Applied Energy 87 (2010) 3514–3525

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Energy optimization in a pulp and paper mill cogeneration facility

D.J. Marshman a, T. Chmelyk b, M.S. Sidhu b, R.B. Gopaluni a,*, G.A. Dumont c

a Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z3b NORPAC Controls Ltd., 7500 Winston Street, Burnaby, BC, Canada V5A 4X5c Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4

a r t i c l e i n f o

Article history:Received 13 February 2010Received in revised form 21 April 2010Accepted 25 April 2010Available online 23 May 2010

Keywords:CogenerationEnergy managementNon-heuristic energy optimizationMILP modelDynamic programmingPulp and paper

0306-2619/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.apenergy.2010.04.023

* Corresponding author. Tel.: +1 604 827 5668; faxE-mail addresses: dmarshman@chbe.ubc.ca (D.J.

paccontrols.com (T. Chmelyk), MSidhu@norpaccontrni@chbe.ubc.ca (R.B. Gopaluni), guyd@ece.ubc.ca (G.A

a b s t r a c t

Alarmingly low pulp prices in early 2009 left pulp and paper mills across North America desperate for anyway to improve thin profit margins. One solution that continues to gain popularity among the industry isimproved energy management systems for cogeneration systems, which use steam for two purposes – toprovide heat for the pulping process and to generate electricity for sale to regional providers. This paperpresents an energy optimization algorithm for use in a pulp and paper mill cogeneration system. Thealgorithm is applicable to a number of popular mill configurations, power sale contracts, and fuel pur-chasing scenarios. The method is also extended to address weather-dependent cooling limitationsencountered by a mill cogeneration facility, in which case an iterative solution is proposed in order tomaintain convexity of the optimization problem. Results are presented in the form of three case studies.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

A cogeneration or combined heat and power (CHP) system pro-duces steam that provides thermal energy to heat exchangers andmechanical energy through expansion to turbine units. The turbineunits then transfer the mechanical energy to generators, which inturn produce electricity. The generation of heat and electricalpower within a single facility, as opposed to separate facilities, of-ten results in efficiency improvements in the range of 10–40% [1].A detailed look at the co-ordination of multiple CHP plants fromboth an economic and environmental perspective by Karlsson etal. [2].

Pulp and paper mills are excellent candidates for cogenerationfacilities. Large scale steam production equipment is already nec-essary for washing, refining and drying stages of the pulping pro-cess, therefore the cost of installation for a cogeneration facilityis significantly offset. Pulp production, depending on the pulpingmethod used, may also yield two additional fuel sources as byprod-ucts – hog fuel and black liquor. Steam production that utilizesthese alternative fuels in the place of natural gas or fossil fuels sig-nificantly reduces cogeneration operating costs.

Pulp mills can alternatively use black liquor to directly generateelectricity using a gasification/gas turbine process, as described by

ll rights reserved.

: +1 604 822 6003.Marshman), TChmelyk@nor

ols.com (M.S. Sidhu), gopalu. Dumont).

Consonni et al. [3], and by Maunsbach et. al. [4]. In this instance,black liquor and hog fuel may also be used to boiler steam for millheating purposes in a parallel process. The utilization of black li-quor to power gas turbines can result in potential reductions inCO2 emissions by up to 6%, compared to reductions of up to 8%with a cogeneration process, as described by Möllersten et al. [5].Alternatively, Klugman et al. [6] provide a mill wide analysis ofheat and electricity use in an effort to economically reduce energyconsumption and potentially make the mill self-sufficient in elec-tricity. The same authors also provide a thorough comparison ofpulp mill energy use variations between major pulp-producingcountries [7]. Although these approaches provide benefits with re-spect to plant economics as well as to the environment, this workwill focus exclusively on the management of cogenerationprocesses.

Successful management of a cogeneration facility is by no meansstraight forward, but is a critical component of recovering profits intoday’s troubled forestry industry. Elaborate plant configurationsresult in complex unit co-dependencies. Market-dependent elec-tricity prices, which typically fluctuate by 200–300% over thecourse of a day, make efficient production scheduling critical toplant management. Most cogeneration facilities have thereforedeveloped and/or employed optimization algorithms to aid in theprocess of plant energy management. These algorithms, often re-ferred to as energy management systems (EMSs), are responsiblefor the optimal scheduling of electrical power and heat generationthrough efficient resource and unit operation management. It isimportant to note that these energy management systems are often

Nomenclature

Ct cost of operation during period tcj

hog cost of hog fuel from supplier number jcng cost of natural gasce,t cost of electricity during period tEt cooling reservoir thermal energy at time tgi

t natural gas consumption by boiler number i during per-iod t

HXi ;Yj

in inlet steam enthalpy to ith unit of type X and jth subunitof type Y. If no subunits exist then the corresponding in-let enthalpy is denoted simply by HXi

inHXi ;Yj

out outlet steam enthalpy to ith unit of type X and jth sub-unit of type Y. If no subunits exist then the correspond-ing outlet enthalpy is denoted simply by HXi

outhi;j

t hog fuel consumption from supplier number j to boilernumber i during period t

fo total energy content of original fuel consumedft energy content of fuel used during time period tkf fuel scaling factormXi ;Yj

t average steam mass flow rate into jth subunit of type Yin ith unit of type X during period t. If no subunits existthen the corresponding mass flow rate is denoted sim-ply by mXi

tDmPRVi

t steam mass flow rate increase through pressure reliefvalve i during period t due to contact with water supplyduring depressurization

mXi ;Yj

MAX max steam mass flow rate into ith unit of type X and jthsubunit of type Y. If no subunits exist then the corre-sponding maximum mass flow rate is denoted simplyby mXi

MAXdmXi ;Yj

MAX rate of change limit for steam mass flow rate into ithunit of type X and jth subunit of type Y over one period.If no subunits exist then the corresponding rate ofchange limit for mass flow rate is denoted simply bydmXi

MAX

nXi ;Y number of subunits of type Y in ith unit of type X.nX number of units of type Xnsup number of hog fuel suppliersn total number of unitsPt power generation during period tQt heat demand during period tqi

t plant heat demand at ith pressure header during periodt. There are usually three pressure headers one each forhigh pressure, for medium pressure and for low pres-sure.

