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Predictive Protective Control for Flexible Energy System
Proceedings, Proceedings, 15th 15th IFAC IFAC Conference Conference on on Programmable Devices and Embedded Systems Proceedings, 15th 15th IFAC and Conference on Systems Programmable Devices Embedded Proceedings, IFAC Conference on Available online at www.sciencedirect.com Ostrava, Republic, May 23-25, 2018 Programmable Devices Embedded Systems Ostrava, Czech Czech Republic, May 23-25,on 2018 Programmable Devices and Embedded Systems Proceedings, 15th IFAC and Conference Ostrava, Czech Czech Devices Republic, May 23-25, 2018 2018 Ostrava, Republic, May 23-25, Programmable and Embedded Systems Ostrava, Czech Republic, May 23-25, 2018
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IFAC PapersOnLine 51-6 (2018) 1–6
Predictive Predictive Predictive
Protective Control Protective Control Energy System Protective Control Energy System ∗ ∗∗ Energy Ozana, Pies, Ozana, S. S. ∗ System Pies, M. M. ∗∗
for for for
Flexible Flexible Flexible
∗∗ Ozana, S. S. ∗∗ Pies, Pies, M. M. ∗∗ Ozana, ∗ Department Engineering, Ozana,and S. Biomedical Pies, M. ∗∗ Department of of Cybernetics Cybernetics and Biomedical Engineering, Faculty Faculty of of Department of Cybernetics and Biomedical Engineering, Faculty Electrical Engineering Engineering andand Computer Science, VSB-Technical Department of Cybernetics Biomedical Engineering, Faculty of of Electrical and Computer Science, VSB-Technical ∗ Electrical and Computer Science, VSB-Technical University of Department of Cybernetics Biomedical Engineering, Faculty of Electrical Engineering Engineering andand Computer Science, VSB-Technical University of Ostrava, Ostrava, University ofCzech Ostrava, 17.listopadu 15, Ostrava, Republic (e-mail: Electrical Engineering and Computer Science, University of Ostrava, 17.listopadu 15, Ostrava, Czech RepublicVSB-Technical (e-mail: 17.listopadu Ostrava, Republic [email protected]). University Ostrava, 17.listopadu 15, 15, Ostrava,ofCzech Czech Republic (e-mail: (e-mail: [email protected]). ∗∗ [email protected]). ∗∗ Department of Cybernetics and Biomedical Engineering, 17.listopadu 15, Ostrava, Czech Republic (e-mail: Faculty [email protected]). Department of Cybernetics and Biomedical Engineering, Faculty of of ∗∗ ∗∗ Department of Cybernetics and Biomedical Engineering, Faculty Electrical Engineering and Computer Science, VSB-Technical [email protected]). Department of Cybernetics Biomedical Engineering, Faculty of of Electrical Engineering andand Computer Science, VSB-Technical ∗∗ Electrical Engineering andand Computer Science, VSB-Technical University of Department of Cybernetics Biomedical Engineering, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, Ostrava, of 17.listopadu 15, Ostrava,University Czech Republic (e-mail: [email protected]) Electrical15, Engineering and Computer Science,[email protected]) VSB-Technical University of Ostrava, Ostrava, 17.listopadu Ostrava, Czech Republic (e-mail: 17.listopadu 15, Ostrava, Czech Republic (e-mail: of Ostrava, 17.listopadu 15, Ostrava,University Czech Republic (e-mail: [email protected]) [email protected]) 17.listopadu 15, with Ostrava, Czech Republic (e-mail: Abstract: The The paper deals deals the predictive predictive control [email protected]) to flexible flexible cogeneration cogeneration energy energy Abstract: paper with the control applied to Abstract: The paper deals with the predictive control applied to energy system (FES). The FES was designed and developed by the POWER Abstract: TheThe paper deals the predictive control by applied to flexible flexible cogeneration cogeneration energy system (FES). FES waswith designed and developed the VITKOVICE VITKOVICE POWER ENGIENGIsystem (FES). The FES was designed and the POWER ENGINEERING joint-stock company and represents aa new solution decentralized cogeneration Abstract: The paper deals the predictive control applied toof cogeneration energy system (FES). The FES waswith designed and developed developed by the VITKOVICE VITKOVICE POWER ENGINEERING joint-stock company and represents new by solution offlexible decentralized cogeneration NEERING joint-stock company and represents a new solution of decentralized cogeneration energy sources. In FES, the heating medium is flue gas generated by combustion of a solid system (FES). The FES was designed and developed by the VITKOVICE POWER ENGINEERING joint-stock company and represents a new solution of decentralized cogeneration energy sources. In FES, the heating medium is flue gas generated by combustion of a solid fuel. fuel. energy sources. In the medium flue gas by combustion of aaPower solid The heated heated medium is company power gas, which is aais gas mixture of air air of and water steam. steam. Power gas NEERING joint-stock and represents a mixture new solution decentralized energy sources. In FES, FES, the heating heating medium is gas flue gas generated generated by combustion ofcogeneration solid fuel. fuel. The medium is power gas, which is of and water gas The heated medium is power gas, which is aais gas of and steam. gas is in exchanger led to gas To protect the main energy sources. In the FES, the heat heating medium flue gas of aPower solid heat fuel. The heated medium ismain power gas, which is and gas mixture of air air by andcombustion water steam. Power gas is superheated superheated in the main heat exchanger and ledmixture to generated gas turbines. turbines. Towater protect the main heat is superheated in heat exchanger and led to gas protect the main exchanger damage by overheating, novel predictive protective control based on the The heatedagainst medium ismain power gas, which isthe a gas of air andTo steam. Power gas is superheated in the the main heat exchanger and ledmixture to gas turbines. turbines. Towater protect the main heat exchanger against damage by overheating, the novel predictive protective control based onheat the exchanger against damage by overheating, the novel predictive protective control based on the mathematical model of exchanger was developed. The paper describes the principle, the design is superheated in the main heat exchanger and led to gas turbines. To protect the main heat exchanger against damage by overheating, the novel predictive protective control based on the mathematical model of exchanger was developed. The paper describes the principle, the design mathematical model of exchanger was The paper the principle, the design and simulation simulation of the the predictive protective method applied todescribes main heat exchanger of FES. exchanger against damage by overheating, the novel predictive protective control based on the mathematical model ofpredictive exchanger was developed. developed. The paperto describes theexchanger principle, the design and of protective method applied main heat of FES. and simulation of the predictive protective method applied to main heat exchanger of FES. mathematical exchangerprotective was developed. papertodescribes theexchanger principle, of the design and simulationmodel of theofpredictive methodThe applied main heat FES. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. and simulation of the control, predictive protective applied to main heat exchanger of FES. Keywords: Predictive control, systems withmethod distributed parameters, cogeneration energy Keywords: Predictive systems with distributed parameters, cogeneration energy Keywords: Predictive control, systems with distributed parameters, cogeneration energy systems, simulation. simulation. Keywords: Predictive control, systems with distributed parameters, cogeneration energy systems, systems, simulation. simulation. Keywords: Predictive control, systems with distributed parameters, cogeneration energy systems, systems, simulation. 1. INTRODUCTION INTRODUCTION In 1. In detail, detail, Fig. Fig. 11 shows shows aa combustion combustion chamber chamber 1 1 which which 1. INTRODUCTION INTRODUCTION In detail, shows combustion chamber 1 burns the Fig. fuel. 11Walls Walls ofaa the the combustion chamber have 1. In detail, Fig. showsof combustion chamber 1 which which burns the fuel. combustion chamber have burns the fuel. of combustion chamber have evaporative pressure water cooling. Water under pressure 1. INTRODUCTION In detail, 1Walls shows combustion chamber 1 which burns the Fig. fuel. Walls ofa the the combustion chamber have evaporative pressure water cooling. Water under pressure In this paper, the new design of predictive protective conIn this paper, the new design of predictive protective con- burns evaporative pressure water cooling. Water under pressure is supplied by pump 2. Generated water steam is injected the fuel. Walls of the combustion chamber have evaporative pressure water cooling. Water under pressure is supplied by pump 2. Generated water steam is injected In this paper, the new design of predictive protective control of the high temperature main heat exchanger (MHE) In paper, new designmain of predictive protective con- to trolthis of the highthe temperature heat exchanger (MHE) is supplied by pump 2. Generated water steam is injected the front mixer 3, where it is added to atmospheric air evaporative pressure water cooling. Water under pressure is supplied by pump 2. Generated water steam is injected to the front mixer 3, where it is added to atmospheric air trol of the the high temperature main heat (MHE) is MHE is basic part of the decentralized In this paper, the new design of predictive con- to trol of high temperature main heat exchanger (MHE) is discussed. discussed. MHE is the the basic part of exchanger theprotective decentralized the front mixer 3, where it is added to atmospheric air supplied to the power circuit by the compressor 4. Portion is supplied by pump 2. Generated water steam is injected to the front mixer 3, where it is added to atmospheric air supplied to the power circuit by the compressor 4. Portion is discussed. MHE is the basic part of the decentralized flexible energy cogeneration system (FES) with combined trol of the high temperature main heat (MHE) of is discussed. MHE is the basic part of exchanger thewith decentralized flexible energy cogeneration system (FES) combined supplied to the power circuit by the compressor 4. Portion the generated steam is available for the protective to the front mixer 3, where it is added to atmospheric air supplied to the power circuit by the compressor 4. Portion of the generated steam is available for the protective