# An Optimal Power and Energy Management by Hybrid Energy Storage Systems in Microgrids

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modelling

#### 2.1. Microgrid

_{i}and l

_{j}, which denote the power delivered by the i-th generator (positive value) and drawn by the j-th load (negative value) respectively. While a positive s value means that the HESS is discharging, otherwise an HESS charging process occurs.

#### 2.2. Hybrid Energy Storage System

_{B}and s

_{S}denote the power exchanged by B and S respectively, with e

_{B}and e

_{S}denoting their corresponding energy levels. These vary in accordance with s

_{B}and s

_{S}as

_{c}and η

_{d}denote the charging and discharging efficiencies. Hence, the power and energy of both B and S are bounded in accordance with the following constraints:

## 3. Optimal Power and Energy Management

^{2}should be minimized. For this purpose, the evolution of s

_{B}over T must be synthesized optimally based on the evolution of the residual power forecasted over the same time window ($\tilde{r}$). In this regard, it is worth noting that only B is considered for Θ

^{2}minimization because energy services generally require high energy density ESS, especially when large T is concerned. In addition, Equation (8) aims at reducing the magnitude of $\tilde{g}$ to the maximum extent, especially when it occurs at high rates. Consequently, it represents a suitable trade-off between peak shaving and reduced grid energy buffering, i.e., the overall energy exchanged between MG and the main grid. In addition, the minimization of Equation (8) leads to an analytical optimal solution, thus enabling fast and effective real-time implementation, especially in comparison with more sophisticated and complex objective functions.

_{r}. Based on $\tilde{r}$, the proposed OPEM synthesizes s

_{B}

^{*}, also in accordance with S charging/discharging needs (Δ

_{S}). Particularly, Δ

_{S}is the average power required by S over t

_{Δ}in order to cope with its unsuitable charging status. Consequently, s

_{B}

^{*}is updated every t

_{B}, which is the minimum value between t

_{r}and t

_{Δ}. Then, s

_{S}

^{*}is determined every t

_{S}based on the errors between $\tilde{r}$ and r. As a result, energy optimization is achieved by B through Θ

^{2}minimization, while power management is accomplished by S, which compensates for unpredictable power mismatches.

_{B}

^{*}and s

_{S}

^{*}have to be computed at certain time refresh rates, namely every t

_{B}and t

_{S}respectively. Consequently, Θ

^{2}is minimized over a sliding time window because s

_{B}

^{*}is updated every t

_{B}, benefiting from more accurate forecasting and the knowledge of the actual B energy level (e

_{B}). The s

_{S}

^{*}is updated every t

_{S}, which should be much smaller than t

_{B}in order to enable the compensation for fast power variations and short-term forecasting errors.

#### 3.1. Energy Optimization

^{2}over T can be achieved by applying the Pontryagin’s minimum principle (PMP), which allows the achievement of s

_{B}

^{*}by satisfying both Equation (6) and Equation (7) simultaneously. Particularly, the PMP was chosen for designing the proposed OPEM in order to achieve an analytical solution, thus easing OPEM implementation. In addition, PMP reveals very important information on the genesis of the optimal solution, giving the possibility of choosing sub-optimal solutions that better fit with HESS features and/or MG goals. Therefore, the Hamiltonian function is introduced at first as

_{B}evolution that does not comply with Equation (7). Hence, the fulfillment of the B energy constraint must be guaranteed by an appropriate choice of Λ.

_{B,k}

^{*}can be either positive or negative in accordance with the following constraints:

^{(+)}and $R$

^{(−)}shown in Figure 3. This reveals that different situations occur depending on the sign of Λ

_{k}, as also pointed out in Table 1. When Λ

_{k}is negative, there is no optimal solution outside $R$

^{(+)}and $R$

^{(−)}because neither Equation (18) nor Equation (19) can be satisfied, as shown in Figure 3a. Consequently, s

_{B,k}

^{*}equals zero until $\tilde{r}$ lies outside the two plane regions. Different considerations have to be made when Λ

_{k}is positive, as detectable in Figure 3b. In this case, $R$

^{(−)}and $R$

^{(+)}are partially overlapped and, thus, both positive and negative s

_{B,k}

^{*}may exist simultaneously. Therefore, in order to select the optimal solution, $\tilde{r}$ can be expressed as

_{B,k}

^{*}values prevail against negative ones in the bottom half of the overlapping region because the former determines lower $H$ values. The opposite occurs in the top half of the region, i.e., when ξ is lower than 0.5.

