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Economic MPC applied to generation scheduling in CSP plants*
Proceedings of the the 20th World World Congress Proceedings of 20th The International Federation of Congress Automatic Control The Federation of Automatic Proceedings of the 20th9-14, World The International International Federation of Congress Automatic Control Control Toulouse, France, July 2017 Available online at www.sciencedirect.com Toulouse, France,Federation July 9-14, 9-14, 2017 2017 The International of Automatic Control Toulouse, France, July Toulouse, France, July 9-14, 2017
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IFAC PapersOnLine 50-1 (2017) 115–120 Economic Economic MPC MPC applied applied to to generation generation ⋆ Economic MPC applied to generation scheduling in CSP plants scheduling in CSP plants ⋆⋆ scheduling in CSP plants ∗ ∗ ∗ ∗
M.J. Vasallo ∗ J.M. Bravo ∗ D. Mar´ın ∗ M.E. Geg´ undez ∗ M.J. Vasallo Vasallo ∗ J.M. J.M. Bravo Bravo ∗ D. D. Mar´ Mar´ın ın ∗ M.E. M.E. Geg´ Geg´ undez ndez ∗ M.J. u ∗ ∗ ∗ M.J. Vasallo J.M. Bravo D. Mar´ ın M.E. Geg´ u ndez ∗ ∗ Departamento de Ingenier´ıa Electr´ onica, de Sistemas Inform´ aticos ∗ ∗ Departamento de Ingenier´ ıa o de a Departamento de ETSI Ingenier´ ıa Electr´ Electr´ onica, nica, de Sistemas Sistemas Inform´ aticos ticos Autom´ atica, Universidad de Huelva, Spain. Inform´ (e-mail: ∗ Departamento de Ingenier´ ıa Electr´ o nica, de Sistemas Inform´ aticos Autom´ a tica, ETSI Universidad de Huelva, Spain. (e-mail: Autom´ [email protected], tica, ETSI Universidad de Huelva, Spain. (e-mail: [email protected], Autom´ [email protected], tica, ETSI Universidad [email protected]) Huelva, Spain. (e-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]) [email protected], [email protected]) [email protected], [email protected])
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Abstract: Abstract: Abstract: This paper proposes a model-based predictive control (MPC) approach with economic objective Abstract: This a predictive control with economic This paper paper proposes a model-based model-based predictive control (MPC) (MPC) approach withplants economic objective function to proposes face the scheduling problem in concentrating solarapproach power (CSP) withobjective thermal This paper proposes a model-based predictive control (MPC) approach with economic objective function to face the scheduling problem in concentrating solar power (CSP) plants thermal functionstorage to face(TES) the scheduling problem in concentrating solarBy power plants with thermal energy in a day-ahead energy market context. this (CSP) approach, thewith most recent function to face the scheduling problem in concentrating solar power (CSP) plants with thermal energy storage storage (TES) in a day-ahead energy market context. By this approach, the most recent energy (TES) in a day-ahead energy market context. By this approach, the most recent prices, weather forecast and the current plant’s state can be used by the proposed in forecast a day-ahead market context. By can this be approach, recent energy prices, weather and the current plant’s state used by proposed energy storage prices, weather forecast and energy the the current plant’s state can be usedtime bythethe the proposed economic MPC(TES) approach to reschedule generation conveniently from tomost time. The energy prices, weather forecast and the current plant’s state can be used by the proposed economic MPC approach to reschedule the generation conveniently from time to time. The economic approach MPC approach to reschedule the generation from time to time. The proposed is applied, in a simulation context, toconveniently a 50 MW parabolic trough collectoreconomic MPC approach to reschedule the generation conveniently from time to time. proposed approach is applied, in a simulation context, to a 50 MW parabolic trough collectorproposed approach is applied, in aassumption simulationofcontext, a 50forecast MW parabolic trough collectorbased CSP with TES under the perfecttoprice and participation in The the proposed approach is applied, in aassumption simulation a a50four-month MW parabolic trough collectorbased CSP CSP with TES TES under the assumption ofcontext, perfect price forecast andperiod participation in the the based with under the of perfect price forecast and participation in Spanish day-ahead energy market. A case study based to on to test several based CSP withconditions TES under the assumption of study, perfect price forecast andperiod participation in the Spanish day-ahead energy A based aa four-month to several Spanish day-ahead energy market. A case case study basedaon on four-month period to test test several meteorological ismarket. performed. In study this complete economic analysis is carried Spanish energy A case based a four-month period to test several meteorological is performed. In this study, aaon complete economic is carried meteorological conditions ismarket. performed. In study thiscost, study, complete economic analysis is Results carried out usingday-ahead actualconditions values of energy price, penalty solar resource data and itsanalysis forecast. meteorological conditions is performed. In this study, a complete economic analysis is carried out using actual values of energy price, penalty cost, solar resource data and its forecast. Results out using actual values of energy price, penalty cost, solar resource data and its forecast. Results show an economic improvement in comparison with a traditional day-ahead scheduling strategy. out actual values of energyin penalty with cost, aasolar resourceday-ahead data and scheduling its forecast.strategy. Results showusing an economic economic improvement inprice, comparison with traditional day-ahead scheduling strategy. show an improvement comparison traditional show anIFAC economic improvement in comparison a traditional scheduling © 2017, (International Federation of Automaticwith Control) Hosting byday-ahead Elsevier Ltd. All rights strategy. reserved. Keywords: Optimal operation and control of power systems, Planning, Energy market Keywords: Optimal Optimal operation and and optimization-based control of of power power systems, systems, Planning, Energy market of Keywords: operation and control market integration, Model predictive control,Planning, ModelingEnergy and simulation Keywords: Optimal operation and control of power systems, Planning, Energy market of integration, Model predictive and optimization-based control, Modeling and simulation of integration, Model predictive and optimization-based control, Modeling and simulation power systems integration, Model predictive and optimization-based control, Modeling and simulation of power systems power systems power systems 1. INTRODUCTION forecasts. In order to reduce the afore-mentioned risk, the 1. INTRODUCTION INTRODUCTION forecasts. In order orderinto to(Vasallo reduce the the afore-mentioned risk, the 1. forecasts. In reduce the authors proposed and afore-mentioned Bravo, 2016) therisk, use of a 1. INTRODUCTION forecasts. In order reduce the afore-mentioned the in and Bravo, 2016) use of aa authors proposed proposed into(Vasallo (Vasallo and(MPC) Bravo, approach 2016) the therisk, usegenof model-based predictive control for Concentrating solar power (CSP) is a promising technol- authors authors proposed in (Vasallo and Bravo, 2016) the use of a model-based predictive control (MPC) approach for genConcentrating solar power (CSP) is a promising technolmodel-based predictive control approach for genConcentrating solar power (CSP) is ainpromising scheduling in CSP plants(MPC) based on a mixed-integer ogy that has drawn much attention countries technolsuch as eration model-based predictive control (MPC) approach for genConcentrating solar power (CSP) is a promising technoleration scheduling in CSP plants based on a mixed-integer ogy that has drawn much attention in countries such as eration scheduling in CSP plants based on a mixed-integer ogy much subsidy attention in countries such as programming (MIP) model. MPC is a control strategy Spainthat andhas the drawn USA, where policies have promoted in CSP plants based a mixed-integer ogy that much subsidy attention in countries such as eration programming (MIP) model. MPC is the control strategy Spain andhas the drawn USA, where subsidy policies have is promoted programming (MIP) model. MPC is aaoncontrol strategy Spain and the USA, where have promoted that hasscheduling been widely adopted both in industry and in its development. Interest in CSP policies technology mainly programming (MIP) model. MPC is a control Spain and the USA, where subsidy policies have promoted that has been widely adopted both in the industry and its development. Interest in CSP technology is mainly that has been adopted both with in thedynamics industrystrategy and in in its development. Interest in CSP technology is mainly givenwidely its ability to deal models based on the semi-dispatchable nature of CSP plants with academia that has been widely adopted both in the industry and in its development. Interest in CSP technology is mainly academia given its ability to deal with dynamics models based on the semi-dispatchable nature of CSP plants with academia given its ability(see to (Mayne, deal with2014; dynamics based on energy the semi-dispatchable CSP plants with and complex constraints Bravomodels et al., thermal storage (TES) nature and/oroffossil-fuel backup academia given its ability to deal with dynamics models based on the semi-dispatchable nature of CSP plants with and complex constraints (see (Mayne, 2014; Bravo et al., thermal energy storage (TES) and/or fossil-fuel backup and complex constraints (see (Mayne, 2014; Bravo et al., thermal energy storage (TES) and/or fossil-fuel backup systems. This attribute favours the participating of CSP 2006)). and complex constraints (see (Mayne, 2014; Bravo et al., thermal storage (TES) and/or fossil-fuel backup 2006)). systems. This attribute favours the to, participating of CSP systems. This attribute favours the participating of CSP plants in energy electricity markets thanks among others, the 2006)). This has been inspired by the question: what is the 2006)). systems. This attribute favours the participating of CSP plants in electricity markets thanks to, among others, the plants in electricity markets thanks to, among others, the This paper capability to displace production from low-price to highpaperimpact has been been inspired by the the