flexible energy cogeneration system (FES) with combined Brayton-Rankine cycle, see Jaluria et al. (2003). The prinis discussed. is the part of the decentralized flexible energyMHE cogeneration system with combined Brayton-Rankine cycle, seebasic Jaluria et(FES) al. (2003). The prin- supplied of the generated generated steam isMHE available for the protective protective predictive control of the 5, see below. Resulting to the power circuit by the compressor 4. Portion of the steam is available for the predictive control of the MHE 5, see below. Resulting Brayton-Rankine cycle, see Jaluria et al. (2003). The principle of FES is shown in Fig. 1. flexible system with combined Brayton-Rankine cycle,insee Jaluria et(FES) al. (2003). The prin- predictive ciple of energy FES is cogeneration shown Fig. 1. control of MHE 5, below. Resulting power gas enters MHE where it issee superheated by the the the gas generated steam available for the protective predictive controlMHE of the the MHE 5, is see below. Resulting power enters 55 is where it superheated by ciple of of FES FES is is shown shown insee Fig. 1. Brayton-Rankine cycle,in Jaluria et al. (2003). The prin- of ciple Fig. 1. power gas enters MHE 5 where it is superheated by the flue gas from combustion chamber. The superheated power predictive control of the MHE 5, see below. Resulting power gas enters MHE 5 where it is superheated by the flue gas from combustion chamber. The superheated power ciple of FES is shown in Fig. 1. flue gas from combustion chamber. The superheated power gas expands in the gas turbines 6 and 7. The compressor power enters 5chamber. where 6itThe is superheated by the flue gasgas from combustion superheated power gas expands in theMHE gas turbines and 7. The compressor gas expands in the gas turbines and 7.generator The compressor compressor turbine 66 drives the compressor The turbine flue gas from combustion chamber. power gas expands in the turbines 664. and 7. The turbine drives thegas compressor 4. The Thesuperheated generator turbine turbine 66the drives the compressor The turbine drives the asynchronous generator that is linked linked to the the gas expands in the turbines 64. 7.generator The compressor turbine drives thegas compressor 4. and The generator turbine 77 drives asynchronous generator 88 that is to 7turbine drives the asynchronous generator 8 that is linked to 50 Hz electric network. 6the drives the compressor 4. The generator 750drives asynchronous generator 8 that is linkedturbine to the the Hz electric network. 50 Hz electric network. 750 drives the asynchronous generator 8 that is linked to the Hz electric network. Residual heat heat that that power power gas gas contains contains after after the the decompresdecompresResidual 50 Hzinelectric network. Residual heat that power gas contains after the decompression the gas turbines is used to generate electricity in Residual heat power is gasused contains after theelectricity decompression in the gasthat turbines to generate in in the gas turbines is used to generate electricity in asion Rankine cycle. The heat exchanger 9 exploits residual Residual heat power gasused contains after theelectricity decompression in the gasthat turbines is to generate in a Rankine cycle. The heat exchanger 9 exploits residual aheat Rankine cycle. The heat exchanger 9 exploits residual flue gas for the preheating of the combustion sion inof the gas turbines is used to generate electricity in aheat Rankine cycle. The heat exchanger 9 exploits residual of flue gas for the preheating of the combustion heat of gas for the combustion air. Discharged combustion products of are cleaned in the the aheat Rankine The heatpreheating exchanger 9 exploits residual of flue fluecycle. gascombustion for the the preheating of the combustion air. Discharged products are cleaned in air. Discharged products are cleaned in purification 10. heat of flueplant gascombustion for the preheating combustion air. Discharged combustion products of arethe cleaned in the the purification plant 10. purification plant 10. air. Discharged combustion products are cleaned in purification plant 10. To support support the the development development of of FES, FES, VPE VPE built built an an the exTo expurification plant 10. To support the FES, an experimental in model To support FES the development development ofMathematical FES, VPE VPE built built an and experimental FES in 2009-2013. 2009-2013.of Mathematical model and perimental FES in 2009-2013. Mathematical model and some basic experimental information concerning this unit To support the development of FES, VPE built an experimental FES in 2009-2013. Mathematical model and some basic experimental information concerning this unit some basic experimental information concerning this unit were presented by Nevriva et al. (2011) and Vilimec et perimental FES in 2009-2013. Mathematical model and some basic experimental information concerning this unit were presented by Nevriva et al. (2011) and Vilimec et al. al. were presented by Nevriva et and Vilimec al. (2010). From the point of information view of (2011) control, FES differs from some basic experimental concerning thiset unit were presented bypoint Nevriva et al. al. (2011) and Vilimec et al. (2010). From the of view of control, FES differs from (2010). From the point of view of control, FES differs from the common cogeneration units in three important control were presented bypoint Nevriva et al. Vilimec et al. (2010). Fromcogeneration the of view ofin(2011) control, FES differs from the common units three and important control the common cogeneration units incontrol, threeof important control loops. In particular it is the the output (2010). From the point ofin FESFES differs from the common cogeneration units three control loops. In particular it of is view the control control ofimportant the FES output loops. In particular it the is units the control ofimportant the FES FES control output power, theparticular control ofit the power gas temperature at the the the common cogeneration in gas three loops. In is the control of the output power, the control of power temperature at power, the control of the power gas temperature at the input of turbines, and the protective control of the MHE loops. In particular it is the control of the FES output power, the control of the power gas temperature at the Fig. 1. The principle scheme of FES input of turbines, and the protective control of the MHE Fig. 1. The principle scheme of FES input of turbines, and the protective control of the MHE Fig. 1. The principle scheme of FES power, controland of the gas control temperature the input ofthe turbines, the power protective of theat MHE Fig. 1. The principle scheme of FES input of turbines, and the protective control of the MHE Fig. 1. The principle scheme of FES Copyright 2018 IFAC 1 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2018, IFAC (International Federation of Automatic Control) ∗ ∗ ∗ ∗
Copyright © 2018 IFAC 1 Peer review© of International Federation of Automatic Copyright 2018 IFAC 1 Copyright ©under 2018 responsibility IFAC 1 Control. 10.1016/j.ifacol.2018.07.120 Copyright © 2018 IFAC 1
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against overheating. Other parts of FES control system are similar to a conventional steam cogeneration energy sources, see Hladky et al. (2014). The paper describes the novel method of protective control of the MHE against damage by overheating. 2. CONTROL TASKS IN FES Changing the amount of fuel within FES makes it possible to change of both the heat and the supplied electrical power. In order to reach maximum effectiveness, the FES operates with very high temperature of power gas and flue gas. The power gas is superheated by flue gas in the MHE from 250 ◦ C to 850 ◦ C. The gases are represented by their state variables (pressure, flow rate, temperature and concentration of power gas). There are three adaptive control tasks associated with the MHE. The first control task is the change and control of the power generated by FES. The FES controller reduces/increases the amount of fuel and reduces/increases the production of air, steam, and flue gas.
Fig. 2. Block scheme of units of the main heat exchanger
surface of the MHE is realized from bundles of thin-walled tubes. Bundles of MHE units are made from different steels and alloys and have the different temperature limits. For each unit of the MHE there exists a certain limit. Every unit may be heated below its specific temperature limit. Temperatures of tubes are measured at the outputs of the units. The procedure has been validated at the experimental FES. The overheating of sections or units of the MHE results from uneven allocation of flow rate of flue gas along the MHE. This temporary anomaly can arise due to change of fuel and/or in case of power changes. The predictive protective control is the novel adaptive method that maintains temperature of tubes under their technological limits.
The main goal of the second control task is to maintain constant power gas temperature of about 850 ◦ C at the output of the MHE. The two gas turbines are fed by the heated power gas directly from the MHE. The turbines are designed for nominal pressure and temperature of the feed gas. Under operating conditions, the pressure and also the temperature of power gas (in a small range) varies with the generated power. The FES controller maintains the temperature of the power gas in the input of the turbines by changing the amount of the power gas at the input of the MHE. It is carried out by changing the speed of the compressor; it is changing the speed of the turbine which drives the compressor. Simultaneously it changes the amount of fuel to change the amount of flue gas and generated steam in order to maintain the concentration of power gas.
3. CONCEPT OF PREDICTIVE PROTECTIVE CONTROL (PPC) The basic motivation for the introduction of predictive protective control (PPC) is the same as regulation by PID controllers in particular loops. Yet the difference lies in the concept. The use of PID control for inner fast loops inevitably leads to some overshoot of process variables. In other words, a certain exceeding of temperature limit occurs over a longer or shorter time within individual component of the superheater approximately between 10 to 15 % (assuming a well-tuned controllers) which is undesirable condition, and the temperature stabilizes below this limit value after a certain amount of time, see Nowakova et al. (2012).
