techniques for quasi-static operating optimization of chp...

PolyCity Workshop, 25th of May 2007, Turin, ITALY 1

Mario Nervi – Univ. Of Genova, Italy

Techniques for quasi-static operating optimization of CHP plants

Mario NerviUniversità di Genova

(Italy)

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Mario Nervi

Associate professor of “Fundamentals of Electrical Engineering” at the University of Genova, Italy.

Author of many scientific papers on electromagnetic field computation, optimization methods, energy applications



Techniques for Quasi StaticOperational Optimization of CHP Plants

P. Girdinio, S. Moccia, G. Molinari, M. Nervi – Università di Genova – Dipart. di Ingegneria Elettrica (DIE), Genova, Italy

A. Pini Prato – Università di Genova – Dipart. di Macchine, Sistemi Energetici e Trasporti (DIMSET), Genova, Italy



A CHP is a machine for the Combined production of Heat and electric Power

It is useful as the combined generation allows tosignificantly improve the energetic efficiency

The cold source heat is not a waste, but a “recycled”resource

In principle CHPs can have any size; usually, for a betterexploitation of the thermal energy, they are medium-smallsize (some tenths of kW to some hundreds of kW)

The term of “micro – cogeneration” is widely used then

What a CHP is?What a CHP is?



A CHP must produce electrical and thermal power, according to the variable requests of the loads

There are constraints on the switching (a CHP cannot beswitched on and off every minute, due to technicalreasons)

The cost of fuel is variable within the year

The costs of electrical power bought from and sold to the grid are variable between night and day (there is a 4 factorfrom the top day price and the night price)

Operational considerationsOperational considerations



An even more important constraint is about the energysaving: the F.E.S.R. (Fuel Energy Savings Ratio), which isdefined as:

Operational considerations (cont’d)Operational considerations (cont’d)

ts

t

es

e

c

Ep

EE

ηη+

⋅

−1

must be greater than 0.1. This means that the fuel saving, compared to that used for the separate production of the same electrical and thermal power, is at least 10%.

This constraint is evaluated at the END of the year!!!



Objective and OptimizationObjective and Optimization

Energy balance

Tax and regulatorycontraints

(by the end of the year)

Technical operationalconstraints

Operational strategies(maintenance planning, etc.)

The correct management is a key issue to have a competivitive behaviour of plants:

The objective is to get the maximum cash-flow



The problem is: how to maximize the differential cash flow, fulfilling all the constraints, especially the limit on F.E.S.R.???

The latter is very critical, as a non-fulfillment (discoveredonly at the end of the year) leads to loose significant taxdiscounts, that in most cases make the difference in termsof the commercial appeal of the CHP

Of course the correct management of a CHP cannot beleft to the operator, as the degrees of freedom are toomany to be chosen by human intervention

The problemThe problem



The objective is:Problem coding – objective - constraintsProblem coding – objective - constraints

( ){( ) }NOTdefFbNOTdefdefFdefQu

WppLoadWss

yFFyFyQ

yWWyWflowcashMAX

__

_

⋅−−⋅−⋅+

+⋅−+⋅=

δ

Subject to the previously defined constraints:Physical congruence (energy balance)Technical congruence (due to machine characteristics)Normative/tax congruence (to achieve tax discounts)Management constraints (for ex. maintenance sched.)



A choice between two main options is necessary

Types of optimization – Quasi StationaryTypes of optimization – Quasi Stationary

Global Optimization

Quasi Stationary Opt.

CHP Optimization



Types of optimization – Q. S. (cont’d)Types of optimization – Q. S. (cont’d)

Global Optimization: the degrees of freedom are all the values of electrical and thermal power, for each time step, within the optimized period (past, present, and future)

Quasi Stationary Optimization: the degrees of freedom are all the values of electrical and thermal power, at ONE time step, within the optimized period (the past is known, the present is optimized, and the future is estimated)

This is the only practical choice (time steps are one hour long), therefore, for a Glob. Opt. over one year the total number of d.o.f. should be multiplied by 8760, leading to an unpractical problem



The management of F.E.S.R. constraint is intrinsicallycomplex: with a Global Optimization approach, it could be“naturally” enforced

Using a Quasi Stationary approach, it has to betransformed into a local problem even though it remainsan integral problem

The problem is how to correctly enforce the constraint, without overconstraining the problem

Case “A” is the result without overconstrainingCase “B” is the result where the constraint (.GE. 10%) isimposed at every iteration