_{B}

^{*}is determined over any operating condition, the corresponding optimal grid profile ($\tilde{g}$

^{*}

_{opt}) can be achieved by means of Equation (9), as depicted in Figure 3. Particularly, when Λ

_{k}is negative, B provides suitable energy buffering within $R$

^{(−)}and $R$

^{(+)}, as highlighted in Figure 3a. Whereas this does not occur outside them, because this would increase Θ

^{2}unsuitably. This phenomenon depends on B charging and discharging efficiencies, i.e., more energy is drawn by B than B delivers back. This is proved by the fact that if both η

_{c,B}and η

_{d,B}were equal to one, β

_{B}would be zero in accordance with Equation (12). Consequently, $R$

^{(−)}and $R$

^{(+)}would span the negative semi-plane, meaning that no “dead-zone” would occur further. However, it is worth noting that this phenomenon preserves B from excessive cycling, thus it can be accepted although it slightly affects peak shaving capability.

^{*}

_{opt}is achieved when Λ

_{k}is positive, as highlighted in Figure 3b. Particularly, $\tilde{g}$

^{*}

_{opt}overcomes $\tilde{r}$ when the latter lies below the average threshold of the overlapping region. Consequently, a local increase of Θ

^{2}occurs, but it is more than compensated by the following Θ

^{2}reduction. However, although Θ

^{2}minimization benefits from such an optimal solution, this does not contribute to peak shaving and reduced grid energy buffering purposes, also leading to B overexploitation. Therefore, the following sub-optimal solution is suggested:

^{*}), as shown in Figure 3b. This slightly impairs Θ

^{2}minimization over T, but peak shaving, reduced grid energy buffering and B cycling are preserved successfully.

#### 3.2. Power Management

^{2}leads to the following result:

_{B}equal to s

_{B}

^{*}, the following result is achieved:

_{r}and δ

_{g}denote the power mismatches occurring on r and g respectively:

_{r}until it does not imply violating Equation (6) and Equation (7), leading to:

_{S,min}or e

_{S,max}, no power compensation can be provided further. Therefore, $\tilde{r}$ can be updated every t

_{Δ}by accounting not only for more accurate forecasting but also for S charging/discharging needs. The latter can be denoted by Δ

_{S}, i.e., the average power that S has to deliver or draw from B over a given time horizon (t

_{Δ}) in order to restore a suitable energy threshold (e

_{S}

^{*}):

_{S}can be assumed to be incorporated into $\tilde{r}$ in order to preserve the validity of Equation (9) and, thus, of all the subsequent equations.

_{S}, thus ensuring its continuous operation.

## 4. Simulation Setup

^{2}, 5181 inhabitants), characterized by both conventional and renewable energy source (RES) power plants, i.e., Combined Heat and Power (CHP), wind and photovoltaic. The overall installed power is about 6.8 MW on both medium and low voltage distribution systems, as pointed out in Table 2. In addition, the PCC consists of four submarine cables that enable a bidirectional power flow with the mainland. The simulations refer to the residual power profile at the PCC, which was achieved based on historical database (@2014). Regarding the HESS, it consists of an active configuration that allows B and S to be managed independently, their main specifications being summarized in Table 3.

_{LF}) is determined by an appropriate digital low-pass filter, whose transfer function deprived from magnitude ripple is shown in Figure 5a. The B power profile is thus determined in accordance with its power and energy constraints, as pointed out in Table 4. In this regard, $\tilde{r}$

_{avg}denotes the averaged power foreseen within the given time horizon T, which is determined by taking into account B charging and discharging efficiencies as

_{avg}represents the average power exchanged between the MG and the main grid if full peak shaving is accomplished, as highlighted in Figure 5b. This power threshold is updated every t

_{r}in order to make the comparison between OPEM and FBM consistent. While the S power profile is computed in accordance with the high-frequency content of the residual power profile (r − r

_{LF}), as still pointed out in Table 4.

_{S}was set as low as possible in accordance with the time resolution of the actual residual power profile, in order to provide an appropriate compensation for both power fluctuations and forecasting errors. Whereas a much greater value of t

_{Δ}was chosen based on the assumption that power fluctuations and short-term forecasting errors are both characterized by poor energy content. However, it is worth noting that t

_{Δ}can be reduced as desired if S is often fully charged and/or discharged. Regarding t

_{B}, it has been set equal to t

_{S}for the FBM, which manages both B and S based on actual residual power profile. In this regard, it is worth noting that FBM prevents B from handling sudden power fluctuations by means of a suitable low-pass filter. Such a filtering action is also provided by OPEM, but by choosing a much greater t

_{B}value, which should be the minimum between t

_{Δ}and t

_{r}, as pointed out in Figure 2.

## 5. Results

#### 5.1. OPEM Testing

_{B}and e

_{B}) and those forecasted at the start of each day ($\tilde{g}$, $\tilde{s}$

_{B}and $\tilde{e}$

_{B}), especially at the end of the time horizon. Particularly, focusing on the first two days, B is foreseen to be fully discharged at the end of each day in order to minimize the objective function within the given time horizon (24 h). As time passes, such discharging actions are postponed appropriately to the first hours of the following days in order to cope with more significant peak load demands, as well shown in Figure 6. This reveals the effectiveness of the proposed OPEM, which adapts the B profile appropriately in accordance with more accurate forecasting and over a sliding time horizon. In addition, the e

_{B}value at the end of each day is adapted every t

_{B}in order to match MG optimization needs of the following day. This does not generally occur in most of the management strategies proposed in the literature, which can only assure piecewise optimization.

