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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

A dynamic optimization-based architecture for polygeneration microgrids with tri-generation, renewables, storage systems and electrical vehicles Stefano Bracco a, Federico Delﬁno a, Fabio Pampararo a, Michela Robba b,⇑,1, Mansueto Rossi a a b

Department of Naval, Electrical, Electronic and Telecommunication Engineering – DITEN, Via Opera Pia 11a, I-16145 Genova, Italy Department of Informatics, Bioengineering, Robotics and Systems Engineering – DIBRIS, Via Opera Pia 13, I-16145 Genova, Italy

a r t i c l e

i n f o

Article history: Received 25 July 2014 Accepted 2 March 2015

Keywords: Smart grids Renewable energy Optimization

a b s t r a c t An overall architecture, or Energy Management System (EMS), based on a dynamic optimization model to minimize operating costs and CO2 emissions is formalized and applied to the University of Genova Savona Campus test-bed facilities consisting of a Smart Polygeneration Microgrid (SPM) and a Sustainable Energy Building (SEB) connected to such microgrid. The electric grid is a three phase low voltage distribution system, connecting many different technologies: three cogeneration micro gas turbines fed by natural gas, a photovoltaic ﬁeld, three cogeneration Concentrating Solar Powered (CSP) systems (equipped with Stirling engines), an absorption chiller equipped with a storage tank, two types of electrical storage based on batteries technology (long term Na–Ni and short term Li-Ion ion), two electric vehicles charging stations, other electrical devices (inverters and smart metering systems), etc. The EMS can be used both for microgrids approximated as single bus bar (or one node) and for microgrids in which all buses are taken into account. The optimal operation of the microgrid is based on a central controller that receives forecasts and data from a SCADA system and that can schedule all dispatchable plants in the day ahead or in real time through an approach based on Model Predictive Control (MPC). The architecture is tested and applied to the case study of the Savona Campus. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction The development of the renewable energy sector, the concept of sustainable energy, and the use of technologies for distributed generation have focused attention on smart grids. Microgrid research ﬁts very well with ongoing smart grid activities throughout the world and several challenges need to be investigated [1]. Microgrids are able to integrate different distributed and heterogeneous sources, either programmable or stochastic (these latter, typically, are the renewables like wind and solar), and require intelligent management methods and efﬁcient design in order to meet the needs of the area they are located in ([2–4]). Generally, microgrids are low voltage distribution networks installed in small

⇑ Corresponding author at: University of Genova, DIBRIS – Department of Computer Science, Bioengineering, Robotics, and Systems Engineering, Via Opera Pia 13, 16145 Genova, Italy. Tel.: +39 0103532804, +39 0103532748, cell: +39 3805105692; fax: +39 0103532154. E-mail address: [email protected] (M. Robba). 1 Address: c/o Campus Savona, Via A. Magliotto 2, 17100 Savona, Italy. Tel.: +39 01923027211. http://dx.doi.org/10.1016/j.enconman.2015.03.013 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

areas (like University Campus sites or districts), but also buildings or industrial plants can themselves be seen as microgrids. Energy Management Systems (EMSs) are vital tools used to optimally operate and schedule microgrids [5]. Experimental tests and demonstration projects are fundamental to derive new methods and tools for the optimal planning and management and for simulation purposes, as described in [6–8]. In the recent literature, different papers can be found about the development of models for the simulation and optimization of microgrids with storage and renewable energies both at planning and at operational level. Chen et al. [9] present a methodology for the optimal allocation and economic analysis of an energy storage system in microgrids. Mohammadi et al. [10] present an optimized design of a microgrid in distribution systems with large penetration of dispersed generation units (among which PV, wind turbines and batteries). Marnay et al. [11] propose an optimization approach to incorporate electrical and thermal storage options in the Berkeley Lab’s Distributed Energy Resources Customer Adoption Model (DER-CAM). Different recent works are also related to operational management problems ([12,13]) and are usually aimed at the best management of intermittent renewable

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Nomenclature Symbol B C CAP D E Ef Ev ef G I LHV N NG P PL pf Q R S SOC Sb t, T, D TES Vb v x Zb

g

phase angle (rad) efﬁciency (-)

Subscript B CHI CR CSP c el HP h in OUT, out PE PV pc pp ppwf RES S SEB SPM Sv t th tx utx W

boiler chiller control room concentrating solar power cool electrical heat pump heat inlet outlet primary energy photovoltaic power conditioning purchasing price purchasing price without fee renewable sources battery storage smart energy building Smart Polygeneration Microgrid vehicle storage time thermal taxed untaxed wind

d beneﬁt (€) cost (€) battery capacity (kW h) electrical/thermal load (kW) emissions (tCO2) emission factor (tCO2/m3 or tCO2/kW h) vehicle stored energy (kW h) electricity fee (€/kW h) solar radiation (kW/m2) current (A) lower heating value (kW h/m3) number () fuel price (€/m3) power (kW) power loss (kW) packing factor () fuel quantity (m3) electrical resistance (X) area (m2) battery state of charge (-) base power (kW) time (h) thermal energy price (€/kW h) base voltage (V) velocity (m/s) electrical reactance (X) base impedance (X)

sources. Marzband et al. [5] compare two algorithms to implement an energy management system based on local energy market in microgrids in islanding mode, based on mixed-integer nonlinear programming. Mohamed and Koivo [14] present a genetic algorithm approach to solve the problem of electric power dispatch optimization of microgrids for a system that includes a fuel cell, a diesel engine, a microturbine, and minimizes total operating costs. Zhang et al. [15] analyze the case of a smart building composed of multiple smart homes (that share a microgrid) and propose a mixed integer linear programming model to minimize total 1-day-ahead expense related to smart building’s energy consumptions, including operation and energy costs. Bracco et al. [7] present a static mixed integer non linear optimization model for the Smart Polygeneration Microgrid (SPM), neglecting the electrical network, the storage systems, and the electrical vehicles. As regards software tools, Homer energy software [16] simpliﬁes the task of evaluating design options for both off grid and grid connected renewable power systems for remote, stand alone, and distributed generation applications. At the industrial side, few software algorithms are available for the optimization of microgrids. One example is the Siemens DEMS (Decentralized Energy Management System) [17] that includes a very good user friendly and ﬂexible interface, in order to monitor data and to obtain necessary forecasts, minimizes overall costs, uses simpliﬁed models for technologies and storage systems, and neglects thermal and electrical distribution networks. A major issue for the optimal operation of microgrids is how to deal with the uncertainties due to the intermittent renewable sources and the variable loads, while minimizing economic and environmental impact objectives. Model Predictive Control (MPC) is a viable approach, as demonstrated by many application areas. MPC is a mature methodology, but there is still a signiﬁcant investigation to carry out concerning with its practical

