboratory of Eco—industry，Northeastem University，Shenyang 1 1 08 1 9，China◎Central South University Press and Springer-Verlag Berlin Heidelberg 20 1 3Abstract：As valuable energy in iron—and steel-making process，by—product gas is widely used in heating and technical processes insteel plant．After being used according to the technical requirements，the surplus by—product gas is usualy used for bufer boilers toproduce steam．With the rapid development of energy conservation technology and energy consumption level，surplus gas in steelplant continues to get larger．Therefore，it is significant to organize surplus gas among bufer boilers．A dynamic programming modelof that issue was established in this work．considering the ramp rate constraint of boilers and the influences of seting gasholders.

Then a case study was done．It is shown that dynamic programming dispatch gets more steam generation and less specific gasconsumption compared with current proportionate dispatch depending on nominal capacities of boilers．The ignored boiler ramp rateconstraint was considered and its contribution to the result validity was pointed out．Finally,the significance of seting gasholderswas studiedKey words：surplus gas；dynamic programming；bufer boiler；steel plant1 Intr0ductiOnIron． and steel—making is a typical iron-coalchemica1 process『1]，in which volumes of by—productgases are generated as consuming fuels，such as coa1.

After being used in main production processes，there arestil1 some surplus gases．So．the optimal dispatch ofsurl：lus gas wins the favor of stee1 plants for reducingproduction cost and energy consumption， Ke印 lngcomprehensive energy consumption per ton of steel closeto the theoretical energy consumption[2]，constructingthe energy flow network [3]，and reducing the C02emissions from gas releasing f4—5]．Litle inform ation isavailable about the optimal dispatch of surplus gas，yetmany researchers have paid their attentions to optimalproduction of steel plant．To dispatch the surplus gas，mixed integer linear programming(MILP)was used tocontro1 the level of gasholder in stee1 plant byAKIM0T0 et a1『6]．They advised a penalty cost in theobiective function of the optimized model when thesurplus gas is released or lacked．SINHA et a1[7]suggested adding the boiler on／of costs overmulti—periods applied to MILP model to obtain themaximum profit．In addition，penalty cost for on／ofstatus of burners in boilers is considered by KIM et al『8-9]and K0NG et al『l0]to study the level fluctuationof gasholder and surplus gas dispatch．Their researchescontributed a lot to the dispatch and utilization of surplusgas；however,some problems not obeying the actualproduction and operation principles also exist in theirmodels．For instance．the quantity of working burners inboilers、 not allowed changing ad 1ibitum．because itdisorganizes the internal flow field of boilers．The ramprate corn,；traint is also ignored in those models『11—12]，which causes the diference between the computedresults and the actual effects.

Additionaly,the optimal dispatch of surplus gasamong tw o or more boilers has not been focused inprevious studies．In actual production，average dispatchand proportionate dispatch depending on nominalcapacities of boilers are applied．However,it has beenproved mat they are not optima1．As a branch ofoperational research， dynamic programmmg 1s anoptimized methodology for solving multistep decisionissues．It has been widely used in resource allocationproblems since its advent 『13-151． Dynamicprogramming is brought to dispatch surplus gas in steelplant in this work，to obtain the maximum steamgeneratlon at given surplus gas.

2 Dynamic programming methodologyElements of one dyn amic programming model foroptimizing a multistep decision process are listed asfollows：Foundation item：Pr0ject(L2012O82)supposed by the Science and Technology Research Funds ofLiaoning Provincial Education Department，ChinaReceived date：2012——05——07；Accepted date：2012—08——21corresponding author：SUN Wen-qiang，PhD Candidate；Tel：+86—24 83672218；E—mail：neu20031542( 163．com2460 J．Cent．South Univ．(2013)20：2459—24651、Step．Step is the natural division of a wholeprocess．To solve the optimal problem in step sequence，step is usually divided in time or space sequence．Stepvariable is expressed as k=l，2，? ，F／.

2、State．State is the initia1 natural condition of eachstep．The variable to express state is state variable．Thestate variable of step k is denoted as sb which is either anumber or a vector．It should describe the characteristicof the process and have no following efects，i．e．，oncethe state variable of a step is given，the evolution of stepsafter it has no relation with the states of steps before it.

31 Decision．Once the state of a ste1)is set，severalchoices could be made and then the state evolves to anew state of next step．The choice is called decision，andthe value of the choice is decision variable．The range ofallowed decision variables is set of admissible decisions.

The decision variables of state Sk at step k is expressed asXk(Sk)，and the set of admissible decisions of state Sk isexpressed as Xk(Sk).

41 State transition equation． For deterministicprocess，once the state and decision of a step are given，the state of next step is achieved uniquely． Statetransition equation is used to describe the evolution rule，and it is expressed ass川 = ( ，xk)，k=1，2，?，n一1 (1)5、0bjective function and optimal value function.

