Optimization of a Network of Compressors in Parallel:

Real Time Optimization (RTO) of Compressors in

Chemical Plants - An Industrial Case Study

Xenos P. Dionysiosa,∗, Matteo Cicciottib,c, Georgios M. Kopanosa, Ala E. F.Bouaswaigc, Olaf Kahrsc, Ricardo Martinez-Botasb, Nina F. Thornhilla

aDepartment of Chemical Engineering, CPSE, Imperial College London, UKbDepartment of Mechanical Engineering, Imperial College London, UK

cAdvance Process Control, Automation Technology, BASF SE, Ludwigshafen, Germany

Abstract

The aim of this paper is to present a methodology for optimizing the op-eration of compressors in parallel in process industries. Compressors in par-allel can be found in many applications for example in compressor stationsconveying gas through long pipelines and in chemical plants in which com-pressors supply raw or processed materials to downstream processes. Thecurrent work presents an optimization framework for compressor stationswhich describe integration of a short term and a long term optimization ap-proach. The short-term part of the framework suggests the best distributionof the load of the compressors (where the time scale is minutes) and thelong-term optimization provides the scheduling of the compressors for largetime periods (where the time scale is days). The paper focuses on the short-term optimization and presents a Real Time Optimization (RTO) frameworkwhich exploits process data in steady-state operation to develop regressionmodels of compressors. An optimization model employs the updated steady-state models to estimate the best distribution of the load of the compressorsto reduce power consumption and therefore operational costs. The paperdemonstrates the application of the RTO to a network of parallel industrialmulti-stage centrifugal compressors, part of a chemical process in BASF SE,Germany. The results from the RTO application showed a reduction in power

∗corresponding authorEmail address: d.xenos@imperial.ac.uk (Xenos P. Dionysios)

Preprint submitted to Applied Energy December 28, 2014

consumption compared to operation with equal load split strategy.

Keywords: real time optimization, industrial compressors, optimal loadsharing, mathematical programming, regression models, energy savings

1. Introduction

Compressors are machines which are used in industrial processes to pro-vide air for combustion, to recirculate fluids through a process and to conveya gas through a pipe. Many researchers have studied the optimal operation ofcompressors (i) considering different applications (e.g. natural gas or supplygas systems), (ii) assuming different levels of operational control tasks (e.g.process control or planning), (iii) studying different scales of systems (e.g. alocal compressor station or large gas networks involving compressor stationsin series) and (iv) examining of compressors using different type of gas (e.g.air or natural gas).

The purpose of this paper is to present a general methodology to opti-mize compressors in parallel. This methodology consists of the integrationof the scheduling of compressors and a real time optimization approach. Thepaper introduces the overall methodology and focuses on the demonstrationof the Real Time Optimization (RTO) method to optimally share the loadamong parallel compressors. The methodology is applied to an industrialcase study. The main aim is to show that the suggested RTO framework canbe applied online, and can reduce the power which is utilized from the motorsof the compressors compared to conventional industrial policies of operation.Moreover the paper introduces the scheduling of the compressors: optimalselection of the compressors taking into account aspects of the operation,such as maintenance plans and minimum, and maximum running times.

The structure of the manuscript is as follows. Section 2 provides an in-troduction to the operation of compressors attached to a downstream systemand the description of the management and operational tasks taking place ina plant. The latter part will help to identify the control actions which takeplace in a compressor station. Section 3 provides a literature review to theoptimization of compressor stations or systems which involve compressors.The integrated framework and the methodology of the RTO for compres-sors is described in Section 4. Section 5 provides the description of the casestudy. Section 6 presents the results and discussions. The paper ends witha summary and conclusions.

2

2. Introduction to the operation of compressors

2.1. Operation of compressors attached to a downstream system

It is generally accepted that compressors consume large amounts of energyin various industrial sectors. Compressors driven by gas turbines are reportedto consume 5% of the transported gas in pipeline networks of natural gas(DeMarco et al., 2011). Moreover the utility for compressed air is consideredto be one of the most expensive in many industries (Saidur et al., 2010).Compressors are assumed to be among the major energy consumers in manyintensive chemical processes such as air separation.

The paper focuses on industrial multi-stage centrifugal compressors. Cen-trifugal compressors are used in applications which request high mass flowrates and low pressure ratios (Boyce et al., 2003). To achieve high ratiosof compression, several single stages of centrifugal compressors are arrangedin series. The single stages in series are attached to a rotating shaft. Thisstructure is called multi-stage centrifugal compressor and it is known as com-pressor train. A compressor train is employed to increase the total dischargepressure compared to the pressure a single-stage compressor can achieve.

More than one single centrifugal stage or compressor train can be con-nected in parallel to increase the total mass flow rate. Compressors operatingin parallel are known as compressor stations.

A compressor is connected with a downstream load and, usually, with anupstream process (in the air separation process, however, the compressor issupplied with ambient air, therefore there is no upstream process). A stan-dard graphical representation used to describe the operation of a compressoris a compressor map, which can be seen in Fig. 1.

A compressor map shows the characteristics, performance and operationallimits of a compressor, i.e surge, choke, minimum and maximum speeds(Dixon et al., 2010). Surge restricts the operation when a compressor worksat lower mass flow rates and higher pressures. When the compressors work athigher flows and lower pressures choke restricts the operation. Moreover, theoperation of a compressor is restricted due to minimum and maximum powerprovided from its driver. These restrictions can be identified in a compressormap considering a minimum and a maximum speed. In the case of a constantspeed compressor with variable Inlet Guide Vanes (IGVs) the operation isrestricted between minimum and maximum opening of the IGVs. Figure 1illustrates the operational region of a compressor between surge and chokefor the minimum (10o) and maximum angle (100o) of the IGVs.

3

surge limit

characteristics

choke limit

efficiency islands

maximumIGV opening

minimumIGV opening

0.75

10o

100o

0.85

0.90

60o

80o

mass flow

pres

sure

Figure 1: A compressor map with Inlet Guide Vanes (IGVs).

The operating point of a compressor is the intersection of its characteristiccurve at a fixed rotational speed (or angle of IGV) and the characteristic curveof the downstream system. The characteristic of the downstream system isknown as load curve or demand curve (Kurz et al., 2012a) . The reasonfor introducing these concepts is to explain that the downstream processinfluences the operation of the compressor, and therefore its performance andpower consumption. Moreover, the data to be used for developing models ofcompressors correspond to various operating points.

Figure 2a illustrates three load curves of different downstream processes.It is assumed that the upstream process does not change the inlet conditionsof the compressor. Kurz et al. (2012a) described three main categories ofdownstream processes a compressor is usually connected with. Load curveA describes a pipeline system in which the pressure becomes greater whenthe mass flow through the pipes increases. Load curve B is used to representsystems which the pressure does not change significantly with the change inmass flow. Refrigeration systems and process systems in which gas is fed intoat a specific discharge pressure are typical examples of this category (Blochet al., 2006). Finally, load curve C describes gas storage applications (Kurzet al., 2010).

4

mass flow

pres

sure

Load curveA

Load curveC

Load curveBp O

P

mOP

100o

0.85

0.90

80o

mass flow

pres

sure

OP

OP 1 OP 2

0.70

mOP1 mOP2 b)a)

ηis,OP

θOP

0.75

Figure 2: Various types of load curves and Operating Point (OP) of a com-pressor connected with load curve A (a) and operating point change by in-creasing the position of the Inlet Guide Vanes (b).

Figure 2a also shows an Operating Point (OP) of the compressor describedfrom this compressor map. The compressor is connected with a downstreamsystem described by load curve A. The OP on the compressor map givesinformation about the mass flow (mOP ), pressure (pOP ) of the gas supplied,opening of the IGV (θOP ) and isentropic efficiency (ηis,OP ).