implementation in the day-by-day management of energy infrastructures [18]. In the ﬁeld of power systems management, Xia et al. [19] focus attention on the optimal control dynamic dispatch and the dynamic economic dispatch formulations, and propose an MPC approach that gives better performances and overcomes technical limits related to ramp rate. Dagdougui et al. [12] present an optimal controller based on MPC and applied to a general building system. With respect to the current literature, the optimization model presented in this paper is dynamic and provides details on the electrical grid, the power losses, the electrical vehicles, the economic assessment of the different plants, the carbon footprint over the whole power ﬂows. Moreover, it allows the inclusion of on/off status of all plants, internal and external grid connections, and thus the possibility to deﬁne/customize in situ intervention and the switching between grid connected and islanded modes. Then, in this work, attention is focused on microgrid optimal control and on the formalization and application of a dynamic decision model to a real case study/test bed facility: the University of Genoa Smart Polygeneration Microgrid (SPM) linked to the Sustainable Energy Building (SEB), which is an intelligent building directly connected to the SPM ([7,8]). The SPM is a three phase low voltage distribution system, connecting three cogeneration micro gas turbines fed by natural gas, a photovoltaic ﬁeld, three cogeneration Concentrating Solar Powered (CSP) systems (equipped with Stirling engines), an absorption chiller equipped with a storage tank, two types of electrical storage based on batteries technology (long term Na–Ni and short term Li-Ion), two electrical vehicles charging stations, and other electrical devices. The grid is integrated with the other generation systems already in operation inside the Savona Campus, such as one cogeneration gas turbine and two traditional boilers, fed by natural gas. The SEB, which is presently under construction, will be supplied with

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different renewable energy units for thermal and electric power generation (photovoltaic, geothermal, wind, etc.) and host ofﬁces and laboratories on building automation and for testing smart grid components and devices. Finally, a MPC control scheme based on the receding horizon technique (like in [20,12]) is applied to derive the optimal solution. Speciﬁcally, the optimization and simulation horizons can be chosen on the basis of the available information about uncertain parameters. The optimization horizon is the length over which the optimization problem is run. This optimization problem is completely deterministic and based on the current states, forecasted demands and prices. Among the results of the optimization problem only the solution related to the ﬁrst time interval is retained. Then, uncertain parameters (new information and new forecasting) are obtained and a new optimization problem is run. The number of times the optimization problem is run constitutes the simulation horizon. This approach allows updating new information when available and to reduce uncertainties related renewables availability and load forecasting. The approach followed in this paper can be applied to any energy system characterized by multiple production, storage systems and distribution systems (building, microgrid, industry, Municipality, etc.) that has a unique decision maker. In fact, the decision model (or similar models more appropriate for another case study) is centralized and any game theory or distributed approach is followed. In fact, the model is representative of a decision maker that owns the microgrid and that has pre-established agreements with other decision makers. In the following, Sections 2 and 3 propose the overall system model, while in Section 4 the general control architecture is described together with the dynamic optimization problem. Results for the SPM are shown in Section 5. Finally, in Section 6, the conclusions are drawn and the possible future developments are outlined.

The controllable generation units are different kinds of microturbines that produce both electrical and thermal energy. The electrical power output is thus related to the primary energy (per unit time) used in the microturbines through empirical functions g k , which vary for each microturbine k, k = 1, . . ., K, and for each time interval (t, t + 1), with t = 0,. . .,T 1. That is ([8,24–26]),

Pel;k;t ¼ g k ðPPE;k;t Þ k ¼ 1; . . . ; K

Pth;k;t ¼ g~k ðPel;k;t Þ k ¼ 1; . . . ; K

Pth;B;t ¼ gB PPE;B;t Pth;HP;t ¼

t ¼ 0; . . . ; T 1

gHP;j Pel;HP;j;t t ¼ 0; . . . ; T 1

PCSP;el;t ¼ SCSP gCSP;el Gt NCSP

t ¼ 0; . . . ; T 1

ð2Þ

PCSP;th;t ¼ SCSP gCSP;th Gt NCSP

t ¼ 0; . . . ; T 1

ð3Þ

The wind turbine power output P W;t [kWe] depends on the output power curves supplied by the manufacturer and on wind velocity vt. Thus,

PW;t ¼ f ðv t Þ t ¼ 0; ::; T 1

ð4Þ

ð8Þ

j¼1

Pth;CHI;t ¼ gCHI Pth;CHI;in;t

t ¼ 0; . . . ; T 1

ð9Þ

PC;CHI;t ¼ Pth;CHI;in;t c t ¼ 0; . . . ; T 1

ð10Þ

where gHP;j and gCHI indicate the efﬁciency (usually called Coefﬁcient Of Performance – COP) of the j-th heat pump and the chiller, whereas c is a constant value. Finally, the state of charge SOC f ;t [adim] of the f-th battery can be expressed by [27]

with

where Spv is the solar cell array area, gPV is the module reference efﬁciency, pf is the packing factor, gpc is the power conditioning efﬁciency (balance of system efﬁciency), and Gt [kW/m2] is the forecasted hourly irradiance. The CSPs electrical and thermal power productions (PCSP,el,t [kWe], PCSP,th,t [kWth]) have been calculated on the basis of the electrical and thermal efﬁciencies (gCSP,el, gCSP,th), as declared in the technical characteristics of the speciﬁc plants. That is,

