Format And Type Fonts CCHHEEMMIICCAALL EENNGGIINNEEEERRIINNGG TTRRAANNSSAACCTTIIOONNSS VOL. 39, 2014 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong Copyright © 2014, AIDIC Servizi S.r.l., ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439010 Please cite this article as: Giaouris D., Papadopoulos A.I. , Seferlis P. , Papadopoulou S., Voutetakis S., Stergiopoulos F., Elmasides C., 2014, Optimum energy management in smart grids based on power pinch analysis, Chemical Engineering Transactions, 39, 55-60 DOI:10.3303/CET1439010 55 Optimum Energy Management in Smart Grids Based on Power Pinch Analysis Damian Giaouris a , Athanasios I. Papadopoulos a , Panos Seferlis b ,Simira Papadopoulou c , Spyros Voutetakis a , Fotis Stergiopoulos c , Costas Elmasides d a Chemical Process and Energy Resources Institute, Centre for Research and Technology-Hellas, 57001 Thermi, Greece b Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece c Department of Automation Engineering, Alexander Technological Educational Institute of Thessaloniki, 57400 Thessaloniki, Greece d Sunlight S.A., Xanthi, Greece spapadopoulos@cperi.certh.gr This work proposes a systemic approach to identify optimum power management strategies (PMS) in renewable energy smart-grids by using the Power Grand Composite Curves (PGCC) approach to adaptively adjust the system operation in short-term power requirements. This is approached by a) using the PGCC to target the optimum power requirements for the subsequent time interval and b) then adjusting the system PMS in the current time-interval to meet the identified target by the end of this interval. First the system PGCC is developed for the subsequent time interval, indicating the external non- renewable input required to satisfy the expected power demands. An appropriate shift in the PGCC sets a target of the minimum power inventory needed by the end of the current interval to completely avoid the use of non-renewable power input in the subsequent interval. The development of this power inventory is then approached in the current interval by identifying the PMS that best satisfies this target. The method is illustrated through a hybrid smart grid considering multiple renewable sources and storage options. 1. Introduction Smart grids based on renewable energy sources (RES) are receiving increased attention worldwide as they required to support isolated and non-grid connected applications. To address the intermittent nature of largely unpredictable environmental phenomena, such systems transform RES into dependable power flows by simultaneous utilisation of different types of conversion equipment and storage media (e.g., PV panels, wind generators, chemical accumulators, hydrogen and so forth). The resulting infrastructures combine multiple subsystems that need to operate efficiently while satisfying power demands ideally based on RES. This is generally approached through the development of power management strategies (PMS) that typically account for decisions regarding the appropriate instance to activate or deactivate different subsystems, the duration of operation of a particular subsystem, the amount or type of energy carrier to use and so forth (Giaouris et al., 2013). Conventional grids mainly utilize a pre-specified PMS repeated throughout the cyclic system operation, which is inefficient in view of the variability observed in RES. An approach involving the recurrent identification and implementation of a new PMS within short time intervals would be more efficient. This involves numerous potential decision combinations resulting from the need to frequently select an optimum system configuration from several available PMS. A systemic method is required which is able to identify optimum performance targets, subsequently interpreted as appropriately fitted operating realizations. The recently proposed Power Pinch Analysis (Wan Alwi et al., 2012a) is one such method, allowing the investigation of complex energy systems based on the identification of insights pointing towards optimum decisions. Focusing on hybrid power systems the method utilizes Composite