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Economic Model Predictive Control for Optimal Operation of Home Microgrid with Photovoltaic-Combined Heat and Power Storage Systems*
Proceedings of the 20th World Congress The International Federation of Congress Automatic Control Proceedings of 20th Proceedings of the the 20th World World The International Federation of Congress Automatic Control Proceedings of the 20th9-14, World Congress Toulouse, France, July 2017 The International Federation of Automatic Control Control The International Federation of Automatic Toulouse, France, July 9-14, 2017 Available online at www.sciencedirect.com The International of Automatic Control Toulouse, France, July Toulouse, France,Federation July 9-14, 9-14, 2017 2017 Toulouse, France, July 9-14, 2017
ScienceDirect
IFAC PapersOnLine 50-1 (2017) 10027–10032 Economic Economic Model Model Predictive Predictive Control Control for for Economic Model Predictive Control for Optimal Operation of Home Microgrid Economic Model Predictive for Optimal Operation of HomeControl Microgrid Optimal Operation of Home Microgrid with Photovoltaic-Combined Heat and Optimal Operation of Home Microgrid with and with Photovoltaic-Combined Photovoltaic-Combined Heat Heat and Power Storage Systems with Photovoltaic-Combined Heat and Power Storage Systems Power Storage Systems Power Storage Systems Diego I. Hidalgo Rodr´ıguez ∗∗ , and Johanna M.A. Myrzik ∗∗
Diego I. Hidalgo Rodr´ıguez ∗∗ , and Johanna M.A. Myrzik ∗∗ Diego I. I. Hidalgo Rodr´ıguez ıguez ∗ ,, and and Johanna Johanna M.A. M.A. Myrzik Myrzik Diego Hidalgo Rodr´ Diego I. Hidalgo∗ Institute Rodr´ıguez , and Johanna M.A. Myrzik ∗ of Energy Systems, ∗ ∗ Institute of Energy Systems, 3 ∗ Institute and of Energy Energy Systems, Energy Energy Economics of ∗ Institute and Energy Efficiency Efficiency EnergySystems, Economics (ie (ie333 )) Institute of Energy Systems, Energy Efficiency and Energy Economics (ie TU Dortmund University, Dortmund, Germany Energy Efficiency and Energy Economics (ie3 )) TU Dortmund University, Dortmund, Germany Energy Efficiency and Energy Economics (ie ) TU Dortmund University, Dortmund, Germany [email protected], [email protected] TU Dortmund University, Dortmund, Germany [email protected], [email protected] TU Dortmund University, Dortmund, Germany [email protected], [email protected] [email protected], [email protected] [email protected], [email protected] Abstract: Abstract: In In this this paper, paper, the the economic economic model model predictive predictive control control operation operation of of aa home home microgrid microgrid Abstract: In this this paper, paper, the theheat economic model predictive control operation of ofThe a home home microgrid with photovoltaic-combined and power storage systems is investigated. purpose of Abstract: In economic model predictive control operation a microgrid with photovoltaic-combined heat and power storage systems is investigated. The purpose of the the Abstract: In this the paper, theheat economic model predictive control operation ofThe a home microgrid with photovoltaic-combined and power storage systems is investigated. purpose of the paper is to present problem formulation, and quantify the impact of uncertainty coming with photovoltaic-combined heat and power storage systems is investigated. The purpose offrom the paper is to present the problem formulation, and quantify the impact of uncertainty coming from with photovoltaic-combined heat and power storage systems is investigated. The purpose of the paper is to present the problem formulation, and quantify the impact of uncertainty coming from the thermal behavior of the mini combined heat and power plant. A model predictive controlpaper is to present the of problem formulation, and quantify the plant. impactAofmodel uncertainty coming from the thermal behavior the mini combined heat and power predictive controlpaper is to present the of problem formulation, and the plant. impact uncertainty coming from the thermal thermal behavior of the mini mini combined heatquantify and power power plant. Aofmodel model predictive controlbased strategy is contrasted with an open loop-based operation and a perfect forecast based the behavior the combined heat and A predictive controlbased strategy is contrasted withcombined an open loop-based operation and a perfect forecastcontrolbased the thermal behavior of the mini heat and such power plant. A model predictive based strategy is contrasted with an openofloop-based loop-based operation and perfect forecast based operation. The paper discusses the effects having an uncertainty, relaying the benefits based strategy is contrasted with an open operation and aa perfect forecast based operation. The paper discusses the effects of having such an uncertainty, relaying the benefits based strategy is contrasted with an openof loop-based operation and a perfect forecast based operation. The paper discusses the effects having such an uncertainty, relaying the benefits of using model predictive control to handle such situations. Additionally, the paper at hand operation. The paper discusses the effects of having such an uncertainty, relaying the benefits of using model predictive control toeffects handle such situations. Additionally,relaying the paper at hand operation. The paper discusses the of having such an uncertainty, the benefits of using model predictive control to handle such situations. Additionally, the paper at presents a sensitivity analysis regarding storage size, concluding that the proposed economic of using model predictive control to handle suchsize, situations. Additionally, the papereconomic at hand hand presents a sensitivity analysis regarding storage concluding that the proposed of using model predictive control to handle such situations. Additionally, the paper at hand presents a sensitivity sensitivity analysis regarding storage size, concluding concluding that the proposed proposed economic economic model predictive control strategy can be used to reduce total annual costs. presents a analysis regarding storage size, that the model predictive control strategy can be used to reduce total annual costs. presents a sensitivity analysis regarding storage size, concluding that the proposed economic model predictive predictive control control strategy strategy can can be be used used to to reduce reduce total total annual annual costs. costs. model model control strategy can used toControl) reduce Hosting total annual costs. © 2017,predictive IFAC (International Federation of be Automatic by Elsevier Ltd. All rights reserved. Keywords: Microgrids, Model predictive control, Optimization, Storage Keywords: Microgrids, Model predictive control, Optimization, Storage systems. systems. Keywords: Microgrids, Microgrids, Model Model predictive predictive control, control, Optimization, Optimization, Storage Storage systems. systems. Keywords: Keywords: Microgrids, Model predictive control, Optimization, Storage systems. 1. the 1. INTRODUCTION INTRODUCTION the economic economic operation. operation. Our Our work work builds builds upon upon the the work work 1. INTRODUCTION INTRODUCTION the economic operation. Our work builds upon the presented in (Kriett and Salani, extend this 1. the economic operation. Our work2012). buildsWe upon the work work presented in (Kriett and Salani, 2012). We extend this 1. INTRODUCTION the economic operation. Our work builds upon the presentedwork in (Kriett (Kriett and Salani, Salani, 2012). contributions: We extend extendwork this previous by including the following Following the incentives of European governments to presented in and 2012). We this work by including the following contributions: Following the incentives of European governments to previous in (Kriett and Salani, 2012). contributions: We extend this previous work work by including including the following following contributions: Following the incentives of European European governments to presented achieve the desired reduction of CO2 emissions by 2050 previous by the Following the incentives of governments to achieve thethe desired reduction of CO2 emissions by 2050 •• A for the dynamic behavior work bymodel including Following incentives of European governments to previous A thermal thermal model for the the following dynamic contributions: behavior for for a a achieve the Commission, desired reduction ofhousehold CO2 emissions emissions byare2050 2050 (European 2011), owners inachieve the desired reduction of CO2 by (European Commission, 2011), household owners are in• A thermal model for the dynamic behavior for ina a commercial internal combustion engine mini CHP • A thermal model for the dynamic behavior for achieve the desired reduction of CO2 emissions by 2050 commercial internal combustion engine mini CHP in (European Commission, 2011), household owners are increasingly investing in new low carbon electricity tech(European Commission, 2011), owners are in• A thermal model for the dynamic behavior for in creasingly investing in new lowhousehold carbon electricity techcommercial internal combustion engine mini CHP CHP ina the optimization problem commercial internal combustion engine mini (European Commission, 2011), household owners are inthe optimization problem creasinglyAsinvesting investing in new low low grids carbon electricity technologies. a distribution are facing pencreasingly new carbon commercial internal combustion engine mini CHP in nologies. Asinvesting a result, result, in distribution grids areelectricity facing the the techpenoptimization problem •• the An analysis impact the problem creasingly new low carbon techAn optimization analysis on on the the impact of of uncertainties uncertainties in in mini mini nologies. of Asrenewable a result, result, in distribution grids areelectricity facing the penetration energy sources (RES), e.g. rooftop nologies. As a distribution grids are facing the penthe optimization problem etration of renewable energy sources (RES), e.g. rooftop • An analysis on the impact of uncertainties in mini CHP thermal power settling times • CHP An analysis the impact uncertainties in mini nologies. of Asrenewable aplants, result, distribution grids(RES), aregenerators, facing penthermalon power settling of times etration of renewable energy sources (RES), e.g.the rooftop photovoltaic energy efficient such etration energy sources e.g. rooftop •• An analysis the impact of uncertainties in mini photovoltaic plants, and and energy efficient generators, such CHP thermalon power settling times A quantification of the added value of CHP thermal power settling times etration of renewable energy sources (RES), e.g. rooftop • A quantification of the added value of MPC MPC compared compared photovoltaic plants, and energy efficient generators, such combined heat and power plants (CHP). In addition, the photovoltaic plants, and energy efficient generators, such CHP thermal power settling times combined heat and power plants (CHP). In addition, the A quantification quantification of the the added added value of ofstrategy MPC compared compared to an optimization •• A of value MPC photovoltaic plants, and energy efficient such an open open loop-based loop-based optimization combined heat and power plants (CHP). generators, In addition, addition, the use of batteries and energy storages combined heat and power plants (CHP). In the •• to A quantification of the on added value ofstrategy MPC compared use of electrical electrical batteries and thermal thermal energy storages to an open loop-based optimization strategy A sensitivity analysis the impacts of battery to an open loop-based optimization strategy combined heat and power plants (CHP). In addition, the • A sensitivity analysis on the impacts of battery size size use of of becomes electricalalso batteries and to thermal energy storages (TES) interesting increase the flexibility. use electrical batteries and thermal energy storages to an open loop-based optimization strategy (TES) becomes also interesting to increase the flexibility. • A sensitivity analysis on the impacts of battery and TES size on the economic operation • and A sensitivity on the impacts of battery size size use these of becomes electrical batteries andmicrogrid, thermal energy storages TES size analysis on the economic operation (TES) becomes also interesting to increase the flexibility. flexibility. All systems form a home which operation (TES) also interesting to increase the • A sensitivity analysis on the impacts of battery size All these systemsalso form a home microgrid, which operation and TES TES size size on on the the economic economic operation operation and (TES) becomes interesting to increase the flexibility. All these systems form a home microgrid, which operation must be efficient and economical. For this reason, operThe paper is organized as follows: Section 2 describes All these systems form a home microgrid, which operation and TES size on the economic operation must be efficient and economical. For this reason, operThe paper is organized as follows: Section 2 describes the the All these systems form a home microgrid, which operation must be efficient and economical. economical. For this reason, operThe paper is as Section the ation of home microgrids is getting the attention of the under investigation, the problem, must be efficient and For this reason, operThe paper is organized organized as follows: follows: Section 22 describes describes the ation of home microgrids is gettingFor thethis attention ofoperthe system system under investigation, the optimization optimization problem, opopmust be efficient and economical. reason, The paper is organized as follows: Section 2 describes the ation of of community, home microgrids microgrids isproposing getting the the attention of the the system system under investigation, the optimization problem, opresearch who is different approaches eration strategies and simulation setup. Then, simulation ation home is getting attention of under investigation, the optimization problem, opresearch community, who is proposing different approaches eration strategies and simulation setup. Then, simulation ation of home microgrids is getting the attention of the system under investigation, the optimization problem, opresearch community, who is proposing different approaches eration strategies and simulation setup. Then, simulation to tackle this based on optiresults and corresponding discussion are presented in research who is proposing approaches strategies and simulation setup. simulation to tacklecommunity, this task. task. Approaches Approaches baseddifferent on numerical numerical opti- eration results and corresponding discussion are Then, presented in SecSecresearch who is promising proposing different approaches eration strategies and simulation setup. Then, simulation to tackle tacklecommunity, this task. task.are Approaches based(Parisio on numerical numerical opti- tion results and corresponding discussion are presented in mization methods very et al., 2014; 3. Finally, Section 4 summarizes the main outcomes to this Approaches based on optiresults and corresponding discussion are presented in SecSecmization methods are very promising (Parisio et al., 2014; tion 3. and Finally, Section 4 summarizes thepresented main outcomes to tackle this task. Approaches based on numerical optiresults corresponding discussion are in Secmization methods methods are veryChen promising (Parisio et al., al.,et2014; 2014; tion 3.paper, Finally, Section summarizes the main outcomes outcomes Oldewurtel et al., 2014; et al., 2013; Zong al., of the its limitations and future work. mization are very promising (Parisio et tion 3. Finally, Section 44 summarizes the main Oldewurtel et al., 2014; Chen et al., 2013; Zong et al., of the paper, its limitations and future work. mization methods are very promising (Parisio et al., 2014; tion 3. Finally, Section 4 summarizes the main outcomes Oldewurtel et al., al., 2014; ChenSossan et al., al.,et2013; 2013; Zong Kriett et al., al., of of the the paper, paper, its its limitations limitations and and future future work. work. 2012; Houwing et al., al., Oldewurtel et Chen et Zong et 2012; Houwing et 2014; al., 2011; 2011; Sossan et2013; al., 2014; 2014; Kriett Oldewurtel et al., 2014; Chen et2015), al.,et Zongbecause et al., of the paper, its limitations and future work. 2012; Houwing et Zhang al., 2011; 2011; Sossan et not al., just 2014; Kriett and Salani, 2012; et al., 2012; Houwing et al., Sossan al., 2014; Kriett 2. SYSTEM DESCRIPTION AND and Salani, 2012; Zhang et al., 2015), not just because 2. SYSTEM DESCRIPTION AND PROBLEM PROBLEM 2012; Houwing etisZhang al., 2011; Sossan et not al., 2014;because Kriett and Salani, Salani, 2012; Zhang et al., al., 2015), not just because system operation explicitly considered through mathe2. AND and 2012; et 2015), just FORMULATION 2. SYSTEM SYSTEM DESCRIPTION DESCRIPTION AND PROBLEM PROBLEM system operation is explicitly considered through matheFORMULATION and Salani, 2012; Zhang et al., 2015), not just because 2. SYSTEM DESCRIPTION AND PROBLEM system operation operation is explicitly explicitly considered through mathematical models, but also because operational constraints FORMULATION system is considered through matheFORMULATION matical models, but also because operational constraints system operation is explicitly considered through matheFORMULATION matical models, but but also because operational constraints and operational goals are included in matical models, also operational constraints In the present work, aa system and operational goals arebecause included in the the formulation. formulation. In the present work, system for for aa multi-family multi-family house house matical models, but also because operational constraints and operational goals are included in the formulation. Within this framework, model predictive control (MPC) and operational goals are included in the formulation. In the present work, a system for a multi-family house (MFH) is investigated, which combines one one In the present work, a system for a house Within this framework, model predictive control (MPC) (MFH) is investigated, which combines multi-family one mini mini CHP, CHP, one and operational goals are included in the formulation. Within thisrelevance framework, model predictive control (MPC) In the present work, a system for a multi-family house is gaining due to its prediction nature and its Within this framework, model predictive control (MPC) (MFH)one is investigated, investigated, which combines oneFig. mini1 CHP, CHP, one TES, PV plant and one battery, as presents. (MFH) is which combines one mini one is gaining relevance due to its prediction nature and its TES, one PV plant and one battery, as Fig. 1 presents. Within this framework, model predictive control (MPC) is gaining gaining relevance relevance due to to its its prediction prediction nature and its its (MFH) isoperation investigated, which combines oneFig. mini CHP, one robustness against uncertainties (Parisio et al., 2014). In is due nature and TES, one PV plant and one battery, as 1 presents. Systems is formulated as a mixed integer linear TES, one PV plant and one battery, as Fig. 1 presents. robustness against uncertainties (Parisio et al., 2014). In operation is and formulated as a mixed integer linear is gaining relevance due to provide its prediction and its robustness against uncertainties (Parisio etnature al., regarding 2014). In Systems TES, one PV plant one battery, as Fig. 1 presents. this paper, the purpose is to new insights robustness against uncertainties (Parisio et al., 2014). In Systems operation is formulated as a mixed integer linear programming (MILP) problem within an MPC framework. Systems operation is formulated as a mixed integer linear this paper, the purpose is to provide new insights regarding (MILP) problem within an MPC framework. robustness against uncertainties (Parisio eteconomic al., regarding 2014). In programming this paper, the the purpose is to to provide provide newan insights regarding operation is formulated as the a mixed integer linear the operation of home using MPC this paper, is new insights programming (MILP) problem within anprinciple MPC framework. This section first briefly describes of MPC programming (MILP) problem within an MPC framework. the operation ofpurpose home microgrids microgrids using an economic MPC Systems This section first briefly describes the principle of MPC this paper, the purpose is to provide new insights regarding the operation operation of home home microgrids using an an economic economic MPC programming (MILP) problem within an MPC framework. approach, more specifically investigating the impact of the of microgrids using MPC This its section first briefly briefly describes the principle of MPC MPC and utilization for the system under investigation, This section first describes the principle of approach, more specifically investigating the impact of and its utilization for the system under investigation, the operation of home microgrids using an economic MPC approach, more specifically specifically investigating the impact of and This section firstcorrespondent briefly describes the principle of MPC mini CHP dynamic behavior prediction and storage size on approach, more investigating the impact of its utilization for the system under investigation, then it presents constraints and objective and its utilization for the system under investigation, mini CHP dynamic behavior prediction and storage size on it presents correspondent constraints and objective approach, more specifically investigating impact of then mini CHP dynamic dynamic behavior prediction prediction and the storage size on on and utilization for the system under investigation, mini behavior storage size then it correspondent constraints and objective function for optimization followed by then its it presents presents constraints and objective ThisCHP workdynamic was supported by prediction the Germanand Federal Ministry of function for the the correspondent optimization problem, problem, followed by the the mini behavior storage size on ThisCHP work was supported by the Germanand Federal Ministry of then it presents correspondent constraints and objective function for the optimization problem, followed by the the description of operation strategies and simulation setup. Education and Research (BMBF) under the grant number 03EK3547 This work was supported by the German Federal Ministry of function for the optimization problem, followed by This work was supported by the German Federal Ministry of description of operation strategies and simulation setup. Education and Research (BMBF) under the grant number 03EK3547 This work was supported by the German Federal Ministry of function forof optimization problem, followed setup. by the description ofthe operation strategies and simulation simulation setup. Education and and Research Research (BMBF) (BMBF) under under the the grant grant number number 03EK3547 03EK3547 description operation strategies and Education description of operation strategies and simulation setup. Education and Research (BMBF) under the grant number 03EK3547
Copyright © 2017 IFAC 10442 Copyright © 2017, 2017 IFAC 10442 2405-8963 © IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2017 2017 IFAC IFAC 10442 Copyright © 10442 Peer review under responsibility of International Federation of Automatic Control. Copyright © 2017 IFAC 10442 10.1016/j.ifacol.2017.08.2039
Proceedings of the 20th IFAC World Congress 10028 Toulouse, France, July 9-14, 2017 Diego I. Hidalgo Rodríguez et al. / IFAC PapersOnLine 50-1 (2017) 10027–10032
Pgas
12,5
PelBatt PelChp
Load
PthSh
Gas boiler PthGboiler
Pel
Pgas
15
Chp
Load
Pel
Space heating
PgasGboiler
PCC Pv
20 P [kW] 17,5
Gas
Grid
Mini CHP
TES
10
Pth
7,5
∑
Pel
5
PthChp
PthDhw
2,5 0
Battery
0
DHW
Electrical power Thermal power Gas
60
120
180
240
300
360
420 Time[min]
Fig. 3. Step responses for a commercial mini CHP (cf. (Thomas, 2011))
Fig. 1. Overview of system components in the home microgrid
2.2 Constraints
2.1 Principle of MPC for the considered home microgrid
Following constraints are valid for each time step k, where k = ki + j|ki for j = 0, ..., Np
MPC is a concept of control systems theory, which consists in optimizing the future behavior of a system by computing optimal trajectories for its inputs. This optimization is performed within a finite time window by solving, in our case, a MILP problem (Boyd and Vandenberghe, 2004). Once an input trajectory is computed, only the first sequence of implementation steps is executed and the rest are discharged. In the next time step, the time window is moved ahead, initial values are updated with actual information and a new optimization is performed. For the actual case study, the goal of the proposed economic MPC-based operation is to find a future trajectory for the electrical and thermal power output of the mini CHP, the state of charge of the storage systems, and the thermal power of the auxiliary gas boiler over a given prediction horizon, to minimize operational costs of the home microgrid. This is done by shifting operation times of the mini CHP using the flexibility provided by the TES and the battery. The MPC strategy considers dynamic models for CHP thermal behavior and evolution of state of charge of the storage systems, as well as measurement data for PV, load, space heating and domestic hot water for a MFH in Germany. The MPC is considered at the management level of the home microgrid automation sysfür Energiesysteme, tem, and power set-points are sent to lowInstitut level controllers Energieeffizienz und Energiewirtschaft of systems components (see Fig. 2).