ð6Þ

ð7Þ

J X

In this section, the considered generation technologies, and storage systems are described. Power plants can be either controllable (i.e., microturbines) or non-controllable (i.e., renewable energies). The latter ones can be forecasted both through black-box ([21,22]), and/or meteorological simulation models [23]. In this work, forecasting data are available through the SPM supervisory software. The photovoltaic plant power output PPV,t [kW] in time interval (t, t + 1) is given by [12]:

ð1Þ

t ¼ 0; . . . ; T 1

being g~k another empirical function. Similarly, equations have been provided for heat production from boilers and heat pumps, and for cool production and electrical consumption from chillers. That is,

SOC f ;tþ1 ¼ SOC f ;t gf ;t

t ¼ 0; . . . ; T 1

ð5Þ

where PPE,k,t [kWPE] and Pel,k,t [kWe] are, respectively, primary energy per unit time (i.e., natural gas ﬂow rate multiplied by its lower heating value) in time interval (t, t + 1) and the electrical power output. As regards the microturbines, the thermal power output Pth,k,t [kWth] in time interval (t, t + 1) can be calculated by (like in [8,26]),

2. Generation units and storage systems

PPV;t ¼ SPV gPV pf gpc Gt

t ¼ 0; . . . ; T 1

(

gf ;t ¼

PS;f ;t D t ¼ 1; . . . ; T CAPS;f

f ¼ 1; . . . ; F

gout;f if P S;f ;t P 0 t ¼ 0; . . . ; T 1 f ¼ 1; . . . ; F gin;f otherwise

ð11Þ

ð12Þ

Speciﬁcally, the storage state of charge at time t + 1 for each kind of battery f, f = 1,. . .,F, (SOC f ;tþ1 ) depends on: the state of charge at time t (SOC f ;t ), the active power PS;f ;t (positive if delivered by the storage, negative if injected), the battery rated capacity CAPS;f [kW h], the time interval D, and gout;f and gin;f (i.e., the efﬁciencies given by the battery and the related inverter). Initial state of charge for each battery is known from in situ measurements available from the supervisory software. Finally, the charging/discharging of electrical vehicles (EVs) through the two available charging stations has to be taken into account. The EVs have ﬁxed times in which they arrive (leave) at (from) the SPM. Each vehicle m, m = 1,. . .,M, is characterized by the stored energy at time t, Ev m;t [kW h], the possible exchange with the SPM of active power P Sv ;m;t (positive if delivered by the electrical vehicle internal storage, negative if injected) [kW], in each time interval (t, t + 1). Moreover, the vehicle is in charging mode or discharging mode only if it is present in the speciﬁc time interval. A binary pre-assigned parameter dSv ;m;t is thus here adopted as regards the presence (1) or absence (0) of each vehicle. Thus, the stored energy in each vehicle is equal to:

Ev m;tþ1 ¼ Ev m;t gsv ;m PSv ;m;t D t ¼ 0; . . . ; T 1 m ¼ 1; . . . ; M ð13Þ with

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P Sv ;m;t ¼

0 if PSv ;m;t

dSv ;m;t ¼ 0 if

dSv ;m;t ¼ 1

t ¼ 0; . . . ; T 1 m ¼ 1; . . . ; M

Pgrid ,t MT

ð14Þ where gsv ;m is the storage efﬁciency of the electrical vehicles.

D

3. The electrical grid

D Del , SEB ,t

In the proposed decision model, any kind of electrical model [28] can be adopted and inserted in the optimization model (as it is explained in [29]). Speciﬁcally, a single bus bar representation can be adopted [8], which means that the electrical grid is not modeled, or alternatively the nodes (i.e., buses) of the electrical grid can be explicitly represented [29]. In this work, the two aforementioned different approaches are formalized and discussed with speciﬁc reference to the Savona Campus SPM. When the single bus bar representation is taken into account all plants are connected to one node. Otherwise, the electrical grid is represented by a set of interconnected nodes at which different generation units and loads are connected, as reported in Fig. 1. In the following, ﬁrst the ‘‘interconnected nodes’’ representation is reported (in connection with Fig. 1) and then the single bus bar equation is considered. The SPM electrical grid is here modeled using the DC load ﬂow approach [28], all the voltages are considered equal to the nominal value (400 V) and a unitary power factor is assumed. Moreover, power losses have been included too. The transformer connecting the microgrid to the medium voltage distribution grid (modeled as node MT) is also taken into account. At each node, the active power balance has been formalized according to [28,29]. In the following, for the sake of clarity, the balance has been formalized for each node, with speciﬁc reference to the structure of the Savona Campus Smart Polygeneration Microgrid. Moreover, its simpliﬁcation to a single bus bar representation is shown too. 3.1. Node MT

0 el,CR,t

Pel,k,t

1

4

PCSP, el ,t

PSv m= 2,t

PC ,CHI ,t

PS ,

f ,t

PPV,

3

2

PSv, m= 1,t

SP M , t

RES SEB ,t

Fig. 1. Schematization of the SPM electrical grid as a set of nodes.

to represent the network constraints, in per unit values in link (i, j), currents are equal to power ﬂows, i.e., ii;j;t ¼ pi;j;t . 3.3. Node 1

Del;CR;t þ Del;SEB;t ¼ P0;1;t P1;2;t þ P CSP;el;t nCSP;t PC;CHI;t t ¼ 0; . . . ; T 1

ð19Þ

(nCSP;t is a binary variable indicating if the CSP production is active or curtailed). 3.4. Node 2

As losses in the transformer are neglected, the power Pgrid;t [kW] from the distribution grid is equal to the power fed by the transformer P MT;0;t [kW], i.e.,:

Pgrid;t ¼ PMT;0;t

el ,C ,t

t ¼ 0; . . . ; T 1

ð15Þ

3.2. Node 0

0¼

F X PS;f ;t þ P1;2;t P2;3;t þ PPV;SPM;t nPV;t þ RESSEB;t nSEB;t f ¼1

t ¼ 0; . . . ; T 1

ð20Þ

with RESSEB;t ¼ P PV;SEB;t þ PW;SEB;t and nPV;t and nSEB;t being binary variables indicating if the power production is curtailed or not.