There are several methods to control a compressor if an operating pointhas to be modified. Liptak et al. (2006) and Kurz et al. (2012a) reported fivemain control methods: (1) suction throttling, (2) discharge throttling, (3)flow recycling, (4) adjustment of the speed of the motor and (5) modificationof the Inlet Guide Vanes. The paper examines compressors with constantspeed and adjustable IGVs. Figure 2b shows an example of changing operat-ing point from OP1 to OP2. It shows that by increasing the opening of theIGVS by 20o the OP changes. The compressor at OP2 provides higher massflow at a relatively higher pressure than in the case of OP1 and moreover theefficiency of the compressor drops to 0.7. This information, pressure, massflow and efficiency, can be used to estimate the power consumed from thecompressor (power in the shaft). Finally, by knowing the efficiency of the

5

driver, the power consumed by the driver can be computed.

2.2. Management and control operational tasks

ERPLevel 4

PCSLevel 0, 1, 2

MESLevel 3

Common actions Time scales

Supply chainDemand planningProduction planningSales and distribution

SchedulingProcess optimizationAdvanced controlAsset monitoring

Real time executionReal time monitoring

Months, weeks,days

Days, shifts, hours,minutes, seconds

Hours, minutes,seconds, less thana second.

ERPLevel 4

PCSLevel 0, 1, 2

PROCESS CONTROL OF INDIVIDUAL COMPRESSORSMONITORING OF COMPRESSORS

OPTIMAL LOAD SHARING,UPDATE OF COMPRESSOR MAPS

MESLevel 3

OPTIMAL SCHEDULE AND MAINTENANCE

DEMAND

(a) (b)

Figure 3: Decision pyramids of a plant (a) and of a compressor station (b)according to the ANSI/ISA-95 (Harjunkoski et al., 2009).

Figure 3a shows a typical decision (or control tasks) pyramid of plant-wide automation according to the ANSI/ISA-95 standard (Harjunkoski etal., 2009). It involves the Process Control System (PCS) which includes realtime set point control and real time monitoring of the process. The time scaleof PCS is seconds or fractions of seconds. The Manufacturing Execution Sys-tem (MES) deals with the manufacturing operations and considers decisionsfor example the scheduling of the units of the operations for the next days orhours and the optimization of the process by improving its performance atreal time. The optimization suggests the best set points of the control sys-tem. On the top of the pyramid is the Enterprise Resource Planning (ERP)considering business planning and logistics. The top level of ERP deals withmarkets, production targets and sales.

Figure 3b presents a decision pyramid of a compressor station. At thetop of this pyramid, in Level 4, there are the production targets from theCentral Dispatch Department (Paparella et al., 2013). These targets are theinput of Level 3. Level 3 includes the scheduling and maintenance of thecompressors. The same level also deals with the optimal distribution of theload among the compressors which provides set points of the speeds of the

6

motors of the compressors to the controllers of the control system. The roleof the controllers is to operate the compressors at the given set points. Thelowest levels, Level 0, 1, 2, involve the control of the individual units and themonitoring of the process. The RTO and the scheduling of compressors areconsidered as control tasks which belong in Level 3 of the decision pyramidsin Figs. 3a and b.

3. Literature review

3.1. Optimization of compressor stations

The optimization of compressor stations is a topic which many researchershave studied in the recent years. Compressors are used in various applica-tions where the nature of each application influences the objectives and theconstraints of the optimization problem. For instance, problems examiningnatural gas systems which transport gas through long pipes can consider thephenomenon of the linepack (Kurz et al., 2012a). The linepack is a time-dependent phenomenon which describes the storage of a gas inside a pipe.The stored gas can be used for example when the operation cannot satisfythe demand due to an unexpected failure of a compressor. On the otherhand, a supply compressor station of a chemical process provides gas at anapproximate constant pressure.

Optimization of compressors regarding the application

Figure 4 presents the classification of the optimization of compressorstations considering four main categories of applications: (i) natural gasnetworks (Shaw, 1994; Wu et al., 2000; Cobos-Zaleta et al., 2002; Borraz-Sanchez, 2010), (ii) utilities (Han et al., 2004; Widell et al., 2010; Xenos etal., 2014a), (iii) gas storage applications (Kurz et al., 2010) and (iv) otherapplications (Camponogara et al., 2012). Furthermore, the examination ofthe optimization problem can consider different time horizons, continuousoperation or/and discrete events.

Optimization of compressors regarding the time horizon

Many authors examined the optimization of different type of gas compres-sors in different applications considering different time horizons. According

7

Optimization ofcompressor stations

Compressor stations innatural gas networks

Utilities (feed gas a process system)

Other applications (e.g. gas oil lifted wells)

Single-period optimization

Optimal selection of compressors

Gas storageA

pplic

atio

ns

Con

tinuo

us

oper

atio

n,di

scre

te e

vent

s

Optimal loadsharing

Multi-period optimization

Pipeline optimization

Tim

e ho

rizon

Pipelineoptimization

(Wu et al., 2000)

(Abbaspour et al., 2005)

(Abbaspour et al., 2007)

(Mahlkeet al., 2010)

(Carter et al., 2010)

(Han et al., 2004)

(Paparellaet al., 2013)

Nguyenet al., 2008)

(Camponogaraet al., 2012)

Optimal selection of compressors

Figure 4: Classification of optimization of compressor stations. The currentpaper focuses on the optimal load sharing of utilities applications in steady-state conditions, i.e. single-period optimization.

to Fig. 4, there is the classification of single- and multi-period optimiza-tion. The single-period optimization considers information of one time in-terval (steady-state) and the multi-period optimization employs informationfrom the future based on forecasting methods. The forecast of the demandand parameters of the constraints are used in the optimization framework.The optimization framework suggests decisions for the current operation andthese decisions are based on future information. An example of a forecastedparameter (i.e. future information) is a scheduled maintenance of a compres-sor, which might influence the decisions for the current operation.

The single-period optimization can be further classified as steady-statepipeline optimization (Wong et al., 1968; Wu et al., 2000; Borraz-Sanchez,2010; Carter et al., 2010), optimal load sharing (Han et al., 2004; Abbaspouret al., 2005; Paparella et al., 2013) and optimal selection of compressors(Wright et al., 1998; Cobos-Zaleta et al., 2002; Widell et al., 2010; Cam-ponogara et al., 2012; Paparella et al., 2013). The steady-state pipeline opti-mization examines the optimal operation of the fuel cost minimization prob-lem (Borraz-Sanchez, 2010) considering information of one period (Carter etal., 2010). The optimal load sharing is the focus on this paper and it will

8

be presented in Section 3.2. The third category involves discrete events inthe formulation of the optimization problem, for example variables whichrepresent which compressor stations operate (on or off) (Cobos-Zaleta et al.,2002) or binary variables for deciding assignments of gas-lift compressors toend-users (wells) (Camponogara et al., 2012).

The multi-period optimal operation of compressors (considering solutionfor more than one time period) includes (1) pipeline optimization with afixed number of operating compressors (Marques et al., 1988; Abbaspour etal., 2007; Carter et al., 2010) and (2) optimal selection (or scheduling) ofcompressors (van den Heever et al., 2003; Nguyen et al., 2008; Mahlke et al.,2010).

3.2. Optimal load sharing

Kurz et al. (2012a) and Garcia-Hernandez et al. (2012) reported that theinstallation of spare stand-by compressors in a station increases its flexibility.Spare compressors are used when the capacity of a station is not enough tosatisfy the demand which is requested due to changes in the demand side ofthe plant. These changes are mainly caused because of changes in the markets(prices of products or electricity) and changes in the internal productionstrategies of the company (products specifications, amount of production).

Many authors and practitioners reported that it is difficult or impossiblefor different compressors in a compressor station to have identical characteris-tics and efficiencies (Abbaspour et al., 2005; Liptak et al., 2006; Milum, 2012;Rolls Royce, 2014). Moreover, these characteristics and efficiencies changeover time due to fouling and erosion (Kurz et al., 2012b), and nonuniformmaintenance plans which result in dissimilar compressor maps for the samecompressor at different time periods (Forsthoffer, 2011; Paparella et al., 2013;Cicciotti et al., 2014a). The use of surrogate models and process data canpredict the performance and characteristics of the compressors (Tirnovan etal. , 2008).