qr;Zt rate of cooling reservoir heat transfer from source Z at

time t where Z denotes either radiation (rad) or inletflow (inf) or vaporization (vap) or sensible heating (sens)or outlet flow (outf)

sj available hog fuel from supplier jt index of a period within the optimization horizonDt duration of an optimization periodtmax total number of periods within the optimization horizonwf,t fuel weighting vector during time period tX major cogeneration units – biolers (denoted boi), tur-

bines (denoted tur), steam headers (denoted sh), pres-sure relief valves (denoted PRV), vents (denoted ven)

Y cogeneration subunits – stages in turbines (denoted sta)aj hog fuel energy content coefficient from supplier ib hog fuel combustion efficiency�Xi ;Yj efficiency of jth subunit of type Y in ith unit of type X. If

no subunit exists then the corresponding efficiency isdenoted simply by �Xi

h natural gas energy content coefficient/ natural gas combustion efficiency

D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525 3515

distinct from individual unit controllers. The EMS often dictatesoptimal unit setpoints, whereas the unit controllers achieve andmaintain those setpoints.

Energy management algorithms emerged from substantialgrowth in computational automation during the 1970s. The major-ity of early methods took advantage of heuristic optimization algo-rithms. A summary of several early energy management strategiesis provided by Gruhl et al. [8].

More recent approaches such by those by Chen et al. [9], Rajanand Mohan [10], Williams et al. [11], Vasebi, Fesanghary and Bat-haee [12], and Sudhakaran and Slochanal [13] utilize one or morewell known heuristic optimization techniques. Chen et al. [9] usean enhanced immune algorithm, while Rajan and Mohan [10] usea method that combines simulated annealing and evolutionaryalgorithms. Williams et al. [11] employ a method known as thesimplex self-directing evolutionary operation procedure (SSDEV-OP). Vasebi et al. [12] a ‘‘harmony search algorithm”, and Sudhak-aran and Slochanal [13] combine the genetic (or immune)algorithm with the tabu search algorithm to produce a heuristicsearch method for a cogeneration system. The above methods areboth accurate and efficient for relatively small or simple systems,but become computationally expensive to use as system complex-ity increases due to the presence of nonlinearities. The industrialpulp mills in this application are relatively complex with severalpotential modes of operation. When combined with the limitedavailable computational equipment in these applications, the solu-tion times are unfeasible for online operation.

Rong et al. have contributed several works on cogenerationoptimization methods; both heuristic [14,15] and non-heuristic[16,17], most of which deal with power generation on a larger scaleand involve the co-ordination of multiple sites. Ren and Gao [18]also provide a very practical approach to multiple-site energy man-agement using a mixed linear programming approach. In this work,they not only address electricity and heat production from gas, oiland biomass, but also from alternative energy sources such as windand solar. Due to the large-scale focus of these works, they are notsufficient in addressing the needs of only a single mill, as is the casein this work.

Non-heuristic energy management solutions were proposedduring the 1970s and 1980s, but computational limitations at thattime led to impractical run times for most reasonably accuratesolutions [19]. Several algorithms in the early 1990s attemptedto make use of non-heuristic methods in the form of linear pro-gramming [20–22], but most of the methods were oversimplified.

Recent advances in mathematical tools and computational tech-nology have led to the development of more complex online calcu-lations in cogeneration facilities. Some mixed integer linearprogramming (MILP) methods, and derivations thereof, have beenproposed in the works of Arroyo and Conejo [23], Thollander et al.[24], Cheng [25], Ferrari-Trecate et al. [26], and Thorin et al. [27].Ferrari-Trecate et al. [26] use MPC reformulation, followed by MILPtechniques. Thorin et al. [27] propose a Lagrangian relaxation iter-ation step to improve robustness. Cai et al. [28] develop a fuzzy-random integral programming model, which is an extension of

3516 D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525

linear programming method specifically tailored to deal addresslarge cases of energy management with multiple uncertainties.Rodriguez-Toral et al. [29] present a sequential quadratic program-ming method, but note that online feasibility may be problematicfor complex systems.

The industrial pulp mills under investigation require an energyoptimization strategy capable of forecasting electricity prices andexploiting the complex unit co-dependencies within a cogenera-tion facility. Reasonable algorithm run times with limited compu-tational equipment are also required for online implementation.Although several of the above methods are both linear and capableof forecasting, many are not equipped to handle alternative cogen-eration configurations as encountered in the industrial applica-tions that are the focus of this paper. For example, therelationships developed between steam generated/fuel combusted,heat supplied, and power generation do not take advantage ofpressure relief valves. These valves may be used to bypass turbinestages while increasing overall steam flow through contact with afresh water supply during de-superheating. This process is ex-plained in further detail in following sections.

This paper therefore aims to develop a non-heuristic approachto energy optimization for industrial application in a pulp and pa-per mill cogeneration facility. The approach should be applicable ina number of cogeneration facilities with variations in plant config-uration. The optimization algorithm should provide significanteconomic improvements over methods currently being used inthe facilities under investigation, and should do so without incur-ring difficulties related to online implementation and run time.

Additionally, this paper will address the unique issue of coolingreservoir limitations to production by developing an economicoptimization algorithm that accounts for thermal absorptioncapacity in extreme weather. Again, short algorithm run time willbe a major focus.

The remainder of this paper is organized as follows: Section 2provides a brief description of the cogeneration process; Section3 shows the development of the plant model; Section 4 presentsthe details of the optimization algorithm; two case studies areexamined in Section 5; Section 6 extends the algorithm to addresscooling limitations; an additional cooling-based case study is pre-sented in Section 7; and conclusions are presented in Section 8.

2. Cogeneration process description

This work is motivated by several industrial applications incogeneration facilities across British Columbia, Canada, and hastherefore been designed with a specific system configuration inmind. The configuration schematic, as shown in Fig. 1, contains as-pects from several of the facilities, which have been combined inorder to create a single, generic system applicable in a number ofmills. The relative complexity of this process and the correspond-ing model (developed in a later section) allows for representationof smaller (but similar) facilities in the industry simply throughunit de-activation. The energy optimization method presentedhere is therefore widely applicable with minimal changes.