Curves (Wan Alwi et al., 2012b) or Grand Composite Curves (Bandyopadhyay, 2011) similarly to the traditional Heat Pinch 56 (Klemeš, 2013). However the associated sink and source streams are plotted in power versus time diagrams. The graphical power pinch analysis method takes the form of numerical tools such as the Power Cascade Analysis (PoCA) and Storage Cascade Table - SCT (Rozali et al., 2013), while the numerical tools are extended to consider power losses (Wan Alwi et al., 2012). The method is applied in the optimisation of a pumped hydro-storage system (Rozali et al., 2013a), while it is also extended to address the optimal sizing of hybrid systems (Rozali et al., 2013b). Recent work (Ho et al., 2013) proposed the stand-alone hybrid system Power Pinch Analysis method (SAHPPA) which employs new ways of utilising the demand and supply Composite Curve methods. Power Pinch methods have also taken the form of a MILP-based transhipment model for targeting the outsourced electricity requirements (Chen et al., 2013) and allocating renewable electricity and storage components to demands in hybrid power systems (Chen et al., 2014). 2. Proposed approach This work proposes a novel approach for the identification of optimum PMSs in RES-based smart grids by using the Power Grand Composite Curves (PGCC) method to adaptively adjust the system operation in short-term power requirements. The main aim is to identify the optimum PMS within recurrent subsequent time intervals in order to minimize external non-RES utilization. The proposed approach builds on a generic smart grid model supporting the development of numerous different PMSs based on an inclusive representation of structural and temporal interactions. 2.1 Generic smart grid operating model The key features of hybrid power generation smart grids involve conversion and accumulation of both material (Mt) and energy (Ng) flows at different time instants. In this context, regardless of equipment characteristics any smart grid may be described through interconnected converters (Cn) and accumulators (Ac) of an overall set E={E Ac , E Cn }, processing flows at different states S of an overall set S={S Ng , S Mt }, (Giaouris et al., 2013). The flows may be calculated as follows:    , , ,,, , ,, , In j j Out j Out j t g nt n t n t g nt l n t l n l g F SF F F          (1) where , , , Ac Cn l E g E n E j S    , , , Out j t l n F  is the output flow of accumulator l directed to device n, in state j, , j t nSF is a possible external signal or flow (e.g., solar radiation) and ,t l n  is a binary variable that becomes 1 when accumulator l feeds device n in state j. The same holds for converters. The accumulators are characterised by the amount of stored energy or material which can be defined as follows: , , , , ( ) / in j out jl l t ln l t l n t t SOAcc SOAcc F F C       (2) where l tSOAcc is the amount of stored energy or material in accumulator l at time instant t, the symbol t - is used to account for the previous observation instant and lC is the total capacity of accumulator l. The investigated accumulators may store only one state hence symbol j is omitted for simplicity. To apply the above balance equations it is necessary to define variables ε of Eq. (1) as they enable the activation/deactivation of connections between devices m and n based on temporally evolving constraints. Variable ,t m n  can be defined in the form of a generic set of logical proposition as follows:  , , ,,, ,ReqAvl Gent m n t m n t m nt m nL      (3)  , , ,, , , , l l l i i SOAcc SOAcc SOAcc Ac t m n m n m n t m n t m nL L r i Avl Req n E m E                   (4) In Eqs. (3)-(4) L is a logical operator and indices Avl and Req correspond to availability or requirement for material or energy as a condition for activation/deactivation of a device. Index Gen represents a free use of variable ε Gen to incorporate any additional desired condition. Binary variables ρ and r are parameters 57 associated with temporal conditions imposed on the power or materials stored in the accumulator l (SOAcc l ). Each converter m is activated/deactivated based on a SOAcc l value of