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sustainability Article

Intelligent Control of a Distributed Energy Generation System Based on Renewable Sources Ciprian Vlad 1 , Marian Barbu 1,2, * and Ramon Vilanova 2 1 2

*

Department of Automatic Control and Electrical Engineering, “Dunarea de Jos” University of Galati, Galati 800008, Romania; [email protected] Department of Telecommunication and Systems Engineering, Universitat Autonoma de Barcelona, Bellaterra, Barcelona 08193, Spain; [email protected] Correspondence: [email protected]; Tel.: +40-336-130-186

Academic Editor: Andrew Kusiak Received: 8 June 2016; Accepted: 29 July 2016; Published: 4 August 2016

Abstract: The control of low power systems, which include renewable energy sources, a local network, an electrochemical storage subsystem and a grid connection, is inherently hierarchical. The lower level consists of the wind energy sources (power limitation at rated value in full load regime and energy optimization in partial load regime) and photovoltaic (energy conversion optimization) control systems. The present paper deals with control problem at the higher level and aims at generating the control solution for the energetic transfer between the system components, given that the powers of the renewable energy sources and the power in the local network have random characteristics. For the higher level, the paper proposes a mixed performance criterion, which includes an energy sub-criterion concerning the costs of electricity supplied to local consumers, and a sub-criterion related to the lifetime of the battery. Three variants were defined for the control algorithm implemented by using fuzzy logic techniques, in order to control the energy transfer in the system. Particular attention was given to developing the models used for the simulation of the distributed energy system components and to the whole control system, given that the objective is not the real-time optimization of the criterion, but to establish by numerical simulation in the design stage the “proper” parameters of the control system. This is done by taking into account the multi-criteria performance objective when the power of renewable energy sources and the load have random characteristics. Keywords: hierarchical control; fuzzy control; storage system; renewable energy PACS: J0101

1. Introduction Distributed systems for the generation and use of electrical energy based on renewable sources is a topic that has been widely treated in the literature, given their involvement in the development of smart grids [1,2]. In this context, an important category is represented by low power systems (up to 5 kW), which provide electricity for local users, predominantly from renewable energy sources. In this case, there is an electrical energy storage system (a battery) and a connection to the national grid to transfer the surplus/deficit of energy from the power flow [3–5]. These distributed systems, which will be addressed in our paper, imply various issues, such as choosing renewable energy sources to simultaneously satisfy the requirements of cost and performance for the energy conversion, ensuring a long lifetime for the battery; ensuring the quality requirements for the electrical energy and, finally, designing a control structure covering a multi-criteria performance indicator. Regarding the renewable energy sources (solar and wind), a key issue is to find the control solutions to ensure the optimal operation in relation with an efficiency criterion given the randomness Sustainability 2016, 8, 748; doi:10.3390/su8080748