F.E.S.R. Constraint managementF.E.S.R. Constraint management



The Quasi Stationary has been implemented using a two stage procedure:

an external procedure, written in high levellanguage (Fortran), that reads all the relevantdata, and manages a loop over the time steps. Thenit calls...an internal commercial state-of-the-art optimizer, able to solve the resulting MILP, then...at the end of the MILP solution the results are passed back to the external driver, checked, and the integral constraints are estimated; then the next step is executed, until the end of the period

S/W ImplementationS/W Implementation



To be mentioned that anyway TWO optimizationsmust be always run:

the first is F.E.S.R. unconstrained, and it is onlyneeded to have a rough estimate of the fuelconsumption;

the second is F.E.S.R. constrained, and it uses the fuel consumption estimates coming from the previous run

S/W Implementation (cont’d)S/W Implementation (cont’d)



Main features of the developed softwareMain features of the developed softwareAt the moment the SW allows to simulate natural gad fedmicro CHP plants

Input data needed:• Monthly/yearly gas consumption of site• Monthly/yearly electric power consumption of site• Location (province) and height above sea level of site• AEEG regulations about gas and electrical power prices

Output data provided:• Production of thermal/electrical power • Switching times (on and off) of CHPs; time of production• Performances (FESR, fuel savings, cash flow)• Financial analyses



Typical plant layout Typical plant layout



Library of available CHPsLibrary of available CHPsAt the moment the following CHPs are included in the library:

Capstone C30, 30 kWeCapstone C60, 60 kWeTurbec T100, 105 kWe

It has been designed an “extendable machine library”, thatneeds in input a matrix of points representing the characteristic of a machine, and builds up the data neede by the optimizer through an “ad hoc” interpolation. This gives to the SW a remarkable use flexibility



Characteristics of Capstone C30Characteristics of Capstone C30



Characteristics of Capstone C60Characteristics of Capstone C60



Characteristics of Turbec T100Characteristics of Turbec T100



Pre ProcessorPre Processor

Input OutputAEEG regulations about

electricity and gas prices, reference efficiency used to

compute the FESR, etc.

Hourly behaviour of electrical and thermal loads, that can

possibly be updated during the analysis

Number and type of (possibly) present boilers

Previous consumption of electrical and thermal power,

and, if available, the records of one week of the electrical loads

Hourly behaviour of site temperature, that can possibly be updated during the analysis

Location (province) of installation site, and height

above sea level (at the moment only the 4 ligurian provinces are

implemented)

The software is split in three “indipendent” modules:

Pre processor tasks are:

Pre processor

Post processor

Supervisor



Supervisor and OptimizerSupervisor and OptimizerFormed by two modules:

InputHourly requests of thermal and

electrical loads, possibly updated during the analysis

Number and type of available CHPs

Hourly behaviour of site temperature, possibly updated

during the analysis Additional consumption during

transients, switch ons and shutdowns

Operational parameters: minimum time between ON and

OFF, etc.Month of beginning of

simulationChoice of objective (max cash flow, minimum emissions, etc.)

OutputComplete estimate of the plant

for each hour of simulated period

Pre processor

Post processor

SupervisorSupervisor, written in Fortran; its

purpose are: 1) to manage and update input data to submit tothe optimizer, and 2) to record optimizer output data

Optimizer, is the commercial code CPLEX, able to solve the resultimg MILP problem; itsoutput allows the supervisor toupdate the integral parameterestimates



Post ProcessorPost ProcessorAllows to display and to save both as picture and as text data the behaviour of all integral parameters and all local quantities

Input OutputComplete state of plant operational constraints

Textual and graphic representation of plant

behaviour

Pre processor

Post processor

SupervisorAllows to performfinancial analyses, such

as NPV, ROI, IRR



Test caseTest caseThe optimized problem is based on:• 2 CHP units, rated electrical power 80kW each, variable

regeneration (the machines have a by-pass valve)• One auxiliary boiler, rated thermal power 500kW

The price structure of electrical power and fuel are obtained from the sites of Italian Regulatory Board for Electrical Energy and Gas

The actual prices of electrical power are obtainedfrom the Italian Electrical Market Manager



ResultsResults

Fuel Energy Savings Ratio (F.E.S.R.)