_{Δ}, thus preventing S from reaching its maximum and minimum energy boundaries. However, such a t

_{Δ}reduction would reduce t

_{B}and increase both the magnitude and frequency of Δ

_{S}, which may lead to an unsuitable B overexploitation.

_{opt}). It is worthy of note that OPEM

_{opt}leads to almost the same Θ

^{2}values achieved by the proposed OPEM, with only differences of the order of 10

^{−4}occurring.

_{opt}reduce the energy exchange over each day and their corresponding results are quite similar to each other. However, the generation decreases more than the load, and consequently the net energy exchange between the MG and the main grid increases compared to the case of no HESS. This was expected due to the additional losses of the HESS charging/discharging processes. However, this drawback is counterbalanced by a more significant reduction in terms of gross energy exchange, revealing reduced energy buffering provided by the main grid.

_{opt}highlights the increased B cycling and reduced S exploitation achieved by the latter. This reveals that the sub-optimal solution defined by Equation (22) is very suitable for preventing B overexploitation and peak shaving issues because the increase of Θ

^{2}is rather negligible, as already pointed out in Table 6. It is also worthy of note that the proposed OPEM accounts inherently for different B and S cycling capabilities by differentiating the services they have to provide, thus achieving optimal HESS exploitation.

#### 5.2. OPEM vs. FBM

_{avg}significantly, better performances are achieved with relatively short time horizons, as pointed out in Table 9. However, it is worth noting that FBM energy management is always worse than that achieved by the proposed OPEM, regardless of the time horizon, thus revealing the effectiveness of the latter, whereas very good performances are achieved by S in compensating for the high-frequency power fluctuations occurring on r, as indicated in Figure 21. Furthermore, Figure 23 reveals that as S never reaches its maximum or minimum energy thresholds, it is thus able to provide this power service continuously over the given time horizon. In this regard, it is worthy of note that the weaker S performances achieved by OPEM is due mainly to the additional service it provides, that is, S compensates not only for sudden power fluctuations but also for short term forecasting errors.