The facility is essentially split into two distinct plants separateddown the middle of Fig. 1, which share supplies of water and fuel.The plant on the left (containing the backpressure turbine) thatmakes up half of the system will be referred to as Plant 1. The planton the right (containing the condensing turbine) that makes uphalf of the system will be referred to as Plant 2. The system fea-tures a total of two recovery boilers and three power boilers, whichburn the fuel supplies in order to generate high pressure steam.The recovery boilers use a byproduct from the pulping processknown as black liquor, which is a hydrocarbon-rich slurry, to heatthe water source at a constant rate. The combustion to steam heat-

ing efficiency in a black liquor fueled recovery boiler is approxi-mately 75% [30]. Alternatively, power boilers produce steam atvariable rates using either hog fuel or natural gas. The combustionto steam heating efficiency in a hog or natural gas fueled powerboiler is approximately 70% [30]. Hog fuel is also a combustiblebyproduct from the pulp mill with a mulch-like consistency. Natu-ral gas can also be used to provide heat to the boilers, but is signif-icantly more expensive than the mill byproduct fuels; hog andblack liquor. For this reason, fuel management is critical to eco-nomically efficient cogeneration plant operation.

High pressure steam from the power boilers passes through ahigh pressure header on its way to either the mill, where it is usedas a heat source for various pulping processes including washing,drying and refining; to a turbine unit, where it expands, rotatingthe turbine, which powers a generator producing electricity; orto a pressure relief valve (PRV), where it descends to a lower pres-sure and picks up additional water during de-superheating. Likeany real process, an efficiency is associated with each of these stepsto account for heat losses.

After passing through either the first stage of the turbine orpressure relief valve, the steam is at medium pressure. From therethe steam is again used to heat mill processes, power the turbine,pick up additional steam through a PRV, or exits through a vent.The vent may be opened either to force additional steam throughthe first stage of the turbine, or for safety purposes. However, atmedium pressure this is rarely performed.

Upon exiting the second stage of turbines or pressure reliefvalves, the steam is at low pressure (which is still well above atmo-spheric pressure). From there, the steam can again enter the mill,the final condensing stage of a turbine, or exit the system througha vent. The low pressure vent is used more frequently than itsmedium pressure counterpart as it allows for more steam to bepassed through two stages of the turbine rather than just one. Iffuel costs are low enough to warrant this measure, it can beexploited to produce additional power in the turbine, increasingplant profitability.

Upon exiting the low pressure header application the steam hasusually condensed back to liquid form, although it is usually toohot to be treated and pumped back to the boilers. To reduce thewater temperature, it is passed through a series of cooling towers,then through a heat exchanger unit. The heat exchanger is cooledby a natural water reservoir, or pond, then pumped for treatmentbefore being sent to the boilers again.

The quantity of heat and electricity cogeneration within a typi-cal kraft pulp mill depends on the size, or more importantly thepulp production capacity, of the mill itself. Francis et al. [30]approximate that for every air dried tonne (ADt) of pulp producedin a typical kraft mill, an average of 15.8 GJ of heat from steam and655 kW h of electricity are produced. However, a typical kraft millconsumes approximately 15.8 GJ/ADt of heat, 638 kW h/ADt ofelectricity, and 1.2 GJ/ADt of natural gas according to Franciset al. [30], leaving an excess of 17 kW h/ADt of electricity for saleand a deficit of 1.2 GJ/ADt of natural gas that must be purchased.Further details behind technical and economic pulp mill operation,including cogeneration, can be found in the works of Francis et al.[30].

In order to maximize the economic output of such a facilitymany factors must be considered, including efficient fuel manage-ment, designation of unit setpoints to customize steam flow paths,and power generation scheduling. This task becomes increasinglycomplex as limitations are introduced such as time-dependantpower and fuel costs, complex power contracts, limited fuel sup-plies, mill heat requirements, and environmental constraints suchas maximum cooling pond temperature. This paper presents an ap-proach to maximizing plant profitability while addressing each ofthese issues.

Fig. 1. Pulp and paper mill cogeneration system schematic.

D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525 3517

The proposed approach involves two major steps; the genera-tion of a working plant model, and the use of that model to formu-late an optimization problem that maximizes profitability of plantoperation. The focus, again, is on industrial application, so unitoperations are approximated using first order models and unit effi-ciencies are approximated as constant around normal operatingconditions. This allows for the establishment of an energy optimi-zation problem relating plant operation to overall profitability,with constraints imposed by various features of the plant model.This optimization problem is convex in nature and it can be imple-mented in an online fashion.

The energy optimization problem, as outlined in the followingthree sections, focuses exclusively on operation within the plant,and ignores the cooling aspects. For many facilities, the coolingside of operation is not a production or profit limiting stage. How-ever, one mill in particular raised concerns around the pond tem-perature, stating that power generation had to be stopped if andwhen the temperature exceeded an environmentally-motivatedupper limit. The scope of the optimization problem was thereforeexpanded to include potential pond temperature limitations as de-scribed in the latter sections of this paper.

3. Cogeneration plant model

A model has been developed to represent a cogeneration systemthat is relatively complex for a pulp and paper mill, and is based ona facility in British Columbia, Canada, as described in the cogenera-tion process description section of this paper and shown in Fig. 1.The model tracks steam and water enthalpy throughout the sys-tem, making state changes and fuel combustion easy to represent.

This model is complex enough to represent the inherent rela-tionships between operating costs, power generation and heat gen-eration, which can be described by sets of differential and algebraicequations of varying levels of complexity [15]. Several model sim-plifying assumptions, such as linearization and model order reduc-tion have been made to allow for the development of a convexenergy optimization problem. For example, by considering onlyturbine inlet and extraction pressures that lie in a normal operat-ing range where operation takes place 99% of the time, a linear tur-bine model fit is sufficiently accurate (as opposed to the full rangeof potential operating conditions, which may account for that addi-tional 1% but require a high order model. See Fig. 2.). This assump-tion is validated and enforced by the presence of turbine and steamheader valve controllers, which operate independently of the en-ergy management system and restrict header pressures to the nor-mal operating range. Likewise, boiler and PRV unit models can beassumed to be linear, due to the consistency of header pressures.Ideally, deviation into regions where linearity does not reasonablyhold will be limited by underlying control mechanisms indepen-dent of the EMS.