MPC controller Constraints
Cost function
Forecast Optimizer
LC1
LC2
M1
LC3
LC4
LC5
M3
M4
Battery
PV
Load
Mini CHP
Gas boiler
TES
DHW
SH
Fig. 2. Structure of the whole setup including microgrid components and MPC controller (LC#:local controllers,
mini CHP This section describes the modeling for the considered internal combustion engine (ICE) mini-CHP. Kriett and Salani (2012) uses an approximated piece-wise linear model, initially developed for large scale CHPs, to describe the behavior of the CHP considered in that work. Thermal and electrical response times from large scale CHPs may significantly differ from response times of mini-CHPs. The authors in (Sossan et al., 2014) introduce a grey-box data-based model for a fuel cell mini-CHP, which is also used within an MPC scheme. As basic principles of fuel cell mini-CHPs and ICE mini-CHPs are different, the representation of the dynamic response of ICE mini-CHPs needs a specific model. Fig. 3 depicts the operation of a commercial ICE mini CHP (Thomas, 2011). The brown line indicates the input power, and the red and green line the thermal and electrical output power respectively. It is noticeable that the two outputs present different step response characteristics. While the electrical output reaches the steady state very fast, in a matter of seconds, the thermal output needs more time to reach the steady state. The figure also shows different step response behaviors for the thermal output. According to (Thomas, 2011), ICE mini-CHPs present two types of step responses for their thermal output: cold-start response and warmstart response. Depending on how long an OFF status of the mini CHP lasts, it takes more or less time to reach a given nominal power set-point. In the figure, for the first start the mini-CHP needs around 60 minutes to reach its nominal power. This is a cold-start. Then, two consecutives warm-starts occur, one at minute 190 and the next at minute 350. For these warm-starts, it takes for the miniCHP around 40 minutes to achieve the steady state. In view of the fact that the dynamic response of the electrical output is faster than the thermal one, and that the settling time of the electrical power output is shorter than the MPC sample, it is reasonably acceptable to describe the relationship between mini CHP power input Chp Pgas and electrical power output PelChp using a steadystate model (static model) as described in (1).
and M#: measurement devices) Chp Chp PelChp = Pgas · ηel
10443
(1)
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Diego I. Hidalgo Rodríguez et al. / IFAC PapersOnLine 50-1 (2017) 10027–10032
Chp A binary variable bChp is used to limit Pel,k to its k minimum and maximum allowable values when the mini CHP is ON. Chp bChp · PelChp,min ≤ Pel,k ≤ PelChp,max · bChp k k
(2)
However, the thermal output dynamic behavior needs a more detailed model. Therefore, we use the data-based model proposed in (Hidalgo Rodriguez et al., 2012), which reproduces the thermal step-response behavior of an ICE mini-CHP. The model is given as continuous-time transfer function. We transform it to state-space representation and discretize it using the same sample time as in the MPC scheme, resulting in the following expression: Chp Chp Chp = Ath,warm · Pth,k + Bth,warm · Pgas,k Pth,k+1
(3)
The following constraint is used to have a continuous operation of the mini CHP for M+1 steps. Chp Chp = Pgas,k+m ∀m ∈ {1, ..., M } Pgas,k
Electrical battery In our model, SocBatt gives the energy level available in the battery in percent. Self-discharge coefficient η Batt,sd , charging and discharging efficiencies, η Batt,char and η Batt,dis , are also taken into account. Similar to (Parisio et al., 2014), battery power at time k is modBatt,char for charging, eled with two different variables Pe,k Batt,dis and Pe,k for discharging to be able to implement separate efficiencies for both processes. To avoid simultaneous battery charging and discharging at a single time step, a binary decision variable bBatt is used which makes both k process mutually exclusive in the optimization problem.
Batt SocBatt · η Batt,sd + k+1 = Sock Batt,dis Pel,k Batt,char Batt,char ·η − Batt,dis · K Batt Pel,k η
with K Batt =
∆T CapBatt
0≤
Batt,dis Pel,k
0≤
≤
Batt,char Pel,k
PelBatt,dis,max ≤
· (1 −
PelBatt,char,max
·
bBatt ) k
(bBatt ) k
(5)
(6)
Auxiliary gas boiler The relationship between gas input power and thermal output power is given by the boiler efficiency η Gboiler . Gboiler = Pth,k · η Gboiler (11) Pth,k
Similar to the CHP, a binary variable is used here to keep Gboiler within its limits. the thermal output power Pth,k Gboiler,min Gboiler,max Gboiler · Pth ≤ Pth,k ≤ Pth,k · bGboiler bGboiler k k (12)
Thermal Energy Storage The following TES model is implemented in this work. It reproduces the evolution of TES state of charge considering stand-by heat loss coefficient, charging efficiency and discharging efficiency. T es = SOCkT es · η T es,sd + SOCk+1 T es,char T es,dis − Pth,k · K T es Pth,k
with K T es =
∆T CapT es
(13)
× 100
SocT es,min ≤ SocTk es ≤ SocT es,max Charging-/discharging for TES T es,char Chp Gboiler · η T es,char = Pth,k + Pth,k Pth,k Sh Dhw Lost + Pth,k + Pth,k Pth,k η T es,dis
(14)
(15) (16)
2.3 Objective function Equation (17) presents the objective function. It gives the total operation costs for the home microgrid over a given time horizon. This function is minimized within the MPC scheme. ki +Np
J1 =
(7)
k=ki
Chp Grid,imp Gboiler Cgas Pgas,k + Pgas,k + Cel · Pel,k
Grid,exp Lost − CF it · Pel,k + C Lost · Pth,k
(8)
(17)
Where ki is any arbitrary initial time step.
Electrical power balance The electrical power balance is given by the following expression: Batt,char Grid,exp Load + Pel,k + Pel,k = Pel,k Chp Batt,dis Grid,imp Pv Pel,k + Pel,k + Pel,k + Pel,k
The constraint below avoids charging the battery from the grid. Grid,imp 0 ≤ Pel,k ≤ PelLoad,max · 1 − bBatt (10) k
T es,dis Pth,k =
× 100
≤ SocBatt,max SocBatt,min ≤ SocBatt k
Batt,char Batt,dis and Pel,k are mutually exclusive, just as Pel,k one of them can be larger than zero at time k. In addition, because costs of power import from the grid are higher Grid,exp than the FIT for Pel,k in the objective function (see (17)), it implies that whenever there is power export to Grid,imp is zero. the grid Pel,k
(4)
In this work, we take just the warm start behavior into account. Considering both, cold start and warm start behavior in the optimization problem is beyond the scope of this paper and is left as future work.
10029
(9)
2.4 Operation strategies To better quantify the advantages or disadvantages of an MPC-based operation, two further operation strategies are simulated for comparison purposes. Table 1 briefly describes the operation strategies.
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Proceedings of the 20th IFAC World Congress 10030 Toulouse, France, July 9-14, 2017 Diego I. Hidalgo Rodríguez et al. / IFAC PapersOnLine 50-1 (2017) 10027–10032
Table 2. Parameters for Simulation
Table 1. Operation strategies for comparison
Perfect
MPC-based
Open loop-based (OL)
Description The optimization problem is solved assuming perfect knowledge of the system. This strategy gives the optimal solution and serves as a lower bound for the other strategies. This is the baseline scenario. Here, uncertainties in thermal behavior of the mini CHP are considered. The mini-CHP model in the optimization problem differs from the real system. The optimization problem is solved for the next 24 hours, but just the set-points for the first hour are sent to the low level controllers. After, one hour, actual states of the system are updated in the model and a new optimization loop starts.
Np
24 (hrs)
∆t
10 (min)
Chp,max Pel
4.5 (kWel )
Chp ηth
0.633
Chp,min Pel
1 (kWel )
Ath,warm
0.088
CapBatt
12 (kWh)
Bth,warm
0.577
Batt,char,max Pel
6 (kWel )
η Batt,char
0.9
Batt,dis,max Pel
6 (kWel )
η Batt,sd
0.999
Load,max Pel Gboiler,max Pth Gboiler,min Pth
10 (kWel )
η Batt,dis
0.92
40 (kWth )
η Gboiler
1
1 (kWth )
P v,nom Pel
9 (kWp )
Cel
28.38 (ct./kWh)
η T es,sd
0.998
η T es,char
0.9
η T es,dis
0.92
CapT es
(kWh)1
11.50
Cgas
6.52 (ct./kWh)
Chp CF it 12 (ct./kWh) ηel 0.238 1 as for a typical water tank with 500l and ∆T = 20K
When there is no PV generation, the CHP runs under a electricity-led strategy, i.e. following the household load in order to reduce electricity costs.
Similar to the MPC-based strategy, uncertainties in the thermal behavior of the mini CHP are present. The optimization problem is solved for the next 24 hours, and the whole sequence is implemented in the real system. After 24 hours, the procedure is repeated.
Electrical Power (kWel )
Operation
3. RESULTS AND DISCUSSION This section present relevant simulation results for the optimal operation of the home microgrid. First, a qualitative analysis of resulting profiles for one exemplary day helps for further understanding the operation of the system. The second part quantifies the overall impact of uncertainty in the mini CHP model on operational costs. In the end, a sensitivity analysis on TES and battery storage sizes shows how costs change if smaller storage systems are used. Fig. 4 presents resulting profiles for the system operation. The first subplot contains the electrical profiles of the system, and the second subplot shows resulting thermal profiles. The last subplot depicts storage systems’ state of charge. When looking at the electrical power output of the CHP, two operation patterns are visible: one during night and early morning hours, and one different during the day.
State of Charge (%)
Time series data in 10 min resolution for space heating, domestic hot water, household load and PV power generation are for Germany over one year. The MFH has an annual electrical consumption of 23655.70 kWh/a, and a thermal consumption of 74888.57 kWh/a. The PV plant has an annual energy yield of 8529.24 kWh/a. Table 2 gives the parameters used for the simulation. Moreover, for the economic analysis, specific investment costs of 1724 EUR/kWh for a 6 kWh battery, and 1108 EUR/kWh for a 12 kWh battery are assumed. Similarly, total investment costs of 1038.87 EUR, 1375.64 EUR, and 2205.07 EUR are used for the 100 liter TES, the 300 liter TES, and the 500 liter TES respectively. The calculation of the annuity factor uses an interest rate of 5% and a useful life-time of 20 years. The implementation is done in Python using Pyomo (Hart et al., 2012, 2011) as modeler, and CPLEX (IBM, 1987,2013) as solver.