_{net}and e

_{gross}compared to the case of no HESS; although the reduction of a positive e

_{net}value implies additional losses, a more significant reduction of e

_{gross}is achieved, especially by OPEM, thus corroborating the effectiveness of the proposed management approach.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Strasser, T.; Andrén, F.; Kathan, J.; Cecati, C.; Buccella, C.; Siano, P.; Leitão, P.; Zhabelova, G.; Vyatkin, V.; Vrba, P.; et al. A Review of Architectures and Concepts for Intelligence in Future Electric Energy Systems. IEEE Trans. Ind. Electron.
**2015**, 62, 2424–2438. [Google Scholar] [CrossRef] - Li, R.; Zhou, F. Microgrid Technology and Engineering Application; Elsevier: Amsterdam, The Netherlands, 2015; ISBN 978-0-12-803630-3. [Google Scholar]
- Olivares, D.E.; Mehrizi-Sani, A.; Etemadi, A.H.; Canizares, C.A.; Iravani, R.; Kazerani, M.; Hajimiragha, A.H.; Gomis-Bellmunt, O.; Saeedifard, M.; Palma-Behnke, R.; et al. Trends in Microgrid Control. IEEE Trans. Smart Grid
**2014**, 5, 1905–1919. [Google Scholar] [CrossRef] - Nejabatkhah, F.; Li, Y.W. Overview of Power Management Strategies of Hybrid AC/DC Microgrid. IEEE Trans. Power Electron.
**2015**, 30, 7072–7089. [Google Scholar] [CrossRef] - Tan, X.; Li, Q.; Wang, H. Advances and trends of energy storage technology in Microgrid. Int. J. Electr. Power Energy Syst.
**2013**, 44, 179–191. [Google Scholar] [CrossRef] - Levron, Y.; Guerrero, J.M.; Beck, Y. Optimal Power Flow in Microgrids with Energy Storage. IEEE Trans. Power Syst.
**2013**, 28, 3226–3234. [Google Scholar] [CrossRef] - European Technology Platform. SmartGrids. Smartgrids Strategic Deployment Document for Europe’s Electricity Networks of the Future. Available online: ftp://ftp.cordis.europa.eu/pub/technology-platforms/docs/smartgrids-sdd-draft-25-sept-2008_en.pdf (accessed on 20 November 2017).
- European Commission. More Microgrids DH1. Microgrid Evolution Roadmap in EU 2009; European Commission: Brussels, Belgium, 2009. [Google Scholar]
- Damiano, A.; Gatto, G.; Marongiu, I.; Porru, M.; Serpi, A. Real-Time Control Strategy of Energy Storage Systems for Renewable Energy Sources Exploitation. IEEE Trans. Sustain. Energy
**2014**, 5, 567–576. [Google Scholar] [CrossRef] - Alnaser, S.W.; Ochoa, L.F. Optimal Sizing and Control of Energy Storage in Wind Power-Rich Distribution Networks. IEEE Trans. Power Syst.
**2016**, 31, 2004–2013. [Google Scholar] [CrossRef] - Ammar, M.; Joós, G. A Short-Term Energy Storage System for Voltage Quality Improvement in Distributed Wind Power. IEEE Trans. Energy Convers.
**2014**, 29, 997–1007. [Google Scholar] [CrossRef] - Mufti, M.D.; Iqbal, S.J.; Lone, S.A.; Ain, Q.U. Supervisory Adaptive Predictive Control Scheme for Supercapacitor Energy Storage System. IEEE Syst. J.
**2015**, 9, 1020–1030. [Google Scholar] [CrossRef] - European Association for Storage of Energy (EASE); European Energy Research Alliance (EERA). European Energy Storage Technology Development Roadmap towards 2030; EASE: Brussels, Belgium, 2013. [Google Scholar]
- International Energy Agency (IEA). Technology Roadmaps—Energy Storage; IEA: Paris, France, 2014. [Google Scholar]
- Hemmati, R.; Saboori, H. Emergence of hybrid energy storage systems in renewable energy and transport applications—A review. Renew. Sustain. Energy Rev.
**2016**, 65, 11–23. [Google Scholar] [CrossRef] - Cau, G.; Cocco, D.; Petrollese, M.; Knudsen Kær, S.; Milan, C. Energy management strategy based on short-term generation scheduling for a renewable microgrid using a hydrogen storage system. Energy Convers. Manag.
**2014**, 87, 820–831. [Google Scholar] [CrossRef] - Torreglosa, J.P.; García-Triviño, P.; Fernández-Ramirez, L.M.; Jurado, F. Control based on techno-economic optimization of renewable hybrid energy system for stand-alone applications. Expert Syst. Appl.
**2016**, 51, 59–75. [Google Scholar] [CrossRef] - Wang, S.; Tang, Y.; Shi, J.; Gong, K.; Liu, Y.; Ren, L.; Li, J. Design and advanced control strategies of a hybrid energy storage system for the grid integration of wind power generations. IET Renew. Power Gener.
**2015**, 9, 89–98. [Google Scholar] [CrossRef] - Shim, J.W.; Cho, Y.; Kim, S.J.; Min, S.W.; Hur, K. Synergistic Control of SMES and Battery Energy Storage for Enabling Dispatchability of Renewable Energy Sources. IEEE Trans. Appl. Supercond.
**2013**, 23, 5701205. [Google Scholar] [CrossRef] - Zhao, P.; Dai, Y.; Wang, J. Design and thermodynamic analysis of a hybrid energy storage system based on A-CAES (adiabatic compressed air energy storage) and FESS (flywheel energy storage system) for wind power application. Energy
**2014**, 70, 674–684. [Google Scholar] [CrossRef] - Dougal, R.A.; Liu, S.; White, R.E. Power and life extension of battery-ultracapacitor hybrids. IEEE Trans. Compon. Packag. Technol.
**2002**, 25, 120–131. [Google Scholar] [CrossRef] - Gao, L.; Dougal, R.A.; Liu, S. Power enhancement of an actively controlled battery/ultracapacitor hybrid. IEEE Trans. Power Electron.
**2005**, 20, 236–243. [Google Scholar] [CrossRef] - Chotia, I.; Chowdhury, S. Battery storage and hybrid battery supercapacitor storage systems: A comparative critical review. In Proceedings of the 2015 IEEE Innovative Smart Grid Technologies—Asia (ISGT ASIA 2015), Bangkok, Thailand, 3–6 November 2015; pp. 1–6. [Google Scholar]
- Micolano, E.; Lazzari, R.; Pellegrino, L. Influence of management and system configuration on performances and lifetime of lithium-ion batteries. In Proceedings of the AEIT International Annual Conference (AEIT 2015), Naples, Italy, 14–16 October 2015; pp. 1–6. [Google Scholar]
- Chong, L.W.; Wong, Y.W.; Rajkumar, R.K.; Rajkumar, R.K.; Isa, D. Hybrid energy storage systems and control strategies for stand-alone renewable energy power systems. Renew. Sustain. Energy Rev.
**2016**, 66, 174–189. [Google Scholar] [CrossRef] - Liu, B.; Zhuo, F.; Zhu, Y.; Yi, H. System Operation and Energy Management of a Renewable Energy-Based DC Micro-Grid for High Penetration Depth Application. IEEE Trans. Smart Grid
**2015**, 6, 1147–1155. [Google Scholar] [CrossRef] - Mendis, N.; Muttaqi, K.M.; Perera, S. Management of Battery-Supercapacitor Hybrid Energy Storage and Synchronous Condenser for Isolated Operation of PMSG Based Variable-Speed Wind Turbine Generating Systems. IEEE Trans. Smart Grid
**2014**, 5, 944–953. [Google Scholar] [CrossRef] - Kollimalla, S.K.; Mishra, M.K.; Narasamma, N.L. Design and Analysis of Novel Control Strategy for Battery and Supercapacitor Storage System. IEEE Trans. Sustain. Energy
**2014**, 5, 1137–1144. [Google Scholar] [CrossRef] - Adhikari, S.; Lei, Z.; Peng, W.; Tang, Y. A battery/supercapacitor hybrid energy storage system for DC microgrids. In Proceedings of the 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia 2016), Hefei, China, 22–26 May 2016; pp. 1747–1753. [Google Scholar]
- Jia, H.; Mu, Y.; Qi, Y. A statistical model to determine the capacity of battery-supercapacitor hybrid energy storage system in autonomous microgrid. Int. J. Electr. Power Energy Syst.