Validation of the linearization assumptions was carried outusing the identification toolbox in MATLAB. Six months of indus-trial operation data were obtained from a facility very similar tothe one represented in Fig. 1. These data included a number ofmonitored variables throughout the system such as flow rates,pressures, and temperatures. The primary, unobserved modelingstate of steam and water enthalpy was calculated based on thesedata using the methods presented in [31]. Enthalpy flow rate ofunit operation input and output streams were imported into theMATLAB identification toolbox, and subsequently fit to lineartransfer function models. While a number of models were built

Fig. 2. Model output versus actual output for several cogeneration unit operations.

Table 1Model quality: percentage fit.

Unit operation Percentage fit (%)

PRV 59.42Condenser 81.32Boiler 60.02Turbine 56.46

3518 D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525

using many process variables, measurements of four importantvariables from four major unit operations and their correspondingpredictions are presented in Fig. 2; PRV (top left), condenser (topright), power boiler (bottom left), and condensing turbine (bottomright) . The corresponding percentage fit values, which are a quan-tification of model quality based on the percentage of the outputvariation reproduced by the model, are presented in Table 1. Itshould be noted that model quality could have potentially beenimproved by selecting large order model structures, but the practi-cal applicability of the algorithm would have suffered. For exam-ple, nonlinear or gain-scheduling approaches may havecompromised the convex nature of the resulting energy optimiza-tion problem, which would greatly increase solution time in mostcases. Linear models were deemed to be both sufficiently accurateand efficient for practical application. The resulting transfer func-tions were used to establish certain equality constraints. Unit timeconstants and delays were used to generate constraints restrictingthe rate of set point changes. For further details, see the section onproblem formulation.

4. Optimization problem formulation

The overall objective of the EMS is to maximize profitabilityover a given time horizon through the co-ordination of individualunit operating conditions within the facility. The time horizon isdivided into a number of equi-spaced time periods and each unitis given a distinct setpoint for every period over the course of thehorizon, subject to operational constraints such as feasible opera-tion limits, rate of change limits, and unit co-dependencies. Thesteady state operational costs are expressed as linear functions offuel flow rate to each boiler, as shown in (1).

Ct ¼Xnboi

i¼1

Xnsup

j¼1

cjhoghi;j

t

� �þ cnggi

t

!: ð1Þ

On the other hand, the primary objective of a cogeneration facil-ity is to generate heat. This is especially true in a pulp and papermill application, where most cogeneration systems in the industryare modified process heating systems. For this reason, the pulp milland the cogeneration facility have a master–slave relationship inreference to heat production. Although there may be contractualobligations associated with electricity production, there is usuallya large degree of flexibility when it comes to the rate of power gen-eration in day-to-day operation. Therefore, plant heat demanddoes not appear in the objective function of the profitability opti-mization problem, but rather as a constraint that must be satisfied.

D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525 3519

The required heat demand can be expressed as a linear function ofheat demands from the pulp and paper mill at each header pres-sure level as per (2).

Q t ¼Xnsh

i¼1

qit: ð2Þ

However, the rate of electricity production, is a defining compo-nent of the EMS objective function along with operating costs.Since the rate of electricity production from a pulp and paper millis relatively small compared to overall grid demands, the relation-ship between power generation and plant profitability is definedby the contractual agreement between the cogeneration facilityand a larger regional power provider. These contracts can be extre-mely complex in nature, and the sale pricing method for electricitycan vary significantly from facility to facility. Prices may fluctuatewith the market, making updated pricing profiles a necessary com-ponent of an effective EMS; or electricity prices may be fixed for anentire year. For this reason the algorithm horizon, iteration periodlength, and pricing structure have not been fixed. Due to theassumption of linearity of individual unit models, the rate of elec-trical power generation can be expressed as a linear function ofsteam flow rate between each extraction point within a turbineat steady state, as shown in (3).

Pt ¼Xntur

i¼1

Xnturi ;sta

j¼1

�turi ;staj Hturi ;staj

in � Hturi ;stajout

� �m

turi ;stajt

� �: ð3Þ

The energy optimization problem can now be defined by Eqs.(4)–(10). The objective function in (4) denotes the overall cost ofoperation, which is obtained by subtracting the revenue of electric-ity sales from the cost of operation. The problem constraints arerepresented by the inequalities in (5)–(7) and the equalities suchas the mass and energy balances as seen in (8)–(10). More specif-ically, (5) represents a limitation on hog fuel supply from each sup-plier over the entire optimization horizon, (6) constrains a steamflow rate m

Xi ;Yjt to physically realizable values for unit Xi (and/or

the corresponding subunit Yj), and (7) is a rate of change limitationto steam flow through unit Xi (and/or the corresponding subunitYj), where dm

Xi ;Yj

MAX is the corresponding maximum physically al-lowed change in steam flow rate from one time period to the next.dm

Xi ;Yj

MAX can be specified using a discrete form of the transfer func-tion of the corresponding unit. (8) enforces enthalpy balancearound a PRV. (9) represents an energy balance around boiler iwhere steam is potentially produced using both natural gas andhog fuel from various different suppliers. The left hand side of (9)represents the energy input to the boiler through hog fuel and nat-ural gas and the right side represents the enthalpy of steam gener-ated. (10) enforces mass balances around a medium pressureheader. It is straightforward to write mass balances around otherpressure headers as well.