The third control task is the protective control. MHE is an expensive part of the FES. The protective control keeps the temperature of the wall of MHE heat transfer surface below the specified temperature limit. The limit depends on the materials used for construction of MHE. This control task is described in this paper in more detail. The heat exchanger is a system with distributed parameters. Its dynamics can be characterized by the dominant time constant. The dominant time constant of the FES MHE is about 10000 s. It is difficult to control the temperature of the wall of the heat transfer surface along their length under such a condition. To allow sufficiently good implementation of the above control task the exchanger was technologically divided into 5 units (UNIT0-UNIT4), see Fig. 2.
The purpose of the protective predictive control is that such exceedances do not occur at all. The mechanism by which this is achieved is demonstrated in the presented case study conducted at two components of MHE, namely UNIT1 and UNIT2. Predictive regulation proposed for FES technology unit uses a process model to calculate future intervention in terms of minimizing a cost function over a finite control horizon.
Each of the units has a dominant time constant of about 2000 s. Units are connected in series. Cool power gas enters the first unit. The superheated power gas is lead from the 5th unit towards turbines, see Filipova et al. (2016). Main heat exchanger is designed as a counter flow. Hot flue gas enters the 5th unit. The cooled flue gas is lead away from the first unit. Temperature of the heat exchanger’s wall that separates the flue gas and power gas therefore increases along the way, starting from the first unit to the fifth unit. The wall of heat transfer
The optimization criterion is a function which itself accumulates all the requirements of the system behavior, such as energy minimization, maximizing the efficiency and the like. Since the partial demands contradict each other, the resulting control design becomes a compromise that fulfills all the prescribed requirements with a minimum penalty of individual contributions to the cost function. 2
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4. IMPLEMENTATION OF PREDICTIVE PROTECTIVE CONTROL (PPC) ON FES
3
ding to the results of the optimization procedure after its completion it immediately prescribes and sets new values of opening positions of the valves RVx at which no exceeding of temperatures will occur. If the disturbance signal subsides at any time and the level of the signal returns to the original value or to any other steady state of the flue gas temperature, this change is evaluated and in case of increasing or decreasing of the predefined percentage value the PPC algorithm is reactivated and it may cause the valves to be set to original or newly computed positions. The control scheme is finally complemented by a block denoted by F, which is in charge of the so-called bumpless switching between PPC and PID control strategies (signals uP P C and uP ID ). This block contains a simple mechanism with the 1st order dynamics which ensures equality of uP P C and uP ID even though one of them is currently inactive (not interfering at the moment). Integration of PPC into existing technology is shown in Fig. 4, showing particular example for UNIT1, the same layout would apply for other exchangers. Technical implementation of the PPC algorithm can use standard hardware and software tools used in industrial automation, such as industrial PC or PLC. In case of using programmable logic controllers the implementation of this task would require transformation of that algorithm to the PLC which is very difficult and complicated task. At the same time, however, the proposed PPC algorithm is an extension of the standard PID control functionality, and in case of any failure or malfunction this situation would not endanger functionality of the entire FES technology. Thus, it would still be true that any wall overheating would be sufficiently compensated by the respective PID control, but it would not be possible to prevent such situations in advance, see Pies et al. (2017).
Recall that the main reason for the proposal of PPC is the requirement for wall temperature not to exceed a given limit at any point of the technology consisting of the heat exchangers. It is supposed that a possible overshooting of the temperature may occur as a result of two situations leading to the change in the physical quantities within the system, considered as disturbance signals in terms of control theory: • change in the power The primary cause of this fault is a speed change of the grate which secondarily leads to the change of the flue gas temperature, and ultimately (in a case of increasing the flue gas temperature) may cause breaking of temperature limit within the wall in a particular location of one of the exchangers. The information about emergence of this disturbance will be available timely (in minutes). The trigger signal for PPC optimization algorithm is a percentage increase or decrease in the current value of the flue gas temperature compared to the previous steady state, for example by 10 %. • change in the calorific value This disturbance signal has a faster dynamics than the change in the performance. Information about this disturbance will not be at disposal in advance. As in the previous case, the trigger signal for PPC optimization algorithm will be a percentage change in the current values of the flue gas temperature compared to the previous stable state, for example by 10 %. The association between the disturbance signals, flue gas temperature, and trigger signals is shown in Fig. 3.
(1)
UNIT1
T2 (L,t)
(1)
T2 (0,t)
(1)
(1)
T1 (L,t)
T1 (0,t)
Tmix1 MIX1
T
T
MAX
Tw1HLIM
Fig. 3. Trigger signal depending on flue gas temperature
SAT high low=0
Trigger signals thus launch PPC optimization procedure. The proposed solution would of course allow timescheduled repetition with a certain period. For the operation of the PPC algorithm it is important to assume that once disturbance occurs and the trigger condition is met, thus after a sufficient increase in flue gas temperature, the new level of this variable persists permanently. Based on the dynamic model, the future steady state of the entire model is calculated, and it is evaluated whether there will or will not be overshooting in the temperature in future at any point in the technological units within heat exchangers. If not, PPC control is not activated (P P CEN ABLE = OF F , see Fig. 4, and only standard lower regulatory levels remain active (outer loop and inner loops with PID controllers). If so, PPC algorithm is activated (P P CEN ABLE = ON , see Fig. 4), and accor-
R11
F
R12
uPID PPC ENABLE
RV1
uPPC STEAM
Fig. 4. Integrating PPC into current technology, illustration for UNIT1
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5. CASE STUDY: PREDICTIVE PROTECTIVE CONTROL OF FES
efficiency of the technology is achieved when the entire amount of steam passes through front mixer MIX0 only, while RVx valves remain closed. Under these ideal circumstances the steam is gradually heated up along its way through particular units and it is not unnecessarily cooled down due to the possible opening of valves RVx. Any action interventions are therefore desirable to be performed in “proximity” of MIX0, such as MIX0 itself + MIX1, optionally at next couple (MIX2 + MIX1) etc., assuming that the action can always be performed via a certain pair of adjacent valves (on adjacent mixers).
This case study serves as a basis for the preparation and follow-up solution of optimization problem demonstrating the PPC control mechanism. The calculation is performed for UNIT1 and UNIT2. Action interventions are calculated for valves RV1 and RV2 which inject steam into the mixers MIX1 and MIX2. Here is the list and meaning of the variables used for this purpose: k1 . . . optimization variable (dimensionless parameter between 0 − 1) representing valve position of RV1
Another important requirement is the minimum temperature gradient at individual mixers, thus a minimum temperature difference marked as ∆T mix2 (corresponding mixer MIX2) in presented case study. From technological point of view these requirements mean that material stress is minimized (in case of repeated cooling and heating), and it ensures good energy balance, because due to the nonlinear dependencies of heat transfer coefficients repetition of heating and cooling at subsequent unit could worsen energy balance compared to the situation without repeating cooling and heating processes.