Many strategies have been used to share the load of compressors. Kurz etal. (2012a) commented that if compressors have identical compressor maps,the load can be equally split or they can operate at the same surge margin.Surge margin is the distance between operating point and surge. In thesame work it was reported that if two compressors have different sizes ordifferent efficiencies the more efficient should provide the base load and thesecond compressor, the less efficient, has to deal with the fluctuations of theload. On the other hand Twohig (2011) reported that parallel compressors

9

in a pharmaceutical fermentation process were decided to operate so as themost aged (and less efficient) compressor worked at its maximum flow rate(where its optimal point was) and the more efficient compressors should varytheir operation to cover the fluctuations of the demand. Moreover, Liptaket al. (2006) suggested a method in which the first step is to estimate theefficiencies of the compressors in units of flow per units of power and thesecond is to load the units in order to their efficiencies.

Another option to distribute optimally the load among the compressors isto formulate an optimization problem. A few researchers (Jenıcek et al., 1995;Han et al., 2004; Abbaspour et al., 2005) studied the optimal load sharingof compressors operating in parallel in order to minimize the fuel consumedby the gas turbines drivers. However, these works did not present an onlineapplication which considers the practical aspects of the implementation ofthe actual optimization, for example update of the maps and steady-statedetection. Paparella et al. (2013) presented an online optimization frame-work which updates the parameters of the models of the compressors online.The optimization framework applied to a gas boosting station. The authorsshowed that surrogate models can be used to predict the performance of thecompressors.

There is significant research contribution in the optimization of utilitysystems for steam production (Luo et al., 2013; Varbanov et al., 2004). Theoptimization in these works involved the estimation of the distribution of loadof each turbine to minimize operational costs. The methodology used in theseworks is very similar to the optimization of the utilities for compressed air.However, there is a little research regarding the optimization of compressorstations for utilities.

3.3. Gap of knowledge and contribution of the paper

Study of the literature revealed a lack of a systematic way to optimallyshare the load of compressors online considering varying operational condi-tions, such as atmospheric temperature and pressure, and demand requestedfrom downstream processes, such as air separation and compressed air forutilities. One of the assumptions mainly used is that individual compressorshave the same characteristics and the same performance behaviour. Regard-ing this assumption, the conventional practice is to distribute the load evenlyamong the compressors or to apply other similar strategies described previ-ously. In addition, a few works presented optimization strategies to sharethe load, however to the best of the authors’ knowledge there is no approach

10

which considers a comprehensive online application with aspects such as up-date of maps and steady-state detection.

The current work suggests a comprehensive framework which deals withthe optimization of compressors in parallel in two different timescales, long-and short-term optimization. After the presentation of the general frame-work, one of the aims of this paper is to present a methodology for generatingmodels of constant speed multi-stage centrifugal compressors with a watercooling system and an Inlet Guide Vane control system. Real industrial dataare used to generate these models.

In the literature, studies of compressor modelling focus on performancemap-based or simulation based cases (Cicciotti et al., 2014b). The paperfocus on a real application involving industrial compressors. The compres-sor maps of the compressors are not available. Therefore, the efficiency fordifferent operational conditions is not given.

Moreover, the compressors are multi-stage involving intercoolers betweenthe stages. The lack of measurements, for example the non availability ofall the temperatures of the intercoolers, is the main reason the the efficiencyof the compressor system cannot be explicitly estimated through thermo-dynamic calculations. For the requirements of the formulation of the op-timization the use of the power of the motors of the compressors includesimplicitly the efficiency of the compressors as this is illustrated in Section6.2. The paper, therefore, suggests a method to minimize the operationalcosts of compressors in parallel when the efficiency of the compressors can-not be explicitly estimated.

Another aim of the paper is to present the part of the framework whichdeals with the short-term optimization. The data-driven models are imple-mented into an optimization model which computes the distribution of theload among the compressors in order to achieve reduced operational costs.The proposed optimization is formulated in a generic way and can be appliedto a compressor station with parallel nonidentical single-or-multi-stage com-pressors in utilities or in process systems when operational data are available.

4. Methodology

4.1. General framework for optimizing compressors in parallel

Figure 5 presents the integrated framework for the optimization of com-pressors in parallel. This framework connects several decisions tasks from

11

Level 0, 1, 2 and 3 of the automation pyramid in Fig. 3b: optimal schedul-ing and maintenance, optimal load sharing and update of the maps and,control and monitoring of the process. The optimal scheduling and mainte-nance focuses on decisions of discrete events such as the switching on or off ofcompressors. The optimal load sharing considers the updates of compressormaps which corresponds to the asset monitoring in Level 3 in the MES ofpyramid in Fig. 3a. The process control applies the set points, given from theoptimal load sharing to the process. Finally, the monitoring system collectsdata, analyses them, detects and diagnoses faults.

A basic Real Time Optimization (RTO) scheme (Mansour et al., 2008)can be tailored to the operation of parallel compressors. The sensors ofthe monitoring system collect process data of the operation such as massflows, pressures and temperatures. A steady-state identification algorithmexamines key process variables and identifies when the operation is in steady-state. If the system is in steady state the collected data are validated (Prataet al., 2010; Mansour et al., 2008). The validated data are used to updatethe models of the compressors.

Operation (compressors)

Validation ofdata

Parameter estimation

Optimization(NLP)

Scheduling(MILP)

Monitoring(sensors)

Raw data

Steady state identification

Validated dataUpdated model

parameters

Set points

Applyset points,

binary decisions

Input parameters

Updated parametersinfeasible NLP

problem

binary decisions

Disturbances (Ambient conditions,

demand)

CostsDemand forecast

Equipment availabilityScheduled maintenance Control

system/operators

Real Time Optimization (RTO)

Scheduling

Figure 5: Framework for optimizing compressor stations.

A NonLinear Programming (NLP) model employs these data-driven mod-

12

els and estimates the optimal load sharing, i.e. the set points of the controlledvariables, i.e. mass flow rates of the compressors. The set points are givento the control system which role is to apply and keep these points to theprocess until the next run of the RTO.

The scheduling problem is a Mixed Integer Linear Programming (MILP)problem which involves both continuous and binary variables as degree offreedom of the optimization. The scheduling gives high-level decisions whichinvolve discrete events (for example switching on or off a compressor) to theRTO. This input is given in a relatively large time interval compared to thetimescale of the RTO.

When the actual demand given in the RTO is significantly different fromthis which is predicted in the scheduling problem, the NLP problem mayresult in an infeasible problem. This is because the online compressors maynot be able to meet the requirements of the demand side. In this case thescheduling problem updates its models and a new schedule of the compressorsis estimated. The new schedule gives the new configuration of the systemwhich can satisfy the demand, for instance by bringing another compressoronline. After these adjustments, the RTO loop is activated considering thenew configuration. The study of the scheduling topic will be presented in thestudy from Kopanos et al. (2015).

4.2. Modeling of compressors with data-driven models for RTO application

This section describes the methodology to develop models of a genericcentrifugal multi-stage compressor, with a cooling system, driven by an elec-trical motor. The models are developed from historical data from operation.The use of data-driven models allows the modelling of a multi-stage compres-sor with available measurements only at the inlet of the first and at the exitof the last stage. A rigorous model requires the availability of measurementsbetween the stages and analytical models of the intercoolers. Moreover, theuse of a data-driven model in the optimization reduces the computationalburden compared to the use of a rigorous model which considers aerody-namics and thermodynamics of the fluid. The computational time of theoptimization plays an important role in an online application such as theRTO.

Steady-state detection

13

Inspection ofraw data

Identification of Steady States

Preprocessing of data

Data ReconcilliationGross Error DetectionTreatment of outliers

Normalisation

Generation of CSET

CSET: calibration setVSET: validation set

Calibration and validation

Models

Generation of VSET

Collect data from process

SENSORS

Figure 6: General methodology for the development of data-driven models.

The steps of the development of data-driven models consist of severalprocedures illustrated in Fig. 6. The description of each step of the method-ology applied to an industrial compressor which has been presented in Xenoset al. (2014a). Data-driven models are black boxes which hold a relation-ship between input and output variables. These input and output variablesshould be close to steady state to hold the validity of the mass and energybalances implied in the black box (Kim et al., 2008). Therefore, the purposeof a steady-state detection algorithm is to identify the steady states of theoperation to develop reliable models.