each accumulator that controls it as follows: , , , , , 1 l l l l SOAcc l SOAcc SOAcc l SOAcc t m n t t m n t m n t t m n t m n SOAcc Lo Lo SOAcc Up                                (5) In Eq. (5) terms Lo and Up refer to lower and upper limits in SOAcc. The first inequality represents the simple ON-OFF behaviour, while the subsequent expression represents the hysteresis behaviour (Giaouris et al., 2013). Hysteresis refers to activation/deactivation of converters based on their state in the previous instant (t - ). The recurring implementation of Eqs. (3)-(5) for a desired interval results in a PMS. Different PMSs result from different combinations of logical operators or values imposed on the upper and lower limits. Parameter r of Eq. (4) is used with ρ to impose or ignore a condition if necessary. 2.2 Adaptive management method Let a hybrid renewable energy and storage grid system operating within an overall horizon time H divided into k equal time intervals and each interval is further divided into subintervals [t0, T]. For example H can be a year that is divided into 365 days, i.e. k[1, 365] and each day divided into intervals of 1h, i.e. t0=1 and T=24. Also let a , , , ( , ) l q k k t qk t PMS f SOAcc from a set of Q overall PMSs realized within an interval k (now added in all previous parameters) as any potential operating combination resulting from Eq(3)-(5). The proposed approach consists of the following main steps: 1. The PGCC of the system is developed at the subsequent time interval k+1 indicating the external non- RES input required to satisfy the power demand. An appropriate shift in the PGCC sets a target of the minimum power inventory needed by the end of the current interval k to completely avoid the use of non-RES power input in the subsequent interval. 2. The optimum PMS is selected in the current time interval k to meet the previously identified target by the end of this interval. For the implementation of step 1 it is necessary to consider all possible PMSs at interval k+1 for the expected weather conditions and power demands. As shown in Figure 1a different PMSs result in different PGCCs and different outsourced electricity supply (OES) requirements for the system. For example, 0, 1kPMS  results in 0 21, 1, l l k OES k OES SOAcc SOAcc    required with the use of 2, 1kPMS  . Note that the OES for different PMSs may also be identified at different instants. Since the goal in step 1 is to develop a sufficient inventory in interval k so that the system may operate autonomously in interval k+1 (i.e. without the use of non-renewable resources) it is necessary to ensure that this goal is satisfied regardless of the PMS employed in interval k+1. This may only be achieved by testing , 1q kPMS  for every q Q and selecting the maximum 1, qk OES SOAcc  . The latter will represent the minimum outsourced electricity supply (MOES) for the system, which will instead be provided as an energy inventory developed in interval k. This may be described by the following equations: 1, 1, max q l l k Shift k OES q Q SOAcc SOAcc     (6) , 0 max, 1 1,, ,targ k k l l l k ShiftT PMS t PMS SOAcc SOAcc SOAcc     (7) Eq. (7) indicates the shift that needs to be implemented in the selected PGCC which is represented by max, 1kPMS  (Figure 1b). It also shows the amount of energy that needs to become available at t=T in interval k. The subscript “max” used in Eq. (7) refers to the q th PMS satisfying Eq(6). Notice that for implementation of Eq. (7), the PMS resulting in the selected 1, l k Shift SOAcc  may not allow the activation of converters which consume energy below the Pinch. In this context, the activation of the appropriate converter may be imposed through Eqs. (3)-(5). The subscript “targ” used in Eq. (7) refers to the PMS best matching the ,, targ k l T PMS SOAcc target and remains to be identified at interval k in step 2. Also notice that the PMS required in order to match the shifted PGCC in this interval will be identified in a subsequent 58 iteration using weather and demand data from interval k+2 (i.e. interval k+2 will become the new interval k+1 and so forth). In order