minXtmax

t¼1

Ct � ce;tPtð Þ ð4Þ

s:t:Xtmax

t¼1

Xnboi

i¼1

hi;jt 6 sj j¼ 1—nsup ð5Þ

06mXi ;Yjt 6m

Xi ;Yj

MAX for all Xi and all Yj ð6Þ

mXi ;Yjt�1 � dm

Xi ;Yj

MAX 6mXi ;Yjt 6m

Xi ;Yjt�1 þ dm

Xi ;Yj

MAX for all Xi and all Yj ð7Þ

HPRViin mPRVi

t ¼ HPRViout mPRVi

t þDmPRVit

� �i¼ 1—nPRV ð8Þ

�boii bXnsup

j¼1

hi;jt aj

� �þ/gi

th

!¼ Hboii

out mboiit i¼ 1—nboi ð9Þ

mtur1 ;sta1t þmPRV1

t þDmPRV1t ¼ q2

t

Htur1 ;sta1out

þmtur1 ;sta2t þmPRV2

t þmven2t ð10Þ

The constraints in the optimization problem shown above arerepresentative of typical mass and energy balance constraints inthe cogeneration facility. There are many more similar constraintsthat are not shown due to space constraints. While these otherconstraints are not shown above, they are used in the energy opti-mization problem during implementation. In order to solve theabove optimization problem, optimal values for all hog and naturalgas fuel combustion rates, and all steam mass flow rates throughevery unit within the system must be chosen. The final optimiza-tion problem contains tmax(2nboinsup + n) optimization variablessubject to nsup + tmax(4n + nboinsup + 2nsh) constraints, several ofwhich may become redundant depending on the complexity ofthe system under investigation. For a mill similar to the one underinvestigation in this article, an optimization problem over a 24 hhorizon involves approximately 1000 optimization variables sub-ject to approximately 2500 constraints. Despite the large size ofthe problem, its convex nature results in reasonable solution timeswith a standard convex optimization tool. The CVX toolbox forMatlab developed by Michael Grant and Stephen Boyd was usedby the authors of this paper.

Online implementation of the energy management optimiza-tion strategy in a real facility requires regular updates to ensurethat continuously optimal operating conditions are maintained,and to update and revise forecasts. Minor disturbances and regularprocess noise will slowly drive conditions away from optimality,but under short time frames local unit control strategies shouldsufficiently negate such effects. However, more significant distur-bances including, but not limited to unit start-up and shut down,mill production variations, significant process disturbances, etc.will have a more severe impact on maintaining optimality. Fre-quency of such events varies greatly between facilities, so thetrade-off between maintaining optimality and frequency of optimi-zation calculations should be assessed on a case by case basis. Gen-erally, it is recommended that the energy managementoptimization problem is revised and resolved every 1–10 min, withincreased solution frequency during periods of known significantdisturbances or start-up/shutdown.

5. Standard case studies

The case studies presented below are based on real power plantmodels and power generation contracts. Process gains, dynamicconstraints and mill heat demands have been approximated fromextensive sets of industrial data. Fuel and electricity prices havebeen estimated based on historical trends.

5.1. Case I: daily production scheduler

The first case study involves an hourly optimization over a 24 hhorizon. Electricity sale prices are assumed to fluctuate hourly overthe course of the day in a standard manner according to market de-mand. Fuel prices are fixed for the course of the day. It is assumedthat an unlimited supply of natural gas is available for use, but thatthe hog fuel supply is limited. The optimization procedure is car-ried out assuming hog fuel supplies of 0, 30, 50, 75 and 100 metrictonnes (T).

Fig. 3 shows the rate of optimal electrical power generation (tomaximize the revenue) by the facility for the five different amountsof hog fuel supplies. The electricity price profile is also included ona second axis for reference.

In the case of no hog fuel availability (see 0 tonne profile inFig. 3), the algorithm assumes only natural gas is available to workwith. Due to the high cost of natural gas relative to the sale price ofelectricity, the rate of steam production over the course of the dayis limited to rates sufficient to satisfy mill heat demands. The

Fig. 3. Electricity production schedule for limited hog fuel supplies over a 24 h period with hourly market-based sale prices.

3520 D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525

steam generated can be sent through the turbines and/or throughthe PRVs as it descends to lower pressure (see Fig. 1). The proposedalgorithm suggests that the path that steam follows as it descendsto satisfy low pressure heat demands should depend on the price ofelectricity at a given time. When the sale price is low the algorithmsends steam through PRVs (from about 3.5 h to 6 h in Fig. 3), wherethe steam is contacted with a water source as it expands (de-superheating). As a result, energy is transferred to the water sup-ply, and thus decreasing the steam enthalpy on a per unit mass ba-sis but increasing the flow rate through PRV. When the sale price issufficiently high, the steam passes through the turbines instead,generating power (from about 6 h to 24 h in Fig. 3).

As hog fuel becomes increasingly available, the proposed algo-rithm uses it to first replace natural gas and then increase steamproduction in order to generate more power. Between the 50 and75 tonne supply profiles in Fig. 3, a shift in maximum electrical gen-eration is observed (from about 9 MW to 11.5 MW). This shift rep-resents a decision by the algorithm to alter the plant configurationby opening a vent in Plant 1, and a PRV in Plant 2 (see Fig. 4). Steamflowing through the PRV is sufficient to satisfy the mill heat de-mands, so no mid pressure extraction is required from the turbine,and more steam can be forced to the back of the condensing turbine.A similar situation is seen in Plant 1, where the steam flow ratethrough the turbine units is restricted by the exhausting capabilities

Fig. 4. Optimized unit inlet valve positions ove

of the low pressure (LP) line. Initially, the only outlet for steam inthe LP line is the mill heat demand; but when it becomes econom-ically feasible to open the vent to provide further exhaust, signifi-cantly more steam can flow through the plant. These alterationsincrease the steam requirement and subsequently operation costs,but the peak sale prices and abundance of cheap fuel make it eco-nomically feasible. Fig. 4 breaks down the individual unit inlet valvesetpoints within the system over the course of the day for the100 tonne hog supply case. Multiple profiles in each plot representthe setpoints for valves controlling fuel streams, turbines, PRVs andvents within each of the two plants.

This case study was compared to an energy management algo-rithm currently being used in a very similar pulp and paper mill inBritish Columbia. The method in use essentially involved proposinga predefined setpoint increase and decrease to every system vari-able and relating that change back to overall mill profitability usinga cost function. If the change was economically advantageous (be-yond a preset deadband) then it was implemented, otherwiseoperation continued unchanged. The mill using this method is fre-quently faced with limited hog fuel supplies, making this casestudy especially applicable.

For the comparison, a 40 tonne supply of hog fuel was assumed(again with an unlimited supply of natural gas) over the 24 hhorizon, and the same electricity price profile was used. Optimal

r 24 hours for a 100 tonne hog fuel supply.