The balance equation for node 0 is

Del;C;t ¼ PMT;0;t P0;1;t þ P4;0;t

t ¼ 0; . . . ; T 1

ð16Þ

where P 0;1;t ; P4;0;t are power exchanges among nodes (0, 1), and (4, 0), respectively. It is important to note that power ﬂows from node 0 (4) to node 1 (0) are positive as a convention of signs. This means that if the power ﬂow is negative, it goes in the opposite direction. Instead, Del;C;t is the summation of different contributions: electrical demand of the Campus Del;t , electricity feeding heat pumps that supply cool, power losses PLt . That is,

Del;C;t ¼ Del;t

J X þ Pel;HP;j;t þ PLt

PSv ;m¼1;t þ P2;3;t ¼ P3;4;t

t ¼ 0; . . . ; T 1

ð21Þ

3.6. Node 4

0 ¼ PSv ;m¼2;t þ P3;4;t P4;0;t þ

K X Pel;k;t

t ¼ 0; . . . ; T 1

ð22Þ

k¼1

t ¼ 0; . . . ; T 1

ð17Þ

j¼1

Power losses are function of both the power ﬂows among nodes and of known parameters. Speciﬁcally [28–29],

As anticipated, the DC load ﬂow is used to model the grid, i.e., the power ﬂows among nodes are expressed in terms of the phases at each node and of the link reactances. That is,

Pi;j;t ¼

PLt ¼ 3 R0;1 I20;1;t þ R1;2 I21;2;t þ R2;3 I22;3;t þ R3;4 I23;4;t þ R4;0 I24;0;t t ¼ 0; . . . ; T 1

3.5. Node 3

ð18Þ

where R0;1 ; R1;2 ; R2;3 ; R3;4 ; R4;0 are the resistances of lines connecting nodes, whereas I0;1;t ; I1;2;t ; I2;3;t ; I3;4;t ; I4;0;t are the currents. Moreover, it should be noted that (like in [29]), as we use the DC load ﬂow

di;t dj;t xi;j Zb

Sb

t ¼ 0; . . . ; T 1 ði; jÞ 2 S

ð23Þ

where di;t ; dj;t are phase angles at each node, xi;j is reactance in each line [X], Z b is the base impedance given by Z b ¼

V 2b , Sb

where Sb is the

base power and V b is the base voltage assumed equal to the nominal voltage (400 V).

S. Bracco et al. / Energy Conversion and Management 96 (2015) 511–520

It is important to note that in case the single bus bar approximation is adopted, for example, constraints (15), (17)–(23) are neglected and substituted by the summation of all balance node equations, posing powers ﬂows among nodes equal to 0. That is,

Pgrid;t þ

F X

PS;f ;t þ PPV;SPM;t nPV;t þ RESSEB;t nSPM;t þ PSv ;m¼1;t þ PSv ;m¼2;t

f ¼1

þ

J K X X Pel;k;t þ PCSP;el;t nCSP;t ¼ Del;t þ Pel;HP;j;t þ Del;CR;t þ Del;SEB;t j¼1

k¼1

þ PC;CHI;t

t ¼ 0; . . . ; T 1

ð24Þ

4. The overall architecture and the dynamic optimization problem Fig. 2 reports the interactions among the MPC controller, the supervisory software, and the different technologies. The approach followed in this paper is based on the repeated formalization and solution of an optimization problem over a ﬁnite horizon, on the basis of the current observed state and on the available forecasts of the quantities of interest. Speciﬁcally, as reported in the introduction section, the optimization and simulation horizons can be chosen on the basis of the available information about uncertain parameters. The architecture is based on a centralized intelligence that receives forecasts for renewable resources availability, demands, prices, and system state (for example the level of charge of the battery system), and, on the basis of an optimization model, gives commands to a sub-set of the generators, to the storage system, and to the connection between the SPM and the external grid. The commands are given to typical hardware (i.e., inverters, switch with the external net, etc.) that are installed in the SPM, through the RTUs (Remote Terminal Units) and the local controllers. Moreover, the central controller can communicate with the local controllers present in all the equipment and in the storage systems. The energy management system can be used for day a-head optimization, intra-day, and real time management. The main goal of the proposed optimization model is that of determining the optimal values over time of electrical and thermal power output from generation plants and boilers, of the storage systems injection/withdrawal, and of the electrical power exchange with the external grid, according to the time-varying thermal and electrical loads, fuel and electricity prices, and available energy forecasts. These optimal values minimize the daily

515

operating costs and the CO2 emissions. Different performance indexes are here formalized as a function of the chosen parameters, state and control variables, to optimize the overall system management, namely: operating costs related to purchasing of electricity and natural gas; beneﬁts due to electricity sales and incentives for local consume of produced energy; the CO2 emissions. State variables are represented by the state of charge of the storage SOCf,t, and the energy stored in the electrical vehicles Ev m;t . Instead, primary control variables are divided in two main classes: generation units scheduling, storage systems management and grid interconnection (i.e., PPE,k,t, PPE,B,t, Pgrid;t ; P el;HP;j;t ; P S;f ;t ; P Sv ;m;t ; Pth;CHI;t ; Pi;j;t , already discussed in the previous section), and binary variables for the on/off status of generation units, grid connections and storage systems (i.e., nk;t ; nB;t ; nj;t ; nCHI;t ; nPV;t ; nSEB;t ; nCSP;t ; ni;j;t ), as described in the following. The detailed formalization of the optimization problem, including objectives and constraints as a function of decision variables and parameters, is described in detail in the following subsections. 4.1. The objective function The overall objective function, to be minimized, is given by the sum of the net operating costs (i.e., costs minus beneﬁts), CTOT [€], and the costs due to CO2 emissions. The net operating costs are given by the sum of boiler costs (CB), microturbine costs (CK), costs (Cgrid) and beneﬁts (Bgrid) related to the electricity exchange with the grid, operating costs due to renewable sources (CRES). The CO2 emissions (ECO2 [tCO2]) are given by the emissions related to consumed primary energy, as detailed in the following. Other emissions (CO, NOx, SOx, . . .) coming from fossil fuel power plants (micro gas turbines and boilers) have not been considered in the optimization model since, in the analyzed operating conditions, the limits imposed by environmental standards have been always respected. On the other hand, the analysis has been focused on CO2 emission since one of the main goals of the present study is that of showing the environmental beneﬁts due to the adoption of high efﬁciency cogeneration technologies [30,31], such as the gas microturbines installed in the Savona Campus Smart Polygeneration Microgrid. The study is part of a more complex research activity aimed at quantifying the carbon footprint of the Savona Campus within the European directive scenario that promotes CO2 emission reduction also in the tertiary and residential sectors. The overall objective function is given by