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Fig. 4. Example of resultant profiles for perfect operation strategy As soon as the MPC predicts the thermal load peak at around 6:00 in the morning (second subplot), the CHP changes to a heat-led operation. It increases the operation point in order to fully charge the TES, so that the coming peak in thermal demand can be covered without using the gas boiler. During PV production hours, the CHP continues under heat-led operation, the electrical load is covered mainly by the PV production, and the electricity surplus is sold into the grid. Due to the high thermal demand during the day, there are just few cases when the TES can be charged (see 10:00 and 14:00 hours). Regarding the battery system, the MPC decides not store the electricity surplus, but to sell it to the grid. Just when the MPC predicts the evening peak in household load around 19:00 hours, it decides to charge the battery at around 13:00 hours to have enough energy to cover
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the coming peak. As PV generation decreases, the CHP switches again to electricity-led operation. As a second point in the results, we quantify the impact of uncertainty in the CHP thermal behavior. For this purpose, we compare the resultant costs for a simulation with optimal operation without uncertainty (perfect knowledge of the system) over a year, with the resultant costs for the open loop optimization operation and the MPC operation, also over a year but including uncertainty in the model. Here, it is assumed that the model in the optimization problem is different from the real system, and this is done by decreasing the time constant of the thermal power system of the CHP. The real system behaves as described in Fig. 3 for the warm start, while the MPC assumes that mini CHP reaches its nominal thermal power in about 10 minutes. To better illustrate the responses, Fig. 5 shows the real, and the mini CHP thermal behavior assumed by the MPC. The brown line shows the gas power input setpoints sent from the MPC to the mini CHP. The purple line is the thermal power output assumed by the MPC, while the red line denotes the real thermal power output of the mini CHP. 20
10
running down, so that no matter what action the MPC takes, the optimization problem is already infeasible. For Lost this reason, the decision variable Pth is included to also enable the MPC to waste some power in order to make the optimization problem feasible. On the contrary, if less energy than expected is given by mini CHP and the storage is almost empty, then the gas boiler has to supply the missing energy. The MPC leads to lower annual operational costs, compared to the open loop strategy, mainly because of its closed loop property, which allows to correct mini CHP schedules every hour. Since the open loop-based operation calculates fixed schedules for the next 24 hours, it must waste more energy due to the presence of uncertainty in the mini CHP thermal behavior. Finally, a sensitivity analysis reveals the effects of storage sizes on home microgrid operational costs. The baseline is the resultant costs for the perfect operation with 500liter TES and battery capacity of 12 kWh. We conduct simulations over a year with variations of TES volume and battery capacity, recording the corresponding additional operation costs. The simulation scenarios correspond to TES volumes of 500 liter, 300 liter and 100 liter, and battery capacities of 12 kWh and 6 kWh, for both operation strategies, MPC-based and open loop-based. Through this experiment, it will be possible to determine how small the storage systems could be, such that under a suitable operation strategy the additional operation costs are still moderated. Fig. 6 helps to visualize the results of the annual simulations.
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Fig. 5. Step responses for the real system and the model in the optimization For the perfect optimal operation the resultant annual operational costs are 7470.79 EUR/a. If uncertainties in the thermal behavior of the mini CHP are present, the annual operational costs increase to 7472.18 EUR/a and 7518.10 EUR/a for the MPC-based operation and the open loop optimization-based operation respectively. These resultant costs can be explained as follows: Because the real system responds slower than assumed by the MPC, this results in the TES receiving less energy than planned when the CHP is running up. On the other hand, when the CHP is running down, slower than assumed by the MPC, the TES receives more energy that initially planned. This may be problematic, if the TES is almost full. In such a situation, the MPC will shut-down the CHP assuming that it will reduce its thermal power very fast, so that the upper limit of the TES will not be reached. In reality, the CHP reduces its thermal power slower than required, meaning that more energy is supplied, leading to an overcharging of the TES. To deal with this issue, the real system has to waste some energy in order to allow further operation, incurring in extra costs. This situation affects the MPC as well, because there may exist situations where in the beginning of MPCs time window the TES is already or almost full, and the CHP is still
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Fig. 6. Sensitivity analysis on operation costs with different storage capacities for MPC and OL As expected, a home microgrid with 500 liter TES and 12 kWh battery gives the minimum operation costs under MPC-based operation. If the system uses a 100 liter TES with a 6 kWh battery under an open loop-based operation, the operation costs increase by ca. 200 EUR/a compared to the baseline case. This configuration presents the larger additional costs. In general, for a given configuration, MPC-based operation is always cheaper than the open loop-based. Another aspect worth to mention, is that a system under MPC-based operation with TES-300 liter and 12 kWh battery shows lower operation costs than a system with the same battery size but with larger TES capacity under open loop-based operation. It is usual that the smaller the storage capacity is, the lower the investment costs are. Therefore, annuity costs, based on investment and operation costs, are shown in Fig. 7.
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REFERENCES
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Fig. 7. Total annual costs with different storage capacities for MPC From this chart, a good compromise between operation costs and storage size is a home microgrid with an MPCbased operation, a TES-300 liter, and 6 kWh battery. 4. CONCLUSIONS Optimal operation of home microgrids is an actual important topic of research. In this paper, the economic MPC operation of a home microgrid with photovoltaic-combined heat and power storage systems was investigated. The purpose of the paper was to present the economic MPC problem formulation, and investigate the impact of uncertainty coming from the thermal behavior of the mini CHP. Additionally, a sensitivity analysis on storage size was also presented. To quantify the effects of this uncertainty in the operation, a ”MPC-based” strategy and a ”open loopbased” strategy were compared with a ”perfect” optimal strategy. The main consequence of having an imperfect model for the thermal response of the mini CHP, is that the TES might be overcharged or undercharged. To overcome these situations, the system has to waste energy, or use the auxiliary gas boiler respectively, incurring in additional costs. Simulation results showed that, even for a minimal mismatch between the optimization model and the real system regarding the settling time of mini CHP thermal power, resultant additional operation costs are essentially different between the ”open loop”-based operation and the ”MPC-based” operation. While the later one achieves operation costs almost equal to the ”perfect” case, the costs for the ”open loop”-based strategy are notably higher. This confirms the robustness of MPC against uncertainties, as well as it advantages for operation of home microgrids. In the end, a sensitivity analysis regarding the impact of storage size on additional operation costs were conducted. Here, the ”MPC-based” operation enabled a better usage of the storage systems, such that it might be possible to reduce both, TES and battery size, with a moderate increased in operational costs, and a reduction in investment costs (smaller storage systems). In future work, other sources of uncertainties will be included in the evaluation, i.e. the impact of forecasts errors from household load, PV generation, and thermal demand on the overall operation costs have to be quantified. Also, a sensitivity analysis regarding larger storage systems (TES larger than 500 liter and battery systems larger than 12 kWh) may provide new insights for determining a maximum feasible capacity for such a home microgrid.
Boyd, S.P. and Vandenberghe, L. (2004). Convex optimization. Cambridge University Press, Cambridge, UK and New York. Chen, C., Wang, J., Heo, Y., and Kishore, S. (2013). MPCBased Appliance Scheduling for Residential Building Energy Management Controller. IEEE Trans. on Smart Grid, 4(3), 1401–1410. doi:10.1109/TSG.2013.2265239. European Commission (2011). Energy Roadmap 2050 Impact Assessment. URL https://ec.europa.eu. Hart, W.E., Laird, C., Watson, J.P., and Woodruff, D.L. (2012). Pyomo – Optimization Modeling in Python, volume 67. Springer US, Boston, MA. doi:10.1007/9781-4614-3226-5. Hart, W.E., Watson, J.P., and Woodruff, D.L. (2011). Pyomo: Modeling and solving mathematical programs in Python. Mathematical Programming Computation, 3(3), 219–260. doi:10.1007/s12532-011-0026-8. Hidalgo Rodriguez, D.I., Spitalny, L., Myrzik, J., and Braun, M. (2012). Development of a control strategy for mini CHP plants for an active voltage management in low voltage networks. In 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe), 1–8. doi:10.1109/ISGTEurope.2012.6465797. Houwing, M., Negenborn, R.R., and de Schutter, B. (2011). Demand Response With Micro-CHP Systems. Proceedings of the IEEE, 99(1), 200–213. doi: 10.1109/JPROC.2010.2053831. IBM (1987,2013). IBM ILOG CPLEX Optimization Studio. URL http://www-03.ibm.com. Kriett, P.O. and Salani, M. (2012). Optimal control of a residential microgrid. Energy, 42(1), 321–330. doi: 10.1016/j.energy.2012.03.049. Oldewurtel, F., Jones, C.N., Parisio, A., and Morari, M. (2014). Stochastic Model Predictive Control for Building Climate Control. IEEE Trans. on Control Systems Technology, 22(3), 1198–1205. doi: 10.1109/TCST.2013.2272178. Parisio, A., Rikos, E., and Glielmo, L. (2014). A Model Predictive Control Approach to Microgrid Operation Optimization. IEEE Trans. on Control Systems Technology, 22(5), 1813–1827. doi: 10.1109/TCST.2013.2295737. Sossan, F., Bindner, H., Madsen, H., Torregrossa, D., Reyes Chamorro, L., and Paolone, M. (2014). A model predictive control strategy for the space heating of a smart building including cogeneration of a fuel cellelectrolyzer system. Electrical Power and Energy Systems, 62, 879–889. doi:10.1016/j.ijepes.2014.05.040. Thomas, B. (2011). Mini-Blockheizkraftwerke: Grundlagen, Ger¨ atetechnik, Betriebsdaten. Vogel, W¨ urzburg, 2., vollst. u ¨berarb. aufl. edition. Zhang, Y., Zhang, T., Wang, R., Liu, Y., and Guo, B. (2015). Optimal operation of a smart residential microgrid based on model predictive control by considering uncertainties and storage impacts. Solar Energy, 122, 1052–1065. doi:10.1016/j.solener.2015.10.027. Zong, Y., Kullmann, D., Thavlov, A., Gehrke, O., and Bindner, H.W. (2012). Application of Model Predictive Control for Active Load Management in a Distributed Power System With High Wind Penetration. IEEE Trans. on Smart Grid, 3(2), 1055–1062. doi: 10.1109/TSG.2011.2177282.