k2 . . . optimization variable (dimensionless parameter between 0 − 1) representing valve position of RV2
T w1HLIM . . . temperature limit, maximal allowable value of the wall temperature, must not be exceeded at any point within UNIT1 T w2HLIM . . . temperature limit, maximal allowable value of the wall temperature, must not be exceeded at any point within UNIT2 T w1max . . . maximal value of the entire temperature profile of the wall of UNIT1 computed by the model and then compared to prescribed maximal allowable value T w1HLIM ; their difference then contributes to the overall cost function with the term in the form of equation (1): (1)
∆T w1max = maxT1 (L, T ) − T w1HLIM
The third requirement is of course no exceeding of the temperature limits in the specific case study marked as T w1HLIM (within UNIT1) and T w2HLIM (within UNIT2). The cost function can be described by equation (3). J = 0.1 · ∆T mix2 + 100 · ∆T w1 + 100 · ∆T w2 (3) where ∆T w1 = T 1max−T w1HLIM at UNIT1, see Fig. 4. Similarly, at UNIT2, ∆T w2 = T w2max − T w2HLIM . The cost function can be expressed in general form of equation (4) for any pair of adjacent mixers: (4) J = w1 · ∆T mixN + w2 · ∆T wM + w3 · ∆T wN where M and N are increasing indexes (order) of adjacent mixers, N=M+1, and w1 ,w2 , w3 represent weight coefficients. The first requirement is interpreted in the way that algorithm determines which pair of valves can ensure prevention from future temperature overshooting. Once a particular pair of the valves is determined, the algorithms continues to compute two specific values representing the optimal valve positions. Decision on the pairs of the valves is carried out according to the following decision tree (with extra RV5) shown in Fig. 6:
(1)
T w2max . . . maximal value of the entire temperature profile of the wall of UNIT2 computed by the model and then compared to prescribed maximal allowable value T w2HLIM ; their difference then contributes to the overall cost function with the term in the form of equation (2): (2)
∆T w2max = maxT1 (L, T ) − T w2HLIM
(2)
∆T mix2 . . . temperature loss (difference) at MIX2 being penalized in the cost function ϑ . . . auxiliary optimization parameter representing relation between positions of RV1 and RV2 valves (ϑ = 100 %: RV1 fully open, RV2 closed, k1 = 1, k2 = 0) Scheme of the situation at UNIT1 and UNIT2 is shown in Fig. 5:
The beginning works of the development of this algorithm included tests of fmincon function (part of Optimization Toolbox for Matlab). This function is intended for general optimization calculations where the cost function and constraints can be nonlinear, having arbitrary number of unknown optimization variables. This function could be used for the jobs not necessarily limited to adjacent pairs of valves only, being capable of determination of optimal positions for all the valves. Optimization job applied for FES technology however does not require such complexity. The use of fmin function also disproportionately increases the computing time, and there is no guarantee of the maximal number of performed iterations (this can be different each time the procedure is started) and thus there is no guarantee of amount of maximum computing time necessary to obtain the results. Therefore, the method of solving this optimization problem was changed as follows: Opening of each of two adjacent valves is represented by
Fig. 5. Situation scheme for UNIT1, UNIT2 5.1 Setting up the Cost Function The first requirement for the cost function takes into account the highest possible efficiency of cascade of exchangers. It can be interpreted in the way that the greatest 4
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5
Fig. 7. Introduction of gains representing valve positions a new variable ϑ [%] is introduced, representing relation between positions of RV1 and RV2 as follows: • ϑ = 100 %: valve RV1 fully open, RV2 closed (k1 = 1, k2 = 0) • ϑ = 0 %: valve RV1 closed, RV2 fully open (k1 = 0, k2 = 1) Simulation experiments have been performed for ϑ in the range of 100, 0 % decreasing by 10%, see Tab. 1. For ϑ = 100 % the job corresponds to the steady state prescribed by static heat computation assigned by provider of the technology.
Fig. 6. Decision tree to determine a pair of action valves a real number between 0 − 1. This interval is first divided into 10 equal sections in which 11 iterations is performed corresponding to the values of the auxiliary variable ϑ - see case studies below (first stage of the calculation). Based on found results ϑ, representing minimum of the objective function is specified. Subsequently there comes the second phase of the calculation which specifies auxiliary calculation interval so that two points from previous stage are considered for further calculations, located to the left and to the right of the found minimum. This interval is again divided into 10 equal sections where it again performs another 11 iterations corresponding to the values of the auxiliary variable ϑ. This is then repeated for the third time which is also the last stage of the calculation. This three-phase mechanism has the following advantages:
Table 1. Results of Simulation Experiments ϑ [%] 100 90 80 70 60 50 40 30 20 10 0
• it ensures sufficient entire achieved accuracy of 0.4 % when searching for optimal value, particularly 10 %, 2 % and 0.4 % during particular stages • it always ensures the same and fixed number of iterations - 33 altogether • it guarantees maximal computing time for a given computation mean (i.e. PC) to complete given optimization job
k1 [−] 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
k2 [−] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
T w1max [◦ C] 476.50 477.00 477.50 478.00 478.40 478.90 479.40 479.90 480.40 480.90 481.40
T w2max [◦ C] 643.20 642.50 641.90 641.20 640.60 639.90 639.20 638.60 637.90 637.20 636.50
∆T mix2 [◦ C] 0.00 1.92 3.85 5.76 7.75 9.71 11.67 13.66 15.70 17.73 19.76
In order to demonstrate PPC functionality the below mentioned restrictions are considered, particularly temperature limits that must not be exceeded at any time and point for both analyzed units. The following values of T w1max, T w2max,∆T mix2 have been indicated for particular steps of algorithm: • Temperature wall limit of UNIT1: T w1HLIM = 479.3 ◦ C (if higher value assigned the result of optimization is the same because there is no exceeding at UNIT1), • Temperature wall limit of UNIT2: T w2HLIM = 639.5 ◦ C.
5.2 Simulation Experiment This case study analyzes situation under which the flue gas temperature is changed from 840 ◦ C to 854.9 ◦ C. In order to perform simulations, flow amounts through RV1 and RV2 valves are represented by parameters (gains) referred to as k1 and k2 , see Fig. 7.
Tab. 1 helps to determine that the desired optimal value ϑ∗ protecting the technology against overheating of unit walls lies between 40 − 50 % (Grey lines of table 1).
5.3 Simulation results
Progress of particular stages of the calculation is documented in Fig. 8, Fig. 9 and Fig. 10. Parameters of the 1st stage of computation: overall achieved accuracy 10%, 11 iterations done, elapsed time 98 seconds. Parameters of the 2nd stage of computation: overall achieved accuracy 2%, 11 iterations done, elapsed time 98 seconds. Parameters of the
The steam is brought to mixers MIX1 and MIX2 with its amount divided in a certain ratio corresponding to k1 and k2 . Because the entire amount of the steam is always consumed, k1 + k2 = 1 holds good. For simulation purpose 5
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Mathematical model describes FES comprising units that can be separated into two groups. In the first group, there are the units where the movement of power gas along the longitudinal space axis can be neglected. The group includes the compressor, mixers, water injectors, safety valves, the compressor turbine, the generator turbine, the asynchronous generator, and controllers. These units are treated as systems with lumped parameters. In the second group there are the evaporator drum boiler, headers, pipelines and heat exchangers. Here, the dynamics of movement of media along the space axis plays the important role. These units are typical systems with distributed parameters. In mathematical model, every unit with lumped parameters is described by a set of ordinary nonlinear differential equations. Every unit with distributed parameters is described by a set of partial nonlinear differential equations. Mathematical model of the simulated PPC task consists of models of water and steam injectors, safety valves, controllers, headers, pipelines and MHE segments.
400
J(k1) 300
200
J(k*1)
100
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 t
Fig. 8. Optimal value k1∗ after the 1st stage of algorithm 50
J(k1) 40 30 20
J(k*1)
10 0 0.3
0.32
0.34
0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5 t
ACKNOWLEDGEMENTS
Fig. 9. Optimal value k1∗ after the 2nd stage of algorithm
This work was supported by the project SP2018/160, Development of algorithms and systems for control, measurement and safety applications IV” of Student Grant System, VSB-TU Ostrava. This work was supported by the European Regional Development Fund in the Research Centre of Advanced Mechatronic Systems project, project number CZ.02.1.01/0.0/0.0/16 019/0000867 within the Operational Programme Research, Development and Education.
10
J(k1) 8 6
J(k*1)
4 2 0 0.42
0.425
0.43
0.435
0.44
0.445
0.45
0.455
0.46
0.465 t
Fig. 10. Optimal value k1∗ after the 3rd stage of algorithm
REFERENCES
rd
3 stage of computation: overall achieved accuracy 0.3 %, 11 iterations done, elapsed time 98 seconds.
FILIPOVA, B., NEVRIVA, P., PIES, M. The Temperature Time Responses of the Heat Exchanger Equipped by the Protective Control. IFAC-PapersOnLine. 2016, vol. 49, iss. 25, pp. 487–492. ISSN 2405-8963. HLADKY, V., BIELEK, R. Modelling and control of thermal system. Advances in Electrical and Electronic Engineering. 2014, vol. 12, iss. 2, pp. 103–110. ISSN 1804-3119. JALURIA, Y., TORRANCE, K. E. Computational Heat Transfer. Second edition. New York: Taylor & Francis, 2003. ISBN 1-56032-477-5, ISBN 1-56032-478-3. NEVRIVA, P., OZANA, S., PIES, M. Simulation of power plant superheater using advanced simulink capabilities. International Journal of Circuits, Systems and Signal Processing. 2011, vol. 5, iss. 1, pp. 86–93. ISSN 19984464. NOWAKOVA, J., POKORNY, M. On PID controller design using knowledge based fuzzy system. Advances in Electrical and Electronic Engineering. 2012, vol. 12, iss. 2, pp. 22–27. PIES, M., FILIPOVA, B., NEVRIVA, P. The control of the output power gas temperature at the heat exchanger. In: Advances in Intelligent Systems and Computing, 527. Cham: Springer, 2017, pp. 114–125. ISBN 978-3-31947363-5. VILIMEC, L., STAREK, K. Power production process with gas turbine from solid fuel and waste heat and the equipment for the performing of this process. US Patent No. US20100199631, 2010.