Fig. 2. The MPC architecture of the developed Energy Management System (EMS).

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S. Bracco et al. / Energy Conversion and Management 96 (2015) 511–520

min

C TOT þ C CO2 ECO2

ð25Þ

where C CO2 is a parameter that corresponds to the price of one ton of CO2 [€/tCO2] [29]. Speciﬁcally, the overall operating costs are given by

C TOT ¼ C B þ C K þ C RES þ C grid þ Bgrid

ð26Þ

where

CB ¼

T1 X P th;B;t TESpp D

ð27Þ

t¼0

CK ¼

T1 X 2 X

4.2. The constraints Different classes of constraints are present in the overall problem formalization. The ﬁrst class includes the modeling of the system technologies given by Eqs. (5)–(14). Other classes of constraints are related to the modeling of the electrical grid, which includes the electrical demand satisfaction constraints, as reported in Eqs. (15), (17)–(23) when the electrical grid is modeled or in (24) when the single bus bar approximation is adopted. As regards other demand satisfaction constraints, the following relations should be added:

~min;m Dv m;t¼t hm 6 Ev m;t¼t h 6 a ~max;m Dv m;t¼t hm a

Q utx;k;t NGppwf þ Q tx;k;t NGpp þ Pel;k;t ef D

t ¼ 0; . . . ; T 1

ð28Þ

ð39Þ

t¼0 k¼1

C RES ¼

T 1 X

PCSP;el;t nCSP;t þ PPV;SPM;t nPV;t þ RESSEBt nSEB;t ef D

ð29Þ

amin Dth;h;t 6

6 amax Dth;h;t

T1 X ¼ cgrid;t maxðP grid;t ; 0ÞD

ð30Þ

t¼0

Bgrid ¼

T 1 X

bgrid;t minðPgrid;t ; 0ÞD

ð31Þ

t¼0

with

Q utx;k;t ¼ ð1 ff ÞbPel;k;t D k ¼ 1; 2 t ¼ 0; . . . ; T 1

ð32Þ

Q tx;k;t ¼ Q k;t Q utx;k;t

ð33Þ

k ¼ 1; 2 t ¼ 0; . . . ; T 1

Pel;k;t ¼ g k ðQ k;t LHVÞ k ¼ 1; 2 t ¼ 0; . . . ; T 1

ð34Þ

where recalling Eq. (5) (that is detailed for the speciﬁc case study in the following sections), P PE;k;t ¼ Q k;t LHV, with LHV the natural gas low heating value. The parameters have the following meaning: TESpp is the thermal energy service purchasing price [€/kW hth], ef is the electricity fee for local production [€/kW hel], Q utx;k;t is the untaxed quantity (due to Italian legislation on high efﬁciency Combined Heat and Power – CHP – systems) of natural gas used in microturbine k [m3], Q tx;k;t is the taxed quantity of natural gas used in the microturbines [m3], NGppwf is the price of untaxed gas [€/m3], NGpp is the full price of gas [€/m3], cgrid,t is the electricity purchasing price [€/kW hel], and bgrid;t the unit beneﬁts coming from the sold electricity [€/kW hel]. Instead, the overall CO2 emissions depend on the sum of emissions related to boilers (ECO2 ;B ), microturbines (ECO2 ;K ), and to the electricity taken from the external grid (ECO2 ;grid ). Thus, the overall emissions are given by

ECO2 ¼ ECO2 ;B þ ECO2 ;K þ ECO2 ;grid

T1 X E f ng D ¼ PPE;B;t e

ECO2 ;K

k¼1

ECO2 ;NET ¼

T1 X

min Dth;c;t 6 P th;HP;t þ P th;CHI;t 6 a max Dth;c;t a

ð40Þ t ¼ 0; . . . ; T 1

ð41Þ

where Pth;CHI;t is function of Pth;CHI;in (reported in the following equations) given by Eq. (9); Pth;k;t is given by Eq. (6); Dv m;t¼t [kW h] is the assigned demand to a speciﬁc time instant; P hm is a parameter given by hm ¼ tt¼0 dSv ;m;t , which is used to activate/deactivate constraint (39); Dth;h;t is the thermal demand for heat, Dth;c;t is the thermal demand for cool; min ; a max ; bmin ; bmax ; amin;m ; amax;m , are bound amin ; amax ; a parameters; Pth;k;CHI;t ; Pth;B;CHI;t are the thermal power generated by the microturbines and the boilers that is used by the chiller, respectively; Pth;k;OUT;t ; P th;B;OUT;t are auxiliary variables and represent the thermal power for the district heating network generated by the microturbines and the boilers, respectively; and:

Pth;CHI;in ¼

K X Pth;k;CHI;t þ P th;B;CHI

t ¼ 0; . . . ; T 1 k ¼ 1; . . . ; K ð42Þ

k¼1

Pth;k;t ¼ P th;k;CHI;t þ Pth;k;OUT;t

t ¼ 0; . . . ; T 1 k ¼ 1; . . . ; K

ð43Þ

Pth;B;t ¼ P th;B;CHI;t þ Pth;B;OUT;t

t ¼ 0; . . . ; T 1

ð44Þ

Then, there are bound constraints for the electrical variables that have to be satisﬁed. That is,