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IFAC PapersOnLine 50-1 (2017) 10027–10032 Economic Economic Model Model Predictive Predictive Control Control for for Economic Model Predictive Control for Optimal Operation of Home Microgrid Economic Model Predictive for Optimal Operation of HomeControl Microgrid Optimal Operation of Home Microgrid with Photovoltaic-Combined Heat and Optimal Operation of Home Microgrid with and with Photovoltaic-Combined Photovoltaic-Combined Heat Heat and Power Storage Systems with Photovoltaic-Combined Heat and Power Storage Systems Power Storage Systems Power Storage Systems Diego I. Hidalgo Rodr´ıguez ∗∗ , and Johanna M.A. Myrzik ∗∗
Diego I. Hidalgo Rodr´ıguez ∗∗ , and Johanna M.A. Myrzik ∗∗ Diego I. I. Hidalgo Rodr´ıguez ıguez ∗ ,, and and Johanna Johanna M.A. M.A. Myrzik Myrzik Diego Hidalgo Rodr´ Diego I. Hidalgo∗ Institute Rodr´ıguez , and Johanna M.A. Myrzik ∗ of Energy Systems, ∗ ∗ Institute of Energy Systems, 3 ∗ Institute and of Energy Energy Systems, Energy Energy Economics of ∗ Institute and Energy Efficiency Efficiency EnergySystems, Economics (ie (ie333 )) Institute of Energy Systems, Energy Efficiency and Energy Economics (ie TU Dortmund University, Dortmund, Germany Energy Efficiency and Energy Economics (ie3 )) TU Dortmund University, Dortmund, Germany Energy Efficiency and Energy Economics (ie ) TU Dortmund University, Dortmund, Germany [email protected], [email protected] TU Dortmund University, Dortmund, Germany [email protected], [email protected] TU Dortmund University, Dortmund, Germany [email protected], [email protected] [email protected], [email protected] [email protected], [email protected] Abstract: Abstract: In In this this paper, paper, the the economic economic model model predictive predictive control control operation operation of of aa home home microgrid microgrid Abstract: In this this paper, paper, the theheat economic model predictive control operation of ofThe a home home microgrid with photovoltaic-combined and power storage systems is investigated. purpose of Abstract: In economic model predictive control operation a microgrid with photovoltaic-combined heat and power storage systems is investigated. The purpose of the the Abstract: In this the paper, theheat economic model predictive control operation ofThe a home microgrid with photovoltaic-combined and power storage systems is investigated. purpose of the paper is to present problem formulation, and quantify the impact of uncertainty coming with photovoltaic-combined heat and power storage systems is investigated. The purpose offrom the paper is to present the problem formulation, and quantify the impact of uncertainty coming from with photovoltaic-combined heat and power storage systems is investigated. The purpose of the paper is to present the problem formulation, and quantify the impact of uncertainty coming from the thermal behavior of the mini combined heat and power plant. A model predictive controlpaper is to present the of problem formulation, and quantify the plant. impactAofmodel uncertainty coming from the thermal behavior the mini combined heat and power predictive controlpaper is to present the of problem formulation, and the plant. impact uncertainty coming from the thermal thermal behavior of the mini mini combined heatquantify and power power plant. Aofmodel model predictive controlbased strategy is contrasted with an open loop-based operation and a perfect forecast based the behavior the combined heat and A predictive controlbased strategy is contrasted withcombined an open loop-based operation and a perfect forecastcontrolbased the thermal behavior of the mini heat and such power plant. A model predictive based strategy is contrasted with an openofloop-based loop-based operation and perfect forecast based operation. The paper discusses the effects having an uncertainty, relaying the benefits based strategy is contrasted with an open operation and aa perfect forecast based operation. The paper discusses the effects of having such an uncertainty, relaying the benefits based strategy is contrasted with an openof loop-based operation and a perfect forecast based operation. The paper discusses the effects having such an uncertainty, relaying the benefits of using model predictive control to handle such situations. Additionally, the paper at hand operation. The paper discusses the effects of having such an uncertainty, relaying the benefits of using model predictive control toeffects handle such situations. Additionally,relaying the paper at hand operation. The paper discusses the of having such an uncertainty, the benefits of using model predictive control to handle such situations. Additionally, the paper at presents a sensitivity analysis regarding storage size, concluding that the proposed economic of using model predictive control to handle suchsize, situations. Additionally, the papereconomic at hand hand presents a sensitivity analysis regarding storage concluding that the proposed of using model predictive control to handle such situations. Additionally, the paper at hand presents a sensitivity sensitivity analysis regarding storage size, concluding concluding that the proposed proposed economic economic model predictive control strategy can be used to reduce total annual costs. presents a analysis regarding storage size, that the model predictive control strategy can be used to reduce total annual costs. presents a sensitivity analysis regarding storage size, concluding that the proposed economic model predictive predictive control control strategy strategy can can be be used used to to reduce reduce total total annual annual costs. costs. model model control strategy can used toControl) reduce Hosting total annual costs. © 2017,predictive IFAC (International Federation of be Automatic by Elsevier Ltd. All rights reserved. Keywords: Microgrids, Model predictive control, Optimization, Storage Keywords: Microgrids, Model predictive control, Optimization, Storage systems. systems. Keywords: Microgrids, Microgrids, Model Model predictive predictive control, control, Optimization, Optimization, Storage Storage systems. systems. Keywords: Keywords: Microgrids, Model predictive control, Optimization, Storage systems. 1. the 1. INTRODUCTION INTRODUCTION the economic economic operation. operation. Our Our work work builds builds upon upon the the work work 1. INTRODUCTION INTRODUCTION the economic operation. Our work builds upon the presented in (Kriett and Salani, extend this 1. the economic operation. Our work2012). buildsWe upon the work work presented in (Kriett and Salani, 2012). We extend this 1. INTRODUCTION the economic operation. Our work builds upon the presentedwork in (Kriett (Kriett and Salani, Salani, 2012). contributions: We extend extendwork this previous by including the following Following the incentives of European governments to presented in and 2012). We this work by including the following contributions: Following the incentives of European governments to previous in (Kriett and Salani, 2012). contributions: We extend this previous work work by including including the following following contributions: Following the incentives of European European governments to presented achieve the desired reduction of CO2 emissions by 2050 previous by the Following the incentives of governments to achieve thethe desired reduction of CO2 emissions by 2050 •• A for the dynamic behavior work bymodel including Following incentives of European governments to previous A thermal thermal model for the the following dynamic contributions: behavior for for a a achieve the Commission, desired reduction ofhousehold CO2 emissions emissions byare2050 2050 (European 2011), owners inachieve the desired reduction of CO2 by (European Commission, 2011), household owners are in• A thermal model for the dynamic behavior for ina a commercial internal combustion engine mini CHP • A thermal model for the dynamic behavior for achieve the desired reduction of CO2 emissions by 2050 commercial internal combustion engine mini CHP in (European Commission, 2011), household owners are increasingly investing in new low carbon electricity tech(European Commission, 2011), owners are in• A thermal model for the dynamic behavior for in creasingly investing in new lowhousehold carbon electricity techcommercial internal combustion engine mini CHP CHP ina the optimization problem commercial internal combustion engine mini (European Commission, 2011), household owners are inthe optimization problem creasinglyAsinvesting investing in new low low grids carbon electricity technologies. a distribution are facing pencreasingly new carbon commercial internal combustion engine mini CHP in nologies. Asinvesting a result, result, in distribution grids areelectricity facing the the techpenoptimization problem •• the An analysis impact the problem creasingly new low carbon techAn optimization analysis on on the the impact of of uncertainties uncertainties in in mini mini nologies. of Asrenewable a result, result, in distribution grids areelectricity facing the penetration energy sources (RES), e.g. rooftop nologies. As a distribution grids are facing the penthe optimization problem etration of renewable energy sources (RES), e.g. rooftop • An analysis on the impact of uncertainties in mini CHP thermal power settling times • CHP An analysis the impact uncertainties in mini nologies. of Asrenewable aplants, result, distribution grids(RES), aregenerators, facing penthermalon power settling of times etration of renewable energy sources (RES), e.g.the rooftop photovoltaic energy efficient such etration energy sources e.g. rooftop •• An analysis the impact of uncertainties in mini photovoltaic plants, and and energy efficient generators, such CHP thermalon power settling times A quantification of the added value of CHP thermal power settling times etration of renewable energy sources (RES), e.g. rooftop • A quantification of the added value of MPC MPC compared compared photovoltaic plants, and energy efficient generators, such combined heat and power plants (CHP). In addition, the photovoltaic plants, and energy efficient generators, such CHP thermal power settling times combined heat and power plants (CHP). In addition, the A quantification quantification of the the added added value of ofstrategy MPC compared compared to an optimization •• A of value MPC photovoltaic plants, and energy efficient such an open open loop-based loop-based optimization combined heat and power plants (CHP). generators, In addition, addition, the use of batteries and energy storages combined heat and power plants (CHP). In the •• to A quantification of the on added value ofstrategy MPC compared use of electrical electrical batteries and thermal thermal energy storages to an open loop-based optimization strategy A sensitivity analysis the impacts of battery to an open loop-based optimization strategy combined heat and power plants (CHP). In addition, the • A sensitivity analysis on the impacts of battery size size use of of becomes electricalalso batteries and to thermal energy storages (TES) interesting increase the flexibility. use electrical batteries and thermal energy storages to an open loop-based optimization strategy (TES) becomes also interesting to increase the flexibility. • A sensitivity analysis on the impacts of battery and TES size on the economic operation • and A sensitivity on the impacts of battery size size use these of becomes electrical batteries andmicrogrid, thermal energy storages TES size analysis on the economic operation (TES) becomes also interesting to increase the flexibility. flexibility. All systems form a home which operation (TES) also interesting to increase the • A sensitivity analysis on the impacts of battery size All these systemsalso form a home microgrid, which operation and TES TES size size on on the the economic economic operation operation and (TES) becomes interesting to increase the flexibility. All these systems form a home microgrid, which operation must be efficient and economical. For this reason, operThe paper is organized as follows: Section 2 describes All these systems form a home microgrid, which operation and TES size on the economic operation must be efficient and economical. For this reason, operThe paper is organized as follows: Section 2 describes the the All these systems form a home microgrid, which operation must be efficient and economical. economical. For this reason, operThe paper is as Section