**2014**, 54, 516–524. [Google Scholar] [CrossRef] - Wang, G.; Ciobotaru, M.; Agelidis, V.G. Power Smoothing of Large Solar PV Plant Using Hybrid Energy Storage. IEEE Trans. Sustain. Energy
**2014**, 5, 834–842. [Google Scholar] [CrossRef] - Kim, Y.; Raghunathan, V.; Raghunathan, A. Design and management of hybrid electrical energy storage systems for regulation services. In Proceedings of the 5th International Green Computing Conference (IGCC 2014), Dallas, TX, USA, 3–5 November 2014; pp. 1–9. [Google Scholar]
- Zeng, A.; Xu, Q.; Ding, M.; Yukita, K.; Ichiyanagi, K. A classification control strategy for energy storage system in microgrid. IEEJ Trans. Electr. Electron. Eng.
**2015**, 10, 396–403. [Google Scholar] [CrossRef] - Li, J.; Xiong, R.; Yang, Q.; Liang, F.; Zhang, M.; Yuan, W. Design/test of a hybrid energy storage system for primary frequency control using a dynamic droop method in an isolated microgrid power system. Appl. Energy
**2017**, 201, 257–269. [Google Scholar] [CrossRef] - Li, J.; Wang, X.; Zhang, Z.; Le Blond, S.; Yang, Q.; Zhang, M.; Yuan, W. Analysis of a new design of the hybrid energy storage system used in the residential m-CHP systems. Appl. Energy
**2017**, 187, 169–179. [Google Scholar] [CrossRef] - Li, J.; Yang, Q.; Robinson, F.; Liang, F.; Zhang, M.; Yuan, W. Design and test of a new droop control algorithm for a SMES/battery hybrid energy storage system. Energy
**2017**, 118, 1110–1122. [Google Scholar] [CrossRef] - Tummuru, N.R.; Mishra, M.K.; Srinivas, S. Dynamic Energy Management of Renewable Grid Integrated Hybrid Energy Storage System. IEEE Trans. Ind. Electron.
**2015**, 62, 7728–7737. [Google Scholar] [CrossRef] - Mohamed, A.; Salehi, V.; Mohammed, O. Real-Time Energy Management Algorithm for Mitigation of Pulse Loads in Hybrid Microgrids. IEEE Trans. Smart Grid
**2012**, 3, 1911–1922. [Google Scholar] [CrossRef] - Ye, Y.; Sharma, R.; Garg, P. An integrated power management strategy of hybrid energy storage for renewable application. In Proceedings of the 40th Annual Conference of the IEEE Industrial Electronics Society (IECON 2014), Dallas, TX, USA, 29 October–1 November 2014; pp. 3088–3093. [Google Scholar]
- Olatomiwa, L.; Mekhilef, S.; Ismail, M.S.; Moghavvemi, M. Energy management strategies in hybrid renewable energy systems: A review. Renew. Sustain. Energy Rev.
**2016**, 62, 821–835. [Google Scholar] [CrossRef] - Hredzak, B.; Agelidis, V.G.; Jang, M. A Model Predictive Control System for a Hybrid Battery-Ultracapacitor Power Source. IEEE Trans. Power Electron.
**2014**, 29, 1469–1479. [Google Scholar] [CrossRef] - Abdeltawab, H.H.; Mohamed, Y.A.-R.I. Market-Oriented Energy Management of a Hybrid Wind-Battery Energy Storage System via Model Predictive Control With Constraint Optimizer. IEEE Trans. Ind. Electron.
**2015**, 62, 6658–6670. [Google Scholar] [CrossRef] - Garcia-Torres, F.; Bordons, C. Optimal Economical Schedule of Hydrogen-Based Microgrids with Hybrid Storage Using Model Predictive Control. IEEE Trans. Ind. Electron.
**2015**, 62, 5195–5207. [Google Scholar] [CrossRef] - Malysz, P.; Sirouspour, S.; Emadi, A. An Optimal Energy Storage Control Strategy for Grid-connected Microgrids. IEEE Trans. Smart Grid
**2014**, 5, 1785–1796. [Google Scholar] [CrossRef] - Palma-Behnke, R.; Benavides, C.; Lanas, F.; Severino, B.; Reyes, L.; Llanos, J.; Sáez, D. A Microgrid Energy Management System Based on the Rolling Horizon Strategy. IEEE Trans. Smart Grid
**2013**, 4, 996–1006. [Google Scholar] [CrossRef] - Zhu, D.; Yue, S.; Chang, N.; Pedram, M. Toward a Profitable Grid-Connected Hybrid Electrical Energy Storage System for Residential Use. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.
**2016**, 35, 1151–1164. [Google Scholar] [CrossRef] - Jiang, W.; Zhang, L.; Zhao, H.; Huang, H.; Hu, R. Research on power sharing strategy of hybrid energy storage system in photovoltaic power station based on multi-objective optimisation. IET Renew. Power Gener.
**2016**, 10, 575–583. [Google Scholar] [CrossRef] - Chen, X.P.; Li, Z.T.; Xiong, W.; Wang, M.H.; Yuan, X.F. Dynamic programming to a CHP-HES system. In Proceedings of the 2014 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Guilin, China, 5–8 August 2014; pp. 178–183. [Google Scholar]
- Zhang, L.; Li, Y. Optimal Energy Management of Wind-Battery Hybrid Power System with Two-Scale Dynamic Programming. IEEE Trans. Sustain. Energy
**2013**, 4, 765–773. [Google Scholar] [CrossRef] - Rouholamini, M.; Mohammadian, M. Heuristic-based power management of a grid-connected hybrid energy system combined with hydrogen storage. Renew. Energy
**2016**, 96, 354–365. [Google Scholar] [CrossRef] - García-Triviño, P.; Llorens-Iborra, F.; García-Vázquez, C.A.; Gil-Mena, A.J.; Fernández-Ramírez, L.M.; Jurado, F. Long-term optimization based on PSO of a grid-connected renewable energy/battery/hydrogen hybrid system. Int. J. Hydrog. Energy
**2014**, 39, 10805–10816. [Google Scholar] [CrossRef] - Geering, H.P. Optimal Control with Engineering Applications; Springer Science & Business Media: Berlin, Germany, 2007; ISBN 978-3-540-69438-0. [Google Scholar]
- Cirocco, L.R.; Belusko, M.; Bruno, F.; Boland, J.; Pudney, P. Controlling stored energy in a concentrating solar thermal power plant to maximise revenue. IET Renew. Power Gener.
**2015**, 9, 379–388. [Google Scholar] [CrossRef] - Lifshitz, D.; Weiss, G. Optimal Control of a Capacitor-Type Energy Storage System. IEEE Trans. Autom. Control
**2015**, 60, 216–220. [Google Scholar] [CrossRef] - Musio, M.; Porru, M.; Serpi, A.; Marongiu, I.; Damiano, A. Optimal Electric Vehicle charging strategy for energy management in microgrids. In Proceedings of the 2nd IEEE International Electric Vehicle Conference (IEVC 2014), Florence, Italy, 17–19 December 2014; pp. 1–8. [Google Scholar]
- Musio, M.; Serpi, A.; Musio, C.; Damiano, A. Optimal management strategy of energy storage systems for RES-based microgrids. In Proceedings of the 41st Annual Conference of the IEEE Industrial Electronics Society (IECON 2015), Yokohama, Japan, 9–12 November 2015; pp. 5044–5049. [Google Scholar]