In this work, a steady-state identification algorithm based on a movingwindow was developed. Figure 7 shows the application of the moving windowto a data-set of a single process variable. A moving data-set window is definedfrom a fixed number of data points of the process variable, ns. The dataincluded in the window are updated at each step τ , recent data are addedand old data are discarded. The window moves every S number of datapoints. A process variable j has value x(i,j,t), where i ∈ I (I is the number ofcompressors), j ∈ J (J is the number of variables) and t ∈ T (T is the totalnumber of data points which corresponds to the total sample time). Variableτ corresponds to a window with data (t− ns + 1, t). The sample rate of thedata set (discretization of T ), the ns and the S are parameters which have to

14

reference pointat τ = 2

data consideredat τ = 2

window τ =1window τ = 2

window τ = 3

t

SnS

proc

ess

varia

ble

Figure 7: Moving time data set window.

be tuned for a desired function of the steady-state identification algorithmregarding to the application.

At each step τ the data-set window moves to t′ = t+S and the standarddeviation of the included data points in the window, σ(i,j,τ), of compressor iand variable j is calculated from:

σ(i,j,τ) =

√1

ns

∑t′∈(t−ns+1,t)

(x(i,j,t′) − µ(i,j,τ))2 (1)

with µ(i,j,τ) is the mean of the data in the window:

µ(i,j,τ) =1

ns

∑t′∈(t−ns+1,t)

(xi,t′) (2)

The steady-state algorithm detects a steady-state episode of a processvariable j when a particular condition holds true, for example if the threetimes the standard deviation 3σ(i,j,τ) is less than a predefined value, h(i,j).This bound is chosen by the user according to their engineering judgementas there are not standarized values for this type of application.

The developed steady-state algorithm is multivariate and involves theexamination of more than one variables to assess if the system is in steady-state. According to Mansour et al. (2008) a system is in steady state whenall the considered variables are in steady state.

15

Hence, if a process variable j of compressor i is in steady state at t thena binary variable Y(ss,i,j,t) is equal to 1, otherwise the variable takes the value0. Therefore, the steady state of the system of I compressors consideringj ∈ J ′ ⊆ J variables is estimated from the value of the variable Yss,system:

Yss,system =∏i∈I

∏j∈J ′

Y(ss,i,j) (3)

The output of the steady-state detection algorithm is a matrix of datawith J ′ rows (variables) and T ∗ columns (number of final steady states ofthe system) where T ∗ ⊆ T .

Development of models

The methods for preprocessing the data and generating the calibrationand validation set of data are the same used in Xenos et al. (2014a). Forexample data have to be normalised before the development of the models.This is because different variables have different units with different ordersof magnitude. For example power is measured in kW and pressure in bar.

The top diagram in Fig. 8 illustrates a generic multi-stage compressordriven by an electrical motor. The development of a black box model of thiscompressor system includes: the multi-stage compressor, the cooling system,the rotating shaft, gearbox and motor. According to the step tests in anindustrial centrifugal compressor presented in Xenos et al. (2014b), it wasshown that the power consumption of the motor mainly depends on the massflow entering the compressor, ma, the ambient conditions, Tin, pin, and thepressure at the exit of the compressor (discharge pressure), pout.

The lower panel in Fig. 8 shows the procedure for the development ofthe model of the operation of a multi-stage compressor. A black box isused to predict the power (output of the model) consumed from the elec-trical driver, Pel, as a function of process variables (input of the model)of the operation, m(a,i,t), Tin, pin, pout . A polynomial regression model isused to develop the black box model of each compressor i. By definingxi,k,t = [m(a,i,t), T(in,t), p(in,t), p(out,t)] with k = 4, number of input variables,and y(i,t) = P(el,i,t), a black box model of compressor i is given by the following

16

Atmospheric air

Stage 1

Stage 2

Intercooler 1

Intercooler 4

Stage 5

AftercoolerPel

Χ = [ ma , pin , Tin , pout ]

outlet pressure pout

Systemenvelope

BLACKBOX

Input measured variables

Output predicted variable

Compressed air

M: MotorG: Gearbox

M G

ma , Tin, pin

Υ = Pel

Figure 8: Regression models of a multi-stage compressor driven by an elec-trical motor.

polynomial:

y∗(i,t) = b(i,0) + b(i,1) · x∗(i,1,t) + b(i,2) · x∗(i,2,t) + b(i,3) · x∗(i,3,t) + b(i,4) · x∗(i,4,t)+b(i,5) · x∗2(i,1,t) + b(i,6) · x∗2(i,2,t) + b(i,7) · x∗2(i,3,t) + b(i,8) · x∗2(i,4,t)+

b(i,9) · x∗(i,1,t) · x∗(i,2,t) + b(i,10) · x∗(i,1,t) · x∗(i,3,t) + b(i,11) · x∗(i,1,t) · x∗(i,4,t)

(4)

where y∗(i,t) = y(i,t)/ymaxi , x∗(i,j,t) = x(i,j,t)/x

max(i,j) are the scaled variables of the

regression models of compressors I. The xmax(i,j) , ymaxi are the maximum vari-

ables of their respective calibration and validation sets. The parameters ofthe models, bm,m = 1 . . . 12 are calculated with regression methods (Rosipalet al., 2006).

Assessment of the accuracy of the prediction of the models.

To evaluate the accuracy of the prediction of the models the Coefficientof Variation of the Root Mean Square Error, CV(RMSE) is used (WikipediaRMSE, 2014):

CV (RMSE) =RMSE

y=

√∑t∈T∗ (y(meas,i,t)−y(i,t))

T ∗

y

17

and the coefficient of determination, known as R squared (RSQ) expresseshow well the data fit the model (Matlab Linear Regression, 2014):

Sres = 1−(∑

t∈T ∗(y(meas,i,t) − y(i,t)))(T ∗ − 1) · vy

where y is the mean and vy is variance of the predicted values of y and ymeasare the measured variables.

4.3. Real Time Optimization (RTO) and optimization model

The offline steady-state identification algorithm, presented in Section 4.2was modified for online applications. The online steady-state identificationexamines if the Yss,system is 1 at the current moment, tr, considering J ′ vari-ables of each compressor i at the window (tr − ns − 1, tr).

According to Fig. 6, raw data are collected from the operation after thesteady-state identification and they are validated through data reconciliation.The validated data are used to update the parameters of the models which areused from the optimization block and to provide the input parameters of theoptimization model. The set points of the mass flows, therefore the output ofthe optimization model, are the input of the control system. The controllercan be a feedback controller. The controller deals with the application ofthe set points and adjusts the position of the actuators, Inlet Guide Vanes(IGVs), to achieve the desired flows.

There is usually a mismatch between models and reality due to fittingerrors and performance changes due to fouling and erosion as previouslymentioned. These errors influence the shape of the objective function of theoptimization problem and consequently the estimation of the minimum ofthe total power consumed. To reduce the influence of these errors, the massflows of the compressors were chosen as degrees of freedom of the optimizationproblem. The position of the IGVs can be then adjusted from the controllers.An analysis on the developments of the models showed that the accuracy inprediction of the models does not improve significantly when the position ofthe IGVs is considered as an input variable in the models.

Defining the input parameter vector of the optimization block (Fig. 5)z∗ = [x∗2,trx

∗3,trx

∗4,tr ] and the optimization variables (degrees of freedom or

manipulated variables of the optimization) mass flows ω∗(j,tr), then the optimalload distribution at a steady-state episode which starts at point t = tr iscomputed by the following optimization formulation:

18

minω∗∑i∈I

P(el,i,tr) (5)

s.t.