0biective function is the quantitative index forevaluating the process．It is the quantitative functionwhich is defined on the whole process and al folowingsub-processes．It is denoted as (sk，xk，sk+1’?，sn)andexpressed aswhere 1，2，? ，n-1，and the function of 斛1 isstrongly monotonous.

Sub-objective function of step J is depended on itsstate and decision xj．It is expresed as vj(sj，xj).

Objective function consists of sub—objective fimctions，i?e(s ，xk，sk小‘‘ (3)According to the state transition equation，objectivefunction can also be expressed as the function of stateSk and policy P (s )={xk(s )，?，xn( n)}．At a givenstate Sk，the optimal value function is( )=opt ( ，P ) (4)where“opt'’represents maximum or minimum depended.

6)Recursion equation．The following equation isthe recursion equationf ( )=Vn(Xn)1 ( )= opt {(sk，xk)+ +1(sk+1)}，k= 一1，?，1【 xkeXk(s )(5)Recursion equation of dynamic programming is thebasis of principle of optimality．It is from n backwardto k=-I for solving the dynamic programming process byusing equation of state transition(Eq．(1))and recursionequation(Eq．(5)；and therefore it is backward solvingprocess.

3 Dynamic programming dispatch modelOptimal dispatch of surplus gas based on dyn amicprogram ing is to reach the optimal value of total steamproduced by involving buffer boilers．which is under theconstraints of surplus gas resources，limits of evaporationcapacity of each boiler,ramp rate of each boiler,andseting gasholder．So，the optimal dispatch of surplus gasamong bufer boilers can be converted into an n．stepdecision process，where n is the number of boilersconcemed with the dispatch process．In this work，fivebuffer boilers are shared in the dispatch of surplus gas.

The nominal capacity of≠≠1-#3 is 220 t／h and that of 4and≠}5 is 65t／h.

Step：Regard the five bufer boilers as five steps.

The st印 variable k=l，2，3，4，5.

State：Define the state variable of steD k at time t assk(t)，which means the total surplus gas could bedispatched to#1-#k boilers．Because backward solvingprocess was used in this work，the state variable of step 5at time t is the total surplus gas at this time口( ．Theactual surplus gas at 0-24 h of 1 d was selected in thiswork．as given in Table 1.

t／h a／(GJ·h- ) t／h a／(GJ·h )0 1314 13 1 5451 1 149 14 2 2802 1 576 15 1 9073 1 659 16 1 4914 1 467 17 1 8935 1 402 18 1 5996 1 898 19 1 1157 1 993 20 l 3158 1 841 21 1 2879 2 190 22 1 821l0 2 015 23 1 769l1 2 059 24 1 93112 1 859、2 ++帅， ～
， 、●， ，L ∑=、+J．Cent．South Univ．(20 1 31 20：2459—2465 2461Decision：Define decision variable of step k at time tas ，which it presents the gas dispatched to# boilerattime t.

Equation of state transition：+1(t)=sk(t)一Xk(t) (6)where S5(t)= (f).

Optimal value function and objective functionk( (f))=(m ax)
Zgj(xj(f) (7)According to the production data，the relationshipbetween steam generation(D and gas consumption(ak)240220}200180160Q1401201000 FielddataDl=96．347 61n(x1／56．262 3)R2=0．820 8200 300 400 500 600Xl／(GJ·h一 )240~(c)220l200180Q 160l4012010O0 Field dataR2=0
．808 482 3、200 300 400 500 600 700x3／(GJ·h一 )of≠1一 5 boilers was fi~ed by least square method．asshown in Fig．1．The obtained fired function is thesub-objective function.

Then，the dynamic programming model of thisproblem is：f ( (f))=D5(X5(f)){fk( (f)：max (( (f)，xk(t)+fk+1( (f)一 (f))，I k=4，3，2，1(8)Subject to surplus gas resource constraint：5∑xAt) 口(f) (9)240200160120807O6050叫 200 300 400 500 600 700 800Xz／(GJ·h一 )(d)。 。

B。 。

D4=41．498 1 In 4／3 1．778 0)R2=0
． 819 760 80 10O 12O 140 160 180x4／(GJ·h一 )Fig．1 Fit curve of relationship between steamgeneration and gas consumption：(a) 1 boiler；(b) 2 boiler；(C)≠}3 boiler；(d) boiler；(d) 5boiler2462 J．Cent．South Univ．(20 1 3)20：2459—2465limits of evaporation capacity constraints( (f)≤pramp rate constraints：一 1
·At Dk(x (f)一Dk(x O一1)) ，IJ·Atseting gasholder constraints：(f)=at( )+ —1)and range constraints：0 Xk(t)≤S (t)(10)(11)(12)(13)where Dk(xk(t) represents the transient evaporationcapacity of boiler at time t with its decision variable( ；D and are the upper and lower limits ofevaporation capacity of# boiler at its working order,respectively； and are the ramp rates of boilerwhen increasing and reducing load，respectively；at( isthe surplus gas from upstream processes of time f；and”(卜1)denotes the remaining gas after the dispatchamong five bufer boilers at time(卜1).