Interpretation of found value: Optimal value k1∗ = 0.44 corresponds to ϑ = 44[%]. As k1 + k2 = 1, then k2∗ = 0.56. These results introduced in this study are easy to interpret in this way: If the positions of the valves RV1 and RV2 bringing the steam into mixers MIX1 and MIX2 are set to k1∗ and k2∗ , then PPC algorithm guarantees that there will be no temperature overshoot at the walls of UNIT1 and UNIT2 in future at any time and point, supposing persisting step change in the flue gas (from 840 ◦ C to 854.9 ◦ C). 6. CONCLUSION The predictive protective control predicts the behavior of MHE over a given time horizon and it calculates the predictive protective control action. The predictive algorithm is based on mathematical model of MHE. At actual FES, the PPC will run in real time and will communicate with FES technology. At present, the PPC algorithm and software is tested off-line using the techniques of computer simulation. The MHE is activated by simulated inputs. To simulate the PPC task the mathematical model of the experimental FES has been used, while parameters of the mathematical model of the experimental FES were adopted for 110 MW. 6
ScienceDirect
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Predictive Predictive Predictive
Protective Control Protective Control Energy System Protective Control Energy System ∗ ∗∗ Energy Ozana, Pies, Ozana, S. S. ∗ System Pies, M. M. ∗∗
for for for
Flexible Flexible Flexible
∗∗ Ozana, S. S. ∗∗ Pies, Pies, M. M. ∗∗ Ozana, ∗ Department Engineering, Ozana,and S. Biomedical Pies, M. ∗∗ Department of of Cybernetics Cybernetics and Biomedical Engineering, Faculty Faculty of of Department of Cybernetics and Biomedical Engineering, Faculty Electrical Engineering Engineering andand Computer Science, VSB-Technical Department of Cybernetics Biomedical Engineering, Faculty of of Electrical and Computer Science, VSB-Technical ∗ Electrical and Computer Science, VSB-Technical University of Department of Cybernetics Biomedical Engineering, Faculty of Electrical Engineering Engineering andand Computer Science, VSB-Technical University of Ostrava, Ostrava, University ofCzech Ostrava, 17.listopadu 15, Ostrava, Republic (e-mail: Electrical Engineering and Computer Science, University of Ostrava, 17.listopadu 15, Ostrava, Czech RepublicVSB-Technical (e-mail: 17.listopadu Ostrava, Republic [email protected]). University Ostrava, 17.listopadu 15, 15, Ostrava,ofCzech Czech Republic (e-mail: (e-mail: [email protected]). ∗∗ [email protected]). ∗∗ Department of Cybernetics and Biomedical Engineering, 17.listopadu 15, Ostrava, Czech Republic (e-mail: Faculty [email protected]). Department of Cybernetics and Biomedical Engineering, Faculty of of ∗∗ ∗∗ Department of Cybernetics and Biomedical Engineering, Faculty Electrical Engineering and Computer Science, VSB-Technical [email protected]). Department of Cybernetics Biomedical Engineering, Faculty of of Electrical Engineering andand Computer Science, VSB-Technical ∗∗ Electrical Engineering andand Computer Science, VSB-Technical University of Department of Cybernetics Biomedical Engineering, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, Ostrava, of 17.listopadu 15, Ostrava,University Czech Republic (e-mail: [email protected]) Electrical15, Engineering and Computer Science,[email protected]) VSB-Technical University of Ostrava, Ostrava, 17.listopadu Ostrava, Czech Republic (e-mail: 17.listopadu 15, Ostrava, Czech Republic (e-mail: of Ostrava, 17.listopadu 15, Ostrava,University Czech Republic (e-mail: [email protected]) [email protected]) 17.listopadu 15, with Ostrava, Czech Republic (e-mail: Abstract: The The paper deals deals the predictive predictive control [email protected]) to flexible flexible cogeneration cogeneration energy energy Abstract: paper with the control applied to Abstract: The paper deals with the predictive control applied to energy system (FES). The FES was designed and developed by the POWER Abstract: TheThe paper deals the predictive control by applied to flexible flexible cogeneration cogeneration energy system (FES). FES waswith designed and developed the VITKOVICE VITKOVICE POWER ENGIENGIsystem (FES). The FES was designed and the POWER ENGINEERING joint-stock company and represents aa new solution decentralized cogeneration Abstract: The paper deals the predictive control applied toof cogeneration energy system (FES). The FES waswith designed and developed developed by the VITKOVICE VITKOVICE POWER ENGINEERING joint-stock company and represents new by solution offlexible decentralized cogeneration NEERING joint-stock company and represents a new solution of decentralized cogeneration energy sources. In FES, the heating medium is flue gas generated by combustion of a solid system (FES). The FES was designed and developed by the VITKOVICE POWER ENGINEERING joint-stock company and represents a new solution of decentralized cogeneration energy sources. In FES, the heating medium is flue gas generated by combustion of a solid fuel. fuel. energy sources. In the medium flue gas by combustion of aaPower solid The heated heated medium is company power gas, which is aais gas mixture of air air of and water steam. steam. Power gas NEERING joint-stock and represents a mixture new solution decentralized energy sources. In FES, FES, the heating heating medium is gas flue gas generated generated by combustion ofcogeneration solid fuel. fuel. The medium is power gas, which is of and water gas The heated medium is power gas, which is aais gas of and steam. gas is in exchanger led to gas To protect the main energy sources. In the FES, the heat heating medium flue gas of aPower solid heat fuel. The heated medium ismain power gas, which is and gas mixture of air air by andcombustion water steam. Power gas is superheated superheated in the main heat exchanger and ledmixture to generated gas turbines. turbines. Towater protect the main heat is superheated in heat exchanger and led to gas protect the main exchanger damage by overheating, novel predictive protective control based on the The heatedagainst medium ismain power gas, which isthe a gas of air andTo steam. Power gas is superheated in the the main heat exchanger and ledmixture to gas turbines. turbines. Towater protect the main heat exchanger against damage by overheating, the novel predictive protective control based onheat the exchanger against damage by overheating, the novel predictive protective control based on the mathematical model of exchanger was developed. The paper describes the principle, the design is superheated in the main heat exchanger and led to gas turbines. To protect the main heat exchanger against damage by overheating, the novel predictive protective control based on the mathematical model of exchanger was developed. The paper describes the principle, the design mathematical model of exchanger was The paper the principle, the design and simulation simulation of the the predictive protective method applied todescribes main heat exchanger of FES. exchanger against damage by overheating, the novel predictive protective control based on the mathematical model ofpredictive exchanger was developed. developed. The paperto describes theexchanger principle, the design and of protective method applied main heat of FES. and simulation of the predictive protective method applied to main heat exchanger of FES. mathematical exchangerprotective was developed. papertodescribes theexchanger principle, of the design and simulationmodel of theofpredictive methodThe applied main heat FES. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. and simulation of the control, predictive protective applied to main heat exchanger of FES. Keywords: Predictive control, systems withmethod distributed parameters, cogeneration energy Keywords: Predictive systems with distributed parameters, cogeneration energy Keywords: Predictive control, systems with distributed parameters, cogeneration energy systems, simulation. simulation. Keywords: Predictive control, systems with distributed parameters, cogeneration energy systems, systems, simulation. simulation. Keywords: Predictive control, systems with distributed parameters, cogeneration energy systems, systems, simulation. 1. INTRODUCTION INTRODUCTION In 1. In detail, detail, Fig. Fig. 11 shows shows aa combustion combustion chamber chamber 1 1 which which 1. INTRODUCTION INTRODUCTION In detail, shows combustion chamber 1 burns the Fig. fuel. 11Walls Walls ofaa the the combustion chamber have 1. In detail, Fig. showsof combustion chamber 1 which which burns the fuel. combustion chamber have burns the fuel. of combustion chamber have evaporative pressure water cooling. Water under pressure 1. INTRODUCTION In detail, 1Walls shows combustion chamber 1 which burns the Fig. fuel. Walls ofa the the combustion chamber have evaporative pressure water cooling. Water under pressure In this paper, the new design of predictive protective conIn this paper, the new design of predictive protective con- burns evaporative pressure water cooling. Water under pressure is supplied by pump 2. Generated water steam is injected the fuel. Walls of the combustion chamber have evaporative pressure water cooling. Water under pressure is supplied by pump 2. Generated water steam is injected In this paper, the new design of predictive protective control of the high temperature main heat exchanger (MHE) In paper, new designmain of predictive protective con- to trolthis of the highthe temperature heat exchanger (MHE) is supplied by pump 2. Generated water steam is injected the front mixer 3, where it is added to atmospheric air evaporative pressure water cooling. Water under pressure is supplied by pump 2. Generated water steam is injected to the front mixer 3, where it is added to atmospheric air trol of the the high temperature main heat (MHE) is MHE is basic part of the decentralized In this paper, the new design of predictive con- to trol of high temperature main heat exchanger (MHE) is discussed. discussed. MHE is the the basic part of exchanger theprotective decentralized the front mixer 3, where it is added to atmospheric air supplied to the power circuit by the compressor 4. Portion is supplied by pump 2. Generated water steam is injected to the front mixer 3, where it is added to atmospheric air supplied to the power circuit by the compressor 4. Portion is discussed. MHE is the basic part of the decentralized flexible energy cogeneration system (FES) with combined trol of the high temperature main heat (MHE) of is discussed. MHE is the basic part of exchanger thewith decentralized flexible energy cogeneration system (FES) combined supplied to the power circuit by the compressor 4. Portion the generated steam is available