P ∗(el,i,tr) = fi(z∗, ω∗(i,tr),bi), i ∈ I (6)

P(el,i,tr) = P ∗(el,i,tr) · ymaxi , i ∈ I (7)

m(a,i,tr) = ω∗(i,tr) · xmax(i,1) , i ∈ I (8)∑

i∈I

m(a,i,tr) = m(D,tr) (9)

mmini ≤ m(a,i,tr), i ∈ I (10)

m(a,i,tr) ≤ xmax(i,1) , i ∈ I (11)

Pmin(el,i) ≤ P(el,i,tr), i ∈ I (12)

P(el,i,tr) ≤ ymaxi , i ∈ I (13)

Equation (5) describes the objective function which is the minimizationof the power consumption at steady state which starts at t = tr and Eq. (6)describes the constraints which give the power of each compressor i as func-tion of the z∗ and normalized mass flows ω∗(i,tr). Equations (7) and (8) refer

to the normalization of the powers and mass flows. Equation (9) providesthe mass balance between summation of the flows of the compressors andthe demand, m(D,tr), requested. Finally, Eqs. (10)-(13) define the regressiondomain.

The above optimization formulation was implemented in MatlabTM usingthe optimization function fmincon (Matlab Optimization Toolbox, 2014) .

5. Description of the industrial case study

This section presents the application of the methodology to an air com-pressor station of multi-stage compressors in parallel, in BASF SE, Germany,which distribute compressed air to different end-users. The end-users areair separation columns and plant-site utilities for compressed air. The aircompressor station consumes the major part of the total energy in an airseparation plant. Moreover, the power rating of the plant is several tens ofMWs.

19

i = 1

i = 3

i = 2

m(a,1) p(out,1)

p(out,2)

pin

p(out,3)

m(a,2)

m(a,3)

mD , popTin

Downstreamprocess

FC1

FT1

FC2

FT2

FC3

FT3

RTO mD

M

M

M

FC4

FT4

Figure 9: The operation of three air multi-stage centrifugal compressorsworking in parallel to supply compressed air a downstream process (air sep-aration column). The suggested control scheme can be seen here.

The case study to be examined involves three air multi-stage centrifugalcompressors similar to the compressor depicted in Fig. 8. The compressorsoperate in parallel to supply an air separation column with compressed air.The air separation column requests compressed air of mass flow rate, mD, at aconstant pressure, pop. The three compressors are assumed to have the samespecifications (power rate, minimum and maximum capacity and efficiencies)at the point of the commissioning of the plant. However, the compressorsare not in the same condition during the time period of the study as will beshown in Section 6.

The implemented control structure in the industrial plant is the following.The set point of the demand mD is given as an input of the system tocontroller FC4. FT4 measures the total mass flow of the compressed airprovided by the compressors. Three controllers FC1, FC2 and FC3 givethe same opening of the Inlet Guide Vanes (IGVs) to each compressor inorder to control the mass flows and meet the demand. By applying thiscontrol strategy the load should be shared equally among the compressors.The summation of the flows, total flow, measured from FT4 has to match

20

with the mD. If there is a mismatch then the IGVs of all the compressorsare adjusted uniformly (open or close for all the compressors) to reach thedesired mD. Referring to Fig. 9, this control structure does not include theRTO block and instead sends the same point signal to each compressor.

The control strategy the current paper suggests for optimal load sharingcan be seen in Fig. 9. Three flow transmitters FT1, FT2 and FT3 are usedto transmit the individual flows at the exit of the compressors. The RTO isplaced between the FC4 and these flow transmitters. In this case controllersFC1, FC2 and FC3 work independently and they receive the values of theflows of the compressors according to the RTO computations. The RTOreceives the demand from FC4 and estimates the best set points for FC1,FC2 and FC3 based also on measurements of Tin, pin and pop. The individualfeedback controllers FC1-FC3 have to independently adjust the position ofthe IGVs of the compressors to reach the set points of the mass flows givenfrom the RTO.

Practical challenges of the case study

The case study of the industrial air separation process revealed severalpractical challenges which are summarised below. These challenges should beconsidered in order to achieve a realistic approach of the proposed method-ology:

The operators did not operate the compressors over their full range inthe collected data set. Therefore, only a partial compressor map is capturedin the regression models. Hence, the feasible area of the model used forthe optimization model is not defined from the actual physical limits of thecompressor, i.e. surge, choke, and minimum and maximum Inlet Guide Vaneopening. Instead, the feasible area of the compressor is defined from thedomain of the regression model (Brooks et al., 1998). The regression domainis a part of the actual operational area.

Figure 10a demonstrates that an operating point of the compressors comesfrom the intersection of the Compressor System (CS) curve and the load curveof the downstream process. The CS curve is defined as the merged individualcompressor characteristics of the parallel compressors assuming that the inletconditions are the same of all compressors. The set of all the operating pointsof the corresponding data set defines the regression domain of the model ofa comrpessor as can be seen in Fig. 10b. It is known from the plant that theoperators operated well within the physical limits (surge and choke) of the

21

compressors during the past operation.

Pre

ssur

e

Flow of compressor i

Characteristics of compressor

maximumIGV opening

Chokeline

Surgeline

minimumIGV opening Regression

domainm(a, i) m(a, i)

pi

Pre

ssur

e

Flow of downstream process

(a) (b)

High demandload curve

Low demandload curve

Partial demandload curve

Operatingpoint

CScurve

min

pimax

maxmin

Figure 10: An operating point of the system defined by intersection betweenload curve and characteristic of the system (CS curve) (a) and the feasiblearea of the compressors, i.e. regression domain (b).

A model is expected to be more accurate when the data set is collectedover a shorter time period, for example one week than a model derived froma data set of several months because for longer period the compressor mighthave been in various states during this period. For example, a compressoris efficient immediately after maintenance and less efficient after many hoursof operation. However, the range of the regression domain of the model issmaller in the case of a more accurate model.

In the case that the compressor was operated close to the surge or chokeline, the regression domain cannot be assumed rectangular (see Fig. 10b)due to the physical restrictions. There are two options to deal with thisissue: a) use a convex hull for describing the regression domain or b) addan extra constraint in the optimization model described by Eqs. (6) - (13).The use of a convex hull can be seen in Brooks et al. (1998) and in Mitraet al. (2012). The extra constraint can be a regression black box model ofthe outlet pressure which relates the mass flow and other parameters such asambient temperature and pressure, pi,out = gi(z,m(a,i), ci), i ∈ I where ci isthe vector of the fitted parameters of the new regression model.

The data reconciliation step requires redundant measurements, for ex-ample extra measurements of the flow apart from these at the exit of thecompressors. Unfortunately the industrial case study did not have these

22

measurements, and hence the data reconciliation step could not be imple-mented.

6. Results

6.1. Models of compressors

Data from fifteen days of operation were used to develop the models ofthe compressors. In the case study examined, it was assumed that the per-formance of the models deteriorates gradually and there was no event whichhas caused a relatively high discontinuous decrease in performance. Data of129600 continuous operating points with 10 s sample interval (0.1 Hz samplerate) were collected. The steady-state algorithm detected 7430 steady-stateepisodes in the examined data set for the system of the compressors. Ofthese episodes, 80% were used for the fitting of the model and the remaining20 % were used to validate the developed model.

Table 1: Statistics of the fitting and validation of the regression models.

Fitting Validation ValidationCompressors RSQ RSQ CV(RMSE)

i1 0.992 0.992 0.54i2 0.968 0.967 0.67i3 0.987 0.988 0.57

Table 1 presents the statistics of the fitting (RSQ) and the validation(RSQ and CV(RMSE)) of the models of the three compressors. The standardfunction LinearModel.fit of Matlab (Matlab Statistics Toolbox, 2014) wasused to fit the data into the polynomial of Eq.(4). Figure. 11 shows theprediction of the normalised power consumption of each compressor versusthe measurements of the power. The axes present normalized values of thepower due to confidentiality restrictions. The normalization of the powerconsumption of each compressor is calculated by dividing the power with theymaxi .