**Figure 3.**The two plane regions $R$

^{(+)}and $R$

^{(−)}for different $\tilde{r}$ and Λ

_{k}values, together with optimal ($\tilde{g}$

^{*}

_{opt}) and sub-optimal ($\tilde{g}$

^{*}) grid profiles achieved assuming that no B power limitation occurs: (

**a**) negative $\tilde{r}$ and Λ

_{k}; (

**b**) positive $\tilde{r}$ and Λ

_{k}.

**Figure 4.**Overall block control scheme of the FBM considered in this paper for comparison purposes, in which LPF denotes the low-pass filter.

**Figure 5.**FBM main details: (

**a**) transfer function of the LPF; (

**b**) averaged power achieved by full peak-shaving ($\tilde{g}$

_{avg}).

**Figure 6.**Residual and grid power profiles achieved by OPEM over three days: $\tilde{r}$ and $\tilde{g}$ (dark orange and orange, forecast at the start of each day), r (dark blue) and g (cyan).

**Figure 7.**The B power profiles achieved by OPEM over three days: $\tilde{s}$

_{B}(orange, forecast at the start of each day) and s

_{B}(red, actual evolution).

**Figure 8.**The B energy evolution achieved by OPEM over three days: $\tilde{e}$

_{B}(orange, forecast at the start of each day) and e

_{B}(green, actual evolution).