Fig. 6. Comparison of profitability for 40 tonne hog fuel supply over a 24 h periodwith hourly market-based sale prices.

Table 2Case II: hog fuel suppliers.

Supplier # Available amount (T) Price per tonne ($/T)

1 375 39.102 300 34.213 750 56.70

D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525 3521

electrical power generation and the corresponding profit (or loss)with the current energy management system is compared withthose of the proposed algorithm in Figs. 5 and 6.

The method currently implemented in the facility begins toforce power generation early in the day, and quickly depletes thesupply. The cheap price of hog fuel relative to the sale price of elec-tricity makes it advantageous to force production (see Fig. 5) de-spite thin profit margins (see Fig. 6). There is no consideration offuture sale prices, which predictably peaks in the early afternoonwell in excess of the prices early in the morning. Once the hog sup-ply is depleted, only the more expensive natural gas remains tosatisfy mill heat demands for the rest of the day, and the algorithmis left trying to minimize losses. The result is a net loss of approx-imately $20–40 per MW of electricity produced with natural gas,depending on the sale price at the time, which brings the overalldaily profitability of the plant to a net loss of $629.65.

The method presented in this paper exploits the sale price trendby reserving the majority of the hog fuel supply and only forcingsteam production during the peak hours. The difference in perfor-mance over the optimization horizon is substantial, as the methodpresented here results in a net profit of $666.81; or in other words,a total of $1296.46 more than the previous method. This amountmay appear to be relatively insignificant for an entire mill, butamounts to an annual difference of $473,279. It is also importantto note that the turbine units in this case study peaked out atroughly 12 MW, but units double and triple that size are notuncommon in pulp and paper applications. Therefore, the proposedalgorithm will likely result in significant yearly profits in largercogeneration facilities.

5.2. Case II: weekly production and purchasing scheduler

The second case study involves an hourly optimization over a168 h period (1 week). Electricity sale prices are assumed to be un-der contract at distinct but constant peak (high) and off-peak (low)values. The peak price is applied to power generated between thehours of 8 am and 8 pm, and the off-peak price is applied to powergenerated between the hours of 8 pm and 8 am, daily. Natural gasis available at a fixed price and in unlimited quantity. Hog fuel isavailable from three suppliers, each with a different total amountavailable at a unique price as outlined in Table 2.

The optimal power generation and fuel usage results are notsurprising with one exception: the power generation schedule iscoordinated with the purchasing schedule, making strategic long-term planning possible where shortsighted decisions would havepreviously been made. As a result, optimization considers not only

Fig. 5. Comparison of electricity production schedules for 40 tonne hog f

current fuel prices, but future prices that will be paid once the cur-rent stock is depleted. Several other algorithms, such as the exist-ing one outlined in the previous section of this paper, use onlycurrent fuel prices to determine profitability. This distinction willnot likely have any short-term impact, but may decrease profitabil-ity over a longer time frame. For example, a decision that requires30% more fuel to increase overall profitability by 10% would bedeemed reasonable by the pre-existing algorithm, regardless ofother vendor supply prices and quantities. The algorithm pre-sented in this paper, on the other hand, may reject a temporary10% increase in profitability in order to make a cheap fuel last30% longer if the only other available hog fuel is from a supplierwith double the price.

Fig. 7 shows the results from this case study by comparing thepower generation profiles using the existing method from the pre-vious case study with the new method developed in this paper. The

uel supply over a 24 h period with hourly market-based sale prices.

Fig. 7. Comparison of electricity production schedules over a seven day period under a two tier electricity sale price contract.

3522 D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525

electricity price profile is also included for reference. Financial re-sults over the 1 week period are presented in Table 3. It is evidentthat the existing method makes inefficient use of the cheap fuel,and is left with only the final, more expensive supplier of hog fuelat roughly the 130 h mark. By instead rationing the fuel supply forthe entire week, the new method achieves a sustainable level ofprofitability and earns over $2000 more over the 1 week period.

6. Special case: cooling reservoir constraint

The most well intended, advanced control strategies may behindered by unexpected obstacles observed only through practicalapplication. For example, one of the mill cogeneration facilitiesinvestigated in this work had a sufficiently profitable energy man-agement system in place that managed the cogeneration operation.For the majority of the year this EMS worked effectively, but if theweather became too warm the cooling pond, which is used to ab-sorb heat from the condensed water (see Fig. 1), rate of evaporationwould increase significantly, jeopardizing the sustainability of thepond, and the pump returning water to the mill would begin to fail.The only feasible solution when this temperature threshold wasexceeded was to cease power generation, allow the pond to cool,then resume operation. Such measures usually required shuttingdown power generation until the following morning.

One proposed solution was to introduce a basic feedback con-trol strategy based on the pond temperature, and to cut back pro-duction as temperature approached a critical point. Although thisapproach would allow sustained power generation, the profitabil-ity of the system would be drastically cut in an uneconomicalway. Power generation during a high-sell price period would betreated no differently than during a period of marginal profitabil-ity. The basic feedback method also failed to incorporate signifi-cant, predictable, and sometimes obvious temperature trends.Such trends include nightly temperature drops, early afternoontemperature peaks, and short-term weather forecasting.

Rather than introducing a supervisory control loop, a forecast-ing algorithm was developed to operate in parallel with the millEMS. By combining readily available meteorological data/forecastswith thermal modeling techniques for small bodies of water, theproduction scheduling algorithm proposed in the previous sections

Table 3Case II: economic results.

MethodUsed

Hog used(T)

Total fuel cost($)

Total revenue($)

Net profit($)

Existing 844.85 34555.78 41623.17 7067.39New 675.00 24926.25 34223.52 9297.27

of this paper was modified to check for future critical temperatureviolations and, if necessary, take economically efficient correctiveaction.

6.1. Reservoir temperature forecasting

Pond thermal energy models developed by Van Buren et al. [32],and Gao and Merrick [33] were employed to forecast future pondtemperatures based on meteorological forecasts and the rate ofheat exchange required by the level of cogeneration operation.Both of these pond models account for five contributing factorsof heat exchange: short (solar) and long wave radiation, vaporiza-tion, sensible heating (convection and conduction), inlet flow, andoutlet flow. Reservoir thermal energy influx/efflux was character-ized by the difference equation in (11). For further pond model de-tails see [32] and [33].