4 Results and discussionThe dispatch result of dynamic programming isshown in Fig．2．It can be seen from Fig．2 that thefluctuation of gas supply is mainly shared by #l一 3boilers but群4 and ≠}5 boilers when large fluctuationoccurs.

Defining that plan A is the dynamic programmingdispatch plan proposed in this work，plan B is the currentproportionate dispatch plan depending the nominalcapacity of each boiler,plan C is a plan A without ram prate constraint，plan D is a plan A without consideringgasholder constraint，and plan E is a plan A without bothramp rate constraint and gasholder constraint． Thedetailed surplus gas dispatches of these five plans areshown in Fig．3，and the comparison of steam generationis showninFig．44．1 Comparison of dynamic programming dispatchand proportionate dispatchIt can be found from the comparison ofplans A andB in Fig． 3 that dynamic programming methoddispatches surplus gas according to the D—x curves ofbuffer boilers shown in Fig．1．whereas proportionatedispatch is according to the nominal capacity of eachbufer boiler．That is why the gas dispatched to#1-#3boilers is the same．and so do≠}4 and≠}5.

From Fig．4，the total steam generation of plan Adnring 0-24 h is 1．69x10 t．which is 105．65 t higherthan that of plan B．It can be calculated that the specifcgas consumption of plan A is 2．5 1 GJ／t．0．02 GJ／t lowerthan that of plan B．Compared with current proportionatedispatch，dyn amic programming dispatch produces moresteam and has lower specific gas consumption．Therefore.

dyn amic programming dispatch has a notable efect onenergy conservation．and it could receive the optimaldispatch with given surplus gas resources.

4．2 Influences of ramp rate and gasholderIn Fig．4，the steam generations produced fromplans C and E are both higher than those of plan A at t=-2，6．14．22 h．That is because ramp rate constraint ofboilers is not considered in plans C and E．which causesthe increasing rates ofgas in≠}1-#3 boilers exceeding thealowed values depending on the combustioncharacteristic of boilers．Take t=-14 h for example，theramp rates ofplans A．C．and E are listed in Tab1e 2.

It can be seen from Table 2 that the ramp rates of1-#3 boilers in plans C and E are too higher to sarisfythe normal combustion of those boilers．The highersteam generations computed by the two plans areunreasonable．So．it is of great significance to considerthe ramp rate constraint of boilers when establishingdyn amic programming models.

t／hFig．2 Steam generation at optimal dynamic dispatch of surplus gas
2464 J
． Cent．South Univ．(20 1 3)20：2459—2465W hen t=-7，23 h in Fig．4，steam generated from planA is higher than those ofplans D and E．It is due to thegasholder constraint． The remaining gases afterdispatch during 0—24 h of plans A，D，and E are given inTlable 3.

Table 3 Comparison ofremaining gases after dispatchIt can be gotten from Table 3 that the remaining gasat any time of plan A could be again used in next timebecause of the set gasholder．That is why only 1．56 GJgas is remained during 0—24 h．and the part can also beused at next moment．There are no gasholders in plans Dand E，so the remained gas at any time has to be released，which causes much energy consumption．Thus，to buferthe remaining gas after its dispatch，seting gasholdersplays a great role in energy conservation and emissionsreduction.

5 Conclusions1)The dynamic programming model of surplus gasdispatch among bufer boilers in steel plant is establishedand a case study is presented．In the model presented inthis work，ramp rate constraints of boilers and gasholderconstraint are considered．Least square method is used tofit the relationship between steam generation and gasconsumption of each boiler．And the fited fimctions areconsidered as sub-objective functions.

2)Compared with current proportionate dispatch，dyn amic programming creates more steam generationand lower specifc gas consumption．It is the optimaldispatch plan at given surplus gas resource.

3)Ramp rate constraint of boilers makes theincreasing or reducing rate of gas consumed by a boilerbe within a reasonable ran ge．And the result of steamgeneration is more reasonable.

4)As a bufer medium，setting gasholders makes itpossible to effectively use the remaining gas of last timeafter its dispatch，which reduces gas releasing，savesby-product gas，increases steam generation，reducesemissions，and therefore has a better environmental andeconomic effectReferences[1】 Y1N Rui—yu．Metallurgical process engineering [M】．Bering：MetallurgicalIndustryPress andSpringer，2011：161—172.

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(Edited by HE Yun-bin)