for the protective to the front mixer 3, where it is added to atmospheric air supplied to the power circuit by the compressor 4. Portion of the generated steam is available for the protective flexible energy cogeneration system (FES) with combined Brayton-Rankine cycle, see Jaluria et al. (2003). The prinis discussed. is the part of the decentralized flexible energyMHE cogeneration system with combined Brayton-Rankine cycle, seebasic Jaluria et(FES) al. (2003). The prin- supplied of the generated generated steam isMHE available for the protective protective predictive control of the 5, see below. Resulting to the power circuit by the compressor 4. Portion of the steam is available for the predictive control of the MHE 5, see below. Resulting Brayton-Rankine cycle, see Jaluria et al. (2003). The principle of FES is shown in Fig. 1. flexible system with combined Brayton-Rankine cycle,insee Jaluria et(FES) al. (2003). The prin- predictive ciple of energy FES is cogeneration shown Fig. 1. control of MHE 5, below. Resulting power gas enters MHE where it issee superheated by the the the gas generated steam available for the protective predictive controlMHE of the the MHE 5, is see below. Resulting power enters 55 is where it superheated by ciple of of FES FES is is shown shown insee Fig. 1. Brayton-Rankine cycle,in Jaluria et al. (2003). The prin- of ciple Fig. 1. power gas enters MHE 5 where it is superheated by the flue gas from combustion chamber. The superheated power predictive control of the MHE 5, see below. Resulting power gas enters MHE 5 where it is superheated by the flue gas from combustion chamber. The superheated power ciple of FES is shown in Fig. 1. flue gas from combustion chamber. The superheated power gas expands in the gas turbines 6 and 7. The compressor power enters 5chamber. where 6itThe is superheated by the flue gasgas from combustion superheated power gas expands in theMHE gas turbines and 7. The compressor gas expands in the gas turbines and 7.generator The compressor compressor turbine 66 drives the compressor The turbine flue gas from combustion chamber. power gas expands in the turbines 664. and 7. The turbine drives thegas compressor 4. The Thesuperheated generator turbine turbine 66the drives the compressor The turbine drives the asynchronous generator that is linked linked to the the gas expands in the turbines 64. 7.generator The compressor turbine drives thegas compressor 4. and The generator turbine 77 drives asynchronous generator 88 that is to 7turbine drives the asynchronous generator 8 that is linked to 50 Hz electric network. 6the drives the compressor 4. The generator 750drives asynchronous generator 8 that is linkedturbine to the the Hz electric network. 50 Hz electric network. 750 drives the asynchronous generator 8 that is linked to the Hz electric network. Residual heat heat that that power power gas gas contains contains after after the the decompresdecompresResidual 50 Hzinelectric network. Residual heat that power gas contains after the decompression the gas turbines is used to generate electricity in Residual heat power is gasused contains after theelectricity decompression in the gasthat turbines to generate in in the gas turbines is used to generate electricity in asion Rankine cycle. The heat exchanger 9 exploits residual Residual heat power gasused contains after theelectricity decompression in the gasthat turbines is to generate in a Rankine cycle. The heat exchanger 9 exploits residual aheat Rankine cycle. The heat exchanger 9 exploits residual flue gas for the preheating of the combustion sion inof the gas turbines is used to generate electricity in aheat Rankine cycle. The heat exchanger 9 exploits residual of flue gas for the preheating of the combustion heat of gas for the combustion air. Discharged combustion products of are cleaned in the the aheat Rankine The heatpreheating exchanger 9 exploits residual of flue fluecycle. gascombustion for the the preheating of the combustion air. Discharged products are cleaned in air. Discharged products are cleaned in purification 10. heat of flueplant gascombustion for the preheating combustion air. Discharged combustion products of arethe cleaned in the the purification plant 10. purification plant 10. air. Discharged combustion products are cleaned in purification plant 10. To support support the the development development of of FES, FES, VPE VPE built built an an the exTo expurification plant 10. To support the FES, an experimental in model To support FES the development development ofMathematical FES, VPE VPE built built an and experimental FES in 2009-2013. 2009-2013.of Mathematical model and perimental FES in 2009-2013. Mathematical model and some basic experimental information concerning this unit To support the development of FES, VPE built an experimental FES in 2009-2013. Mathematical model and some basic experimental information concerning this unit some basic experimental information concerning this unit were presented by Nevriva et al. (2011) and Vilimec et perimental FES in 2009-2013. Mathematical model and some basic experimental information concerning this unit were presented by Nevriva et al. (2011) and Vilimec et al. al. were presented by Nevriva et and Vilimec al. (2010). From the point of information view of (2011) control, FES differs from some basic experimental concerning thiset unit were presented bypoint Nevriva et al. al. (2011) and Vilimec et al. (2010). From the of view of control, FES differs from (2010). From the point of view of control, FES differs from the common cogeneration units in three important control were presented bypoint Nevriva et al. Vilimec et al. (2010). Fromcogeneration the of view ofin(2011) control, FES differs from the common units three and important control the common cogeneration units incontrol, threeof important control loops. In particular it is the the output (2010). From the point ofin FESFES differs from the common cogeneration units three control loops. In particular it of is view the control control ofimportant the FES output loops. In particular it the is units the control ofimportant the FES FES control output power, theparticular control ofit the power gas temperature at the the the common cogeneration in gas three loops. In is the control of the output power, the control of power temperature at power, the control of the power gas temperature at the input of turbines, and the protective control of the MHE loops. In particular it is the control of the FES output power, the control of the power gas temperature at the Fig. 1. The principle scheme of FES input of turbines, and the protective control of the MHE Fig. 1. The principle scheme of FES input of turbines, and the protective control of the MHE Fig. 1. The principle scheme of FES power, controland of the gas control temperature the input ofthe turbines, the power protective of theat MHE Fig. 1. The principle scheme of FES input of turbines, and the protective control of the MHE Fig. 1. The principle scheme of FES Copyright 2018 IFAC 1 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2018, IFAC (International Federation of Automatic Control) ∗ ∗ ∗ ∗
Copyright © 2018 IFAC 1 Peer review© of International Federation of Automatic Copyright 2018 IFAC 1 Copyright ©under 2018 responsibility IFAC 1 Control. 10.1016/j.ifacol.2018.07.120 Copyright © 2018 IFAC 1
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against overheating. Other parts of FES control system are similar to a conventional steam cogeneration energy sources, see Hladky et al. (2014). The paper describes the novel method of protective control of the MHE against damage by overheating. 2. CONTROL TASKS IN FES Changing the amount of fuel within FES makes it possible to change of both the heat and the supplied electrical power. In order to reach maximum effectiveness, the FES operates with very high temperature of power gas and flue gas. The power gas is superheated by flue gas in the MHE from 250 ◦ C to 850 ◦ C. The gases are represented by their state variables (pressure, flow rate, temperature and concentration of power gas). There are three adaptive control tasks associated with the MHE. The first control task is the change and control of the power generated by FES. The FES controller reduces/increases the amount of fuel and reduces/increases the production of air, steam, and flue gas.
Fig. 2. Block scheme of units of the main heat exchanger
surface of the MHE is realized from bundles of thin-walled tubes. Bundles of MHE units are made from different steels and alloys and have the different temperature limits. For each unit of the MHE there exists a certain limit. Every unit may be heated below its specific temperature limit. Temperatures of tubes are measured at the outputs of the units. The procedure has been validated at the experimental FES. The overheating of sections or units of the MHE results from uneven allocation of flow rate of flue gas along the MHE. This temporary anomaly can arise due to change of fuel and/or in case of power changes. The predictive protective control is the novel adaptive method that maintains temperature of tubes under their technological limits.
The main goal of the second control task is to maintain constant power gas temperature of about 850 ◦ C at the output of the MHE. The two gas turbines are fed by the heated power gas directly from the MHE. The turbines are designed for nominal pressure and temperature of the feed gas. Under operating conditions, the pressure and also the temperature of power gas (in a small range) varies with the generated power. The FES controller maintains the temperature of the power gas in the input of the turbines by changing the amount of the power gas at the input of the MHE. It is carried out by changing the speed of the compressor; it is changing the speed of the turbine which drives the compressor. Simultaneously it changes the amount of fuel to change the amount of flue gas and generated steam in order to maintain the concentration of power gas.
3. CONCEPT OF PREDICTIVE PROTECTIVE CONTROL (PPC) The basic motivation for the introduction of predictive protective control (PPC) is the same as regulation by PID controllers in particular loops. Yet the difference lies in the concept. The use of PID control for inner fast loops inevitably leads to some overshoot of process variables. In other words, a certain exceeding of temperature limit occurs over a longer or shorter time within individual component of the superheater approximately between 10 to 15 % (assuming a well-tuned controllers) which is undesirable condition, and the temperature stabilizes below this limit value after a certain amount of time, see Nowakova et al. (2012).