to implement step 2 it is necessary to consider all PMSs at interval k and find PMSopt,k so that: , ,, , min( ) targ k q kT PMS T PMS q Q SOAcc SOAcc   (8) The procedure is illustrated in Figure 2 where the PGCC is shifted first in interval k+1 and then from implementation of Eqs. (6)-(7) it is found that PMSopt,k= PMS0,k. The correct way to read Figure 2 is from right to left. In the next iteration, the current interval k+1 becomes the new k and the procedure is repeated. Eqs. (6) -(7) may take the following form to account for different potential limits and operating goals: 1, 1, max h q l l k Shift k OES q Q h SOAcc SOAcc             (9) , 0 max, 1, , 1, 1 1 ( ) 1 lm lm targ k k h N N l l l h hT PMS t PMS k Shift h h SOAcc SOAcc c SOAcc c         with (10) Nlm is the total number of limits imposed on SOAcc depending on the considered converters (each limit determines when to activate/deactivate a converter). Note that during implementation of Eqs. (6)-(7) converters consuming power should be allowed to operate only above the Pinch. This may be imposed though Eqs. (3)-(5). Upper limits may be treated in the same way as lower limits. In such a case there would be a shift-down (instead of the shift-up of Figure 1b) to Pinch an upper limit, below a max SOAcc level. The coefficient ch determines the sign depending on energy is supply (i.e. Lower Level Pinch) or utilization (i.e. Upper Level Pinch). If ch=1 the use of external sources is avoided through Eq. (8). If ch=-1, Eq. (10) shows the energy that should be utilized before violation of an upper limit, indicating the undesired de-activation of a converter. If both limits are applicable the choice of ch allows the prioritization of the actions. Eqs. (9)-(10) hold for Nlm = 2. In case of Nlm > 2 Eq. (11) is repeated depending on the shape of the PGCC. Time (interval k+1) t0 T Le v e l in A cc u m u la to r (S O A cc ) min PMS0,k+1 Lo PMS2,k+1 tmin OES0 0 1 PMS1,k+1 OES2 (a) Time (interval k+1) t0 T Le v e l in A cc u m u la to r (S O A cc ) min PMSmax,k+1 Lo tmin Shift 0 1 Pinch (b) PGCC Figure 1: a) PGCCs for different PMSs, b) Pinch Point generated by shifted PGCC Time (interval k) t0 T Le ve l i n A cc u m u la to r (S O A cc ) min PMS0,k Lo PMSq,k 0 1 PMS1,k Time (interval k+1)t0 T Shifted PGCC PMStarg,k Figure 2: Matching of PGCCs from different PMSs between intervals k and k+1 59 3. Implementation The considered hybrid smart grid consists of PV panels (PV) and wind generators (WG). Surplus energy is supplied to an electrolyzer (EL) after the specified load demand (LD) is satisfied. The produced H2 is stored in pressurized cylinders (BT) and in cases of energy deficit, is utilized in a fuel cell (FC) to power the system. Lead-acid batteries (BAT) are used to regulate the power flows through frequent charging and discharging cycles induced by the RES variability. In case of energy excess, units such as the H2 compressor (CP) utilize this energy to store H2 in long-term storage tanks (FT). A diesel generator (DSL) is also utilized in cases of emergency (i.e. power demands of the application cannot be covered by RES or stored H2). To illustrate the proposed method (considering space restrictions), it is applied for 2 PMS previously detailed in Giaouris et al. (2013). Both PMS activate the associated sub-systems as follows: 1. FC is activated ( , Avl t FC BAT  =1) if , BAT BAT SOAcc t t FC BAT SOAcc Lo   and hysteresis is imposed until , BAT SOAcc t FC BAT Up  . 2. EL is activated ( Re , q t BAT EL   =1) if , BAT BAT SOAcc t t BAT EL SOAcc Up   and hysteresis is imposed until , BAT SOAcc t BAT EL Lo  . 3. DSL is activated if , BAT BAT SOAcc t t DSL BAT SOAcc Lo   and hysteresis is imposed until , BAT SOAcc t DSL BAT Up  . 4. PV is activated if , BAT BAT SOAcc t t PV BAT SOAcc Lo   without a hysteresis zone. 5. WG is activated if , BAT BAT SOAcc t t WG BAT SOAcc Lo   without a hysteresis zone. While the above points are common between the two PMS, additional conditions differentiating the two PMSs are that , 1 Gen t FC BAT   if , , , 0 Out Pow Out Pow Out Pow PV BAT WG BAT BAT LD F F F          and . 