Compressor i1 shows the most accurate match between prediction andactual measurements of the power. The fitting of the model has also higher

23

0.75 0.8 0.85 0.9 0.95 10.75

0. 8

0.85

0. 9

0.95

1

Normalized actual mass flow (-)

Nor

mal

ized

pre

dict

ed m

ass

flow

(-)

(a) Compressor i1

0.75 0.8 0.85 0.9 0.95 1

0. 8

0.85

0. 9

0.95

1

Normalized actual mass flow (-)

Nor

mal

ized

pre

dict

ed m

ass

flow

(-)

(b) Compressor i2

0.75 0.8 0.85 0.9 0.95 10.75

0. 8

0.85

0. 9

0.95

1

Normalized actual mass flow

Nor

mal

ized

pre

dict

ed m

ass

flow

(c) Compressor i3

Figure 11: Prediction versus actual values of mass flow of compressors i1, i2and i3 in the validation set.

24

RSQ value than in the other cases. In the case of compressor i2 the accuracyof the prediction is relatively less than the other two compressors. The reasonfor this is that the measurements of the mass flow and power of compressori2 are relatively more noisy than in the case the other two compressors. TheCV(RMSE) of the models ranges between 0.54 and 0.67 %. By comparingthe mean RMSE results with other results from similar case studies (Hanet al., 2004; Xenos et al., 2014a) these models can be considered of highaccuracy for predicting power consumption of compressors.

Table 2: Boundaries of mass flows and power consumptions. The units aredimensionless and scaled.

Compressors mmin(a,i) xmax(i,1) Pmin

(el,i) ymaxi

i1 0.670 0.924 0.304 0.406i2 0.676 0.836 0.295 0.365i3 0.624 0.842 0.286 0.374

Table 2 presents the minimum and maximum bounds of the mass flowsand powers of the three compressors. The values shown in Table 2 representthe boundaries of mass flows and powers where they are divided by twoscaling factors to keep the confidentiality agreement with the provider ofthe case study. The table shows that compressors have different regressiondomains with compressor i1 having a larger feasible area than the other two.

6.2. Illustrative example with industrial compressors

An illustrative example of the two compressors i1 and i2 explains theoptimal load sharing using the optimization presented in Section 4.3. In thisexample, only two compressors are taken into account into the optimizationmodel. The rate of total mass flow which has to be delivered from the twocompressors is m∗D. The summation of the mass flows of the two compressorsm(a,i1) and m(a,i2) has to be equal to the mass flow rate of the demand.

Figure 12 presents the normalized power consumed from the two com-pressors individually and the combined normalized power consumption onvertical axis as a function of the normalized mass flow of the first compres-sor, m(a,i1) on horizontal axis. Therefore, given the m(a,i1), the m(a,i2) equals

25

m∗D −m(a,i1). By increasing the mass flow of the first compressor the com-pressor i1 consumes more and on the other hand compressor i2 less power,assuming that all the other parameters are kept fixed, e.g. inlet temperatureand pressure of the downstream process. Moreover, the compressors are re-stricted to operate from a minimum mass flow rate boundary, correspondingto compressor i1 equal to max{mmin

(a,i1),m∗D−mmax

(a,i2)} = 0.670 and a maximum

equal to min{mmax(a,i1),m

∗D −mmin

(a,i2)} = 0.795 when the value of the mass flowof the demand is 1.471.

0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8

0.3

0.4

0.5

0.6

0.7

X: 0.735Y: 0.651

X: 0.735Y: 0.322

X: 0.735Y: 0.329

0.65 0.7 0.75 0.80.64

0.65

0.66

0.67

X: 0.735Y: 0.651

X: 0.795Y: 0.641

Nor

mal

ized

pow

erco

nsum

ptio

n (%

)

Normalized mass flow of compressor i1 (%)

Comp. i1+i2

OptimalActual

Comp. i2

Comp. i1

Figure 12: Example of the optimization of two compressors in parallel.

The actual operation (point described in Fig. 12) is defined as the op-eration which took place in reality and the power consumed from the com-pressors is a result of the mass flows from the existing control scheme. Com-pressors i1 and i2 operated at m(a,i1) = 0.735 and m(a,i2) = 0.736 which canbe assumed that the load was split evenly. As can be seen from Fig. 12,compressor i1 consumes more power than i2 by 2.1% under these conditions.This means that the compressor are in a different condition.

From the combined curve (Comp. i1 + i2) it can be observed that inthe actual compressor operation the mass flow of i1 is m(a,i1) = 0.735. Inthis case the total consumption is higher than operating at the point whichcompressor i1 has mass flow rate m(a,i1) = 0.795. The reduction in poweris 1.54 % in this case. In other words, this observation demonstrates thatcompressor i1 is more efficient than compressor i2. The more the compressor

26

i1 operates against compressor i2 the higher is the total power reduction inthe available search space. The upper boundary results due to the minimummass flow boundary of compressor i1.

The above analysis and graphical representation is feasible for two com-pressors but when more than two compressors are involved in a networkthen optimization (i.e. mathematical programming) deals with the estima-tion of the minimum value of the objective function while ensuring that theconstraints hold valid.

6.3. Demonstration of Real Time Optimization application in parallel withreal operation

Section 6.3 examines the application of the developed RTO methodologyon a simulation of real time operation. The historical data are simulated asif given in real time and the RTO runs in parallel with the operation of thesystem in Fig. 9. The RTO estimates the optimal load sharing and the resultscoming from these computations are compared with the operation that tookplace in reality. The RTO methodology was applied to the compressor systemof the three parallel compressors for more than 12 hours.

The steady-state detection is configured to examine when the three com-pressors are in steady state simultaneously for 40 s. The inputs of the op-timization are collected during this period. After the RTO calculations, thesystem is examined if it is still in steady state and if this holds true the RTOresults are given to the proposed control system (see Fig. 9). The onlinesteady-state identification algorithm detected 50 steady state episodes wherethe first 16 can be seen in Fig. 13.

Table 3: Three different cases of operation.

Case Mass flows to estimate power using Eq. (4.2)Actual operation The mass flows are given from the real dataEqual split operation The demand is split to equal mass flow ratesOptimal operation The mass flows are given from the optimization

It was assumed that the compressor conditions does not change signif-icantly during the 15 days period of the collected data in Section 4.2 and

27

the updated compressor maps from the 15 days time window were used inthe optimization. Figure 14 shows the normalized power consumption of thethree compressors in three different cases for the examined 12 hours: a) ac-tual operation, b) equal split operation and c) optimal operation. Table 3describes the assumptions to be taken to estimate the power consumed inthese three different cases.

The power consumption in Fig. 14 is a calculated quantity whose errorsdepend on errors in the quantities used in the calculation. The differencebetween the actual operation and equal split operation might be attributed torandom variability in the data. However the power consumption for optimaloperation is systematically lower and the difference cannot be accounted forby random statistical variation.

The measurement error in the mass flow is less than +/-0.005 on thenormalized mass flow scale. This applies to the results in Figs. 14 - 20.

7.7 7.72 7.74 7.76 7.78 7.8 7.82x 105

0.72

0.73

0.74

0.75

0.76

0.77

0.78

0.79

0. 8

Comp.i1

Comp.i2

Comp.i3

Time (s)

Nor

mal

ised

pow

er c

onsu

mpt

ion

(%)

SteadyStates

1 6 9 13 148432 5 10

Past operation

Figure 13: The first sixteen steady-state episodes of the system of the com-pressors.

Figure 14 shows that the actual operation and the equal split strategydo not show an important difference in the total power consumed from thecompressors. Moreover, Figs. 15 - 17 show that the compressors are not

28

equally split in the actual operation and especially in the case of compressori3 it can be seen that there is a difference between the mass flow from equalsplit operation and actual operation. Although the values of the mass flowsin the case of the equal split are different from the mass flows from the actualoperation, there is not much difference in the total power consumption.

5 10 15 20 25 30 35 40 45 500.94

0.95

0.96

0.97

0.98

0.99

1

Number of steady state episodes

Nom

raliz

ed p

ower

con

sum

ptio

n (%

)

Actual operationEqual split operationOptimal operation

Figure 14: Normalized total power consumption of the three compressorsfrom actual, equal split and optimal operation.