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Sustainability 2016, 8, 748

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of these primary energy resources [5–8]. For small power wind energy systems, the permanent magnet synchronous generator (PMSG) is preferred, as it allows the direct coupling to the wind turbine. The control solution ensures in this case the optimal regimes for the wind turbine (in terms of energy criterion), i.e., to ensure the maximum power conversion in the operating region corresponding to a partial load regime as well as power limitation in full load operating region [9,10]. In the full load operating region, the “stall speed regulation” strategy is used, which limits the shaft power by bringing the turbine in stall mode, based on shaft rotational speed reduction. On the other hand, control solution for solar energy systems ensures the operation on the optimal regimes characteristics, based on a mathematical model of the photovoltaic panel [11]. A crucial problem, insufficiently solved in the multisource systems with renewable energy conversion, is to ensure a long lifetime of the battery. Naturally, lifetime depends on the type of the adopted battery, which corresponds to the investment cost. When the battery has already been chosen on the basis of the quality/cost tradeoff, the question is to ensure the longest possible battery lifetime. What will be referred to in this paper is the fact that such an issue as the battery lifetime can be addressed on the basis of the control of the sources from the system, also taking into account that the power output of the renewable energy sources and the power required by the local network are random variables. Compliance with the supplied electrical energy quality, as imposed by technical rules authorizing the coupling of energy distributed system to the grid, implies the use of active power filters which by means of its control systems should provide a good performance/cost ratio [12,13]. The control of the distributed energy system with renewable sources was extensively approached in the literature. One of the first papers was published in 2001 and concerns intelligent energy management considering energy sources like photovoltaic, wind and conventional power plants, and dealing with the optimization of the system using energetic, ecological and economical criteria [14]. One of the approaches used in the following years was the supervisory control, considering different structures for the distributed energy systems: stand-alone system, including wind and solar energy sources [15], or grid-connected system [16], also including wind and solar energy sources, where multiple supervisory control strategies are considered. The efficient use of the storage capacities prove to be an efficient solution in increasing the performances of these distributed systems which are deeply influenced by the randomness of the energy provided by the renewable sources. Thus, in [17] a micro-wind energy system uses the battery unit as buffer for high demand periods, and also and to maintain the power quality norms, and in [18] the energy management systems minimize the power outage to critical loads, and maximize the utilization of renewable energy sources. Other applications include the use of SCADA systems to implement the management system for the Distributed Energy Systems [19]. However, the most widely used approach in the past few years is the optimal control of these systems: in [20] an optimal control strategy for an isolated system is proposed to coordinate energy storage and diesel generators to maximize wind penetration while maintaining system economics and normal operation performance; in [21] an Economic Model Predictive Control scheme is proposed in order to achieve the optimal economic performance in the operational costs of the micro-grid, but without considering the lifetime of the battery; in [22] a novel dissipativity-based distributed economic model prediction control approach is proposed to allow micro-grid users to optimize their own benefits, but the application only considers solar energy sources. This paper deals with the hierarchical control of distributed systems for the generation and use of electrical energy based on renewable sources based on artificial intelligence techniques. The proposed structure of the control system distinguishes itself from the proposals in the literature [14–22] by the following features: ‚ ‚

using a mixed performance criterion, which includes both the cost of the electricity supplied to the local consumers and a component expressing the battery lifetime; establishing a fuzzy based solution for the higher level control of the distributed system, which will correspond to the requirements imposed by the use of the mixed performance criterion; and


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

‚

establishing a fuzzy based solution for the higher level control of the distributed system, which will correspond to the requirements imposed by the use of the mixed performance criterion; obtaining the control solution and the parameters of the appropriate fuzzy controller based on and numerical simulation of the hybrid system using plausible scenarios regarding the random  obtaining the control solution and the parameters of the appropriate fuzzy controller based on evolution of the renewable energy sources and the local network. Within each scenario, numerical simulation of the hybrid system using plausible scenarios regarding the random the controller are established in order to satisfy the designer requirements regarding evolution parameters of the renewable energy sources and the local network. Within each scenario, the the performance criterion components. The final values of the controller parameters controller parameters are established in order to satisfy the designer requirements regarding are determined on the basis of the values obtained in all scenarios in the simulation. the performance criterion components. The final values of the considered controller parameters are determined on the basis of the values obtained in all scenarios considered in the simulation. Therefore, the controller parameters are not obtained through a real time optimization procedure the controller parameters are they not obtained real for time optimization of theTherefore, mixed performance criterion because would bethrough suitablea only a given instance of procedure of the mixed performance criterion because they would be suitable only for a given the mentioned random powers, used in the optimization procedure. instance of the mentioned random powers, used in the optimization procedure.

The rest of the article is organized Section22presents presents structure of proposed the proposed The rest of the article is organizedasasfollows: follows: Section thethe structure of the distributed energy system, the models of the renewable energy sources (wind and solar energy) and of distributed energy system, the models of the renewable energy sources (wind and solar energy) and of the and the intelligent control algorithms for theofcontrol of the system under the load, andload, the intelligent control algorithms used for used the control the system under consideration. same section, a performance criterion is introduced, including the cost of In theconsideration. same section,Ina the performance criterion is introduced, including both the cost of both electricity supplied electricity supplied local consumers and Section the battery lifetime. 3 deals with thewhen resultsusing to local consumers andtothe battery lifetime. 3 deals withSection the results obtained obtained when using the intelligent control algorithmsand, shown previously and, based onresults, the obtained the intelligent control algorithms shown previously based on the obtained proposes results, proposes an improved version of the control algorithm. The last section is dedicated to an improved version of the control algorithm. The last section is dedicated to conclusions. conclusions.