The third control task is the protective control. MHE is an expensive part of the FES. The protective control keeps the temperature of the wall of MHE heat transfer surface below the specified temperature limit. The limit depends on the materials used for construction of MHE. This control task is described in this paper in more detail. The heat exchanger is a system with distributed parameters. Its dynamics can be characterized by the dominant time constant. The dominant time constant of the FES MHE is about 10000 s. It is difficult to control the temperature of the wall of the heat transfer surface along their length under such a condition. To allow sufficiently good implementation of the above control task the exchanger was technologically divided into 5 units (UNIT0-UNIT4), see Fig. 2.
The purpose of the protective predictive control is that such exceedances do not occur at all. The mechanism by which this is achieved is demonstrated in the presented case study conducted at two components of MHE, namely UNIT1 and UNIT2. Predictive regulation proposed for FES technology unit uses a process model to calculate future intervention in terms of minimizing a cost function over a finite control horizon.
Each of the units has a dominant time constant of about 2000 s. Units are connected in series. Cool power gas enters the first unit. The superheated power gas is lead from the 5th unit towards turbines, see Filipova et al. (2016). Main heat exchanger is designed as a counter flow. Hot flue gas enters the 5th unit. The cooled flue gas is lead away from the first unit. Temperature of the heat exchanger’s wall that separates the flue gas and power gas therefore increases along the way, starting from the first unit to the fifth unit. The wall of heat transfer
The optimization criterion is a function which itself accumulates all the requirements of the system behavior, such as energy minimization, maximizing the efficiency and the like. Since the partial demands contradict each other, the resulting control design becomes a compromise that fulfills all the prescribed requirements with a minimum penalty of individual contributions to the cost function. 2
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4. IMPLEMENTATION OF PREDICTIVE PROTECTIVE CONTROL (PPC) ON FES
3
ding to the results of the optimization procedure after its completion it immediately prescribes and sets new values of opening positions of the valves RVx at which no exceeding of temperatures will occur. If the disturbance signal subsides at any time and the level of the signal returns to the original value or to any other steady state of the flue gas temperature, this change is evaluated and in case of increasing or decreasing of the predefined percentage value the PPC algorithm is reactivated and it may cause the valves to be set to original or newly computed positions. The control scheme is finally complemented by a block denoted by F, which is in charge of the so-called bumpless switching between PPC and PID control strategies (signals uP P C and uP ID ). This block contains a simple mechanism with the 1st order dynamics which ensures equality of uP P C and uP ID even though one of them is currently inactive (not interfering at the moment). Integration of PPC into existing technology is shown in Fig. 4, showing particular example for UNIT1, the same layout would apply for other exchangers. Technical implementation of the PPC algorithm can use standard hardware and software tools used in industrial automation, such as industrial PC or PLC. In case of using programmable logic controllers the implementation of this task would require transformation of that algorithm to the PLC which is very difficult and complicated task. At the same time, however, the proposed PPC algorithm is an extension of the standard PID control functionality, and in case of any failure or malfunction this situation would not endanger functionality of the entire FES technology. Thus, it would still be true that any wall overheating would be sufficiently compensated by the respective PID control, but it would not be possible to prevent such situations in advance, see Pies et al. (2017).
Recall that the main reason for the proposal of PPC is the requirement for wall temperature not to exceed a given limit at any point of the technology consisting of the heat exchangers. It is supposed that a possible overshooting of the temperature may occur as a result of two situations leading to the change in the physical quantities within the system, considered as disturbance signals in terms of control theory: • change in the power The primary cause of this fault is a speed change of the grate which secondarily leads to the change of the flue gas temperature, and ultimately (in a case of increasing the flue gas temperature) may cause breaking of temperature limit within the wall in a particular location of one of the exchangers. The information about emergence of this disturbance will be available timely (in minutes). The trigger signal for PPC optimization algorithm is a percentage increase or decrease in the current value of the flue gas temperature compared to the previous steady state, for example by 10 %. • change in the calorific value This disturbance signal has a faster dynamics than the change in the performance. Information about this disturbance will not be at disposal in advance. As in the previous case, the trigger signal for PPC optimization algorithm will be a percentage change in the current values of the flue gas temperature compared to the previous stable state, for example by 10 %. The association between the disturbance signals, flue gas temperature, and trigger signals is shown in Fig. 3.
(1)
UNIT1
T2 (L,t)
(1)
T2 (0,t)
(1)
(1)
T1 (L,t)
T1 (0,t)
Tmix1 MIX1
T
T
MAX
Tw1HLIM
Fig. 3. Trigger signal depending on flue gas temperature
SAT high low=0
Trigger signals thus launch PPC optimization procedure. The proposed solution would of course allow timescheduled repetition with a certain period. For the operation of the PPC algorithm it is important to assume that once disturbance occurs and the trigger condition is met, thus after a sufficient increase in flue gas temperature, the new level of this variable persists permanently. Based on the dynamic model, the future steady state of the entire model is calculated, and it is evaluated whether there will or will not be overshooting in the temperature in future at any point in the technological units within heat exchangers. If not, PPC control is not activated (P P CEN ABLE = OF F , see Fig. 4, and only standard lower regulatory levels remain active (outer loop and inner loops with PID controllers). If so, PPC algorithm is activated (P P CEN ABLE = ON , see Fig. 4), and accor-
R11
F
R12
uPID PPC ENABLE
RV1
uPPC STEAM
Fig. 4. Integrating PPC into current technology, illustration for UNIT1
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5. CASE STUDY: PREDICTIVE PROTECTIVE CONTROL OF FES
efficiency of the technology is achieved when the entire amount of steam passes through front mixer MIX0 only, while RVx valves remain closed. Under these ideal circumstances the steam is gradually heated up along its way through particular units and it is not unnecessarily cooled down due to the possible opening of valves RVx. Any action interventions are therefore desirable to be performed in “proximity” of MIX0, such as MIX0 itself + MIX1, optionally at next couple (MIX2 + MIX1) etc., assuming that the action can always be performed via a certain pair of adjacent valves (on adjacent mixers).
This case study serves as a basis for the preparation and follow-up solution of optimization problem demonstrating the PPC control mechanism. The calculation is performed for UNIT1 and UNIT2. Action interventions are calculated for valves RV1 and RV2 which inject steam into the mixers MIX1 and MIX2. Here is the list and meaning of the variables used for this purpose: k1 . . . optimization variable (dimensionless parameter between 0 − 1) representing valve position of RV1
Another important requirement is the minimum temperature gradient at individual mixers, thus a minimum temperature difference marked as ∆T mix2 (corresponding mixer MIX2) in presented case study. From technological point of view these requirements mean that material stress is minimized (in case of repeated cooling and heating), and it ensures good energy balance, because due to the nonlinear dependencies of heat transfer coefficients repetition of heating and cooling at subsequent unit could worsen energy balance compared to the situation without repeating cooling and heating processes.
k2 . . . optimization variable (dimensionless parameter between 0 − 1) representing valve position of RV2
T w1HLIM . . . temperature limit, maximal allowable value of the wall temperature, must not be exceeded at any point within UNIT1 T w2HLIM . . . temperature limit, maximal allowable value of the wall temperature, must not be exceeded at any point within UNIT2 T w1max . . . maximal value of the entire temperature profile of the wall of UNIT1 computed by the model and then compared to prescribed maximal allowable value T w1HLIM ; their difference then contributes to the overall cost function with the term in the form of equation (1): (1)
∆T w1max = maxT1 (L, T ) − T w1HLIM
The third requirement is of course no exceeding of the temperature limits in the specific case study marked as T w1HLIM (within UNIT1) and T w2HLIM (within UNIT2). The cost function can be described by equation (3). J = 0.1 · ∆T mix2 + 100 · ∆T w1 + 100 · ∆T w2 (3) where ∆T w1 = T 1max−T w1HLIM at UNIT1, see Fig. 4. Similarly, at UNIT2, ∆T w2 = T w2max − T w2HLIM . The cost function can be expressed in general form of equation (4) for any pair of adjacent mixers: (4) J = w1 · ∆T mixN + w2 · ∆T wM + w3 · ∆T wN where M and N are increasing indexes (order) of adjacent mixers, N=M+1, and w1 ,w2 , w3 represent weight coefficients. The first requirement is interpreted in the way that algorithm determines which pair of valves can ensure prevention from future temperature overshooting. Once a particular pair of the valves is determined, the algorithms continues to compute two specific values representing the optimal valve positions. Decision on the pairs of the valves is carried out according to the following decision tree (with extra RV5) shown in Fig. 6:
(1)
T w2max . . . maximal value of the entire temperature profile of the wall of UNIT2 computed by the model and then compared to prescribed maximal allowable value T w2HLIM ; their difference then contributes to the overall cost function with the term in the form of equation (2): (2)
∆T w2max = maxT1 (L, T ) − T w2HLIM
(2)
∆T mix2 . . . temperature loss (difference) at MIX2 being penalized in the cost function ϑ . . . auxiliary optimization parameter representing relation between positions of RV1 and RV2 valves (ϑ = 100 %: RV1 fully open, RV2 closed, k1 = 1, k2 = 0) Scheme of the situation at UNIT1 and UNIT2 is shown in Fig. 5:
The beginning works of the development of this algorithm included tests of fmincon function (part of Optimization Toolbox for Matlab). This function is intended for general optimization calculations where the cost function and constraints can be nonlinear, having arbitrary number of unknown optimization variables. This function could be used for the jobs not necessarily limited to adjacent pairs of valves only, being capable of determination of optimal positions for all the valves. Optimization job applied for FES technology however does not require such complexity. The use of fmin function also disproportionately increases the computing time, and there is no guarantee of the maximal number of performed iterations (this can be different each time the procedure is started) and thus there is no guarantee of amount of maximum computing time necessary to obtain the results. Therefore, the method of solving this optimization problem was changed as follows: Opening of each of two adjacent valves is represented by
Fig. 5. Situation scheme for UNIT1, UNIT2 5.1 Setting up the Cost Function The first requirement for the cost function takes into account the highest possible efficiency of cascade of exchangers. It can be interpreted in the way that the greatest 4
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Fig. 7. Introduction of gains representing valve positions a new variable ϑ [%] is introduced, representing relation between positions of RV1 and RV2 as follows: • ϑ = 100 %: valve RV1 fully open, RV2 closed (k1 = 1, k2 = 0) • ϑ = 0 %: valve RV1 closed, RV2 fully open (k1 = 0, k2 = 1) Simulation experiments have been performed for ϑ in the range of 100, 0 % decreasing by 10%, see Tab. 1. For ϑ = 100 % the job corresponds to the steady state prescribed by static heat computation assigned by provider of the technology.