**Figure 9.**Power fluctuations and forecasting errors on residual power (δ

_{r}, light purple) and grid power (δ

_{g}, blue) achieved by employing the proposed OPEM over three days, together with the S power demand (Δ

_{S}, magenta).

**Figure 12.**Residual and grid power profiles achieved by OPEM over a generic week by employing different time horizons.

**Figure 13.**The B power profiles achieved by OPEM over a generic week by employing different time horizons.

**Figure 14.**The B energy evolutions achieved by OPEM over a generic week by employing different time horizons.

**Figure 15.**Power fluctuations and forecasting errors on residual power (δ

_{r}light purple) and grid power (δ

_{g}, blue) by employing the proposed OPEM over a generic week at T = 24 h, together with the S power demand (Δ

_{S}, magenta).

**Figure 18.**Residual and grid power profiles achieved by FBM over a generic week by employing different time horizons.

**Figure 19.**The B power profiles achieved by FBM over a generic week by employing different time horizons.

**Figure 20.**The B energy evolutions achieved by FBM over a generic week by employing different time horizons.

**Figure 21.**Power fluctuations and forecasting errors on residual power (δ

_{r}, light purple) and grid power (δ

_{g}, blue) by employing the proposed FBM over a generic week at T = 24 h, together with the S power demand (Δ

_{S}, magenta).

**Figure 24.**Pareto diagram of r (gray) and g achieved by OPEM (blue) and FBM (red) at T = 12 h when the MG acts as a generator (values on the

**left**) and as a load (sign-changed values on the

**right**).

Λ_{k} | $\tilde{\mathit{r}}$ | s_{B}^{*} |
---|---|---|

<0 | $>{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}-{\beta}_{B}\right)$ | ${\left(-\tilde{r}+{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}-{\beta}_{B}\right)\right)\rangle}_{{s}_{B,\mathit{min}}}^{{s}_{B,\mathit{max}}}$ |

$<{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}-{\beta}_{B}\right)and>{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}+{\beta}_{B}\right)$ | 0 | |

$<{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}+{\beta}_{B}\right)$ | ${\left(-\tilde{r}+{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}+{\beta}_{B}\right)\right)\rangle}_{{s}_{B,\mathit{min}}}^{{s}_{B,\mathit{max}}}$ | |

>0 | $<{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}{\alpha}_{B}$ | ${\left(-\tilde{r}+{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}+{\beta}_{B}\right)\right)\rangle}_{{s}_{B,\mathit{min}}}^{{s}_{B,\mathit{max}}}$ |

$>{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}{\alpha}_{B}$ | ${\left(-\tilde{r}+{\scriptscriptstyle \frac{1}{2}}{\Lambda}_{\text{\hspace{0.17em}}k}\left({\alpha}_{B}-{\beta}_{B}\right)\right)\rangle}_{{s}_{B,\mathit{min}}}^{{s}_{B,\mathit{max}}}$ |

Voltage Level | Power Plant | Installed Power (kW) |
---|---|---|

Medium Voltage | Wind | 3600 |

Photovoltaic | 1387 | |

Total | 4987 | |

Low Voltage | Photovoltaic | 953 |

CHP | 891 | |

Total | 1844 | |

Total | 6831 |

ESS | Parameter | Value | Unit |
---|---|---|---|

B | Rated Charging Power | 250 | kW |

Rated Discharging Power | 500 | kW | |

Total (Usable) Energy | 500 (400) | kWh | |

Max (min) Stored Energy | 450 (50) | kWh | |

Round-Trip Efficiency | 92 | % | |

S | Rated Power | 1108 | kW |

Total (Usable) Energy | 9 (6) | kWh | |

Max (min) Stored Energy | 11.4 (2.4) | kWh | |

Round-Trip Efficiency | 90 | % |

Variable | e_{B} = e_{B,max} | e_{B,min} < e_{B} < e_{B,max} | e_{B} = e_{B,min} |

s_{B}^{*} | 0 | ${s}_{B}={\left(-{r}_{LF}+{\tilde{r}}_{avg}\right)\rangle}_{{s}_{B,\mathit{min}}}^{{s}_{B,\mathit{max}}}$ | 0 |

Variable | e_{S} = e_{S,max} | e_{S,min} < e_{S} < e_{S,max} | e_{S} = e_{S,min} |

s_{S}^{*} | 0 | ${s}_{S}={\left(-r+{r}_{LF}\right)\rangle}_{{s}_{S,\mathit{min}}}^{{s}_{S,\mathit{max}}}$ | 0 |