2. Methods

2. Methods

2.1. The Structure of the Distributed Electrical Energy Generation System Based on Renewable Sources 2.1. The Structure of the Distributed Electrical Energy Generation System Based on Renewable Sources

The simplified blockblock scheme, illustrating the structure of energy distributed system and highlighting The simplified scheme, illustrating the structure of energy distributed system and the proposed higher control level, is shown in Figure 1. highlighting the proposed higher control level, is shown in Figure 1.

Figure 1. Simplified block scheme of the proposed system. Figure 1. Simplified block scheme of the proposed system.

The system includes two power sources based on the conversion of renewable energies: wind

The system two panels. power sources based inject on thethe conversion energies: turbine and includes photovoltaic These sources currents Iof WT renewable and IPV into the DCwind turbine and photovoltaic panels. These sources inject the currents IWT and IPV into the DC intermediate circuit, and from here the energy flow can be transferred either to the local network or, eventually, to the grid or to the battery. In the first case, as long as the national grid is connected and available, the block labeled “Inverter/APF” has enabled the active power filter function and can achieve a bidirectional energy transfer, ensuring the power quality requirements for grid connection. If the renewable sources


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produce more energy than the one required to satisfy the local consumers as well as the charging battery requirements, a transfer of energy to the grid is ordered based on the energy balance. However, if the energy provided from the renewable sources is insufficient and there is a need to ensure a power flow from the grid for charging the battery then the “Inverter/APF” works in a rectifier PWM mode. If the national grid is not available, the block “Inverter/APF” only works as a voltage inverter, supplying the local consumers based on available energy in the battery and from the renewable sources. The second case refers to the transfer to/from the battery. An important condition imposed on the system by the performance criterion is to ensure a regularly charging/discharging regime of the battery (to the extent possible, given that both the renewable sources and the load have random characteristics) and at a low frequency, so that it results in a longer battery lifetime. This requirement is imposed through the control of the bidirectional converter “Cdc-dc ”, simultaneously with another concurrent requirement: reducing the energy transfer from the grid to the local network. The hierarchical control system contains two levels: the lower control level which refers to the control systems related to the system components and the higher level which refers to the management of the energy flows, taking into account a mixed criterion which considers energy cost as well as battery lifetime. The implemented lower level for the wind energy system ensures the optimal regimes for wind turbine (in terms of energy criterion), i.e., ensures the maximum power conversion in region 2 (partial load regime) and power limitation in region 3 (full load operating region) [9,10]. The control solution for solar energy system ensures operation on the optimal regimes characteristics, based on a mathematical model of the photovoltaic panel [11]. The control system for the “Inverter/APF” performs the regime inverter/rectifier PWM providing the output voltage level and the power quality requirements imposed to the active power filter. The control system of the “Cdc-dc ” converter provides direction and intensity of the transfer energy. The higher control level is implemented in the “Intelligent Management and Operation Control Block” and its design and implementation will be shown in the next sections. 2.2. Modeling the Random Energetic Flows In the energy balance of the distributed system the following energetic flows with random evolution take place: power is generated by renewable energy sources (wind and solar) and power is consumed in the local network (the load). 2.2.1. Modeling of the Power Generated by the Wind Source The electrical power provided by the wind source, Pwe , is modeled as: Pwe “ ηg Pwm “ ηg ¨ 0.5πρR2 CP pλqv3

(1)

where Pwm is the mechanical power, ηg is the efficiency of the electric generator, ρ is the air density, R is the turbine blade length, v is the wind speed, and CP pλq is the turbine power coefficient, which depends on the tip speed ratio λ “ RΩ{v. In the partial load region, the control system of the wind source ensures the operation of the turbine on the optimal regimes characteristics by maintaining the tip speed ratio at the optimal value, λopt . The dependence of electric power on the wind speed is of the form: Pwe “ K Pe ¨ v3 , in which K Pe “ ηg ¨ 0.5πρR2 CPmax is obtained from knowing the nominal value of electrical power and wind speed: K Pe “ Pwe,r {v3r . In the full load region, when v ą vr , the turbine control system should keep the power at the nominal value. The wind speed is a non-stationary random variable that can be presented as: v ptq “ v ptq ` vt ptq

(2)

where v ptq is the medium- and long-term component and vt ptq is the turbulence component. For the time scale corresponding to the turbulence component, v ptq may be considered as the constant average of the wind speed. Both components are important in distributed systems for electricity