question: what is the the This paper has inspired by question: is economic of using a MPC approach forwhat generating plants in electricity markets thanks to, among others, the capability to displace production from low-price to highcapability to displace production from low-price to highprice periods. Therefore, it is interesting to approach the This paper has been inspired by the question: what is the economic impact of using a MPC approach for generating economic impact of using a MPC approach for generating in CSP plants?. In this sense an economic capability to displace production from low-price to highprice periods. Therefore, it is is interesting interesting to approach approach the scheduling price periods. Therefore, it to the optimal generation scheduling problem (also called selfeconomic impact of using a MPC approach for generating scheduling in CSP plants?. In this sense an economic scheduling in general CSP plants?. In this presented sense anineconomic of the MPC approach (Vasallo price periods. it is interesting to approach the version optimal generation scheduling problemelectricity (also called selfoptimal generation scheduling problem (also called selfscheduling). InTherefore, a deregulated market, producscheduling in CSPis plants?. Inand this senseItanisin version of general MPC presented (Vasallo version of the the general MPC approach approach presented ineconomic (Vasallo and Bravo, 2016) proposed tested. based on optimal generation scheduling problem (also called selfscheduling). In a deregulated market, electricity producscheduling). In a deregulated market, electricity produc- version ers aim to maximize profits from energy sales. Moreover, of the general MPC approach presented in (Vasallo and Bravo, 2016) is proposed and tested. It is based on and Bravo, 2016) is proposed and tested. It is based on the fact that the cost function used to track the commitscheduling). In a deregulated market, electricity producers aim to maximize profits from energy sales. Moreover, ers aim to maximize energy sales. Moreover, in electricity markets,profits powerfrom plant owners have to offer the and Bravo, 2016) is proposed and tested. It the is based on fact that the cost function used to track committhe fact that the cost function used to track the committed generation schedule is defined such that pricing and ersdaily aim to maximize profits energy sales. Moreover, electricity markets, powerfrom plant owners have to offer offer the fact that the cost function used to track the commitin electricity markets, power plant owners have to ain production schedule in advance. Consequently, ted generation schedule is defined such that pricing and ted generation schedule is defined pricingcould and penalty information is added. Thissuch way,that penalties in electricity markets, power forecast plant owners have to offer a daily daily production schedule in advance. advance. Consequently, aelectricity production in price and schedule weather must Consequently, be taken into penalty ted generation schedule is increasing defined that pricing and information is added. This way, penalties could penalty information is by added. Thissuch way, penalties could be partially balanced revenues thanks to a daily production schedule in advance. Consequently, electricity price and weather forecast must be taken into electricity and weatherproblem. forecast must be taken into penalty account in price the optimization information is added. This way, penalties could be partially balanced by increasing revenues thanks to be partially balanced by increasing revenues thanks to the use of economic information. The proposed approach electricity price and weather forecast must be taken into account in the optimization problem. account in the optimization problem. be partially balanced by increasing revenues thanks to the use of economic information. The proposed approach the use of economic information. The proposed approach is applied, in a simulation context, to a 50 MW PTCOne of the firstoptimization works about problem. optimal CSP plant operation account in the the use of economic information. The proposed approach is applied, in a simulation context, to a 50 MW PTCOne of the first works about optimal CSP plant operation is applied, a simulation context, to a TES 50 MW PTCOne the first works about optimal plant operation CSP in plant with molten-salt-based under the was of (Sioshansi and Denholm, 2010).CSP Two models were based is applied, simulation context, to aparticipation 50 MW PTCOne of thewidely-used first works about optimal CSP plant operation based CSP in plant with price molten-salt-based TES under the was (Sioshansi and Denholm, Denholm, 2010). Two models were CSP plant with molten-salt-based TES under the was (Sioshansi and 2010). Two models assumption of aperfect forecast and in used, the tool SAM (SAM, 2016) and anwere op- based based CSP plant with molten-salt-based TES under the was (Sioshansi and Denholm, 2010). Two models were assumption of perfect price forecast and participation in used, the widely-used tool SAM (SAM, 2016) and an opassumption of perfect price forecast and participation in used, the widely-used tool SAM (SAM, 2016) and an optimization model based on mixed-integer linear program- the Spanish day-ahead energy market. assumption perfect price forecast used, the widely-used (SAM, and an op- the day-ahead energy market. timization model basedtool on SAM mixed-integer linear programthe Spanish Spanish of day-ahead energy market.and participation in timization model based on mixed-integer linear programming (MILP). Further examples using the2016) MILP approach A the economic thegeneral Spanishdescription day-aheadofenergy market. MPC approach is timization model basedexamples on mixed-integer ming (MILP). Further examples using the linear MILP approach ming using the MILP approach can be(MILP). found inFurther (Usaola, 2012) and (Kost et al., program2013). A general description ofcase thestudy, economic MPC approach approach is A general description of the economic MPC is given in Section 2. The the results and discusming (MILP). Further examples using the MILP approach can be found in (Usaola, 2012) and (Kost et al., 2013). can be found in (Usaola, 2012) and (Kost et al., 2013). A general description ofcase thestudy, MPC approach is in Section 2. The results and given in explained Section 2. in The case study, the results and discusdiscussion are Section 3economic and the finally, conclusions are CSP plants on 2012) electricity markets run2013). the risk given can be foundoperating in (Usaola, and (Kost et al., given in Section 2. The case study, the results and discussion are explained in Section 3 and finally, conclusions are CSP plants operating on electricity markets run the risk sion forward are explained in Section 3 and finally, conclusions are CSP plants operating electricity run the genrisk put in Section 4. of being penalized for on deviating frommarkets the scheduled sion forward are explained in Section 3 and finally, conclusions are CSP plants operating electricity run the risk put put forward in Section Section 4. of being penalized for on deviating frommarkets the scheduled genin 4. of being penalized for deviating from the scheduled generation due to imperfect direct normal irradiance (DNI) of beingdue penalized for deviating from the scheduled(DNI) gen- put forward in Section 4. eration due to imperfect imperfect direct normal normal irradiance (DNI) eration to direct irradiance ⋆ This work was supported by DPI2016-76493-C3-2-R of Ministerio eration due to imperfect direct normal irradiance (DNI) ⋆ ⋆
This work was was supported by by DPI2016-76493-C3-2-R DPI2016-76493-C3-2-R of Ministerio Ministerio work supported of deThis Economia y Competitividad (Spain). ⋆ de Economia y (Spain). work was supported by DPI2016-76493-C3-2-R of Ministerio deThis Economia y Competitividad Competitividad (Spain). de Economia y Competitividad (Spain). Copyright © 2017 IFAC 117 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2017 117 Copyright © 2017, 2017 IFAC IFAC 117 Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Copyright © 2017 IFAC 117Control. 10.1016/j.ifacol.2017.08.020
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 116 M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120
Fig. 1. Sliding window of the economic MPC 2. DESCRIPTION OF THE ECONOMIC MPC APPROACH Fig. 2. Block diagram of the economic MPC The proposed approach assumes participation in a dayahead energy market and the producer’s price-taking property (i.e., its production schedules do not influence market prices). The dual purpose of the proposed MPC approach is: (1) the convenient, periodical tracking of the generation schedule that has been committed to, and (2) the development of the optimal generation schedule for the next trading day at the appropriate time. The MPC approach proposed in this paper uses a cost function that included pricing and penalty information in order to achieve the dual objective. Therefore, all terms of the cost function are economic and the proposed MPC approach can be classified as an economic MPC, see (Amrit et al., 2011; Touretzky and Baldea, 2014). The two objectives for the MPC approach requires its sliding window to be divided into two intervals (see Fig. 1): the tracking interval (TI) and the next schedule interval (NSI). The generation schedule must be updated to track the schedule that has been committed to within the interval TI, while the interval NSI is used to maximize future profits and to generate the schedule for the next day at the appropriate time. Several variables and parameters related to the sliding window are defined next: • t(i) = i∆tw where i = 0, 1, ... are the time instants when MPC control output is generated. The beginning time of the sliding window when it is in position i is set to instant t(i). Case i = 0 refers to instant 0.0h of the current day D. ∆tw is the time step for control update. • tschedule del is defined as the deadline hour in the day D for the delivery of the generation schedule for the next day D+1. This deadline hour depends on the market of each country. • tschedule end is the final time of the committed generation schedule. If the current time has not reached the time tschedule del , tschedule end is usually 24.0h of the day D. On the contrary, tschedule end is 24.0h of the day D+1 because the generation schedule for this day has been already delivered. • ∆w is the constant sliding window length.