1 Gen t EL BF   if , , , 0 Out Pow Out Pow Out Pow PV BAT WG BAT BAT BATF F F       for PMS2, while for PMS1 the two conditions don’t apply 4. Results and discussion The method is applied to find the PMS that avoids the activation of the DSL during two days considering local, hourly averaged weather data. The goal is to ensure that the SOAcc BAT remains above 0.2 (Lo limit) to satisfy a constant load of 2 kW. Initially the hysteresis zone of the FC is from 0.3 to 0.35 while for the DSL from 0.2 to 0.205. The initial SOAcc was set at 0.3 for the BAT and 0.7 for the FT, BF and WT. The remaining parameters (e.g., size of BAT, FT and so forth) are described in Giaouris et al. (2013). To find the optimum PMS in Day 1 we investigate the power generation profile of Day 2 considering the 2 PMSs. Eq. (6) indicates that the PMS resulting in the largest shift (i.e. in the minimum SOAcc BAT at t=tmin as shown in Figure 1) should be selected. However, each PMS may start from any possible SOAcc BAT at t=0, whereas different values of SOAcc BAT at t=0 may also result in identical values of SOAcc BAT at t=tmin. It is necessary to identify those SOAcc BAT values (at t=0) prior to implementing Eq(6). Using a step size of 0.001 we calculate the estimated PGCC for all values of SOAcc BAT from 0.2 to 0.8 for both PMS (in Day 2). This generates 1,200 PGCC graphs which indicate 3 initial values (i.e. SOAcc BAT at t=0) for PMS1 and 2 for PMS2. These are shown in Table 1 and illustrated in Figure 3b with different lines for PMS1. The highest value is selected as SOAcc BAT at t=0 for each PMS, ensuring that the resulting curve will not violate the Lo limit. The shift in the PGCC of PMS1 and PMS2 to Pinch at the Lo limit is 0.016 and 0.007 (Table1). Based on Eq. (6) the selected PGCC (i.e. PMSmax,k+1) corresponds to PMS1 and the SOAcc BAT (at t=tmin) is shifted by 0.016 in order to Pinch the limit of 0.2. Based on Eq. (7) the targeted SOAcc BAT for Day 1 should be at 0.241. Hence if for PMS1 the initial SOAcc BAT is 0.241 and the operating regions of DSL and FC are also shifted by 0.016 we can be sure that regardless of PMS the SOAcc BAT will not drop below 0.2. Therefore the chosen PMS for Day 1 is the one that will generate a final value of the SOAcc BAT as close to 0.241 as possible, based on Eq. (8). The latter is the level of charge that should be stored in the battery in Day 1 in order to avoid using the DSL in Day 2. Again it is possible to calculate the PGCC for Day 1 and Table 1: SOAcc BAT values considered in the case study SOAcc BAT PMS1 PMS2 Minimum limit (min) 0.184 0.193 Lower limit (Lo) 0.2 0.2 Shift 0.2-0.184=0.016 0.2-0.193=0.007 Initial 0.201, 0.209, 0.225 0.208, 0.232 Targeted (targ) 0.225+0.2-0.184=0.241 0.232+0.2-0.193=0.239 60 a) 5 10 15 20 0.15 0.2 0.25 0.3 0.35 0.4 Time, h (Day 1) S O A c c B A T PMS 1 PMS 2 Target 0.241 b) 5 10 15 20 25 0.2 0.25 0.3 0.35 0.4 Time, h (Day 2) S O A c c B A T 0.184 Figure 3: a) PGCC curves for Day 1 for PMS1 and PMS2, b) Initial and shifted PGCC for PMS1 in Day 2 starting from the given initial conditions (0.3 for BAT and 0.7 for the other accumulators) we see that PMS1 will produce the best result and a final SOAcc BAT at 0.2790 while the FT will be at 0.561. Repeating for Day 2, we focus on Day 3 and PMS1 produces a SOAcc BAT (at t=tmin) of 0.194 for initial SOAcc BAT at 0.229 imposing a shift at 0.235. The chosen PMS for Day 2 is again PMS1, producing a final SOAcc BAT at 0.28. 5. Conclusions The use of the PGCC method was presented as formal and generic mathematical formulations supporting the graphical tools and facilitating the recursive implementation of the method for long time horizons. Although the presented case study considered daily time intervals, the proposed method may be implemented for shorter time intervals. This is very important because the potential combination of the method with short-term weather forecasts could enable a very efficient adaptation of the system in view of variable weather conditions. As this is on-going work, more extensive case studies are developed addressing multiple PMS. 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