8,00%

10,00%

12,00%

14,00%

16,00%

18,00%

20,00%

22,00%

1 611 1221 1831 2441 3051 3661 4271 4881 5491 6101 6711 7321 7931 8541

hours [h]

Case ACase B



Results (cont’d)Results (cont’d)

Differential Cash Flow

0

10000

20000

30000

40000

50000

1 611 1221 1831 2441 3051 3661 4271 4881 5491 6101 6711 7321 7931 8541

hours [h]

[€] Case A

Case B



Results (cont’d)Results (cont’d)Machines' productions

-10

0

10

20

30

40

50

60

70

80

90

1 26 51 76 101 126 151 176 201 226 251 276 301

hours [h]

kW Electrical Pwr Machine 1Electrical Pwr Machine 2



Results (cont’d)Results (cont’d)

44,38%45,61%

43,15%73,31%

53,16%26,48%

89,40%10,60%

41,04%45,70%

36,39%50,13%

63,24%13,37%

84,55%15,45%

0,00% 10,00% 20,00% 30,00% 40,00% 50,00% 60,00% 70,00% 80,00% 90,00% 100,00%

Case A

Case B

General operational parameters comparison

Total thermal energy produced by the auxiliary boiler (compared to user's request)Total thermal energy produced by the plant (compared to user's request)Total electrical energy sold to the grid (compared to user's request)Total electrical energy purchased from the grid (compared to user's request)Total electircal energy produced by the plant (compared to user's request)Time utilization coefficient of the machine 2 Time utilization coefficient of the machine 1 Time utilization coefficient of the plant



It is apparent (even though paradoxical) that case “A”option leads to better results than case “B”

This can be explained observing that using the Q.S. Opt. approach, we loose the complete control of the system

If we used Glob. Opt., every d.o.f. (in past, present, and future) could potentially be modified in a single optimization, and all the integral constraints could beexactly evaluated

With Q.S. Opt., this is not possible (and unrealistic, as wecannot change the past, and the future is only estimated)

DiscussionDiscussion



Therefore, with the Q.S. Approach, becomes of the utmost importance how to impose integral constraints

If their enforcing is too hard, it can lead to differentchoices, perfectly logical in the Q.S. logic, but leading toworse results if considered over the period

Several tests confirmed this fact, leading us to search fora different and less critical technique...

Discussion (cont’d)Discussion (cont’d)



Case study: comparison between three solutionsCase study: comparison between three solutionsThe site is a National Health Service hospital, characterizedby the following parameters:Max thermal consumption : 460 kWtMax electrical consumption : 250 kWeSimulations of different possible solutions were run:

Capstone C30 Capstone C60 Turbec T100

Case 1 4 0 0

Case 2 0 4 0

Case 3 0 0 2



Simulation parametersSimulation parameters

Max number of CHPs: 4

Minimum time between CHP switch: 6h

For each type of CHP the following additional consumptionwere chosen:• during transients: 0.5 % of the difference of required electrical

power• during switch ons: 25 % of the rated consumption• during switch offs: 8 % of the rated consumption



Hourly behaviour of:

1. Yearly thermal load [kWh];

2. Yearly temperature [°C];

3. Electrical load over a forthnight [kWh].

Case study – site characterizationCase study – site characterization



Case 1 – Integral operational variablesCase 1 – Integral operational variables


Caso 1 4 0 0

Caso 2 0 4 0

Caso 3 0 0 2



Case 1 – Integral performance indicatorsCase 1 – Integral performance indicators

IRE : 30.8 %CASH FLOW: 33858 €BURNT FUEL IN BOILER: 743 MWhBURNT FUEL IN BOILER IN CHP: 1493 MWhFUEL SAVING: 665 MWh





Caso 1 4 0 0

Caso 2 0 4 0

Caso 3 0 0 2



An interesting development is about the setup of a different way to enforce the F.E.S.R. constraint

This must be done in order to have a good accuracy, butavoiding unphysical abort of optimization, and to avoidsolutions so constrained to be economically meaningless

Basically there are two ways to impose the F.E.S.R., and the control logic can switch from one to the other, according to the behaviour of optimization

The first results are encouraging, but they are notmature enough, yet

Future developmentsFuture developments



It is worth mentioning that the Q.S. approach, due to itsinherently low requirements, is excellent to build an online optimizer, and it is the logical choice to optimize a long operational period (for example, to assess the economicappeal of a particular co-generating plant)

To have a more reliable optimizer, in shorter periods(like one day, up to a fortnight) the Glob. Opt. should lead to better results, as in the case of online optimizers

Anyway it is of critical importance the quality of the estimates of fuel/electrical power/thermal power requested

Future developments (cont’d)Future developments (cont’d)



Future developments (cont’d)Future developments (cont’d)

We are working on the modelling of InternalCombustion Engines for CHP applications; therefore it is appearing a distinction between the recovery of thermal energy with HIGH and LOW energy content

We are also working to setup a defintion of FESR simpler to use (less constraining), but anywayfulfilling all operatioal constraints

techniques for quasi-static operating optimization of chp...

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