According to the previous definitions, the endpoints of the intervals TI and NSI are shown in Fig. 1. Notice that the sliding window length is constant but the lengths of both intervals are time-variant. When t(i) = tschedule del , the generation schedule solved by the MPC control for the interval NSI until 24.0h of the day D+1 can be given as the generation schedule for this day. Since the typical optimal scheduling problem has an optimization horizon based on the next one or 118
two trading days (Wittmann et al., 2011), and a constant sliding window length is assumed, this length (∆w) can have a value between 24 − tschedule del +24 hours (oneday strategy) and 24 − tschedule del +48 hours (two-day strategy). Fig. 2 shows the block diagram of the MPC approach. At each sliding window position i, MPC control receives the following information: (1) Current continuous state of the CSP plant (xc (t(i))), e.g., the TES energy level and thermal state in the solar field (SF). (2) Current discrete state of the plant (xd (t(i))), e.g., active operating phases in the SF, TES or turbine. (3) Electricity price forecast made at time t(i) (p(j/i), for j = 1, .., N ), where j indicates each step in the MPC model, N = ∆w/∆to is the number of steps in the sliding window, and ∆to is the time step expressed in hours of the MPC model. (4) Predictions made at time t(i) of average value of the maximum thermal power available from the SF (PSF max (j/i), for j = 1, .., N ). The qualifying ’maximum’ is added to indicate that partial defocus in the SF can lead to a decrease in the thermal power available. A CSP plant model, DNI and other meteorological variables forecast and initial conditions xc (t(i)) and xd (t(i)) are used to generate these predictions. (5) Committed generation schedule to be met (Peref (j/i), for j = 1, .., NT I ), expressed in average gross electric power, where NT I = (tschedule end − t(i))/∆to is the number of steps in the interval TI. As a result of the optimization at the sliding window position i, the following outputs are generated: (1) Decision variables at time t(i) (u(j/i), for j = 1, .., N ). Only the decision variables u(1/i) are applied to the plant as common in MPC approaches. (2) Average values of turbine-generated gross electric power calculated at time t(i) (Pe (j/i), for j = 1, .., N ). When t(i) = tschedule del , values inside the interval NSI until 24.0h of the next day are given as the new generation schedule for this day (Peref (j/i) = Pe (j/i), for j = NT I + 1, .., NT′ I , where NT′ I = NT I + 24/∆to is the new number of steps in the interval TI). The objective function to minimize is expressed by Equation (1)
Proceedings of the 20th IFAC World Congress M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
Strategy
Model
Rescheduling
MPC DAS
MIP-MPC MIP-DAS
Hourly No
Short term forecast Hourly No
Feedback of the plant’s state Hourly Daily
Turbine capacity (gross) Solar field capacity Thermal capacity in solar-only mode Thermal capacity in TES-only mode Solar multiple TES capacity (TES-only mode) Turbine efficiency (full load) Fossil backup only for preventing HTF freezing
Table 1. Information about scheduling strategies and models
117
52.5 MW-e 250 MW-t 140 MW-t 119 MW-t 1.8 8 hours 38%
Table 2. Characteristics of the CSP plant J(i) = − ∆to
N TI ∑
[p(j/i)Penet (j/i)
j=1
− ϕ(j/i)(Peref net (j/i) − Penet (j/i)) − fcost (.)] − ∆to
N ∑
j=NT I +1
[p(j/i)Penet (j/i) − fcost (.)]
− s(E(N + 1/i))
(1)
where ϕ(j/i) is an estimation of the penalty cost per kW-h of deviation at hour j, Penet (j/i) is the turbine-generated net electric power, Peref net (j/i) is the committed net electric power, fcost (.) represents generation costs, and s(E(N + 1/i)) is a terminal value term applied to the final TES energy level. Notice that function −J(i) represents the profits along the sliding window. In this work it is assumed that the electricity production does not exceed the committed schedule, then the term ϕ(j/i) refers to falling penalty. 3. CASE STUDY In this section, the economic MPC approach proposed by this paper is applied, in a simulation context, to a 50 MW PTC-based CSP plant with molten-salt-based TES. Two scheduling strategies are compared, the proposed economic MPC strategy and a traditional day-ahead scheduling (DAS strategy). The MPC strategy uses the MIP-MPC model (see subsection 3.1 for more details), hourly rescheduling, hourly short-term forecast and hourly feedback of the plants’s state. The DAS strategy is characterized by the following: (1) The schedule for the day D+1 is generated at tschedule del of day D. At this moment, initial conditions for day D+1 are estimated using the current plant state, the day-ahead forecast and the schedule still to be met. (2) The generation schedule is tracked without any rescheduling. Then the generation each hour is the maximum that can be reached according to the committed value. The optimization model to generate the schedule in the DAS strategy is refereed as MIP-DAS model in this paper (see subsection 3.1 for more details). Table 1 summarizes all information about optimization models used and scheduling strategies. The CSP plant used in this study is based on the model presented in (Garc´ıa et al., 2011) and also used in (Vasallo and Bravo, 2016), which describes the plant Andasol 2 in Granada, Spain. Some characteristics of this model (adapted to this case study) are shown in Table 2. 119
Next, the main features of the simulation scenario developed for this case study are enumerated. An enough long time period is considered (from 01/02/2013 to 31/05/2013) with the purpose of testing several meteorological conditions. The Spanish day-ahead energy market and the producer’s price-taking property are considered. Price forecasts are assumed to be perfect and were obtained from data of the Iberian market operator OMIE, ((OMIE, 2016)). No premium per MWh is considered. Penalty costs per MWh of deviation are also obtained from OMIE. In order to keep things simple, generation costs are not taken into consideration. The generation schedule and MIP-MPC model resolutions are hourly. The frequency of the rescheduling is also hourly. Therefore, ∆to = ∆tw = 1.0 h (see Fig. 1). Parameter tschedule del is set to 10.0 h (Spanish market in 2013). Parameter ∆w is set to 48 h to reach a compromise between computation time of the MIP-MPC model and the possibility to conserve energy for sale after the end of the next day. Therefore, the length of the interval NSI at 10.0 h is 34 h, and the scheduling problem for the next day is based on the next 1+5/12 days (i.e., an intermediate scheme between the one-day and two-day strategies). To generate predictions PSF max (j/i) (see Fig.2), the detailed CSP plant model from (Vasallo and Bravo, 2016) is used. DNI and ambient temperature are the only meteorological variables considered and ambient temperature forecasts are assumed to be perfect and created from TMY2 data (TMY2, 2016). The CSP plant is represented by an onehour-resolution model to avoid very high simulation times, as in (Kraas et al., 2013; Law et al., 2016). Specifically, a MIP model derived from the itself MIP-MPC model is employed. Therefore, performance differences are only due to DNI forecast errors. This model is referred in this work as MIP-plant model. A set of day-ahead forecasts of solar radiation, obtained by the Integrated Forecast System model (IFS) of the European Centre for Medium-range Weather Forecasts (ECMWF), is available. Moreover, a set of solar radiation measures is also available. Both sets are converted to maximum thermal power available from SF by simulation with the detailed CSP plant model. Short-term DNI forecasts are also taken into account in this study. Several methods can be consulted in (Law et al., 2014). In the absence of short-term forecast data, a synthetic predictor is developed, which works directly with the variable PSF max (j/i) to avoid conversion from DNI values. Equation (2) describes the synthetic shortterm predictor used to incorporate the influence of shortterm DNI forecasts: PSF max ST F (k/i) = PSF max actual (k/i)+ +r(k)(PSF max DA (k/i) − PSF max actual (k/i))
(2)
Proceedings of the 20th IFAC World Congress 118 M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
for k=1 to NST F + 1; where NST F is the scope (hours) of the short-term forecast; r(k) is a function linear with index k, r(1) = 0; r(NST F + 1) = 1; PSF max ST F (k/i) and PSF max actual (k/i) and PSF max DA (k/i) are the shortterm forecasted, actual and day-ahead forecasted maximum thermal power available from SF. Notice that the percentage of day-ahead forecast error to be added to the actual value to generate the short-term forecast of the first hour is 0%. This percentage grows linearly with time and it is 100% when k = NST F + 1 (i.e., out of the scope of the short-term forecast). Typical values for NST F are 5 or 6 hours (Law et al., 2014, 2016).
lower than the minimum electricity price in the simulation period. This way, the terminal value term of the objective function makes the defocused thermal energy be as low as possible once the maximum economic profits (without terminal value term) have been obtained. In the Spanish market, deviation from the scheduled generation produces penalty costs if it requires the intervention of the transmission system operator. These penalties are associated with the costs incurred to stabilize the system, and do not follow any pre-given function. Therefore, these costs are difficult to estimate. An average value for ϕ(j/i) is assumed in Subsection 3.2.
MIP models are explained in Subsection 3.1. Subsection 3.2 describes the characteristics of the following input data: solar resource, its day-ahead forecast and the penalty costs per MWh of deviation. Finally, results and discussion are shown in Subsection 3.3.
MIP-DAS model. The MIP-DAS model is an optimization model which generates the generation schedule for the day D+1 when t(i) = tschedule del at the day D in case of DAS strategy. The MIP-DAS model is derived from the MIP-MPC model: the TI interval is removed and the NSI interval begins the hour 0 of the day D+1. Initial values for the moment before hour 0 of day D+1 are estimated at tschedule del of day D using the current status of the plant, day-ahead forecast and the schedule still to be met.