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production from renewable sources. The medium- and long-term component is particularly important for medium and high power wind systems. They have slow dynamics and react to low frequency variations of the wind speed, which determines the sequence of situations regarding the wind energy potential (high, medium, low). Small turbines, as the one considered in this paper, have fast dynamics and also react to the turbulence component of the wind speed. For modeling the wind speed the starting point was the generic broadband model of Van der Hoven [23], valid for the temperate zone, which provides information on the power spectral density of wind speed, Svv pωq, for both components on the medium- and long-term, as well for the turbulence component. To generate the time series which represents athe component v ptq a shaping filter has been used. The gain characteristics of such filter Gpωq “ Svv pωq have been obtained on the basis of the Van der Hoven power spectral density, Svv pωq, taking into account only the region corresponding to the low frequencies ω P t1e ´ 6, 1e ´ 3u (rad/s). It has been found that, in this region, the nonparametric Bode characteristics can be parameterized by the asymptotic characteristic of a first f order filter, GdB pωq. This filter was used as a shaping filter for the medium- and long-term components. The turbulence properties at a given time when the value of medium- and long-term components is considered to be constant, v, depend on the mean value of the wind speed through two parameters: ‚

turbulence intensity, I, defined by the equation: I“

‚

σ v

(3)

where σ is the turbulence standard deviation, turbulence length, Lt , which influences the spectral bandwidth of the time series, vt ptq.

These parameters depend on the average wind speed, surface roughness and the height from the ground. They are calculated by relations given in [23,24], in accordance with various standards (e.g., IEC Standard, DS 472 Danish Standard, etc.). The usual spectral models of fixed point turbulence are those of von Karman and Kaimal [25]. In this paper, the first model has been adopted as it is simpler to use. Therefore, based on the von Karman spectral model, the transfer function of the shaping filter for generating a turbulence, w f ptq, with unitary standard deviation is obtained as a fractional model: H f psq “

Kv pTv s ` 1q5{6

(4)

where Tv “ Lt {v, and Kv is chosen in order for the filter output, w f ptq, to have a standard deviation equal to one. In these conditions, for a given turbulence intensity, I, the standard deviation is computed as, σ “ I ¨ v, and the fixed point turbulence is: vt ptq “ I ¨ v ¨ w f ptq

(5)

with m1 = 0.4 and m2 = 0.25. The scheme for numerical generation of the wind speed is given in Figure 2 [26]. Kv pm1 Tv s ` 1q (6) H Kar f 1 “ pT s ` 1qpm T s ` 1q v 2 v


H Kar f1 

K v (m1Tv s  1) (Tv s  1)(m2Tv s  1)

H Kar f1 

K v (m1Tv s  1) (Tv s  1)(m2Tv s  1)


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(6)

6 of (6)23

Figure 2. Scheme of the system for numerical generation of the wind speed. Figure 2. Scheme generation of of the the wind wind speed. speed. Figure 2. Scheme of of the the system system for for numerical numerical generation

Figure 3a shows a fragment of the wind speed variation obtained using the scheme from Figure Figure 3a shows a fragment of the wind speed variation obtained using the scheme from Figure 2, when Figure the turbulence is the I = wind 0.12.speed The mediumand long-term of the 2,wind 3a shows aintensity fragment of variation obtained using the component scheme from Figure 2, when the turbulence intensity is I = 0.12. The medium- and long-term component of the wind when the turbulence intensity is I = 0.12. The mediumand long-term component of the wind is kW, speed is shown in red. For the wind power generation, a source with the nominal powerspeed of 1.5 speed is shown in red. For the wind power generation, a source with the nominal power of 1.5 kW, shownatinared. For the wind wind power a source the nominal of 1.5 kW, obtained obtained nominal speedgeneration, v  11 m/s, was with considered. Thepower source begins to produce obtained at a nominal wind speed vr  11 m/s, was considered. The source begins to produce at a nominal wind speed v “ 11 m/s, rwas considered. The source begins to produce energy at the

r energy at the turbine cut-in speed By neglecting neglecting thedynamics dynamics of the power wind energy at the turbine speedvdvd3.5 3.5 m/s. m/s. By of the lowlow power turbine cut-in speed vcut-in neglecting the dynamicsthe of the low power wind sourcewind and d “ 3.5 m/s. By source andinto taking into account that by thewind wind source varies the cube source and taking into account thatthe thepower power generated generated by the source withwith the cube of of taking account that the power generated by the wind source varies withvaries the cube of the wind the wind speed, thethe resulting distribution of wind power sensibly different from the one the wind resulting distribution of the the windispower isissensibly different from the theof the speed, thespeed, resulting distribution of the wind power sensibly different from the one of one the of wind wind speed (Figure 3b). windspeed speed (Figure 3b). (Figure 3b). 1600