Etþ1 ¼ Et þ Dt � ðqr;radt þ qr;inf

t � qr;vapt � qr;sens

t � qrr;outft Þ ð11Þ

The radiation, vaporization, and sensible heating terms arefunctions of, among other factors, environmental conditionsincluding temperature, wind speed, humidity, pressure, and cloudcover. It is these three terms that raise the pond temperature aboveits feasible operating limit under conditions of extreme weather. Inthe event of precipitation the inlet energy flow terms are also sig-nificantly effected. For optimization horizons of 24 hours or less,hourly forecasts are generally available online from local or na-tional sources such as http://www.theweathernetwork.com. Forlonger horizons and areas where hourly forecasts are unavailableor insufficient, less detailed or daily forecasts can be supplementedusing historical weather trends. An extensive database of hourly,historical meteorological data in Canada is available at http://www.climate.weatheroffice.ec.gc.ca.

For a given power production schedule and weather forecast, itis possible to use (11) in order to predict the peak reservoir tem-perature. If the peak forecasted temperature exceeds the operatinglimit, it may be possible to refine the cogeneration plant operationschedule in order to stay below the critical pond temperaturedepending on the severity of the climate at the mill reservoir. Byincorporating the forecasting technique into the economic opti-mizer, a safe pond temperature profile may be achieved while min-imizing lost revenue.

6.2. Reservoir temperature limited production scheduling

One major challenge that must be overcome when addressingthe co-ordination of production scheduling with reservoir thermalenergy forecasting is the unconventional relationship between

D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525 3523

cooling rate, time of day, and peak temperature. On a normal day,an undisturbed pond will typically experience a peak temperaturein the late afternoon. The exact time that the pond hits this peaktemperature is dependent on the weather conditions and the resi-dence time of water in the pond (assuming that the pond is not iso-lated from other natural water sources). Therefore, a different peaktemperature may be achieved depending on the time of day thatthe reservoir contacts the mill’s condensed stream. It is entirelypossible that depending on whether the pond absorbs 30 kJ of heatat 9 am, 2 pm, or 8 pm, it may reach a daily peak temperature of18 �C, 24 �C, or 22 �C respectively.

The important conclusion from the above observation is thatthe relationship between peak reservoir temperature and powergeneration scheduling is both non-trivial and non-convex. Due tothe need for online implementation, however, a non-convex opti-mizer may not be practical for an industrial application. The pro-posed solution is therefore an algorithm that determines thecogeneration operation schedule using convex optimization tech-niques, but which undergoes an iterative (but still convex) optimi-zation process in the event of reservoir temperature constraintviolation.

The proposed solution begins by posing an optimization prob-lem in the form of Eqs. (4)–(10). The resulting production scheduleis used to determine the mill contribution to the reservoir inlet en-ergy flow over the optimization horizon. By combining reservoircooling requirements with meteorological forecasting, the differ-ence Eq. (11) can be used to determine the reservoir temperatureprofile, and consequently the peak temperature, over the horizon.

If the solution of (11) yields a peak temperature below the max-imum allowable limit, then the overall profitability of the plant isnot jeopardized and therefore no corrective action needs to be ta-ken. On the other hand, if the peak reservoir temperature is greaterthan the upper limit, then some corrective action must be taken inorder to avoid the last minute safety measure of shutting downpower generation. In this temperature limiting case, an additionalconstraint in the form of (12) can be added to the overall optimiza-tion problem, where wf,t is the fuel usage weight factor, kf is a totalfuel scaling factor, ft is the energy content of fuel used during timeperiod t, and fo is the total energy content of fuel used in the solu-tion to the original optimization problem in the form of Eqs. (4)–(10).

Xtmax

t¼1

ftwf ;t 6fo

kf: ð12Þ

The weights, wf,t are calculated using the following method:

1. Solve for the maximum allowable heat exchange (using (11))with reservoir during the first optimization period such thatthe temperature is still below the threshold, assuming no heatis exchanged for the rest of the time periods. Then wf,t isassigned the inverse of the maximum allowable heat exchange.

2. Find wf,t for every optimization period in the horizon.3. Rescale the weight factors by dividing each weight factor with

the sum of all weight factors and thus ensuring that eachweight factor satisfies 0 < wf,t < 1.

The vector wf,t effectively redistributes the usage of fuel in away that allows for sustainable power production by exploitingthe degree to which thermal energy is retained by the ponddepending on the ambient conditions throughout the day. Forexample, heat typically dissipates readily into the environment inthe cool, early morning, so large cooling duties can be offset. How-ever, the rate of transfer from the pond to its surroundings slows asthe air heats and humidity increases throughout the day. Other fac-tors such as precipitation, cloud cover, solar radiation, etc. also

contribute to the ability of the pond to reject heat. By incorporatingthe fuel weighting vector into the original problem, time periodswhere thermal energy transferred to the reservoir is easily dissi-pated are favoured and allotted additional fuel, whereas periodswhere thermal energy is retained are penalized and therefore allot-ted less fuel. However, such penalties may still be offset by signif-icantly high sale prices during those periods. The end result is aneconomically efficient, sustainable production schedule.

Once wf,t are known, the fuel scaling factor (kf) is assigned a va-lue of 1 and an iterative process used to lower the maximum pondtemperature in the most cost effective way possible begins. Thefuel usage weighting vector is incorporated into the schedulingproblem as additional constraints in the form of (12), the originalscheduling optimizer is re-run, and the maximum observed reser-voir temperature is again noted. If it still exceeds the upper limit, kf

is increased, and the optimizer is run again. By increasing the valueof kf, the total fuel usage will gradually decrease until the reservoirtemperature is maintained below its limit.