3.1 MIP models In this subsection the three one-hour-resolution MIP models are described. The MIP-DAS and MIP-plant models are derived from the MIP-MPC model. The formulation of the three MIP models for this case study was carried out without any non-linear element, except for binary variables. Thus they are MILP models. A clarification is important to do at this moment: it is supposed that the plant operator and control systems of the plant under study take decisions based on two goals with different priority (Vasallo and Bravo, 2016). The high-priority goal is to minimize the generation error. Once this objective is met, the low-priority goal can be applied, which consists in minimizing the defocused thermal power in the SF. Therefore, the plant under study has an only independent decision variable in relation to power sharing, e.g., the setpoint for electricity generation. Then, the MPC action u(1/i) = Pe SP (1/i). Equation Pe SP (1/i) = Pe (1/i) is used to obtain the setpoint, where Pe (1/i) is a value generated by the MPC control. MIP-MPC model. The set of equations and inequalities that composes the MIP-MPC model and values for its parameters can be consulted in (Vasallo and Bravo, 2016). The objective function to minimize is expressed in equation (3), which is a specific case of the objective function in Section 2. Minimize
J(i) =
−∆to
N TI ∑
[p(j/i)Penet (j/i)
j=1
−ϕ(j/i)(Peref net (j/i) − Penet (j/i))] −∆to
N ∑
(p(j/i)Penet (j/i))
j=NT I +1
−KE(N + 1/i)
(3)
In this objective function, generation costs are not taken into consideration and KE(N + 1/i) is the terminal value term formed by a value proportional to the final TES energy level, with constant K defined by equation K = ηpvlow , where η is a efficiency factor to convert stored energy to net electric energy, and pvlow is a value much 120
MIP-plant model. In order to avoid high simulation time, the representation of the CSP plant is made by a MIP model of one-hour resolution. It is composed of two consecutive optimization models derived from the MIPMPC model. The two goals with different priority which guide the decisions of the plant operator and control systems (see the beginning of Section 3.1) explains this scheme. This model receives each hour the setpoint generated from the MPC or DAS strategy. Then, the evolution of the electrical generation and the plant’s state is obtained based on this hourly update of setpoint, the actual value for solar resource and the aforementioned goals. 3.2 Input data description The characteristics of the solar resource, its day-ahead forecast and the penalty costs per MWh of deviation for the studied time period are described in this Subsection. Fig. 3 shows the hourly average values of the maximum thermal power available from the SF, PSF max actual (j), that have been obtained using solar radiation data and the detailed CSP plant model. As can be seen in the figure, as the days advance, the profile of PSF max actual (j) increases in intensity and length. Furthermore, approximately the first one seventy days present a high meteorological variability, while the stability increases the last fifty days. An important variable that can influence the performance of the scheduling strategies is, obvioursly, the day-ahead forecast error of the maximum thermal power available from the SF. In general, the forecast error increases with the meteorology variability, that is, winter days presents higher prediction errors than clean summer days. In order to characterise the day-ahead forecast error, some metrics are shown in Table 3 in a monthly basis. Note that only daylight hours are used to obtain the metrics because in night hours the prediction error is absent. The mean of the maximum thermal power available from SF is denoted by P¯SF max actual . The Relative Root Mean Absolute Error and the Relative Mean Bias Error are denoted by rM AE and rM BE respectively, (see (Kraas et al., 2013) for
Proceedings of the 20th IFAC World Congress M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
February 4.4%
119
March 7.3%
April 3.4%
May 0.9%
Table 5. Monthly percentage of improvement Hourly mean value Generation (MWh-e) Deviation (MWh-e) Defocused energy (MWh-t) TES energy level (%) Equivalent sale price (Euros/MWh-e)
DAS 12.42 1.46 4.26 23.29 64
MPC 12.37 1.76 4.39 28.04 65.49
% -0.43% 20.68% 3% 20.37 % 2.33%
Table 6. Energy results of DAS and MPC
40
Month February March April May
P¯SF max
actual
(MW)
82.5 87.6 152.4 164.4
rM AE (%) 32.1 52.8 25.7 17.8
rM BE (%) 3.8 8.4 -5.3 10.6
Table 3. Metrics of day-ahead forecast error for maximum thermal power from the SF
30 Percentage of total generation
Fig. 3. Hourly average values for maximum thermal power available from the SF (kW)
20
10
0
−10
−20
Revenues (Euros) Penalty costs (Euros) Profits (Euros)
DAS 2148321 38969 2109352
∆Profit of MPC (%) DAS (%) MPC (%)
MPC 2228481 58949 2169532
0
10
20
30 40 50 60 Prices Interval (Euros/MWh)
70
80
90
Fig. 4. Distribution of generation with price intervals for DAS and MPC strategies (%)
Table 4. Economic results of DAS and MPC strategies expresions of these metrics). Some observations may be useful. The mean of the maximum thermal power available from the SF increases near of 100% from February to May. The relative error is higher in winter months. In fact, March has been particularly bad in the studied period. Finally, the monthly bias error can vary widely. The proposed economic MPC approach uses a constant ¯ where ϕ¯ = 7.69 ϕ(j, i) value. In this case ϕ(j, i) = ϕ, Euros/MWh is the mean value for the penalty costs per MWh during the first half-year period. 3.3 Results and discussion In this Subsection, simulation results are shown and commented. It is important to remark that there are many factors which affect the economic results of scheduling strategies, e.g., electricity market regulations, plant site local climate, forecasts, plant design, simplification hypothesis and models used (Law et al., 2016). Therefore, the conclusions drawn from this case study could be different in other scenarios. Next, the following analysis will be performed: (1) economic comparison between MPC and DAS strategies; (2) calculation of the percentage of improvement in profits of the MPC strategy respect to the DAS strategy on a monthly basis; and (3) energy analysis of both strategies. Table 4 shows the economic results of the DAS and MPC strategies. It should be underlined that the results 121
obtained by the MPC scheduler outperform the profits obtained by the DAS scheduler. Table 5 shows, for each month, the percentage of improvement in profits of MPC strategy with respect to the DAS strategy. As can be seen, the MPC strategy obtains substantial improvements when the meteorological instability is present. In fact, the best result is obtained in March, that is, the month with worse forecast for the maximum thermal power available form the SF. In this sense, the MPC strategy can compensate bad forecast situations. Next, some energy results of DAS and MPC strategies are shown in Table 6. It is shown that generation is slightly lower with MPC strategy. Moreover, values for deviation and defocused energy with MPC strategy are also worse. The economic improvement of MPC strategy is shown in parameter equivalent sale price. This parameter is defined as the ratio between total profits and total generation. The worse energy results of MPC strategy are explained by its capability to admit deviation in order to reserve energy for higher possible revenues, as its higher mean TES energy level clarifies. This capability is based on the hourly slide of the MPC window, which is incorporating new information (precise or not). In any case, although total deviation can be higher with the MPC strategy, this strategy distributes it by taking advantage of the most favorable hours obtaining an improvement of 2.33% in the equivalent sale price. Fig. 4 shows the distribution of electric generation with price interval for both strategies. It can be observed the displacement of generation to high prices of the MPC strategy over the DAS strategy.
Proceedings of the 20th IFAC World Congress 120 M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
In summary, the following conclusions can be drawn after analyzing the results: (1) The MPC strategy obtains higher total profits than the DAS strategy during the period of four months. (2) The improvement in profits of the MPC strategy in relation to the DAS strategy are higher in periods with bad forecast. In this sense, the percentage of improvement during March is higher than 7%. (3) The improvement of the MPC strategy is based on the hourly rescheduling, which adapts to the current situation and displaces generation to highprice hours. In the opinion of the authors, the proposed economic MPC could reach better results in the following situations: (1) In the real case of not perfect forecast of energy price, the economic MPC could outperform more clearly the DAS strategy due to the perfect knowledge of the prices of the current day from a certain hour. (2) In scenarios with a higher level of penalty costs per MWh of deviation, the performance of the economic MPC can have more importance. (3) More complex models to form the penalization term in the optimization function can be evaluated. (4) Other aspects as analyzing the effect in results of the length of the sliding window, or including robust terms in the optimization problem are interesting to explore. 4. CONCLUSION An economic MPC approach is proposed to address the optimal generation scheduling in CSP plants with TES. One of the main obstacles tackled in this class of problems is the penalty cost charged by the electricity market when deviation from the committed generation schedule arises due to limited accuracy of the solar resource forecast. The proposed approach faces this pitfall with a dual purpose: (1) the economically advantageous, periodic update of the generation schedule to track the committed schedule using the most recent forecast and the current plant’s state and (2) the generation, at the appropriative time, of a more practicable schedule for the next day thanks to the use of a better estimation for the initial conditions based on short-term forecast. In order to achieve the proposed aims, the objective function of the MPC consists of economic terms where forecasted electricity prices and estimations of penalty costs are used. The proposed approach is applied, in a simulation context, to a 50 MW parabolic-troughcollector based CSP plant with TES under the assumption of participation in the Spanish day-ahead energy market and perfect price forecast. A time period of four months is taken into account in this case study to test several meteorological conditions. The proposed approach is compared with a reference strategy based on a traditional day-ahead scheduling. The comparative analysis covers economic and energy results. A significant economic improvement is observed, especially in periods with bad forecast of solar resource. Several future research lines are indicated: (1) the analysts of scenarios with imperfect forecast of electricity prices or higher level of penalty costs, (2) the development of more complex methods to estimate the penalty cost per 122
MWh of deviation, and (3) the provision of robustness for the proposed approach. REFERENCES Amrit, R., Rawlings, J.B., and Angeli, D. (2011). Economic optimization using model predictive control with a terminal cost. Annual Reviews in Control, 35(2), 178 – 186. Bravo, J.M., Alamo, T., and Camacho, E.F. (2006). Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets. Automatica, 42(10), 1745–1751. ´ Garc´ıa, I.L., Alvarez, J.L., and Blanco, D. (2011). Performance model for parabolic trough solar thermal power plants with thermal storage: Comparison to operating plant data. Solar Energy, 85(10), 2443 – 2460. Kost, C., Flath, C.M., and Most, D. (2013). Concentrating solar power plant investment and operation decisions under different price and support mechanisms. Energy Policy, 61(0), 238 – 248. Kraas, B., Schroedter-Homscheidt, M., and Madlener, R. (2013). Economic merits of a state-of-the-art concentrating solar power forecasting system for participation in the Spanish electricity market. Solar Energy, 93(0), 244 – 255. Law, E.W., Kay, M., and Taylor, R.A. (2016). Calculating the financial value of a concentrated solar thermal plant operated using direct normal irradiance forecasts. Solar Energy, 125, 267 – 281. Law, E.W., Prasad, A.A., Kay, M., and Taylor, R.A. (2014). Direct normal irradiance forecasting and its application to concentrated solar thermal output forecasting — A review. Solar Energy, 108(0), 287 – 307. Mayne, D.Q. (2014). Model predictive control: Recent developments and future promise. Automatica, 50(12), 2967 – 2986. OMIE (2016). OMIE. Last access: 02.11.16. http://www.omie.es/. SAM (2016). The SAM website. Last access: 02.11.16. https://sam.nrel.gov/. Sioshansi, R. and Denholm, P. (2010). The value of concentrating solar power and thermal energy storage. Sustainable Energy, IEEE Transactions on, 1(3), 173– 183. TMY2 (2016). User’s Manual for TMY2s. Last access: 02.11.16. http://rredc.nrel.gov/solar/pubs/tmy2/. Touretzky, C.R. and Baldea, M. (2014). Integrating scheduling and control for economic MPC of buildings with energy storage. Journal of Process Control, 24(8), 1292 – 1300. Economic nonlinear model predictive control. Usaola, J. (2012). Operation of concentrating solar power plants with storage in spot electricity markets. Renewable Power Generation, IET, 6(1), 59–66. Vasallo, M.J. and Bravo, J.M. (2016). A MPC approach for optimal generation scheduling in CSP plants. Applied Energy, 165, 357 – 370. Wittmann, M., Eck, M., Pitz-Paal, R., and MllerSteinhagen, H. (2011). Methodology for optimized operation strategies of solar thermal power plants with integrated heat storage. Solar Energy, 85(4), 653 – 659. SolarPACES 2009.