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v [m/s]

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[W] Pw eP[W] we

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(a)of the wind speed evolution (blue) and of the medium(b) Figure 3. (a) Sample and long-term component (red); and (b) power of the wind source for the wind speed sample. Figure 3. 3. (a)(a)Sample wind evolution and ofand the mediumand long-term Figure Sample ofofthethe wind speedspeed evolution (blue) and (blue) of the mediumlong-term component (red); component (red); and (b) power of the wind source for the wind speed sample. (b) power the wind source forby thethe wind speed sample. 2.2.2.and Modeling theofPower Generated Solar Energy Source In orderthe to conduct the numerical simulation analysis of the distributed system, the summer 2.2.2.2.2.2. Modeling Power Generated Energy Source Modeling the Power Generatedby bythe the Solar Solar Energy Source

regime was considered when the solar energy source can generate electricity from 6.00 a.m. till 9.00 In order to conduct the numerical simulation distributed system, thea summer In order to conduct the numerical simulation analysis ofthe the distributed system, the summer p.m. [27]. The calculated and adopted values for theanalysis optical of and electrical power during regime considered when the solar energy source can generate electricity from a.m. daywas arewas shown in Table 1. the It has been considered that the photovoltaic cells from have 6.00 a conversion regime considered when solar energy source can generate electricity 6.00 a.m. till 9.00 9.00 p.m. [27]. The calculated and adopted values for the optical and electrical power during a summer efficiency of about 12%. Due to the fact that the irradiance may be affected by the movement of p.m. [27]. The calculated and adopted values for the optical and electrical power during a summer shown Table It It hashas been considered that thethat photovoltaic have acells conversion clouds, irradiance was1.1. considered as a considered random variable with slowcells evolution which is subtracted day day are are shown ininTable been the photovoltaic have aefficiency conversion of about 12%. Due to the fact that the with irradiance may be affected by of thedaytime movement of clouds, irradiance from the electrical power corrected temperature. A sample evolution of the power of efficiency of about 12%. Due to the fact that the irradiance may be affected by the movement was considered as a random variable with slow evolution which is subtracted from the electrical power provided by the solar energy source is shown in Figure 4. clouds, irradiance was considered as a random variable with slow evolution which is subtracted corrected with temperature. A sample of daytime evolution of the power provided by the solar energy fromsource the electrical power corrected with temperature. A sample of daytime evolution of the power is shown in Figure 4.

provided by the solar energy source is shown in Figure 4.

Sustainability 2016, 2016, 8, 8, 748 748 Sustainability Sustainability 2016, 8, 748

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Table 1. Parameters considered for the solar energy source in the summer regime. Table Table 1. Parameters Parameters considered considered for the solar energy source in the summer regime. Time Time During During aa Day Day

Time During a Day

12 12 a.m.–6.00 a.m.–6.00 a.m. a.m. 12a.m.–7.00 a.m.–6.00 a.m. 6.00 6.00 a.m.–7.00 a.m. a.m. 6.00a.m.–8.00 a.m.–7.00a.m. a.m. 7.00 7.00 a.m.–8.00 7.00 a.m.–8.00a.m. a.m. 8.00 a.m.–11.00 a.m. 8.00 8.00a.m.–11.00 a.m.–11.00a.m. a.m. 11 p.m. 1111a.m.–4.00 a.m.–4.00 a.m.–4.00p.m. p.m. 4.00 4.00p.m.–7.00 p.m.–7.00p.m. p.m. 4.00 p.m.–7.00 p.m. 7.00 p.m.–8.00 p.m. 7.00 p.m.–8.00 p.m. 7.00 p.m.–8.00 p.m. 8.00p.m.–9.00 p.m.–9.00p.m. p.m. 8.00 8.00 p.m.–9.00 p.m. 9.00p.m.–12.00 p.m.–12.00a.m. a.m. 9.00 9.00 p.m.–12.00 a.m.