In the event of temperature constraint violations the solutiontime of the EMS optimizer is increased, typically by a factor rang-ing from 2 to 20, due to the iterative nature of the solution. How-ever, online solution time may be minimized by infrequentupdating of the fuel scaling factor (kf) and the fuel weighting fac-tors (wf,t). Since these variables will only change with varyingweather conditions, the iterative procedure only needs to be car-ried out a few times per hour, depending on the climatic conditionsat the facility. Additionally, minor changes in the weather forecastrequire very few iterations given a reasonable step size. In anyevent, the implementation of this iterative convex procedure ismore practical than its highly non-convex counterpart.

It should also be noted that the ability of the EMS to handle po-tential reservoir temperature violations is highly dependent onweather forecasting accuracy. For best results, it is recommendedthat on-site temperature, pressure, wind speed and humidity read-ings are used whenever possible. Local weather forecasting can beadjusted based on discrepancies between on-site and weather sta-tion readings.

The validity of the uniform pond temperature assumptionshould be analyzed on a case by case basis. For small, round, shal-low ponds the approximation should hold reasonably well. How-ever, as the pond increases in depth and length, temperaturegradients will likely grow. In any case, temperature readingsshould be taken near the surface, downstream from the mill heatexchanger exhaust.

7. Thermal reservoir-limited case study

The case study presented in this section is based on a real powerplant model and power generation contract. The general structureof the mill is depicted in Fig. 1. Unit gains, dynamic constraints andmill heat demands have been approximated from extensive sets ofindustrial data. Fuel and electricity prices have been estimatedbased on historical trends. A set of recorded weather data from July2009 local to the mill in question was also used.

The study involves an hourly optimization over a 24 h horizon.Electricity sale prices are assumed to fluctuate hourly over thecourse of the day in a standard manner according to market de-mand. Fuel prices are fixed over the course of the day. It is assumedthat an unlimited supply of natural gas is available for use, but thatthe hog fuel supply is limited to a maximum of 20 tonnes. Ambientatmospheric conditions are assumed to behave according to the re-corded historical data set. During practical application, a forecastedset of data would be used instead. The optimization algorithmwould be updated hourly according to fluctuations in both weatherand market electricity prices.

Fig. 9. Power generation profile over a 24 h period for the original EMS and thetemperature constraint modified version of the EMS.

Table 4Thermal reservoir-limited case: results summary.

EMS version Max. res.temp (�C)

Final res.temp (�C)

Total powergen. (MW h)

Netprofit($)

Unmodified (tempignored)

23.8 23.8 250.8 1653.03

Unmodified (withshut down)

22.0 21.8 179.2 1290.35

Modified 21.6 21.6 203.0 1378.69

3524 D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525

In this instance, the reservoir is a 600 m3 pond with a surfacearea of 400 m2. A river flowing at an average rate of 4.3 m3/h andan average temperature of 11.2 �C feeds into the pond. Water exitsthe pond at a similar rate and at the mean pond temperature,which is assumed to be uniform throughout. Current operatingprocedure calls for the cessation of power generation if the pondtemperature exceeds 21.7 �C at any point.

Using only the EMS schedule optimizer presented in the previ-ous sections of this paper, and not the modified version presentedin Section 5, operation of the cogeneration facility results in a vio-lation of the pond temperature limit at approximately 6 pm. Con-tinued operation for the remainder of the day results in a finalpond temperature of 23.8 �C.

As mentioned previously, current operating procedure in placeat the mill calls for power generation to be stopped in the eventof a reservoir temperature violation, but the entire pulp mill can-not be shut down. Therefore, the cogeneration facility will stopgenerating steam for power production, but will continue to pro-duce heat to satisfy the mill demand. Under those guidelines a finaltemperature of 21.8 �C would be achieved, but the peak tempera-ture would still reach 22.03 �C at approximately 9 pm due to steamproduction in order to satisfy mill heat demands.

The reservoir temperature constraint modification to the EMSwas then used in place of the original optimizer. As expected, noviolation of the pond temperature occurred over the optimizationhorizon. A peak temperature of 21.6 �C was observed at the endof the day. A plot comparing the reservoir temperature profiles thatresult from the original and modified versions of the EMS over thecourse of the 24 h period can be seen in Fig. 8.

The unmodified EMS, if allowed to run for the full 24 h periodregardless of pond temperature, would produce 250.8 MW h overthe period for a total profit of $1653.03. In practice, however,power generation would be shut down at approximately 6 pmafter generating a total of 179.2 MW h of electricity for a total prof-it of $1290.35.

By applying the reservoir temperature constraint modificationto the EMS, a total of 203.0 MW h would be produced for a netprofit of $1378.69. More importantly, however, is that this profitwould be achieved while maintaining a pond temperature belowthe 21.7 �C limit. A plot comparing the power generation profilesthat result from the original and modified versions of the EMS over

Fig. 8. Thermal reservoir temperature profile over a 24 h period for the originalEMS and the temperature constraint modified version of the EMS.

the course of the 24 h period can be seen in Fig. 9. A summary offinancial results can be found in Table 4.

8. Conclusions

A practical energy optimization algorithm for use in a pulp andpaper mill cogeneration plant has been developed. The proposedapproach is applicable to a wide range of mills in the industry, withthe potential to address a variety of plant configurations and powercontracts over a given horizon due to a relatively flexible problemstructure. By coordinating fuel pricing and availability with electri-cal price forecasts over the optimization horizon, an economicallyefficient plant management strategy is obtained. This strategy pro-vides significant economic benefits over classical methods thatmake use of basic current-state optimization, as demonstrated byseveral case studies. The magnitude of the aforementioned benefitsvaries significantly from case to case, but increased profit in therange of 10–50% has been regularly observed. Additionally, sincethe optimization problem is posed in a convex format, solutiontimes are relatively fast making online implementation feasible.

The proposed optimization algorithm was modified to accountfor temperature constraints on a cooling reservoir. By implement-ing a thermal energy forecaster based on operational and meteoro-logical data in parallel with the original algorithm, operational-limiting thermal constraints can be satisfied in an economicallyfeasible way. This was demonstrated in a case study dealing withthermal reservoir limitations. Solution time increased with theadditional thermal constraint, but convexity of the optimization

D.J. Marshman et al. / Applied Energy 87 (2010) 3514–3525 3525

problem was preserved through the utilization of an iterative opti-mization strategy, which made online implementation possible.

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