the ation of home microgrids is getting the attention of the under investigation, the problem, must be efficient and For this reason, operThe paper is organized organized as follows: follows: Section 22 describes describes the ation of home microgrids is gettingFor thethis attention ofoperthe system system under investigation, the optimization optimization problem, opopmust be efficient and economical. reason, The paper is organized as follows: Section 2 describes the ation of of community, home microgrids microgrids isproposing getting the the attention of the the system system under investigation, the optimization problem, opresearch who is different approaches eration strategies and simulation setup. Then, simulation ation home is getting attention of under investigation, the optimization problem, opresearch community, who is proposing different approaches eration strategies and simulation setup. Then, simulation ation of home microgrids is getting the attention of the system under investigation, the optimization problem, opresearch community, who is proposing different approaches eration strategies and simulation setup. Then, simulation to tackle this based on optiresults and corresponding discussion are presented in research who is proposing approaches strategies and simulation setup. simulation to tacklecommunity, this task. task. Approaches Approaches baseddifferent on numerical numerical opti- eration results and corresponding discussion are Then, presented in SecSecresearch who is promising proposing different approaches eration strategies and simulation setup. Then, simulation to tackle tacklecommunity, this task. task.are Approaches based(Parisio on numerical numerical opti- tion results and corresponding discussion are presented in mization methods very et al., 2014; 3. Finally, Section 4 summarizes the main outcomes to this Approaches based on optiresults and corresponding discussion are presented in SecSecmization methods are very promising (Parisio et al., 2014; tion 3. and Finally, Section 4 summarizes thepresented main outcomes to tackle this task. Approaches based on numerical optiresults corresponding discussion are in Secmization methods methods are veryChen promising (Parisio et al., al.,et2014; 2014; tion 3.paper, Finally, Section summarizes the main outcomes outcomes Oldewurtel et al., 2014; et al., 2013; Zong al., of the its limitations and future work. mization are very promising (Parisio et tion 3. Finally, Section 44 summarizes the main Oldewurtel et al., 2014; Chen et al., 2013; Zong et al., of the paper, its limitations and future work. mization methods are very promising (Parisio et al., 2014; tion 3. Finally, Section 4 summarizes the main outcomes Oldewurtel et al., al., 2014; ChenSossan et al., al.,et2013; 2013; Zong Kriett et al., al., of of the the paper, paper, its its limitations limitations and and future future work. work. 2012; Houwing et al., al., Oldewurtel et Chen et Zong et 2012; Houwing et 2014; al., 2011; 2011; Sossan et2013; al., 2014; 2014; Kriett Oldewurtel et al., 2014; Chen et2015), al.,et Zongbecause et al., of the paper, its limitations and future work. 2012; Houwing et Zhang al., 2011; 2011; Sossan et not al., just 2014; Kriett and Salani, 2012; et al., 2012; Houwing et al., Sossan al., 2014; Kriett 2. SYSTEM DESCRIPTION AND and Salani, 2012; Zhang et al., 2015), not just because 2. SYSTEM DESCRIPTION AND PROBLEM PROBLEM 2012; Houwing etisZhang al., 2011; Sossan et not al., 2014;because Kriett and Salani, Salani, 2012; Zhang et al., al., 2015), not just because system operation explicitly considered through mathe2. AND and 2012; et 2015), just FORMULATION 2. SYSTEM SYSTEM DESCRIPTION DESCRIPTION AND PROBLEM PROBLEM system operation is explicitly considered through matheFORMULATION and Salani, 2012; Zhang et al., 2015), not just because 2. SYSTEM DESCRIPTION AND PROBLEM system operation operation is explicitly explicitly considered through mathematical models, but also because operational constraints FORMULATION system is considered through matheFORMULATION matical models, but also because operational constraints system operation is explicitly considered through matheFORMULATION matical models, but but also because operational constraints and operational goals are included in matical models, also operational constraints In the present work, aa system and operational goals arebecause included in the the formulation. formulation. In the present work, system for for aa multi-family multi-family house house matical models, but also because operational constraints and operational goals are included in the formulation. Within this framework, model predictive control (MPC) and operational goals are included in the formulation. In the present work, a system for a multi-family house (MFH) is investigated, which combines one one In the present work, a system for a house Within this framework, model predictive control (MPC) (MFH) is investigated, which combines multi-family one mini mini CHP, CHP, one and operational goals are included in the formulation. Within thisrelevance framework, model predictive control (MPC) In the present work, a system for a multi-family house is gaining due to its prediction nature and its Within this framework, model predictive control (MPC) (MFH)one is investigated, investigated, which combines oneFig. mini1 CHP, CHP, one TES, PV plant and one battery, as presents. (MFH) is which combines one mini one is gaining relevance due to its prediction nature and its TES, one PV plant and one battery, as Fig. 1 presents. Within this framework, model predictive control (MPC) is gaining gaining relevance relevance due to to its its prediction prediction nature and its its (MFH) isoperation investigated, which combines oneFig. mini CHP, one robustness against uncertainties (Parisio et al., 2014). In is due nature and TES, one PV plant and one battery, as 1 presents. Systems is formulated as a mixed integer linear TES, one PV plant and one battery, as Fig. 1 presents. robustness against uncertainties (Parisio et al., 2014). In operation is and formulated as a mixed integer linear is gaining relevance due to provide its prediction and its robustness against uncertainties (Parisio etnature al., regarding 2014). In Systems TES, one PV plant one battery, as Fig. 1 presents. this paper, the purpose is to new insights robustness against uncertainties (Parisio et al., 2014). In Systems operation is formulated as a mixed integer linear programming (MILP) problem within an MPC framework. Systems operation is formulated as a mixed integer linear this paper, the purpose is to provide new insights regarding (MILP) problem within an MPC framework. robustness against uncertainties (Parisio eteconomic al., regarding 2014). In programming this paper, the the purpose is to to provide provide newan insights regarding operation is formulated as the a mixed integer linear the operation of home using MPC this paper, is new insights programming (MILP) problem within anprinciple MPC framework. This section first briefly describes of MPC programming (MILP) problem within an MPC framework. the operation ofpurpose home microgrids microgrids using an economic MPC Systems This section first briefly describes the principle of MPC this paper, the purpose is to provide new insights regarding the operation operation of home home microgrids using an an economic economic MPC programming (MILP) problem within an MPC framework. approach, more specifically investigating the impact of the of microgrids using MPC This its section first briefly briefly describes the principle of MPC MPC and utilization for the system under investigation, This section first describes the principle of approach, more specifically investigating the impact of and its utilization for the system under investigation, the operation of home microgrids using an economic MPC approach, more specifically specifically investigating the impact of and This section firstcorrespondent briefly describes the principle of MPC mini CHP dynamic behavior prediction and storage size on approach, more investigating the impact of its utilization for the system under investigation, then it presents constraints and objective and its utilization for the system under investigation, mini CHP dynamic behavior prediction and storage size on it presents correspondent constraints and objective approach, more specifically investigating impact of then mini CHP dynamic dynamic behavior prediction prediction and the storage size on on and utilization for the system under investigation, mini behavior storage size then it correspondent constraints and objective function for optimization followed by then its it presents presents constraints and objective ThisCHP workdynamic was supported by prediction the Germanand Federal Ministry of function for the the correspondent optimization problem, problem, followed by the the mini behavior storage size on ThisCHP work was supported by the Germanand Federal Ministry of then it presents correspondent constraints and objective function for the optimization problem, followed by the the description of operation strategies and simulation setup. Education and Research (BMBF) under the grant number 03EK3547 This work was supported by the German Federal Ministry of function for the optimization problem, followed by This work was supported by the German Federal Ministry of description of operation strategies and simulation setup. Education and Research (BMBF) under the grant number 03EK3547 This work was supported by the German Federal Ministry of function forof optimization problem, followed setup. by the description ofthe operation strategies and simulation simulation setup. Education and and Research Research (BMBF) (BMBF) under under the the grant grant number number 03EK3547 03EK3547 description operation strategies and Education description of operation strategies and simulation setup. Education and Research (BMBF) under the grant number 03EK3547
Copyright © 2017 IFAC 10442 Copyright © 2017, 2017 IFAC 10442 2405-8963 © IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2017 2017 IFAC IFAC 10442 Copyright © 10442 Peer review under responsibility of International Federation of Automatic Control. Copyright © 2017 IFAC 10442 10.1016/j.ifacol.2017.08.2039
Proceedings of the 20th IFAC World Congress 10028 Toulouse, France, July 9-14, 2017 Diego I. Hidalgo Rodríguez et al. / IFAC PapersOnLine 50-1 (2017) 10027–10032
Pgas
12,5
PelBatt PelChp
Load
PthSh
Gas boiler PthGboiler
Pel
Pgas
15
Chp
Load
Pel
Space heating
PgasGboiler
PCC Pv
20 P [kW] 17,5
Gas
Grid
Mini CHP
TES
10
Pth
7,5
∑
Pel
5
PthChp
PthDhw
2,5 0
Battery
0
DHW
Electrical power Thermal power Gas
60
120
180
240
300
360
420 Time[min]
Fig. 3. Step responses for a commercial mini CHP (cf. (Thomas, 2011))
Fig. 1. Overview of system components in the home microgrid
2.2 Constraints
2.1 Principle of MPC for the considered home microgrid
Following constraints are valid for each time step k, where k = ki + j|ki for j = 0, ..., Np
MPC is a concept of control systems theory, which consists in optimizing the future behavior of a system by computing optimal trajectories for its inputs. This optimization is performed within a finite time window by solving, in our case, a MILP problem (Boyd and Vandenberghe, 2004). Once an input trajectory is computed, only the first sequence of implementation steps is executed and the rest are discharged. In the next time step, the time window is moved ahead, initial values are updated with actual information and a new optimization is performed. For the actual case study, the goal of the proposed economic MPC-based operation is to find a future trajectory for the electrical and thermal power output of the mini CHP, the state of charge of the storage systems, and the thermal power of the auxiliary gas boiler over a given prediction horizon, to minimize operational costs of the home microgrid. This is done by shifting operation times of the mini CHP using the flexibility provided by the TES and the battery. The MPC strategy considers dynamic models for CHP thermal behavior and evolution of state of charge of the storage systems, as well as measurement data for PV, load, space heating and domestic hot water for a MFH in Germany. The MPC is considered at the management level of the home microgrid automation sysfür Energiesysteme, tem, and power set-points are sent to lowInstitut level controllers Energieeffizienz und Energiewirtschaft of systems components (see Fig. 2).