Irradiance Irradiance 2 Irradiance (W/m (W/m2))2 (W/m 00 ) 0 200 200 200 800 800 800 1000 1000 1000 800 800 800 1000 1000 1000 800 800 800 200 200 200 000

Optical Optical Electrical Power (kW) Power (kW) Optical PowerElectrical Electrical Power Power Power (kW) (kW) (kW) (kW) 00 00 0 0 3.12 0.312 3.12 0.312 3.12 0.312 12.4 1.248 12.4 1.248 12.4 1.248 15.0 1.56 15.0 1.56 15.0 1.56 12.48 1.56 12.48 1.56 12.48 1.56 15.0 1.56 15.0 1.56 15.0 1.56 12.4 1.248 12.4 1.248 12.4 1.248 3.12 0.312 3.12 0.312 3.12 0.312 00 0 00 0

Electrical Electrical Power Power Corrected Corrected Electrical Power Corrected with Temperature with Temperature (kW) (kW) with Temperature (kW) 00 0 0.312 0.312 0.312 1.248 1.248 1.248 1.56 1.56 1.56 1.404 1.404 1.404 1.56 1.56 1.56 1.248 1.248 1.248 0.312 0.312 0.312 000

Figure Figure4. 4.Sample Sampleof ofthe thepower powergenerated generatedby bythe thesolar solarenergy energysource sourceover overaaaday, day, in regime. Figure 4. Sample of the power generated by the solar energy source over day, in summer summer regime.

2.2.3. 2.2.3. Modeling Modeling the Power Consumed by by the the Load Load Modeling the the Power Power Consumed The aa house, aa small farm, aa The representative electrical loads for the distributed systems can bebe small farm, The representative representative electrical electricalloads loadsfor forthe thedistributed distributedsystems systemscan canbe ahouse, house, a small farm, hostel, etc. In the local network, there may be consumers, such as a fridge, freezer, microwave, hostel, etc. thethe local a hostel, etc.In In localnetwork, network,there theremay maybebeconsumers, consumers,such suchasasaa fridge, fridge, freezer, freezer, microwave, microwave, washing small machines, etc., as well as the lighting installation. Coupling these washing machine, machine, small machines, etc., as well as the lighting installation. Coupling these units to machine, machines, Coupling these units units to the local network is determined by the daytime activities and can have a significant variability [3]. the the local local network network is is determined determined by by the the daytime daytime activities activities and and can can have have aa significant significant variability variability [3]. [3]. Most Most important important aspect of the diurnal distribution of the consumed consumed electrical power is the possibility possibility important aspect aspect of of the the diurnal diurnal distribution distribution of of the consumed electrical electrical power power is is the possibility of of having having significant significant variations of power power relative to to the the average power. Figure Figure shows diurnal significant variations variations of power relative average power. Figure 555 shows shows aa diurnal variation profile in the local network considered in the analysis by numerical simulation variation of the the variation profile in the local network considered in the analysis by numerical simulation simulation of distributed system. distributed system.

Figure Figure 5. 5. Daily Daily evolution evolution of of the the power power consumed consumed in in the the local local network. network. Figure 5. Daily evolution of the power consumed in the local network.


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2.3. Intelligent Control Algorithms for the Distributed Energy System 2.3.1. Approaches in the Intelligent Control of the Distributed Energy System The higher level control of the system relates to the design of the control algorithm that is in charge of transferring the electrical energy between the system components: renewable energy sources, public grid, energy storage unit (battery) and the local network (the load). The algorithm in question refers to two aspects: (a) energy transfer direction; and (b) the magnitude of the energy transfer, i.e., the transferred power. The fact that the power required by the load and power output from the renewable energy sources are random variables determines a variety of the control situations. The presence of the battery is very important, not only as a storage unit for the energy excess from the renewable sources (which contributes to the supply to the load during the energy deficit), but also as a “sensor” for the level of the system energy. The evolution of the battery voltage, which is directly correlated to stored energy, largely reflects the energy context of the distributed system. This context can be characterized by a set of “states” in which the integrated system can be found. The “states” vector can be defined by: the current value of the battery voltage, Vb , which is considered proportional with the accumulated energy in the system, by the variation of the accumulated energy, ∆V, and by the predicted values of the power for the renewable energy sources and for the load, de p . Using predictions for each one of the three powers is unreasonable and excessive; what matters is the deficit/surplus prediction of energy in the distributed system, i.e., the difference between the power for the renewable energy sources and for the load. Therefore, the “states” which reflects the context of the system energy, may be defined by the vector: xs “ rVb ∆V de p sT (7) Based on these states, the control system establishes the direction and the magnitude of the electrical energy transfer between the distributed system and the grid. The control algorithm can consider two approaches, as follows: (1)