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IFAC PapersOnLine 50-1 (2017) 115–120 Economic Economic MPC MPC applied applied to to generation generation ⋆ Economic MPC applied to generation scheduling in CSP plants scheduling in CSP plants ⋆⋆ scheduling in CSP plants ∗ ∗ ∗ ∗
M.J. Vasallo ∗ J.M. Bravo ∗ D. Mar´ın ∗ M.E. Geg´ undez ∗ M.J. Vasallo Vasallo ∗ J.M. J.M. Bravo Bravo ∗ D. D. Mar´ Mar´ın ın ∗ M.E. M.E. Geg´ Geg´ undez ndez ∗ M.J. u ∗ ∗ ∗ M.J. Vasallo J.M. Bravo D. Mar´ ın M.E. Geg´ u ndez ∗ ∗ Departamento de Ingenier´ıa Electr´ onica, de Sistemas Inform´ aticos ∗ ∗ Departamento de Ingenier´ ıa o de a Departamento de ETSI Ingenier´ ıa Electr´ Electr´ onica, nica, de Sistemas Sistemas Inform´ aticos ticos Autom´ atica, Universidad de Huelva, Spain. Inform´ (e-mail: ∗ Departamento de Ingenier´ ıa Electr´ o nica, de Sistemas Inform´ aticos Autom´ a tica, ETSI Universidad de Huelva, Spain. (e-mail: Autom´ [email protected], tica, ETSI Universidad de Huelva, Spain. (e-mail: [email protected], Autom´ [email protected], tica, ETSI Universidad [email protected]) Huelva, Spain. (e-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]) [email protected], [email protected]) [email protected], [email protected])
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Abstract: Abstract: Abstract: This paper proposes a model-based predictive control (MPC) approach with economic objective Abstract: This a predictive control with economic This paper paper proposes a model-based model-based predictive control (MPC) (MPC) approach withplants economic objective function to proposes face the scheduling problem in concentrating solarapproach power (CSP) withobjective thermal This paper proposes a model-based predictive control (MPC) approach with economic objective function to face the scheduling problem in concentrating solar power (CSP) plants thermal functionstorage to face(TES) the scheduling problem in concentrating solarBy power plants with thermal energy in a day-ahead energy market context. this (CSP) approach, thewith most recent function to face the scheduling problem in concentrating solar power (CSP) plants with thermal energy storage storage (TES) in a day-ahead energy market context. By this approach, the most recent energy (TES) in a day-ahead energy market context. By this approach, the most recent prices, weather forecast and the current plant’s state can be used by the proposed in forecast a day-ahead market context. By can this be approach, recent energy prices, weather and the current plant’s state used by proposed energy storage prices, weather forecast and energy the the current plant’s state can be usedtime bythethe the proposed economic MPC(TES) approach to reschedule generation conveniently from tomost time. The energy prices, weather forecast and the current plant’s state can be used by the proposed economic MPC approach to reschedule the generation conveniently from time to time. The economic approach MPC approach to reschedule the generation from time to time. The proposed is applied, in a simulation context, toconveniently a 50 MW parabolic trough collectoreconomic MPC approach to reschedule the generation conveniently from time to time. proposed approach is applied, in a simulation context, to a 50 MW parabolic trough collectorproposed approach is applied, in aassumption simulationofcontext, a 50forecast MW parabolic trough collectorbased CSP with TES under the perfecttoprice and participation in The the proposed approach is applied, in aassumption simulation a a50four-month MW parabolic trough collectorbased CSP CSP with TES TES under the assumption ofcontext, perfect price forecast andperiod participation in the the based with under the of perfect price forecast and participation in Spanish day-ahead energy market. A case study based to on to test several based CSP withconditions TES under the assumption of study, perfect price forecast andperiod participation in the Spanish day-ahead energy A based aa four-month to several Spanish day-ahead energy market. A case case study basedaon on four-month period to test test several meteorological ismarket. performed. In study this complete economic analysis is carried Spanish energy A case based a four-month period to test several meteorological is performed. In this study, aaon complete economic is carried meteorological conditions ismarket. performed. In study thiscost, study, complete economic analysis is Results carried out usingday-ahead actualconditions values of energy price, penalty solar resource data and itsanalysis forecast. meteorological conditions is performed. In this study, a complete economic analysis is carried out using actual values of energy price, penalty cost, solar resource data and its forecast. Results out using actual values of energy price, penalty cost, solar resource data and its forecast. Results show an economic improvement in comparison with a traditional day-ahead scheduling strategy. out actual values of energyin penalty with cost, aasolar resourceday-ahead data and scheduling its forecast.strategy. Results showusing an economic economic improvement inprice, comparison with traditional day-ahead scheduling strategy. show an improvement comparison traditional show anIFAC economic improvement in comparison a traditional scheduling © 2017, (International Federation of Automaticwith Control) Hosting byday-ahead Elsevier Ltd. All rights strategy. reserved. Keywords: Optimal operation and control of power systems, Planning, Energy market Keywords: Optimal Optimal operation and and optimization-based control of of power power systems, systems, Planning, Energy market of Keywords: operation and control market integration, Model predictive control,Planning, ModelingEnergy and simulation Keywords: Optimal operation and control of power systems, Planning, Energy market of integration, Model predictive and optimization-based control, Modeling and simulation of integration, Model predictive and optimization-based control, Modeling and simulation power systems integration, Model predictive and optimization-based control, Modeling and simulation of power systems power systems power systems 1. INTRODUCTION forecasts. In order to reduce the afore-mentioned risk, the 1. INTRODUCTION INTRODUCTION forecasts. In order orderinto to(Vasallo reduce the the afore-mentioned risk, the 1. forecasts. In reduce the authors proposed and afore-mentioned Bravo, 2016) therisk, use of a 1. INTRODUCTION forecasts. In order reduce the afore-mentioned the in and Bravo, 2016) use of aa authors proposed proposed into(Vasallo (Vasallo and(MPC) Bravo, approach 2016) the therisk, usegenof model-based predictive control for Concentrating solar power (CSP) is a promising technol- authors authors proposed in (Vasallo and Bravo, 2016) the use of a model-based predictive control (MPC) approach for genConcentrating solar power (CSP) is a promising technolmodel-based predictive control approach for genConcentrating solar power (CSP) is ainpromising scheduling in CSP plants(MPC) based on a mixed-integer ogy that has drawn much attention countries technolsuch as eration model-based predictive control (MPC) approach for genConcentrating solar power (CSP) is a promising technoleration scheduling in CSP plants based on a mixed-integer ogy that has drawn much attention in countries such as eration scheduling in CSP plants based on a mixed-integer ogy much subsidy attention in countries such as programming (MIP) model. MPC is a control strategy Spainthat andhas the drawn USA, where policies have promoted in CSP plants based a mixed-integer ogy that much subsidy attention in countries such as eration programming (MIP) model. MPC is the control strategy Spain andhas the drawn USA, where subsidy policies have is promoted programming (MIP) model. MPC is aaoncontrol strategy Spain and the USA, where have promoted that hasscheduling been widely adopted both in industry and in its development. Interest in CSP policies technology mainly programming (MIP) model. MPC is a control Spain and the USA, where subsidy policies have promoted that has been widely adopted both in the industry and its development. Interest in CSP technology is mainly that has been adopted both with in thedynamics industrystrategy and in in its development. Interest in CSP technology is mainly givenwidely its ability to deal models based on the semi-dispatchable nature of CSP plants with academia that has been widely adopted both in the industry and in its development. Interest in CSP technology is mainly academia given its ability to deal with dynamics models based on the semi-dispatchable nature of CSP plants with academia given its ability(see to (Mayne, deal with2014; dynamics based on energy the semi-dispatchable CSP plants with and complex constraints Bravomodels et al., thermal storage (TES) nature and/oroffossil-fuel backup academia given its ability to deal with dynamics models based on the semi-dispatchable nature of CSP plants with and complex constraints (see (Mayne, 2014; Bravo et al., thermal energy storage (TES) and/or fossil-fuel backup and complex constraints (see (Mayne, 2014; Bravo et al., thermal energy storage (TES) and/or fossil-fuel backup systems. This attribute favours the participating of CSP 2006)). and complex constraints (see (Mayne, 2014; Bravo et al., thermal storage (TES) and/or fossil-fuel backup 2006)). systems. This attribute favours the to, participating of CSP systems. This attribute favours the participating of CSP plants in energy electricity markets thanks among others, the 2006)). This has been inspired by the question: what is the 2006)). systems. This attribute favours the participating of CSP plants in electricity markets thanks to, among others, the plants in electricity markets thanks to, among others, the This paper capability to displace production from low-price to highpaperimpact has been been inspired by the the question: what is the the This paper has inspired by question: is economic of using a MPC approach forwhat generating plants in electricity markets thanks to, among others, the capability to displace production from low-price to highcapability to displace production from low-price to highprice periods. Therefore, it