On the other hand, Fig. 14 shows that the optimization achieves reduc-tion in the total power consumption in all 50 steady-state periods. Figure 15shows that compressor i1 should work at higher mass flows than in the caseof the actual and equal split operation and Fig. 16 shows that compressori2 should work at lower mass flows. Figure 17 demonstrates that the opti-mal operation suggests that compressor i3 has to work at mass flow ratesvery close to the mass flows the actual operation which took place. In otherwords, the optimization estimated that compressor i3 was operated well dur-ing the actual operation but compressor i1 as more efficient should be loadedmore than compressor i2 which seems to be less efficient under the currentoperational conditions.

It was observed that in actual operation compressor i1 and i2 were oper-ated with equal load and compressor i3 dealt with the remaining load. The

29

5 10 15 20 25 30 35 40 45 500.65

0.7

0.75

0.8

0.85

0.9

Number of steady state episodes

Com

pres

sor i

1 no

rmal

ized

mas

s flo

w (%

)Actual operationEqual split operation

Min/max boundariesOptimal operation

Figure 15: Compressor i1 normalised mass flow rate from three differentcases.

5 10 15 20 25 30 35 40 45 500.65

0.7

0.75

0.8

0.85

0.9

Number of steady state episodes

Com

pres

sor i

2 no

rmal

ized

mas

s flo

w (%

) Actual operationEqual split operation

Min/max boundariesOptimal operation

Figure 16: Compressor i2 normalised mass flow rate from three differentcases.

30

5 10 15 20 25 30 35 40 45 500.65

0.7

0.75

0.8

0.85

0.9

Number of steady state episodes

Com

pres

sor i

3 no

rmal

ized

mas

s flo

w (%

) Actual operationEqual split operation

Min/max boundariesOptimal operation

Figure 17: Compressor i3 normalised mass flow rate from three differentcases.

RTO method was applied exclusively to the two compressors i1 and i2 inthe case of the 50 steady-state episodes. This is because the previous re-sults from the optimization showed that compressor i3 should not changeoperating point from this of the actual operation, therefore the mass flow ofcompressor i3 does not consist any degree of freedom in the optimization.

In this new study, Figure 18a shows the power consumption of the twocompressors from the actual and optimal operation. It can be seen thatcompressor i1 consumes more power compared to compressor i2 in the ac-tual operation in all 50 cases where the equal split strategy was applied.This shows again that compressors are in different performance conditions.Moreover, compressor i1 is less efficient that compressor i2 when the load isequally shared.

Optimization results give a lower total power consumption of the compres-sors compared to the power consumption coming from the actual operation.The compressor i1 loaded more and compressor i2 less which results in givinga lower total power consumption. This means that the compressor i1 and i2work more efficiently when they operate at the mass flows the RTO suggests.These mass flows can be seen in Figs. 19 and 20.

The suggested RTO framework can be applied to multiple compressors inparallel. The RTO can provide the automation of the optimization of com-

31

5 10 15 20 25 30 35 40 45 500.29

0.30

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

Optimal operation (i2)Optimal operation (i1)Actual operation (i2)Actual operation (i1)

Nor

mal

ized

pow

er c

onsu

mpt

ion

(%)

Number of steady state episodes

(a) Compressors power consumption

0.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

5 10 15 20 25 30 35 40 45 50Number of steady state episodes

Nor

mal

ized

tota

l pow

er c

onsu

mpt

ion

(%)

Actual operationOptimal operation

(b) Total power consumption

Figure 18: Power consumption of compressors i1 and i2 from optimizationand actual operation (equal split).

pressors in real-time. The online steady-state detection algorithm detectswhen the operation is constant and the RTO scheme computes the optimaldistribution of the load among the online compressors considering their up-dated characteristics and performances. The duration of transient operationbetween two steady states is much smaller compared to the length of timethe compressors stay at their new operating point, hence the optimization ofthe transients of the system can be neglected.

The configuration of the online compressors is given from the second partof the framework in Fig. 5. Therefore, the scheduling of the compressorsis also needed to provide the best selection of compressors. The study fromKopanos et al. (2015) will explain the optimal scheduling of the compressors.

7. Conclusions

The paper presented the state-of-the-art of the optimization of compres-sor stations involving multiple industrial compressors operating in parallel.It also suggested an integrated framework to optimize the operation of com-pressors for short and long time periods. The contribution of this paper isthe presentation of an integrate framework focusing on an online Real TimeOptimization (RTO) method which collects raw data from the process. Thedata are used to update the models of the compressors which are used into an

32

5 10 15 20 25 30 35 40 45 500.65

0.7

0.75

0.8

0.85

0.9

Number of steady state episodes

Com

pres

sor i

1 no

rmal

ised

mas

s flo

w (%

)

Actual operation

Min/max boundariesOptimal operation

Figure 19: Compressor i1 normalised mass flow rate from actual and optimaloperation.

5 10 15 20 25 30 35 40 45 500.65

0.7

0.75

0.8

0.85

0.9

Number of steady state episodes

Com

pres

sor i

2 no

rmal

ised

mas

s flo

w (%

)

Actual operation

Min/max boundariesOptimal operation

Figure 20: Compressor i2 normalised mass flow rate from actual and optimaloperation.

33

optimization framework which reduces the power consumption in a steady-state period. The optimization deals with different operational conditionssuch as inlet temperature and pressure.

A real industrial case study of an air compressors station, part of anintensive chemical process in BASF SE, Germany consuming several tens ofMW was optimized using the developed RTO methodology. The comparisonbetween the RTO application and the actual operation taken place in realityshowed that the RTO method has the potential to reduce the total powerconsumption of the compressors.

8. Acknowledgments

Financial support from the Marie Curie FP7-ITN project ”Energy sav-ings from smart operation of electrical, process and mechanical equipment -ENERGY SMARTOPS”, Contract No: PITN-GA-2010-264940 is gratefullyacknowledged.

The authors would like to thank BASF SE for providing a case study andtechnical support.

References

Abbaspour M., Chapman K.S., Krishnaswami P., 2005, Nonisothermal com-pressor station optimisation, Journal of Energy Resources Technology,Transactions of the ASME, Vol. 127, pp. 131-141.

Abbaspour M., Krishnaswami P., Chapman K.S., 2007, Transient optimisa-tion in natural gas compressor stations for linepack operation, Journal ofEnergy Resources Technology, Transactions of the ASME, Vol. 129, pp.314-324.

Bloch H.P., 2006, A Practical Guide to Compressor Technology (2nd edition),John Wiley & Sons, Inc., Hoboken, New Jersey.

Borraz-Sanchez C., 2010, Optimisation Methods for Pipeline Transportationof Natural Gas, PhD Dissertation, University of Bergen, Department ofInformatics, Norway.

Boyce M.P.P.E., 2003, Centrifugal Compressors: A Basic Guide, Pen WellCorporation, Oklahoma.

34

Brooks D.G., Carroll S.S., Verdini W.A., 1998, Characterizing the domain ofa regression model, The American Statician, Vol. 42, No.3, pp. 187-190.

Camponogara E., Nazari L.F., Meneses C.N., 2012, A revised model forcompressor design and scheduling in gas-lifted oil fields, IIE Transactions,Vol. 44 (5), pp. 342-351.

Carter R., Denton N., Reisner M., OMV, Sekirnjak E., ADES, 2010, Tran-sient optimization - Examples and directions, PSIG 1011, PSIG AnnualMeeting, Florida 11 May - 14 May 2010.

Cicciotti M., Xenos D.P., Bouaswaig A.E.F., Thornhill N.F., Martinez-BotasR., 2014a, Online performance monitoring of industrial comperssors us-ing meanline modelling, Proceedings of ASME Turbo Expo 2014,GT2014-25088, June 16-20, 2014, Dussedorf, Germany.

Cicciotti M., Xenos D.P., Bouaswaig A.E.F., Thornhill N.F., Martinez-BotasR., 2014b, Physical modelling of industrial multistage centrifugal compres-sors for monitoring and simulation, Journal of Mechanical EngineeringScience.

Cobos-Zaleta D., Rıos-Mercado R.Z., 2002, A MINLP model for minimizingfuel consumption on natural gas pipeline networks, Memorias del XI Con-greso Latino Iberoamericano de Investigacion de Operaciones (CLAIO),27-31 October 2002, Chile.