Crisp type approach, which uses a simple algorithm for “control situations” recognition. Let us consider the following discrete commands: C1 : C2 : C3 : C4 : C5 :

important transfer from the grid to the distributed system (Pgs “ 100%); medium transfer from the grid to the distributed system (Pgs “ 50%); null transfer between the grid to the distributed system (Pgs “ 0%); medium transfer from the distributed system to the grid (Psg “ 50%); and important transfer from the distributed system to the grid (Psg “ 100%).

In the above, Pgs ptq and Psg ptq are the transferred powers from the grid to the distributed system, and from the distributed system to the grid, respectively. These discrete commands are put in correspondence and adopted as “prototype states” set by the pi q

designer. Let us denote xs , i “ 1, 5 as these states. They are numerically defined in accordance with Equation (7), by imposing values for the variables Vb , ∆V and de p . For example, for the “prototype p1q

state” xs the numeric value of Vb should reflect a reduced accumulation of power in the battery, ∆V should be negative (i.e., there is an energy deficit in the system) and the prediction de p still indicates energy deficit. Obviously, in this case, an important command for energy transfer from the grid to distributed system (Pgs “ 100%) is justified. For any current “state” xs , the discrete command is determined by the following algorithm: ! Min

i“1,...,5

) p jq pi q dpxs , xs q “ dpxs , xs q ñ C “ Cj

(8)


pi q

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pi q

where dpxs , xs q is a function that reflects the degree of proximity between xs and xs . This function can be the Euclidean distance between the two vectors. Obviously, the components of the state vectors must be normalized before assessing this distance. The decision rule given by Equation (10) is very simple: determine which “prototype state” is closest to the current state vector and adopt the command corresponding to that “prototype state”. (2)

Fuzzy type approach, in which the energy state of the system is evaluated in linguistic terms. In this case, the control principle shown above is preserved, but all the variables involved in the system, including the command setting the direction and the magnitude of the energy transfers, are obtained by fuzzy evaluation, and the control law is obtained by means of fuzzy inference.

An assessment of the two approaches reveals that the fuzzy approach allows a more nuanced control of energy transfers. The method based on crisp variables may be presented as a special case of the fuzzy techniques, when in the implementation makes use of special membership functions, thus avoiding the calculation of the distance between vectors. The design and testing of the higher level control system is performed by taking into account several working regime scenarios. Generating these scenarios is in relation to the following requirements: ‚

‚

testing the system operation in different situations regarding the renewable energy sources. For the distributed system design it is necessary to consider at least two regimes: summer and winter; and testing the system operation in two operating modes of the battery: buffer regime—considered as the standard one—and periodic regime, in which the charging and discharging cycles are taking place during the normal operation of the distributed system. These cycles are recommended to increase the battery lifetime.

2.3.2. Prediction of the Random Variables from the Distributed Energy System Prediction of power from the renewable energy sources is an important challenge [28–30]. The prediction algorithms were implemented based on the linear AR and ARMA time series models. The results obtained with these classical algorithms were very different, depending on the physical nature of the predicted time series. Thus, the medium- and long-term components of the wind speed have an autocorrelation function with a very slow decreasing variation, offering a good opportunity for prediction. The good results obtained in this case are illustrated by the sample shown in Figure 6 where different values of the prediction horizon where considered when using an ARMA type model. The turbulence component prediction has more modest results, the prediction can be acceptable only for a few sampling steps (Ts “ 1 psq was used). The explanation is very simple: the turbulence properties are very close to those of a white noise, since the shaping filter for the turbulence component is of second order with unitary pole excess (see Equation (6)). In these conditions, the autocorrelation function has a fast decreasing variation and consequently the prediction is very difficult (especially when using very simple approaches, such as linear predictors). However, for low power wind systems, as considered in this paper, even a prediction on a very short horizon time (a few seconds) can avoid some switching of the type discharging–charging–discharging from the operating regime of the battery. As mentioned, the predicted variable in the system is the difference between the sum of powers of the renewable energy sources and the consumed power by load. In the case of this variable, there are two components that severely limit the prediction performances. One is the turbulence component of the wind speed. The other is the random variation of the load power (local network). As the average value of this load is lower, the percentage random variations of the power are more important (when coupling and uncoupling different consumers) and the prediction of the power surplus/deficit is more difficult. Two versions of the fuzzy control algorithm of the distributed system, shown in the next sub-section,