is interesting to approach the This paper has been inspired by the question: what is the economic impact of using a MPC approach for generating economic impact of using a MPC approach for generating in CSP plants?. In this sense an economic capability to displace production from low-price to highprice periods. Therefore, it is is interesting interesting to approach approach the scheduling price periods. Therefore, it to the optimal generation scheduling problem (also called selfeconomic impact of using a MPC approach for generating scheduling in CSP plants?. In this sense an economic scheduling in general CSP plants?. In this presented sense anineconomic of the MPC approach (Vasallo price periods. it is interesting to approach the version optimal generation scheduling problemelectricity (also called selfoptimal generation scheduling problem (also called selfscheduling). InTherefore, a deregulated market, producscheduling in CSPis plants?. Inand this senseItanisin version of general MPC presented (Vasallo version of the the general MPC approach approach presented ineconomic (Vasallo and Bravo, 2016) proposed tested. based on optimal generation scheduling problem (also called selfscheduling). In a deregulated market, electricity producscheduling). In a deregulated market, electricity produc- version ers aim to maximize profits from energy sales. Moreover, of the general MPC approach presented in (Vasallo and Bravo, 2016) is proposed and tested. It is based on and Bravo, 2016) is proposed and tested. It is based on the fact that the cost function used to track the commitscheduling). In a deregulated market, electricity producers aim to maximize profits from energy sales. Moreover, ers aim to maximize energy sales. Moreover, in electricity markets,profits powerfrom plant owners have to offer the and Bravo, 2016) is proposed and tested. It the is based on fact that the cost function used to track committhe fact that the cost function used to track the committed generation schedule is defined such that pricing and ersdaily aim to maximize profits energy sales. Moreover, electricity markets, powerfrom plant owners have to offer offer the fact that the cost function used to track the commitin electricity markets, power plant owners have to ain production schedule in advance. Consequently, ted generation schedule is defined such that pricing and ted generation schedule is defined pricingcould and penalty information is added. Thissuch way,that penalties in electricity markets, power forecast plant owners have to offer a daily daily production schedule in advance. advance. Consequently, aelectricity production in price and schedule weather must Consequently, be taken into penalty ted generation schedule is increasing defined that pricing and information is added. This way, penalties could penalty information is by added. Thissuch way, penalties could be partially balanced revenues thanks to a daily production schedule in advance. Consequently, electricity price and weather forecast must be taken into electricity and weatherproblem. forecast must be taken into penalty account in price the optimization information is added. This way, penalties could be partially balanced by increasing revenues thanks to be partially balanced by increasing revenues thanks to the use of economic information. The proposed approach electricity price and weather forecast must be taken into account in the optimization problem. account in the optimization problem. be partially balanced by increasing revenues thanks to the use of economic information. The proposed approach the use of economic information. The proposed approach is applied, in a simulation context, to a 50 MW PTCOne of the firstoptimization works about problem. optimal CSP plant operation account in the the use of economic information. The proposed approach is applied, in a simulation context, to a 50 MW PTCOne of the first works about optimal CSP plant operation is applied, a simulation context, to a TES 50 MW PTCOne the first works about optimal plant operation CSP in plant with molten-salt-based under the was of (Sioshansi and Denholm, 2010).CSP Two models were based is applied, simulation context, to aparticipation 50 MW PTCOne of thewidely-used first works about optimal CSP plant operation based CSP in plant with price molten-salt-based TES under the was (Sioshansi and Denholm, Denholm, 2010). Two models were CSP plant with molten-salt-based TES under the was (Sioshansi and 2010). Two models assumption of aperfect forecast and in used, the tool SAM (SAM, 2016) and anwere op- based based CSP plant with molten-salt-based TES under the was (Sioshansi and Denholm, 2010). Two models were assumption of perfect price forecast and participation in used, the widely-used tool SAM (SAM, 2016) and an opassumption of perfect price forecast and participation in used, the widely-used tool SAM (SAM, 2016) and an optimization model based on mixed-integer linear program- the Spanish day-ahead energy market. assumption perfect price forecast used, the widely-used (SAM, and an op- the day-ahead energy market. timization model basedtool on SAM mixed-integer linear programthe Spanish Spanish of day-ahead energy market.and participation in timization model based on mixed-integer linear programming (MILP). Further examples using the2016) MILP approach A the economic thegeneral Spanishdescription day-aheadofenergy market. MPC approach is timization model basedexamples on mixed-integer ming (MILP). Further examples using the linear MILP approach ming using the MILP approach can be(MILP). found inFurther (Usaola, 2012) and (Kost et al., program2013). A general description ofcase thestudy, economic MPC approach approach is A general description of the economic MPC is given in Section 2. The the results and discusming (MILP). Further examples using the MILP approach can be found in (Usaola, 2012) and (Kost et al., 2013). can be found in (Usaola, 2012) and (Kost et al., 2013). A general description ofcase thestudy, MPC approach is in Section 2. The results and given in explained Section 2. in The case study, the results and discusdiscussion are Section 3economic and the finally, conclusions are CSP plants on 2012) electricity markets run2013). the risk given can be foundoperating in (Usaola, and (Kost et al., given in Section 2. The case study, the results and discussion are explained in Section 3 and finally, conclusions are CSP plants operating on electricity markets run the risk sion forward are explained in Section 3 and finally, conclusions are CSP plants operating electricity run the genrisk put in Section 4. of being penalized for on deviating frommarkets the scheduled sion forward are explained in Section 3 and finally, conclusions are CSP plants operating electricity run the risk put put forward in Section Section 4. of being penalized for on deviating frommarkets the scheduled genin 4. of being penalized for deviating from the scheduled generation due to imperfect direct normal irradiance (DNI) of beingdue penalized for deviating from the scheduled(DNI) gen- put forward in Section 4. eration due to imperfect imperfect direct normal normal irradiance (DNI) eration to direct irradiance ⋆ This work was supported by DPI2016-76493-C3-2-R of Ministerio eration due to imperfect direct normal irradiance (DNI) ⋆ ⋆
This work was was supported by by DPI2016-76493-C3-2-R DPI2016-76493-C3-2-R of Ministerio Ministerio work supported of deThis Economia y Competitividad (Spain). ⋆ de Economia y (Spain). work was supported by DPI2016-76493-C3-2-R of Ministerio deThis Economia y Competitividad Competitividad (Spain). de Economia y Competitividad (Spain). Copyright © 2017 IFAC 117 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2017 117 Copyright © 2017, 2017 IFAC IFAC 117 Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Copyright © 2017 IFAC 117Control. 10.1016/j.ifacol.2017.08.020
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 116 M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120
Fig. 1. Sliding window of the economic MPC 2. DESCRIPTION OF THE ECONOMIC MPC APPROACH Fig. 2. Block diagram of the economic MPC The proposed approach assumes participation in a dayahead energy market and the producer’s price-taking property (i.e., its production schedules do not influence market prices). The dual purpose of the proposed MPC approach is: (1) the convenient, periodical tracking of the generation schedule that has been committed to, and (2) the development of the optimal generation schedule for the next trading day at the appropriate time. The MPC approach proposed in this paper uses a cost function that included pricing and penalty information in order to achieve the dual objective. Therefore, all terms of the cost function are economic and the proposed MPC approach can be classified as an economic MPC, see (Amrit et al., 2011; Touretzky and Baldea, 2014). The two objectives for the MPC approach requires its sliding window to be divided into two intervals (see Fig. 1): the tracking interval (TI) and the next schedule interval (NSI). The generation schedule must be updated to track the schedule that has been committed to within the interval TI, while the interval NSI is used to maximize future profits and to generate the schedule for the next day at the appropriate time. Several variables and parameters related to the sliding window are defined next: • t(i) = i∆tw where i = 0, 1, ... are the time instants when MPC control output is generated. The beginning time of the sliding window when it is in position i is set to instant t(i). Case i = 0 refers to instant 0.0h of the current day D. ∆tw is the time step for control update. • tschedule del is defined as the deadline hour in the day D for the delivery of the generation schedule for the next day D+1. This deadline hour depends on the market of each country. • tschedule end is the final time of the committed generation schedule. If the current time has not reached the time tschedule del , tschedule end is usually 24.0h of the day D. On the contrary, tschedule end is 24.0h of the day D+1 because the generation schedule for this day has been already delivered. • ∆w is the constant sliding window length.