Variable | Symbol | OPEM | FBM |
---|---|---|---|

Time Horizon | T | 24/12/6 h | 24/12/6 h |

Forecasting Service | t_{r} | 15 min | 15 min |

S energy reinstatement | t_{Δ} | 15 min | 15 min |

Energy Optimization (B) | t_{B} | 15 min | 1 s |

Power Management (S) | t_{S} | 1 s | 1 s |

Case | Day 1 | Day 2 | Day 3 | TOT |
---|---|---|---|---|

no HESS | 0.729 | 1.173 | 1.273 | 1.084 |

OPEM & OPEM_{opt} | 0.677 | 1.133 | 1.218 | 1.037 |

Energy | Case | e (MWh) | |||
---|---|---|---|---|---|

Day 1 | Day 2 | Day 3 | TOT | ||

e_{gen} | no HESS | 6.765 | 0.385 | 6.167 | 13.317 |

OPEM | 6.239 | 0.060 | 5.888 | 12.187 | |

OPEM_{opt} | 6.235 | 0.060 | 5.907 | 12.202 | |

e_{load} | no HESS | −8.400 | −23.669 | −21.311 | −53.380 |

OPEM | −8.205 | −23.452 | −20.998 | −52.655 | |

OPEM_{opt} | −8.203 | −23.451 | −21.000 | −52.654 | |

e_{net} | no HESS | −1.635 | −23.284 | −15.144 | −40.063 |

OPEM | −1.966 | −23.392 | −15.110 | −40.468 | |

OPEM_{opt} | −1.968 | −23.391 | −15.093 | −40.452 | |

e_{gross} | no HESS | 15.165 | 24.054 | 27.478 | 66.697 |

OPEM | 14.444 | 23.512 | 26.886 | 64.842 | |

OPEM_{opt} | 14.439 | 23.511 | 26.906 | 64.857 |

ESS | Case | Day 1 | Day 2 | Day 3 | TOT |
---|---|---|---|---|---|

B | OPEM | 2.28 | 1.71 | 2.10 | 6.09 |

OPEM_{opt} | 2.45 | 1.74 | 2.27 | 6.46 | |

S | OPEM | 41.6 | 41.9 | 41.7 | 125.2 |

OPEM_{opt} | 38.7 | 38.7 | 38.3 | 115.7 |

Case | T (h) | |||
---|---|---|---|---|

24 | 12 | 6 | 3 | |

no HESS | 1.379 | 1.379 | 1.379 | 1.379 |

OPEM | 1.336 | 1.336 | 1.336 | 1.337 |

FBM | 1.365 | 1.356 | 1.344 | 1.340 |

T (h) | Case | g (MW) | |
---|---|---|---|

Peak Power delivered by MG | Peak Power drawn by MG | ||

no HESS | 3.62 | 2.11 | |

24 | OPEM | 3.27 (−9.7%) | 1.86 (−11.8%) |

FBM | 3.52 (−2.8%) | 1.99 (−5.7%) | |

12 | OPEM | 3.27 (−9.7%) | 1.86 (−11.8%) |

FBM | 3.52 (−2.8%) | 1.99 (−5.7%) | |

6 | OPEM | 3.27 (−9.7%) | 1.86 (−11.8%) |

FBM | 3.52 (−2.8%) | 1.99 (−5.7%) | |

3 | OPEM | 3.27 (−9.7%) | 1.86 (−11.8%) |

FBM | 3.27 (−9.7%) | 1.95 (−7.6%) |

T (h) | Case | e (MWh) | |||
---|---|---|---|---|---|

e_{gen} | e_{load} | e_{net} | e_{gross} | ||

no HESS | 103.67 | −72.16 | 31.51 | 175.83 | |

24 | OPEM | 99.74 | −69.41 | 30.33 | 169.16 |

FBM | 102 | −71.16 | 30.84 | 173.16 | |

12 | OPEM | 99.73 | −69.40 | 30.34 | 169.13 |

FBM | 101.07 | −70.32 | 30.75 | 171.39 | |

6 | OPEM | 99.78 | −69.43 | 30.34 | 169.21 |

FBM | 100.31 | −69.7 | 30.61 | 170.01 | |

3 | OPEM | 99.76 | −69.43 | 30.33 | 169.18 |

FBM | 100.16 | −69.67 | 30.49 | 169.84 |

Variable | OPEM | FBM | ||||||
---|---|---|---|---|---|---|---|---|

T (h) | 24 | 12 | 6 | 3 | 24 | 12 | 6 | 3 |

B | 18.35 | 18.25 | 18.24 | 18.67 | 5.58 | 7.42 | 10.81 | 13.83 |

S | 296.3 | 276.0 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Serpi, A.; Porru, M.; Damiano, A.
An Optimal Power and Energy Management by Hybrid Energy Storage Systems in Microgrids. *Energies* **2017**, *10*, 1909.
https://doi.org/10.3390/en10111909

**AMA Style**

Serpi A, Porru M, Damiano A.
An Optimal Power and Energy Management by Hybrid Energy Storage Systems in Microgrids. *Energies*. 2017; 10(11):1909.
https://doi.org/10.3390/en10111909

**Chicago/Turabian Style**

Serpi, Alessandro, Mario Porru, and Alfonso Damiano.
2017. "An Optimal Power and Energy Management by Hybrid Energy Storage Systems in Microgrids" *Energies* 10, no. 11: 1909.
https://doi.org/10.3390/en10111909