MPC controller Constraints
Cost function
Forecast Optimizer
LC1
LC2
M1
LC3
LC4
LC5
M3
M4
Battery
PV
Load
Mini CHP
Gas boiler
TES
DHW
SH
Fig. 2. Structure of the whole setup including microgrid components and MPC controller (LC#:local controllers,
mini CHP This section describes the modeling for the considered internal combustion engine (ICE) mini-CHP. Kriett and Salani (2012) uses an approximated piece-wise linear model, initially developed for large scale CHPs, to describe the behavior of the CHP considered in that work. Thermal and electrical response times from large scale CHPs may significantly differ from response times of mini-CHPs. The authors in (Sossan et al., 2014) introduce a grey-box data-based model for a fuel cell mini-CHP, which is also used within an MPC scheme. As basic principles of fuel cell mini-CHPs and ICE mini-CHPs are different, the representation of the dynamic response of ICE mini-CHPs needs a specific model. Fig. 3 depicts the operation of a commercial ICE mini CHP (Thomas, 2011). The brown line indicates the input power, and the red and green line the thermal and electrical output power respectively. It is noticeable that the two outputs present different step response characteristics. While the electrical output reaches the steady state very fast, in a matter of seconds, the thermal output needs more time to reach the steady state. The figure also shows different step response behaviors for the thermal output. According to (Thomas, 2011), ICE mini-CHPs present two types of step responses for their thermal output: cold-start response and warmstart response. Depending on how long an OFF status of the mini CHP lasts, it takes more or less time to reach a given nominal power set-point. In the figure, for the first start the mini-CHP needs around 60 minutes to reach its nominal power. This is a cold-start. Then, two consecutives warm-starts occur, one at minute 190 and the next at minute 350. For these warm-starts, it takes for the miniCHP around 40 minutes to achieve the steady state. In view of the fact that the dynamic response of the electrical output is faster than the thermal one, and that the settling time of the electrical power output is shorter than the MPC sample, it is reasonably acceptable to describe the relationship between mini CHP power input Chp Pgas and electrical power output PelChp using a steadystate model (static model) as described in (1).
and M#: measurement devices) Chp Chp PelChp = Pgas · ηel
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(1)
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Diego I. Hidalgo Rodríguez et al. / IFAC PapersOnLine 50-1 (2017) 10027–10032
Chp A binary variable bChp is used to limit Pel,k to its k minimum and maximum allowable values when the mini CHP is ON. Chp bChp · PelChp,min ≤ Pel,k ≤ PelChp,max · bChp k k
(2)
However, the thermal output dynamic behavior needs a more detailed model. Therefore, we use the data-based model proposed in (Hidalgo Rodriguez et al., 2012), which reproduces the thermal step-response behavior of an ICE mini-CHP. The model is given as continuous-time transfer function. We transform it to state-space representation and discretize it using the same sample time as in the MPC scheme, resulting in the following expression: Chp Chp Chp = Ath,warm · Pth,k + Bth,warm · Pgas,k Pth,k+1
(3)
The following constraint is used to have a continuous operation of the mini CHP for M+1 steps. Chp Chp = Pgas,k+m ∀m ∈ {1, ..., M } Pgas,k
Electrical battery In our model, SocBatt gives the energy level available in the battery in percent. Self-discharge coefficient η Batt,sd , charging and discharging efficiencies, η Batt,char and η Batt,dis , are also taken into account. Similar to (Parisio et al., 2014), battery power at time k is modBatt,char for charging, eled with two different variables Pe,k Batt,dis and Pe,k for discharging to be able to implement separate efficiencies for both processes. To avoid simultaneous battery charging and discharging at a single time step, a binary decision variable bBatt is used which makes both k process mutually exclusive in the optimization problem.
Batt SocBatt · η Batt,sd + k+1 = Sock Batt,dis Pel,k Batt,char Batt,char ·η − Batt,dis · K Batt Pel,k η
with K Batt =
∆T CapBatt
0≤
Batt,dis Pel,k
0≤
≤
Batt,char Pel,k
PelBatt,dis,max ≤
· (1 −
PelBatt,char,max
·
bBatt ) k
(bBatt ) k
(5)
(6)
Auxiliary gas boiler The relationship between gas input power and thermal output power is given by the boiler efficiency η Gboiler . Gboiler = Pth,k · η Gboiler (11) Pth,k
Similar to the CHP, a binary variable is used here to keep Gboiler within its limits. the thermal output power Pth,k Gboiler,min Gboiler,max Gboiler · Pth ≤ Pth,k ≤ Pth,k · bGboiler bGboiler k k (12)
Thermal Energy Storage The following TES model is implemented in this work. It reproduces the evolution of TES state of charge considering stand-by heat loss coefficient, charging efficiency and discharging efficiency. T es = SOCkT es · η T es,sd + SOCk+1 T es,char T es,dis − Pth,k · K T es Pth,k
with K T es =
∆T CapT es
(13)
× 100
SocT es,min ≤ SocTk es ≤ SocT es,max Charging-/discharging for TES T es,char Chp Gboiler · η T es,char = Pth,k + Pth,k Pth,k Sh Dhw Lost + Pth,k + Pth,k Pth,k η T es,dis
(14)
(15) (16)
2.3 Objective function Equation (17) presents the objective function. It gives the total operation costs for the home microgrid over a given time horizon. This function is minimized within the MPC scheme. ki +Np
J1 =
(7)
k=ki
Chp Grid,imp Gboiler Cgas Pgas,k + Pgas,k + Cel · Pel,k
Grid,exp Lost − CF it · Pel,k + C Lost · Pth,k
(8)
(17)
Where ki is any arbitrary initial time step.
Electrical power balance The electrical power balance is given by the following expression: Batt,char Grid,exp Load + Pel,k + Pel,k = Pel,k Chp Batt,dis Grid,imp Pv Pel,k + Pel,k + Pel,k + Pel,k
The constraint below avoids charging the battery from the grid. Grid,imp 0 ≤ Pel,k ≤ PelLoad,max · 1 − bBatt (10) k
T es,dis Pth,k =
× 100
≤ SocBatt,max SocBatt,min ≤ SocBatt k
Batt,char Batt,dis and Pel,k are mutually exclusive, just as Pel,k one of them can be larger than zero at time k. In addition, because costs of power import from the grid are higher Grid,exp than the FIT for Pel,k in the objective function (see (17)), it implies that whenever there is power export to Grid,imp is zero. the grid Pel,k
(4)
In this work, we take just the warm start behavior into account. Considering both, cold start and warm start behavior in the optimization problem is beyond the scope of this paper and is left as future work.
10029
(9)
2.4 Operation strategies To better quantify the advantages or disadvantages of an MPC-based operation, two further operation strategies are simulated for comparison purposes. Table 1 briefly describes the operation strategies.
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Table 2. Parameters for Simulation
Table 1. Operation strategies for comparison
Perfect
MPC-based
Open loop-based (OL)
Description The optimization problem is solved assuming perfect knowledge of the system. This strategy gives the optimal solution and serves as a lower bound for the other strategies. This is the baseline scenario. Here, uncertainties in thermal behavior of the mini CHP are considered. The mini-CHP model in the optimization problem differs from the real system. The optimization problem is solved for the next 24 hours, but just the set-points for the first hour are sent to the low level controllers. After, one hour, actual states of the system are updated in the model and a new optimization loop starts.
Np
24 (hrs)
∆t
10 (min)
Chp,max Pel
4.5 (kWel )
Chp ηth
0.633
Chp,min Pel
1 (kWel )
Ath,warm
0.088
CapBatt
12 (kWh)
Bth,warm
0.577
Batt,char,max Pel
6 (kWel )
η Batt,char
0.9
Batt,dis,max Pel
6 (kWel )
η Batt,sd
0.999
Load,max Pel Gboiler,max Pth Gboiler,min Pth
10 (kWel )
η Batt,dis
0.92
40 (kWth )
η Gboiler
1
1 (kWth )
P v,nom Pel
9 (kWp )
Cel
28.38 (ct./kWh)
η T es,sd
0.998
η T es,char
0.9
η T es,dis
0.92
CapT es
(kWh)1
11.50
Cgas
6.52 (ct./kWh)
Chp CF it 12 (ct./kWh) ηel 0.238 1 as for a typical water tank with 500l and ∆T = 20K
When there is no PV generation, the CHP runs under a electricity-led strategy, i.e. following the household load in order to reduce electricity costs.
Similar to the MPC-based strategy, uncertainties in the thermal behavior of the mini CHP are present. The optimization problem is solved for the next 24 hours, and the whole sequence is implemented in the real system. After 24 hours, the procedure is repeated.
Electrical Power (kWel )
Operation
3. RESULTS AND DISCUSSION This section present relevant simulation results for the optimal operation of the home microgrid. First, a qualitative analysis of resulting profiles for one exemplary day helps for further understanding the operation of the system. The second part quantifies the overall impact of uncertainty in the mini CHP model on operational costs. In the end, a sensitivity analysis on TES and battery storage sizes shows how costs change if smaller storage systems are used. Fig. 4 presents resulting profiles for the system operation. The first subplot contains the electrical profiles of the system, and the second subplot shows resulting thermal profiles. The last subplot depicts storage systems’ state of charge. When looking at the electrical power output of the CHP, two operation patterns are visible: one during night and early morning hours, and one different during the day.
State of Charge (%)
Time series data in 10 min resolution for space heating, domestic hot water, household load and PV power generation are for Germany over one year. The MFH has an annual electrical consumption of 23655.70 kWh/a, and a thermal consumption of 74888.57 kWh/a. The PV plant has an annual energy yield of 8529.24 kWh/a. Table 2 gives the parameters used for the simulation. Moreover, for the economic analysis, specific investment costs of 1724 EUR/kWh for a 6 kWh battery, and 1108 EUR/kWh for a 12 kWh battery are assumed. Similarly, total investment costs of 1038.87 EUR, 1375.64 EUR, and 2205.07 EUR are used for the 100 liter TES, the 300 liter TES, and the 500 liter TES respectively. The calculation of the annuity factor uses an interest rate of 5% and a useful life-time of 20 years. The implementation is done in Python using Pyomo (Hart et al., 2012, 2011) as modeler, and CPLEX (IBM, 1987,2013) as solver.