Pmax 6 P i;j;t 6 Pmax i;j i;j

ði; jÞ 2 S t ¼ 0; . . . ; T 1

ð45Þ

Imax 6 Ii;j;t 6 Imax i;j i;j

ð36Þ

Then, available generators and storage systems are characterized by rated performance values (minimum/maximum values) that should be respected. Thus,

t¼0

( ) K T1 X X ¼ Q k;t Ef ng D

t ¼ 0; . . . ; T 1

ð35Þ

where

ECO2 ;B

Pth;k;OUT;t þ Pth;B;OUT;t þ PCSP;th;t nCSP;t

k¼1

t¼0

C grid

K X

ð37Þ

ði; jÞ 2 S t ¼ 0; . . . ; T 1

ð46Þ

pmin;k nk;t 6 Pel;k;t 6 Pmax t ¼ 0; . . . ; T 1 k ¼ 1; . . . ; K el;k nk;t

ð47Þ

pmin;B nB;t 6 Pth;B;t 6 Pmax t ¼ 0; . . . ; T 1 th;B nB;t

ð48Þ

t¼0

pmin;HP;j nj;t 6 gHP;j PPE;HP;j;t 6 Pmax t ¼ 0; . . . ; T 1 j ¼ 1; . . . ; J th;HP;j nj;t maxð0; Pgrid;t ÞEf n D

ð49Þ

ð38Þ

t¼0

E f ng are the emission factors of the fuel, respecwhere Ef ng and e tively expressed in [tCO2/m3, tCO2/kW hPE]), whereas Ef n is the average emission factor of the national electrical mix [tCO2/kW hel].

pmin;CHI nCHI;t 6 Pth;CHI;t 6 Pmax t ¼ 0; . . . ; T 1 th;CHI nCHI;t

ð50Þ

pmin;SOC;f 6 SOC f ;t 6 pmax;SOC;f t ¼ 0; . . . ; T 1 f ¼ 1; . . . ; F

ð51Þ

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S. Bracco et al. / Energy Conversion and Management 96 (2015) 511–520

pmin;SOC;m 6 Ev m;t 6 pmax;SOC;m t ¼ 0; . . . ; T 1 m ¼ 1; . . . ; M ð52Þ Prated;f 6 P S;f ;t 6 Prated;f

t ¼ 0; . . . ; T 1 f ¼ 1; . . . ; F

P rated;m dSv ;m;t 6 P Sv ;m;t 6 P rated;m dSv ;m;t

ð53Þ

t ¼ 0; . . . ; T 1 m ¼ 1; . . . ; M

load for the system, and RES_SPM is the sum of the SPM PV and CSPs contribution. Finally, for microturbines (in the results only two microturbines are active, that is the C65 and the C30 Capstone microturbines (K = 2)) the following equations have been used [26]:

Pel;k;t ¼ lk;t P PE;k;t þ mk;t nk;t

k ¼ 1; . . . ; K

t ¼ 0; . . . ; T 1

ð61Þ

k;t P PE;k;t þ m k;t nk;t Pth;k;t ¼ l

k ¼ 1; . . . ; K

t ¼ 0; . . . ; T 1

ð62Þ

ð54Þ Finally, there are constraints that relate continuous and binary variables (like in [7]), for activation/deactivation of some constraints, for the imposition of maintenance interventions, and for the switching between islanded mode and grid-connected mode. That is,

Pel;k;t Mnk;t 6 0 t ¼ 0; . . . ; T 1 k ¼ 1; . . . ; K

ð55Þ

Pth;B;t MnB;t 6 0 t ¼ 0; . . . ; T 1

ð56Þ

Pel;HP;j;t Mnj;t 6 0 t ¼ 0; . . . ; T 1 J ¼ 1; . . . ; J

ð57Þ

Pth;CHI;t MnCHI;t 6 0 t ¼ 0; . . . ; T 1

ð58Þ

Pi;j;t ¼

Pgrid;t ¼

0 if

ni;j;t ¼ 0

Pi;j;t

otherwise

0 if P grid;t

ngrid;t ¼ 0 otherwise

t ¼ 0; . . . ; T 1 i; j ¼ 1; . . . ; N

t ¼ 0; . . . ; T 1

ð59Þ

ð60Þ

where M is a big number and ni;j;t ; ngrid;t are binary parameters set by the user. 5. Application to the Savona Campus case study The developed decision architecture has been tested with available data for the SPM and the SEB at the Savona University Campus [32–34]. The SPM was born from the ‘‘2020 Energy’’ Project (special project fully funded by the Italian Ministry of Education, University and Research, MIUR, started in 2011 and inaugurated in February 2014) whereas the SEB Project comes from ﬁnancial resources by the Italian Ministry for the Environment for the construction of a sustainable building (that will be connected to the SPM as an energy ‘‘prosumer’’) equipped by renewable power plants and characterized by energy efﬁciency measures and it is presently in progress (foreseen completion date: February 2016). The system case study related to the SPM and SEB at the Savona Campus is reported in Fig. 3. The following parameters (described in the above sections) have been used for the solution of the optimization problem: TESpp = 85.3103 €/kW hth; NGppwf = 0.53 €/m3; NGpp = 0.73 €/m3; ef = 0.0125 €/kW hel; cgrid,t has been set to 0.256 €/kW hel between 8 a.m. and 8 p.m., and 0.198 €/kW hel in the other time intervals; bgrid,t = 0.08 [€/kW hel]; C CO2 = 10 [€/tCO2]; ff = 0.12; b = 0.25 m3/ e f ng = 0.000202 tCO2/kW hPE; Ef-ng = kW hel; LHV = 9.7 kW hPE/m3; E 0.00195 tCO2/m3; Ef-n = 0.465103 tCO2/kW hel; gB ¼ 0:9; gout;f ¼ 1:15; gin;f ¼ 0:85; NB = 1; gHP;j ¼ 3:5; gCHI = 0.74; c = 0.06; CAPS;1 ¼ 141D kW h; Imax i;j

CAPS;2 ¼ 124D kW h;