DeMarco F.C.G., Elias G.P., 2011, Fuel consumption model on natural gascompression stations driven by two-shaft gas turbine, PSIG 1107, PSIGAnnual Meeting, Napa Valley, California, 24 May - 27 May 2011.

Dixon S.L., Hall C.A., 2010, Fluid Mechanics and Thermodynamics of Tur-bomachinery, Sixth Edition, Elsevier, Oxford, UK.

Forsthoffer W.E., 2011, Forsthoffer’s Best Practice Handbook for RotatingMachinery, Butterworth-Heinemann, Boston.

Garcia-Hernandez A., Brun K., 2012, Energy usage in natural gas pipelineapplications, ASME Journal of Engineering for Gas Turbines and Power,Vol. 134, pp. 022402-1 to 022402-9.

35

Han I.-S, Han C., Chung C.-B., 2004, Optimisation of the air-and gas-supplynetwork of a chemical plant, Trans IChemE, Part A, Chemical EngineeringResearch and Design, Vol. 82 (A10), pp. 1337-1343.

Harjunkoski I., Nystrom R., Horch A., 2009, Integration of scheduling andcontrol - Theory and practice, Computers and Chemical Engineering, Vol.33, pp. 1909-1918.

Jenıcek T., Kralık J., 1995, Optimised control of generalized compressorstation, 27th Annual Meeting Pipeline Simulation Interest Group (PSIG),October 18-20, Albuquerque, New Mexico.

Kim M., Yoon S.H., Domanski P.A., Payne, W.V, 2008, Design of a steady-state detector for fault detection and diagnosis of a residential air condi-tioner, International Journal of Refrigeration, Vol. 31, pp. 790-799.

Kopanos G.M., Xenos D.P., Cicciotti M., Pistikopoulos E.F., Thonrhill N.F.,2015, Operational planning of networks of compressor stations: The airseparation plant case, Applied Energy

Kurz R., Brun K., 2010, Assessment of compressors in gas storage applica-tions, Journal of Engineering for Gas Turbines and Power, Vol. 132, pp.062402-1:7, DOI: 10.1115/1.4000147.

Kurz R., Lubomirsky M., Brun K., 2012a, Gas compressor station economicoptimization, International Journal of Rotating Machinery, Vol. 12, pp.1-9; DOI: 10.1155/2012/715017.

Kurz R., Brun K., 2012b, Fouling mechanisms in axial compressors, Journalof Engineering for Gas Turbines and Power, Vol. 134, pp. 032401-1:032401-9; DOI: 10.1115/1.4004403.

Liptak B.G, Process Control and Optimization, Compressor Control and Op-timization, 2006 Instrument Engineer’s Handbook, Vol. II, Fourth Edition,Chapter 8.15, pp. 1763- 1792.

Luo, X., Zhang B., Chen Y., Mo S., 2013, Operational planning optimiza-tion of steam power plants considering equipment failure in petrochemicalcomplex, Applied Energy, Vol. 11., pp. 1247-1264.

36

Mahlke D., Martin A., Moritz S., 2009, A mixed integer approach for time-dependent gas network optimisation, Optimisation Methods and Software,Vol. 25, No. 4, pp. 625-644.

Mansour M., Ellis J.E., 2008, Methodology of on-line optimisation applied toa chemical reactor, Applied Mathematical Modelling, Vol. 32, pp. 170-184.

Marques D., Morari M., 1988, On-line optimisation of gas pipeline networks,Automatica, Vol. 24, No. 4, pp. 455-469.

Matlab Statistics Toolbox : mathworks.co.uk/help/stats/linearmodel.fit.html;accessed 25/04/2014

Matlab Optimization Toolbox: mathworks.co.uk/help/optim/ug/fmincon.html; accessed 25/04/2014

Matlab Linear Regression: mathworks.co.uk/help/matlab/data analysis/linear-regression.html; accessed 25/04/2014

Milum R., 2012, Multi-compressor capacity optimization, Petrotech, 7thPipeline Technology Conference 2012, A Petrotch, Inc. White paper.

Mitra S., Grossmann I.E., Pinto J.M., Arora N., 2012, Optimal produc-tion planning under time-sensitive electricity prices for continuous power-intensive processes, Computers and Chemical Engineering, Vol. 38, pp.171-184.

Nguyen H.H., Uraikul V., Chan C.W., Tontiwachwuthikul P., 2008, A com-parison of automation techniques for optimization of compressor schedul-ing, Advances in Engineering Software, Vol. 39, 178-188.

Paparella F., Domınguez L., Cortinovis A., Mercangoz M., Pareschi, D., Bit-tanti S., 2013, Load sharing optimization of parallel compressors, EuropeanControl Conference (ECC), July 17-19, 2013, Zurich, Switzerland.

Martinez Prata D., Schwaab M., Luis Lima E., Carlos Pinto J., 2010, Simul-taneous robust data reconciliation and gross error detection through parti-cle swarm optimization for an industrial polypropylene reactor, ChemicalEngineering Science, Vol. 65, pp. 4943-4954.

37

Rosipal R., Kramer N., 2006, Overview and recent advances in partialleast squares, Subspace, Latent Structure and Feature Selection: Statisti-cal and Optimization Perspectives Workshop (SLSFS 2005), Revised Se-lected Papers (Lecture Notes in Computer Science 3940). Berlin, Germany:Springer-Verlag, pp. 3451.

Rolls Royce: www.rolls-royce.com/energy/energy products/ accessed6/02/2014.

Saidur R., Rahim N.A., Hasanuzzaman M., 2010, A review on compressed-air energy use and energy savings, Renewable and Sustainable EnergyReviews, Vol. 14, pp. 1135-1153.

Shaw, D.C., 1994, Pipeline system optimization: a tutorial, ScientificSoftware-Intercomp, Houston.

Tirnovan R., Giurgea S., Miraoui A., Cirrincione M., 2008, Surrogate mod-elling of compressor characteristics for fuel-cell applications, Applied En-ergy, Vol. 85, pp. 394-403.

Twohig, D., 2011, Utility optimization: Driving economic performancethrough the utilization of automation technologies, Automation Island,InTech, www.isa.org, accessed 28.09.2013.

van den Heever S.A., Grossmann I.E., 2003, A strategy for the integrationof production planning and reactive scheduling in the optimisation of ahydrogen supply network, Computers and Chemical Engineering, Vol. 27,pp. 1813-1839.

Varbanov P.S., Doyle S., Smith R., 2004, Modeling and optimization of util-ity systems, Trans IChemE, Part A, Chemical Engineering Research andDesign, Vol. 82 (A5), pp. 561-578.

Wu S., Rios-Mercado R.Z., Boydm E.A., Scott L.R, 2000, Model relaxationsfor the fuel cost minimization of steady-state gas pipeline networks, Math-ematical and Computer Modelling, Vol. 31, pp. 197-220.

Widell K.N., Eikevik T., 2010, Reducing power consumption in multi-compressor refrigeration systems, International Journal of Refrigeration,Vol. 33, pp. 88-94.

38

Wikipedia, Root-mean-square deviation: en.wikipedia.org/wiki/Root-mean-square deviation; accessed 25/04/2014.

Wong J.P., Larson E.R., 1968, Optimisation of tree-structured natural-gastransmission networks, Journal of Mathematical Analysis and Applica-tions,Vol. 24, pp. 613-626.

Wright S., Somani M., Ditzel C., 1998, Compressor station optimization,Pipeline Simulation Interest Group (PSIG), Denver, Colorado, October28-30, 1998.

Xenos D.P., Cicciotti M., Bouaswaig A.E.F., Thornhill N.F., Martinez-BotasR., 2014a, Modeling and optimization of industrial centrifugal compres-sor stations employing data-driven methods, Proceedings of ASME TurboExpo 2014, GT2014-25089, June 16-20, 2014, Dussedorf, Germany.

Xenos D.P., Cicciotti M., Bouaswaig A.E.F., Thornhill, 2014b, Preprocessingof raw data for developing steady-state data-driven models for optimizingcompressor stations, 10th International Conference on Control, Control2014, Loughborough, UK.

39