Fig. 6. Decision tree to determine a pair of action valves a real number between 0 − 1. This interval is first divided into 10 equal sections in which 11 iterations is performed corresponding to the values of the auxiliary variable ϑ - see case studies below (first stage of the calculation). Based on found results ϑ, representing minimum of the objective function is specified. Subsequently there comes the second phase of the calculation which specifies auxiliary calculation interval so that two points from previous stage are considered for further calculations, located to the left and to the right of the found minimum. This interval is again divided into 10 equal sections where it again performs another 11 iterations corresponding to the values of the auxiliary variable ϑ. This is then repeated for the third time which is also the last stage of the calculation. This three-phase mechanism has the following advantages:
Table 1. Results of Simulation Experiments ϑ [%] 100 90 80 70 60 50 40 30 20 10 0
• it ensures sufficient entire achieved accuracy of 0.4 % when searching for optimal value, particularly 10 %, 2 % and 0.4 % during particular stages • it always ensures the same and fixed number of iterations - 33 altogether • it guarantees maximal computing time for a given computation mean (i.e. PC) to complete given optimization job
k1 [−] 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
k2 [−] 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
T w1max [◦ C] 476.50 477.00 477.50 478.00 478.40 478.90 479.40 479.90 480.40 480.90 481.40
T w2max [◦ C] 643.20 642.50 641.90 641.20 640.60 639.90 639.20 638.60 637.90 637.20 636.50
∆T mix2 [◦ C] 0.00 1.92 3.85 5.76 7.75 9.71 11.67 13.66 15.70 17.73 19.76
In order to demonstrate PPC functionality the below mentioned restrictions are considered, particularly temperature limits that must not be exceeded at any time and point for both analyzed units. The following values of T w1max, T w2max,∆T mix2 have been indicated for particular steps of algorithm: • Temperature wall limit of UNIT1: T w1HLIM = 479.3 ◦ C (if higher value assigned the result of optimization is the same because there is no exceeding at UNIT1), • Temperature wall limit of UNIT2: T w2HLIM = 639.5 ◦ C.
5.2 Simulation Experiment This case study analyzes situation under which the flue gas temperature is changed from 840 ◦ C to 854.9 ◦ C. In order to perform simulations, flow amounts through RV1 and RV2 valves are represented by parameters (gains) referred to as k1 and k2 , see Fig. 7.
Tab. 1 helps to determine that the desired optimal value ϑ∗ protecting the technology against overheating of unit walls lies between 40 − 50 % (Grey lines of table 1).
5.3 Simulation results
Progress of particular stages of the calculation is documented in Fig. 8, Fig. 9 and Fig. 10. Parameters of the 1st stage of computation: overall achieved accuracy 10%, 11 iterations done, elapsed time 98 seconds. Parameters of the 2nd stage of computation: overall achieved accuracy 2%, 11 iterations done, elapsed time 98 seconds. Parameters of the
The steam is brought to mixers MIX1 and MIX2 with its amount divided in a certain ratio corresponding to k1 and k2 . Because the entire amount of the steam is always consumed, k1 + k2 = 1 holds good. For simulation purpose 5
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Mathematical model describes FES comprising units that can be separated into two groups. In the first group, there are the units where the movement of power gas along the longitudinal space axis can be neglected. The group includes the compressor, mixers, water injectors, safety valves, the compressor turbine, the generator turbine, the asynchronous generator, and controllers. These units are treated as systems with lumped parameters. In the second group there are the evaporator drum boiler, headers, pipelines and heat exchangers. Here, the dynamics of movement of media along the space axis plays the important role. These units are typical systems with distributed parameters. In mathematical model, every unit with lumped parameters is described by a set of ordinary nonlinear differential equations. Every unit with distributed parameters is described by a set of partial nonlinear differential equations. Mathematical model of the simulated PPC task consists of models of water and steam injectors, safety valves, controllers, headers, pipelines and MHE segments.
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ACKNOWLEDGEMENTS
Fig. 9. Optimal value k1∗ after the 2nd stage of algorithm
This work was supported by the project SP2018/160, Development of algorithms and systems for control, measurement and safety applications IV” of Student Grant System, VSB-TU Ostrava. This work was supported by the European Regional Development Fund in the Research Centre of Advanced Mechatronic Systems project, project number CZ.02.1.01/0.0/0.0/16 019/0000867 within the Operational Programme Research, Development and Education.
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REFERENCES
rd
3 stage of computation: overall achieved accuracy 0.3 %, 11 iterations done, elapsed time 98 seconds.
FILIPOVA, B., NEVRIVA, P., PIES, M. The Temperature Time Responses of the Heat Exchanger Equipped by the Protective Control. IFAC-PapersOnLine. 2016, vol. 49, iss. 25, pp. 487–492. ISSN 2405-8963. HLADKY, V., BIELEK, R. Modelling and control of thermal system. Advances in Electrical and Electronic Engineering. 2014, vol. 12, iss. 2, pp. 103–110. ISSN 1804-3119. JALURIA, Y., TORRANCE, K. E. Computational Heat Transfer. Second edition. New York: Taylor & Francis, 2003. ISBN 1-56032-477-5, ISBN 1-56032-478-3. NEVRIVA, P., OZANA, S., PIES, M. Simulation of power plant superheater using advanced simulink capabilities. International Journal of Circuits, Systems and Signal Processing. 2011, vol. 5, iss. 1, pp. 86–93. ISSN 19984464. NOWAKOVA, J., POKORNY, M. On PID controller design using knowledge based fuzzy system. Advances in Electrical and Electronic Engineering. 2012, vol. 12, iss. 2, pp. 22–27. PIES, M., FILIPOVA, B., NEVRIVA, P. The control of the output power gas temperature at the heat exchanger. In: Advances in Intelligent Systems and Computing, 527. Cham: Springer, 2017, pp. 114–125. ISBN 978-3-31947363-5. VILIMEC, L., STAREK, K. Power production process with gas turbine from solid fuel and waste heat and the equipment for the performing of this process. US Patent No. US20100199631, 2010.
Interpretation of found value: Optimal value k1∗ = 0.44 corresponds to ϑ = 44[%]. As k1 + k2 = 1, then k2∗ = 0.56. These results introduced in this study are easy to interpret in this way: If the positions of the valves RV1 and RV2 bringing the steam into mixers MIX1 and MIX2 are set to k1∗ and k2∗ , then PPC algorithm guarantees that there will be no temperature overshoot at the walls of UNIT1 and UNIT2 in future at any time and point, supposing persisting step change in the flue gas (from 840 ◦ C to 854.9 ◦ C). 6. CONCLUSION The predictive protective control predicts the behavior of MHE over a given time horizon and it calculates the predictive protective control action. The predictive algorithm is based on mathematical model of MHE. At actual FES, the PPC will run in real time and will communicate with FES technology. At present, the PPC algorithm and software is tested off-line using the techniques of computer simulation. The MHE is activated by simulated inputs. To simulate the PPC task the mathematical model of the experimental FES has been used, while parameters of the mathematical model of the experimental FES were adopted for 110 MW. 6