According to the previous definitions, the endpoints of the intervals TI and NSI are shown in Fig. 1. Notice that the sliding window length is constant but the lengths of both intervals are time-variant. When t(i) = tschedule del , the generation schedule solved by the MPC control for the interval NSI until 24.0h of the day D+1 can be given as the generation schedule for this day. Since the typical optimal scheduling problem has an optimization horizon based on the next one or 118
two trading days (Wittmann et al., 2011), and a constant sliding window length is assumed, this length (∆w) can have a value between 24 − tschedule del +24 hours (oneday strategy) and 24 − tschedule del +48 hours (two-day strategy). Fig. 2 shows the block diagram of the MPC approach. At each sliding window position i, MPC control receives the following information: (1) Current continuous state of the CSP plant (xc (t(i))), e.g., the TES energy level and thermal state in the solar field (SF). (2) Current discrete state of the plant (xd (t(i))), e.g., active operating phases in the SF, TES or turbine. (3) Electricity price forecast made at time t(i) (p(j/i), for j = 1, .., N ), where j indicates each step in the MPC model, N = ∆w/∆to is the number of steps in the sliding window, and ∆to is the time step expressed in hours of the MPC model. (4) Predictions made at time t(i) of average value of the maximum thermal power available from the SF (PSF max (j/i), for j = 1, .., N ). The qualifying ’maximum’ is added to indicate that partial defocus in the SF can lead to a decrease in the thermal power available. A CSP plant model, DNI and other meteorological variables forecast and initial conditions xc (t(i)) and xd (t(i)) are used to generate these predictions. (5) Committed generation schedule to be met (Peref (j/i), for j = 1, .., NT I ), expressed in average gross electric power, where NT I = (tschedule end − t(i))/∆to is the number of steps in the interval TI. As a result of the optimization at the sliding window position i, the following outputs are generated: (1) Decision variables at time t(i) (u(j/i), for j = 1, .., N ). Only the decision variables u(1/i) are applied to the plant as common in MPC approaches. (2) Average values of turbine-generated gross electric power calculated at time t(i) (Pe (j/i), for j = 1, .., N ). When t(i) = tschedule del , values inside the interval NSI until 24.0h of the next day are given as the new generation schedule for this day (Peref (j/i) = Pe (j/i), for j = NT I + 1, .., NT′ I , where NT′ I = NT I + 24/∆to is the new number of steps in the interval TI). The objective function to minimize is expressed by Equation (1)
Proceedings of the 20th IFAC World Congress M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
Strategy
Model
Rescheduling
MPC DAS
MIP-MPC MIP-DAS
Hourly No
Short term forecast Hourly No
Feedback of the plant’s state Hourly Daily
Turbine capacity (gross) Solar field capacity Thermal capacity in solar-only mode Thermal capacity in TES-only mode Solar multiple TES capacity (TES-only mode) Turbine efficiency (full load) Fossil backup only for preventing HTF freezing
Table 1. Information about scheduling strategies and models
117
52.5 MW-e 250 MW-t 140 MW-t 119 MW-t 1.8 8 hours 38%
Table 2. Characteristics of the CSP plant J(i) = − ∆to
N TI ∑
[p(j/i)Penet (j/i)
j=1
− ϕ(j/i)(Peref net (j/i) − Penet (j/i)) − fcost (.)] − ∆to
N ∑
j=NT I +1
[p(j/i)Penet (j/i) − fcost (.)]
− s(E(N + 1/i))
(1)
where ϕ(j/i) is an estimation of the penalty cost per kW-h of deviation at hour j, Penet (j/i) is the turbine-generated net electric power, Peref net (j/i) is the committed net electric power, fcost (.) represents generation costs, and s(E(N + 1/i)) is a terminal value term applied to the final TES energy level. Notice that function −J(i) represents the profits along the sliding window. In this work it is assumed that the electricity production does not exceed the committed schedule, then the term ϕ(j/i) refers to falling penalty. 3. CASE STUDY In this section, the economic MPC approach proposed by this paper is applied, in a simulation context, to a 50 MW PTC-based CSP plant with molten-salt-based TES. Two scheduling strategies are compared, the proposed economic MPC strategy and a traditional day-ahead scheduling (DAS strategy). The MPC strategy uses the MIP-MPC model (see subsection 3.1 for more details), hourly rescheduling, hourly short-term forecast and hourly feedback of the plants’s state. The DAS strategy is characterized by the following: (1) The schedule for the day D+1 is generated at tschedule del of day D. At this moment, initial conditions for day D+1 are estimated using the current plant state, the day-ahead forecast and the schedule still to be met. (2) The generation schedule is tracked without any rescheduling. Then the generation each hour is the maximum that can be reached according to the committed value. The optimization model to generate the schedule in the DAS strategy is refereed as MIP-DAS model in this paper (see subsection 3.1 for more details). Table 1 summarizes all information about optimization models used and scheduling strategies. The CSP plant used in this study is based on the model presented in (Garc´ıa et al., 2011) and also used in (Vasallo and Bravo, 2016), which describes the plant Andasol 2 in Granada, Spain. Some characteristics of this model (adapted to this case study) are shown in Table 2. 119
Next, the main features of the simulation scenario developed for this case study are enumerated. An enough long time period is considered (from 01/02/2013 to 31/05/2013) with the purpose of testing several meteorological conditions. The Spanish day-ahead energy market and the producer’s price-taking property are considered. Price forecasts are assumed to be perfect and were obtained from data of the Iberian market operator OMIE, ((OMIE, 2016)). No premium per MWh is considered. Penalty costs per MWh of deviation are also obtained from OMIE. In order to keep things simple, generation costs are not taken into consideration. The generation schedule and MIP-MPC model resolutions are hourly. The frequency of the rescheduling is also hourly. Therefore, ∆to = ∆tw = 1.0 h (see Fig. 1). Parameter tschedule del is set to 10.0 h (Spanish market in 2013). Parameter ∆w is set to 48 h to reach a compromise between computation time of the MIP-MPC model and the possibility to conserve energy for sale after the end of the next day. Therefore, the length of the interval NSI at 10.0 h is 34 h, and the scheduling problem for the next day is based on the next 1+5/12 days (i.e., an intermediate scheme between the one-day and two-day strategies). To generate predictions PSF max (j/i) (see Fig.2), the detailed CSP plant model from (Vasallo and Bravo, 2016) is used. DNI and ambient temperature are the only meteorological variables considered and ambient temperature forecasts are assumed to be perfect and created from TMY2 data (TMY2, 2016). The CSP plant is represented by an onehour-resolution model to avoid very high simulation times, as in (Kraas et al., 2013; Law et al., 2016). Specifically, a MIP model derived from the itself MIP-MPC model is employed. Therefore, performance differences are only due to DNI forecast errors. This model is referred in this work as MIP-plant model. A set of day-ahead forecasts of solar radiation, obtained by the Integrated Forecast System model (IFS) of the European Centre for Medium-range Weather Forecasts (ECMWF), is available. Moreover, a set of solar radiation measures is also available. Both sets are converted to maximum thermal power available from SF by simulation with the detailed CSP plant model. Short-term DNI forecasts are also taken into account in this study. Several methods can be consulted in (Law et al., 2014). In the absence of short-term forecast data, a synthetic predictor is developed, which works directly with the variable PSF max (j/i) to avoid conversion from DNI values. Equation (2) describes the synthetic shortterm predictor used to incorporate the influence of shortterm DNI forecasts: PSF max ST F (k/i) = PSF max actual (k/i)+ +r(k)(PSF max DA (k/i) − PSF max actual (k/i))
(2)
Proceedings of the 20th IFAC World Congress 118 M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
for k=1 to NST F + 1; where NST F is the scope (hours) of the short-term forecast; r(k) is a function linear with index k, r(1) = 0; r(NST F + 1) = 1; PSF max ST F (k/i) and PSF max actual (k/i) and PSF max DA (k/i) are the shortterm forecasted, actual and day-ahead forecasted maximum thermal power available from SF. Notice that the percentage of day-ahead forecast error to be added to the actual value to generate the short-term forecast of the first hour is 0%. This percentage grows linearly with time and it is 100% when k = NST F + 1 (i.e., out of the scope of the short-term forecast). Typical values for NST F are 5 or 6 hours (Law et al., 2014, 2016).
lower than the minimum electricity price in the simulation period. This way, the terminal value term of the objective function makes the defocused thermal energy be as low as possible once the maximum economic profits (without terminal value term) have been obtained. In the Spanish market, deviation from the scheduled generation produces penalty costs if it requires the intervention of the transmission system operator. These penalties are associated with the costs incurred to stabilize the system, and do not follow any pre-given function. Therefore, these costs are difficult to estimate. An average value for ϕ(j/i) is assumed in Subsection 3.2.
MIP models are explained in Subsection 3.1. Subsection 3.2 describes the characteristics of the following input data: solar resource, its day-ahead forecast and the penalty costs per MWh of deviation. Finally, results and discussion are shown in Subsection 3.3.
MIP-DAS model. The MIP-DAS model is an optimization model which generates the generation schedule for the day D+1 when t(i) = tschedule del at the day D in case of DAS strategy. The MIP-DAS model is derived from the MIP-MPC model: the TI interval is removed and the NSI interval begins the hour 0 of the day D+1. Initial values for the moment before hour 0 of day D+1 are estimated at tschedule del of day D using the current status of the plant, day-ahead forecast and the schedule still to be met.