Pmax ¼ 137:2 kW; i;j

¼ 250 A. As regards other electrical parameters, in Table 1, resistance and reactance for each line are reported. For the solution of the optimization problem, all grid lines are here considered working, all renewable plants on, and electrical vehicles are charged from 10 p.m. till 8 a.m with a known electrical request. Fig. 4 reports the available power from the overall renewables (primary y-axis) and the thermal and electrical demand (secondary y-axis). Speciﬁcally, the reported electrical demand is the overall

k;t are parameters that depend on time-varying k;t ; m where lk;t ; mk;t ; l external air temperature and load condition, and that are calculated at each optimization run on the basis of the meteorological forecasting. In fact, as assessed by Bracco et al. [35], it is important to consider the inﬂuence of the ambient temperature on the gas turbine performance, since its variation has a direct effect on the power output and the efﬁciency of the plant. The developed decision model is nonlinear. In particular, the results here reported refer to an optimization horizon of 4 h, a time interval of 15 min and a simulation horizon of 24 h. The optimization problem has been solved through the use of Lingo 9.0, Non Linear Solver, Multistart option (10 attempts). The time necessary for each optimization run is about 10 s. The overall cost to be payed by the energy manager for the considered day is 1648 €, while CO2 emissions are 4.31 tCO2. Figs. 5 and 6 report the values of control variables for the generation units for electrical and thermal power, respectively. It is important to highlight from the optimal solution that microturbine C65 is the most convenient, followed by microturbine C30, while the boiler is only used because the two microturbines are not sufﬁcient to satisfy the Campus energy needs. Instead, power ﬂows inside the grid are reported in Fig. 7. In the optimal solution, power ﬂows directions are: from node MT to node 0, from node 4 to node 0, and mainly from node 1 to node 0. This is because the highest electrical demand is at node 0. Then other power ﬂows are from node 4 (where there are microturbines) to nodes 3, 2, and 1. Finally, the batteries state of charge is reported in Fig. 8. It is important to note that battery is charged in the hours in which the energy price is low and is discharged when the energy price is higher. The optimal results have been compared with a not optimized scenario, i.e., storage systems do not work and the gas turbines produce the maximum power between 8 a.m. and 8 p.m., and are off in other time intervals. In this case, the optimal cost (i.e., the value of the real operating costs, found by subtracting the CO2 contribution to objective function (26)) is in this case 1754 € and CO2 emissions are 4.43 tCO2. Moreover, the results have been compared with a case in which all microturbines and storage systems are not working. The optimal value in this case is equal to 1930 € and 4.65 tCO2. The beneﬁts of using the SPM are thus at least (because the contribution of renewables is here considered, and the boiler use still optimized) equal to a saving of 15% in costs and of 8% in CO2 emissions for the considered day. This is a very good result, also considering the fact that only two microturbines are active in the considered day. Then, in order to evaluate the inﬂuence of the CO2 emission contribution in the objective function, the optimal results are compared to a problem formalization in which only CO2 emissions are minimized in the objective function. The optimal cost is in this case 1657 € (in spite of 1648 €) and CO2 emissions are 4.295 tCO2 (in spite of 4.31 tCO2). Thus, the decision maker has to decide if he/ she wants to spend additional 9 € to reduce the CO2 of about 0.02 tCO2. Finally, to see the inﬂuence of the line connections inside the SPM, link 0–1 has been disconnected. Optimal results show that the optimal cost is in this case 1650 € (higher than in

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S. Bracco et al. / Energy Conversion and Management 96 (2015) 511–520

Micro Wind Turbine 3 kWp

Photovoltaic unit 20 kWp (PV2)

+Q03

Plug-in Electrical Vehicles Electrical Storage 141 kWh Smart Energy Building

+Q02 284

270

N. 3 CSP 1 kWel each Sub-Station MV-LV National Grid Connection Point

+Q01

Operation Centre

Photovoltaic unit 77 kWp (PV1)

Thermal Storage & Chiller

+Q04 Plug-in Electrical Vehicles

Micro-Gas Turbines C30 - C65 Thermal Boilers

Fig. 3. The map of the University of Genoa SPM and SEB facilities. Table 1 Resistance and reactance of the SPM electric lines. Line

Resistance (X)

Reactance (X)

MT-0 0–1 1–2 2–3 3–4 4–0

0.00000 0.00371 0.01855 0.00583 0.01961 0.02915

0.012 0.003178 0.01589 0.004994 0.016798 0.02497

the case all lines are connected but of only two euros). This is mainly due to the location and size of loads, storage systems, grid connection (injecting at node 0), microturbines (see Fig. 1). The

results are conﬁrmed by disconnecting link 3–4: the cost is 1649.8 €. Thus, lines disconnection creates an increase of costs that for the SPM is very low but that in other case studies should be considered. A further analysis is related to the augmentation of renewable energy connected to the SPM at node 2: if it is doubled the cost is about 1585 €; however if renewable energy is ten times its initial value power lines constraints are not respected and thus curtailment actions have to be introduced. Then, the inﬂuence of power losses has been investigated for the SPM. In fact, posing power losses equal to zero, the cost is about 1640 € (instead of 1648 €). Finally, this last optimal solution

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S. Bracco et al. / Energy Conversion and Management 96 (2015) 511–520

Opmal power ﬂows

Renewable resources and power demand 250

100

1000

200

900 150

700 600

kWel

800

50

500

0

400

-50

300

PMT_0 P01 P12 P23 P34 P40

100

-100 0

200

5

0

0 0

5

10

RES_SPM [kW]

15

RES_SEB [kW]

20

10

15

20

hours

100

Fig. 7. Optimal power ﬂows among the lines of the SPM.

25

Electrical Demand [kWe]

Thermal Demand [kWt]

Baeries state of charge Fig. 4. Available renewable power and electrical/thermal power demands.

0.9 0.8 0.7 0.6

Opmal electrical power producon

0.5

350

0.4 300

0.3

kW

250

0.2 0.1

200 Pgrid

150

0 0

5

10

15

20

25

PelC30 SOC

100

SOC1

PelC65

50

Fig. 8. Batteries state of charge.