Thermal Power (kWth )
2.5 Simulation setup
14 12
PelChp
10 8
PelPv
6
PelLoad
4 2 0 30 25
Chp Pth
20
Gboiler Pth
15
Dhw Pth
10
Sh Pth
5 0
100 80
Soc Tes Soc Batt
60 40 20 0 00
:00
02
:00
04
:00
06
:00
08
:00
10
:00
12
:00
14
:00
16
:00
18
:00
20
:00
22
:00
00
:00
Time
Fig. 4. Example of resultant profiles for perfect operation strategy As soon as the MPC predicts the thermal load peak at around 6:00 in the morning (second subplot), the CHP changes to a heat-led operation. It increases the operation point in order to fully charge the TES, so that the coming peak in thermal demand can be covered without using the gas boiler. During PV production hours, the CHP continues under heat-led operation, the electrical load is covered mainly by the PV production, and the electricity surplus is sold into the grid. Due to the high thermal demand during the day, there are just few cases when the TES can be charged (see 10:00 and 14:00 hours). Regarding the battery system, the MPC decides not store the electricity surplus, but to sell it to the grid. Just when the MPC predicts the evening peak in household load around 19:00 hours, it decides to charge the battery at around 13:00 hours to have enough energy to cover
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the coming peak. As PV generation decreases, the CHP switches again to electricity-led operation. As a second point in the results, we quantify the impact of uncertainty in the CHP thermal behavior. For this purpose, we compare the resultant costs for a simulation with optimal operation without uncertainty (perfect knowledge of the system) over a year, with the resultant costs for the open loop optimization operation and the MPC operation, also over a year but including uncertainty in the model. Here, it is assumed that the model in the optimization problem is different from the real system, and this is done by decreasing the time constant of the thermal power system of the CHP. The real system behaves as described in Fig. 3 for the warm start, while the MPC assumes that mini CHP reaches its nominal thermal power in about 10 minutes. To better illustrate the responses, Fig. 5 shows the real, and the mini CHP thermal behavior assumed by the MPC. The brown line shows the gas power input setpoints sent from the MPC to the mini CHP. The purple line is the thermal power output assumed by the MPC, while the red line denotes the real thermal power output of the mini CHP. 20
10
running down, so that no matter what action the MPC takes, the optimization problem is already infeasible. For Lost this reason, the decision variable Pth is included to also enable the MPC to waste some power in order to make the optimization problem feasible. On the contrary, if less energy than expected is given by mini CHP and the storage is almost empty, then the gas boiler has to supply the missing energy. The MPC leads to lower annual operational costs, compared to the open loop strategy, mainly because of its closed loop property, which allows to correct mini CHP schedules every hour. Since the open loop-based operation calculates fixed schedules for the next 24 hours, it must waste more energy due to the presence of uncertainty in the mini CHP thermal behavior. Finally, a sensitivity analysis reveals the effects of storage sizes on home microgrid operational costs. The baseline is the resultant costs for the perfect operation with 500liter TES and battery capacity of 12 kWh. We conduct simulations over a year with variations of TES volume and battery capacity, recording the corresponding additional operation costs. The simulation scenarios correspond to TES volumes of 500 liter, 300 liter and 100 liter, and battery capacities of 12 kWh and 6 kWh, for both operation strategies, MPC-based and open loop-based. Through this experiment, it will be possible to determine how small the storage systems could be, such that under a suitable operation strategy the additional operation costs are still moderated. Fig. 6 helps to visualize the results of the annual simulations.
Chp Pgas
5
Additional operation costs [EUR]
Power [kW]
15
^ Chp P th Chp Pth
0 0
5
10
15
20
25
30
35
40
Time [Minutes]
Fig. 5. Step responses for the real system and the model in the optimization For the perfect optimal operation the resultant annual operational costs are 7470.79 EUR/a. If uncertainties in the thermal behavior of the mini CHP are present, the annual operational costs increase to 7472.18 EUR/a and 7518.10 EUR/a for the MPC-based operation and the open loop optimization-based operation respectively. These resultant costs can be explained as follows: Because the real system responds slower than assumed by the MPC, this results in the TES receiving less energy than planned when the CHP is running up. On the other hand, when the CHP is running down, slower than assumed by the MPC, the TES receives more energy that initially planned. This may be problematic, if the TES is almost full. In such a situation, the MPC will shut-down the CHP assuming that it will reduce its thermal power very fast, so that the upper limit of the TES will not be reached. In reality, the CHP reduces its thermal power slower than required, meaning that more energy is supplied, leading to an overcharging of the TES. To deal with this issue, the real system has to waste some energy in order to allow further operation, incurring in extra costs. This situation affects the MPC as well, because there may exist situations where in the beginning of MPCs time window the TES is already or almost full, and the CHP is still
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200
MPC
100 100
150
100
300
OL
500 Liter
300
300 100
100
300 Liter
500 50
500
500
100 Liter
300 500
0
6
12
Battery capacity [kWh]
Fig. 6. Sensitivity analysis on operation costs with different storage capacities for MPC and OL As expected, a home microgrid with 500 liter TES and 12 kWh battery gives the minimum operation costs under MPC-based operation. If the system uses a 100 liter TES with a 6 kWh battery under an open loop-based operation, the operation costs increase by ca. 200 EUR/a compared to the baseline case. This configuration presents the larger additional costs. In general, for a given configuration, MPC-based operation is always cheaper than the open loop-based. Another aspect worth to mention, is that a system under MPC-based operation with TES-300 liter and 12 kWh battery shows lower operation costs than a system with the same battery size but with larger TES capacity under open loop-based operation. It is usual that the smaller the storage capacity is, the lower the investment costs are. Therefore, annuity costs, based on investment and operation costs, are shown in Fig. 7.
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REFERENCES
Total annual costs [EUR/a]
8750
8700
TES 500l 8650
8600
TES 300l
8550
TES 100l
8500
8450 6
9
12
Battery capacity [kWh]
Fig. 7. Total annual costs with different storage capacities for MPC From this chart, a good compromise between operation costs and storage size is a home microgrid with an MPCbased operation, a TES-300 liter, and 6 kWh battery. 4. CONCLUSIONS Optimal operation of home microgrids is an actual important topic of research. In this paper, the economic MPC operation of a home microgrid with photovoltaic-combined heat and power storage systems was investigated. The purpose of the paper was to present the economic MPC problem formulation, and investigate the impact of uncertainty coming from the thermal behavior of the mini CHP. Additionally, a sensitivity analysis on storage size was also presented. To quantify the effects of this uncertainty in the operation, a ”MPC-based” strategy and a ”open loopbased” strategy were compared with a ”perfect” optimal strategy. The main consequence of having an imperfect model for the thermal response of the mini CHP, is that the TES might be overcharged or undercharged. To overcome these situations, the system has to waste energy, or use the auxiliary gas boiler respectively, incurring in additional costs. Simulation results showed that, even for a minimal mismatch between the optimization model and the real system regarding the settling time of mini CHP thermal power, resultant additional operation costs are essentially different between the ”open loop”-based operation and the ”MPC-based” operation. While the later one achieves operation costs almost equal to the ”perfect” case, the costs for the ”open loop”-based strategy are notably higher. This confirms the robustness of MPC against uncertainties, as well as it advantages for operation of home microgrids. In the end, a sensitivity analysis regarding the impact of storage size on additional operation costs were conducted. Here, the ”MPC-based” operation enabled a better usage of the storage systems, such that it might be possible to reduce both, TES and battery size, with a moderate increased in operational costs, and a reduction in investment costs (smaller storage systems). In future work, other sources of uncertainties will be included in the evaluation, i.e. the impact of forecasts errors from household load, PV generation, and thermal demand on the overall operation costs have to be quantified. Also, a sensitivity analysis regarding larger storage systems (TES larger than 500 liter and battery systems larger than 12 kWh) may provide new insights for determining a maximum feasible capacity for such a home microgrid.
Boyd, S.P. and Vandenberghe, L. (2004). Convex optimization. Cambridge University Press, Cambridge, UK and New York. Chen, C., Wang, J., Heo, Y., and Kishore, S. (2013). MPCBased Appliance Scheduling for Residential Building Energy Management Controller. IEEE Trans. on Smart Grid, 4(3), 1401–1410. doi:10.1109/TSG.2013.2265239. European Commission (2011). Energy Roadmap 2050 Impact Assessment. URL https://ec.europa.eu. Hart, W.E., Laird, C., Watson, J.P., and Woodruff, D.L. (2012). Pyomo – Optimization Modeling in Python, volume 67. Springer US, Boston, MA. doi:10.1007/9781-4614-3226-5. Hart, W.E., Watson, J.P., and Woodruff, D.L. (2011). Pyomo: Modeling and solving mathematical programs in Python. Mathematical Programming Computation, 3(3), 219–260. doi:10.1007/s12532-011-0026-8. Hidalgo Rodriguez, D.I., Spitalny, L., Myrzik, J., and Braun, M. (2012). Development of a control strategy for mini CHP plants for an active voltage management in low voltage networks. In 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe), 1–8. doi:10.1109/ISGTEurope.2012.6465797. Houwing, M., Negenborn, R.R., and de Schutter, B. (2011). Demand Response With Micro-CHP Systems. Proceedings of the IEEE, 99(1), 200–213. doi: 10.1109/JPROC.2010.2053831. IBM (1987,2013). IBM ILOG CPLEX Optimization Studio. URL http://www-03.ibm.com. Kriett, P.O. and Salani, M. (2012). Optimal control of a residential microgrid. Energy, 42(1), 321–330. doi: 10.1016/j.energy.2012.03.049. Oldewurtel, F., Jones, C.N., Parisio, A., and Morari, M. (2014). Stochastic Model Predictive Control for Building Climate Control. IEEE Trans. on Control Systems Technology, 22(3), 1198–1205. doi: 10.1109/TCST.2013.2272178. Parisio, A., Rikos, E., and Glielmo, L. (2014). A Model Predictive Control Approach to Microgrid Operation Optimization. IEEE Trans. on Control Systems Technology, 22(5), 1813–1827. doi: 10.1109/TCST.2013.2295737. Sossan, F., Bindner, H., Madsen, H., Torregrossa, D., Reyes Chamorro, L., and Paolone, M. (2014). A model predictive control strategy for the space heating of a smart building including cogeneration of a fuel cellelectrolyzer system. Electrical Power and Energy Systems, 62, 879–889. doi:10.1016/j.ijepes.2014.05.040. Thomas, B. (2011). Mini-Blockheizkraftwerke: Grundlagen, Ger¨ atetechnik, Betriebsdaten. Vogel, W¨ urzburg, 2., vollst. u ¨berarb. aufl. edition. Zhang, Y., Zhang, T., Wang, R., Liu, Y., and Guo, B. (2015). Optimal operation of a smart residential microgrid based on model predictive control by considering uncertainties and storage impacts. Solar Energy, 122, 1052–1065. doi:10.1016/j.solener.2015.10.027. Zong, Y., Kullmann, D., Thavlov, A., Gehrke, O., and Bindner, H.W. (2012). Application of Model Predictive Control for Active Load Management in a Distributed Power System With High Wind Penetration. IEEE Trans. on Smart Grid, 3(2), 1055–1062. doi: 10.1109/TSG.2011.2177282.
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