3.1 MIP models In this subsection the three one-hour-resolution MIP models are described. The MIP-DAS and MIP-plant models are derived from the MIP-MPC model. The formulation of the three MIP models for this case study was carried out without any non-linear element, except for binary variables. Thus they are MILP models. A clarification is important to do at this moment: it is supposed that the plant operator and control systems of the plant under study take decisions based on two goals with different priority (Vasallo and Bravo, 2016). The high-priority goal is to minimize the generation error. Once this objective is met, the low-priority goal can be applied, which consists in minimizing the defocused thermal power in the SF. Therefore, the plant under study has an only independent decision variable in relation to power sharing, e.g., the setpoint for electricity generation. Then, the MPC action u(1/i) = Pe SP (1/i). Equation Pe SP (1/i) = Pe (1/i) is used to obtain the setpoint, where Pe (1/i) is a value generated by the MPC control. MIP-MPC model. The set of equations and inequalities that composes the MIP-MPC model and values for its parameters can be consulted in (Vasallo and Bravo, 2016). The objective function to minimize is expressed in equation (3), which is a specific case of the objective function in Section 2. Minimize
J(i) =
−∆to
N TI ∑
[p(j/i)Penet (j/i)
j=1
−ϕ(j/i)(Peref net (j/i) − Penet (j/i))] −∆to
N ∑
(p(j/i)Penet (j/i))
j=NT I +1
−KE(N + 1/i)
(3)
In this objective function, generation costs are not taken into consideration and KE(N + 1/i) is the terminal value term formed by a value proportional to the final TES energy level, with constant K defined by equation K = ηpvlow , where η is a efficiency factor to convert stored energy to net electric energy, and pvlow is a value much 120
MIP-plant model. In order to avoid high simulation time, the representation of the CSP plant is made by a MIP model of one-hour resolution. It is composed of two consecutive optimization models derived from the MIPMPC model. The two goals with different priority which guide the decisions of the plant operator and control systems (see the beginning of Section 3.1) explains this scheme. This model receives each hour the setpoint generated from the MPC or DAS strategy. Then, the evolution of the electrical generation and the plant’s state is obtained based on this hourly update of setpoint, the actual value for solar resource and the aforementioned goals. 3.2 Input data description The characteristics of the solar resource, its day-ahead forecast and the penalty costs per MWh of deviation for the studied time period are described in this Subsection. Fig. 3 shows the hourly average values of the maximum thermal power available from the SF, PSF max actual (j), that have been obtained using solar radiation data and the detailed CSP plant model. As can be seen in the figure, as the days advance, the profile of PSF max actual (j) increases in intensity and length. Furthermore, approximately the first one seventy days present a high meteorological variability, while the stability increases the last fifty days. An important variable that can influence the performance of the scheduling strategies is, obvioursly, the day-ahead forecast error of the maximum thermal power available from the SF. In general, the forecast error increases with the meteorology variability, that is, winter days presents higher prediction errors than clean summer days. In order to characterise the day-ahead forecast error, some metrics are shown in Table 3 in a monthly basis. Note that only daylight hours are used to obtain the metrics because in night hours the prediction error is absent. The mean of the maximum thermal power available from SF is denoted by P¯SF max actual . The Relative Root Mean Absolute Error and the Relative Mean Bias Error are denoted by rM AE and rM BE respectively, (see (Kraas et al., 2013) for
Proceedings of the 20th IFAC World Congress M.J. Vasallo et al. / IFAC PapersOnLine 50-1 (2017) 115–120 Toulouse, France, July 9-14, 2017
February 4.4%
119
March 7.3%
April 3.4%
May 0.9%
Table 5. Monthly percentage of improvement Hourly mean value Generation (MWh-e) Deviation (MWh-e) Defocused energy (MWh-t) TES energy level (%) Equivalent sale price (Euros/MWh-e)
DAS 12.42 1.46 4.26 23.29 64
MPC 12.37 1.76 4.39 28.04 65.49
% -0.43% 20.68% 3% 20.37 % 2.33%
Table 6. Energy results of DAS and MPC
40
Month February March April May
P¯SF max
actual
(MW)
82.5 87.6 152.4 164.4
rM AE (%) 32.1 52.8 25.7 17.8
rM BE (%) 3.8 8.4 -5.3 10.6
Table 3. Metrics of day-ahead forecast error for maximum thermal power from the SF
30 Percentage of total generation
Fig. 3. Hourly average values for maximum thermal power available from the SF (kW)
20
10
0
−10
−20
Revenues (Euros) Penalty costs (Euros) Profits (Euros)
DAS 2148321 38969 2109352
∆Profit of MPC (%) DAS (%) MPC (%)
MPC 2228481 58949 2169532
0
10
20
30 40 50 60 Prices Interval (Euros/MWh)
70
80
90
Fig. 4. Distribution of generation with price intervals for DAS and MPC strategies (%)
Table 4. Economic results of DAS and MPC strategies expresions of these metrics). Some observations may be useful. The mean of the maximum thermal power available from the SF increases near of 100% from February to May. The relative error is higher in winter months. In fact, March has been particularly bad in the studied period. Finally, the monthly bias error can vary widely. The proposed economic MPC approach uses a constant ¯ where ϕ¯ = 7.69 ϕ(j, i) value. In this case ϕ(j, i) = ϕ, Euros/MWh is the mean value for the penalty costs per MWh during the first half-year period. 3.3 Results and discussion In this Subsection, simulation results are shown and commented. It is important to remark that there are many factors which affect the economic results of scheduling strategies, e.g., electricity market regulations, plant site local climate, forecasts, plant design, simplification hypothesis and models used (Law et al., 2016). Therefore, the conclusions drawn from this case study could be different in other scenarios. Next, the following analysis will be performed: (1) economic comparison between MPC and DAS strategies; (2) calculation of the percentage of improvement in profits of the MPC strategy respect to the DAS strategy on a monthly basis; and (3) energy analysis of both strategies. Table 4 shows the economic results of the DAS and MPC strategies. It should be underlined that the results 121
obtained by the MPC scheduler outperform the profits obtained by the DAS scheduler. Table 5 shows, for each month, the percentage of improvement in profits of MPC strategy with respect to the DAS strategy. As can be seen, the MPC strategy obtains substantial improvements when the meteorological instability is present. In fact, the best result is obtained in March, that is, the month with worse forecast for the maximum thermal power available form the SF. In this sense, the MPC strategy can compensate bad forecast situations. Next, some energy results of DAS and MPC strategies are shown in Table 6. It is shown that generation is slightly lower with MPC strategy. Moreover, values for deviation and defocused energy with MPC strategy are also worse. The economic improvement of MPC strategy is shown in parameter equivalent sale price. This parameter is defined as the ratio between total profits and total generation. The worse energy results of MPC strategy are explained by its capability to admit deviation in order to reserve energy for higher possible revenues, as its higher mean TES energy level clarifies. This capability is based on the hourly slide of the MPC window, which is incorporating new information (precise or not). In any case, although total deviation can be higher with the MPC strategy, this strategy distributes it by taking advantage of the most favorable hours obtaining an improvement of 2.33% in the equivalent sale price. Fig. 4 shows the distribution of electric generation with price interval for both strategies. It can be observed the displacement of generation to high prices of the MPC strategy over the DAS strategy.
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In summary, the following conclusions can be drawn after analyzing the results: (1) The MPC strategy obtains higher total profits than the DAS strategy during the period of four months. (2) The improvement in profits of the MPC strategy in relation to the DAS strategy are higher in periods with bad forecast. In this sense, the percentage of improvement during March is higher than 7%. (3) The improvement of the MPC strategy is based on the hourly rescheduling, which adapts to the current situation and displaces generation to highprice hours. In the opinion of the authors, the proposed economic MPC could reach better results in the following situations: (1) In the real case of not perfect forecast of energy price, the economic MPC could outperform more clearly the DAS strategy due to the perfect knowledge of the prices of the current day from a certain hour. (2) In scenarios with a higher level of penalty costs per MWh of deviation, the performance of the economic MPC can have more importance. (3) More complex models to form the penalization term in the optimization function can be evaluated. (4) Other aspects as analyzing the effect in results of the length of the sliding window, or including robust terms in the optimization problem are interesting to explore. 4. CONCLUSION An economic MPC approach is proposed to address the optimal generation scheduling in CSP plants with TES. One of the main obstacles tackled in this class of problems is the penalty cost charged by the electricity market when deviation from the committed generation schedule arises due to limited accuracy of the solar resource forecast. The proposed approach faces this pitfall with a dual purpose: (1) the economically advantageous, periodic update of the generation schedule to track the committed schedule using the most recent forecast and the current plant’s state and (2) the generation, at the appropriative time, of a more practicable schedule for the next day thanks to the use of a better estimation for the initial conditions based on short-term forecast. In order to achieve the proposed aims, the objective function of the MPC consists of economic terms where forecasted electricity prices and estimations of penalty costs are used. The proposed approach is applied, in a simulation context, to a 50 MW parabolic-troughcollector based CSP plant with TES under the assumption of participation in the Spanish day-ahead energy market and perfect price forecast. A time period of four months is taken into account in this case study to test several meteorological conditions. The proposed approach is compared with a reference strategy based on a traditional day-ahead scheduling. The comparative analysis covers economic and energy results. A significant economic improvement is observed, especially in periods with bad forecast of solar resource. Several future research lines are indicated: (1) the analysts of scenarios with imperfect forecast of electricity prices or higher level of penalty costs, (2) the development of more complex methods to estimate the penalty cost per 122
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