0 0

2

4

6

8

10

12

14

16

18

20

22

hours Fig. 5. Optimal electrical power production.

Opmal thermal power producon 1000 900 800 700

kWth

600 500

PthB PthC30

400

PthC65

300 200 100 0 0

2

4

6

8

10

12

14

16

18

20

22

hours Fig. 6. Optimal thermal power production.

has been compared with the optimization problem solved under the single bus bar approximation. The optimal results are the same. 6. Conclusions Microgrids with local controllers and a variety of generation units (tri-generation, renewables), storage systems (electrical, thermal) and loads (residential buildings, ofﬁces, electrical vehicles, etc.) represent a challenge for the development of business models, strategies and approaches for local optimal scheduling,

demand response programs, contribution to Distribution System Operators services and city demand satisfaction. The University of Genoa test-bed facilities at the Savona Campus have been described in connection with the different sub-systems that compose the overall system. An optimal control problem has been formalized that can be used both for day-ahead optimization and real time operational management. The novelty lies in the formalization and application of a dynamic decision model based on an MPC approach that provides modeling details on the storage systems, the electrical vehicles, the power losses, and on the formalization of detailed issues in the performance indicators (costs, beneﬁts, CO2 emissions). Many analyses have been reported as well as the comparison between the single bus bar approximation and the interconnected nodes representation of the grid. Uncertainties are here faced through the possibility of activating an MPC architecture based on the repeated formalization and solution of an optimization problem over a ﬁnite horizon, on the basis of the current observed state and on the available forecasts of the quantities of interest. Future developments could regard the definition of a stochastic optimization problem in which uncertainties in the model, in available renewable resources, in demands and prices will be explicitly reported in the problem formalization. It is important to highlight that the overall cost to be payed in the case of detailed formalization of the grid (i.e., interconnected nodes) by the energy manager for the considered day is 1648 €, while CO2 emissions are 4.31 tCO2. The optimal results have been compared with a not optimized scenario, i.e., storage systems do not work and the gas turbines operate at the maximum power between 8 a.m. and 8 p.m., and are off in other time intervals. In this case, the optimal cost is 1754 €/day and CO2 emissions are 4.43 tCO2/day. Moreover, the results have been compared with a case in which all microturbines and storage systems are not working. The optimal value in this case is equal to 1930 €/day and 4.65 tCO2/day. The beneﬁts of using the SPM are thus at least (because the contribution of renewables is here considered, and

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S. Bracco et al. / Energy Conversion and Management 96 (2015) 511–520

the boiler use still optimized) equal to a saving of 15% in costs and of 8% in CO2 emissions for the considered day. This is a very good result, also considering the fact that only two microturbines are active in the considered day. Then, in order to evaluate the inﬂuence of the CO2 emission contribution in the objective function, the optimal results are compared to a problem formalization in which only CO2 emissions are minimized in the objective function: the decision maker has to decide if he/she wants to spend additional 9 € to reduce the CO2 of about 0.02 tCO2. Then, the inﬂuence of power losses has been investigated for the SPM. In fact, posing power losses equal to zero, the cost is about 1640 €/day (instead of 1648 €/day). This could suggest measures to reduce power losses also in small microgrids like the one present at the Savona Campus. Finally, this last optimal solution has been compared with the optimization problem solved under the single bus bar approximation. The optimal results are the same. This means that, for the SPM, if electrical constraints are not violated, one can use the single bus bar approximation. However, the interconnected nodes representation is obviously advantageous for curtailment management and for lines disconnection interventions. It is important to note that, in this work, a centralized decision architecture and a centralized optimization problem has been taken into account. However, distributed, decentralized and hierarchical architectures can also be considered inside a single microgrid [29,36]. The speciﬁc test-bed facility could of course be detailed to make these approaches more attractive, either in terms of frequency regulation or in terms of different decision makers related to ‘‘internal sub-microgrids’’ (i.e., the SPM, the SEB, the laboratories), or in terms of local controllers associated to each local controller. Finally, the model of the microgrid could be used as a ‘‘virtual power plant’’ to study the interactions among many microgrids (also buildings), many decision makers, and the external grid manager, that are typical of large scale systems. References [1] Zamora R, Srivastava AK. Controls for microgrids with storage: review, challenges, and research needs. Renew Sustain Energy Rev 2010;14:2009–18. [2] Kriett PO, Salani M. Optimal control of a residential microgrid. Energy 2012;42:321–30. [3] Asano H, Hatziargyriou N, Iravani R, Marnay C. Microgrids: an overview of on going research, development, and demonstration projects. IEEE Power Energy Mag 2007:78–94. [4] Basu AK, Chowdhury SP, Chowdhury S, Paul S. Microgrids: energy management by strategic deployment of DERs—a comprehensive survey. Renew Sustain Energy Rev 2011;15:4348–56. [5] Marzband M, Sumper A, Dominguez-Garcia JL, Gumara-Ferret R. Experimental validation of a real time energy management system for microgrids in islanded mode using a local day-ahead electricity market and MINLP. Energy Convers Manage 2013;76:314–22. [6] Lidula WA, Rajapakse AD. Microgrids research: a review of experimental microgrids and test systems. Renew Sustain Energy Rev 2011;15:186–202. [7] Bracco S, Delﬁno F, Pampararo F, Robba M, Rossi M. A mathematical model for the optimal operation of the University of Genoa Smart Polygeneration Microgrid: evaluation of technical, Economic and Environmental Performance Indicators. Energy 2014;64:912–22. [8] Bracco S, Delﬁno F, Pampararo F, Robba M, Rossi M. A system of systems model for the control of the University of Genoa Smart Polygeneration Microgrid. In: IEEE 7th international conference on system of systems engineering (SOSE 2012). Genova; 16–19 luglio 2012. [9] Chen C, Duan S, Cai T, Liu B, Hu G. Optimal allocation and economic analysis of energy storage system in microgrids. IEEE Trans Power Electron 2011;26:2762–73.

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