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are using information provided by the predictor with a short time horizon. The transfer function of this predictor is: Sustainability 2016, 8, 748

Hpz

10 of 22

´1

´1

´2

´3

q “ 6.558 ´ 5.959z ` 0.04215 z ` 0.2391 z ` 0.01096 z 1 2 3 ´5  5.959 z´ 7 0.2391 z ´ 8 0.01096 z´94  H0.2945z ( z 1 )  6.558 z ´  ´ 0.5238z 6`0.04215 0.02858z ` 1.281z  ´ 1.024z

´4

`

0.2945 z 5  0.5238 z 6  0.02858 z 7  1.281z 8  1.024 z 9

Figure 6. seasonal component of the wind speed, (blue line), overover 10, 20, v  t v ptq Figure 6. Prediction Predictionofofthe the seasonal component of the wind speed, (blue line), 10,and 20, and 30 min green, respectively). 30 min (red,(red, blackblack and and green, respectively).

2.3.3. Fuzzy Controllers for the Distributed Energy System System Based on sections, the the control algorithm for transferring the electrical energy between onthe theprevious previous sections, control algorithm for transferring the electrical energy the system is implemented as a battery voltagevoltage feedback controlcontrol system,system, using fuzzy between thecomponents system components is implemented as a battery feedback using techniques. The controller of thisof loop designed in twoin variants, as follows: fuzzy techniques. The controller thiswas loop was designed two variants, as follows: (1) Variant Variant 11 of of the the control control algorithms algorithms is is illustrated illustrated in in the scheme given in Figure 7. 7. The controller inputs are the components of the x vector defined by Equation (7). These variables inputs are the components of the ss vector defined by Equation (7). These variables are scaled using the the coefficients 1.3,, kk2 “44 and and kk3 “0.8 0.8.. The The battery battery voltage, voltage, V (t), reflects reflects the using coefficients kk11 “  1.3 Vbb(t), the 2 3 accumulated energy at the current time t and is calculated in accordance with the simplified accumulated energy at the current time t and is calculated in accordance with the simplified model [3] on the basis of the following equation: model [3] on the basis of the following equation: VMV´ Vm m VVb ptq “ Vm `VM  )  Wm´ Wm(trWptq  Wm s b (t )  Vm  W ´W MW WM  m

(9) (9)

energy fed fed to to the the input, input, and and VVMM and V Vm m are the voltage value for the maximum maximum where W(t) is the energy energy,WW M , and the minimum energy, W m, accumulated into the battery, respectively. In the energy, , and the minimum energy, W , accumulated into the battery, respectively. In the simulation m M simulation program, a battery with the nominal voltage of 48 V was considered. In Equation (9), the program, a battery with the nominal voltage of 48 V was considered. In Equation (9), the following following values wereVadopted: Vand M = 49.5 and m = 47 V. Assuming a battery 800 Ah, it values were adopted: Vm =V47 V. V Assuming a battery capacity of capacity 800 Ah, itofresults that M = 49.5 V results that W M = 138.24 MJ. The minimum value of the stored energy, when the battery is practically WM = 138.24 MJ. The minimum value of the stored energy, when the battery is practically discharged, discharged, WmWith = 17.28 MJ. With the value M =the 138.24 MJ forstored the maximum the is Wm = 17.28isMJ. the value WM = 138.24 MJWfor maximum energy, thestored batteryenergy, can supply battery can supply an electrical of energy 1.6 kW transferred for 24 h. The energy transferred into thetime battery an electrical load of 1.6 kW for 24load h. The into the battery at the current t is: at the current time t is: żt t Wptq “ (10) W (t )  rP ( ) ´  PPo(pτqs  )  ddτ  Pi pτq (10)



00

i

o

where ‚

PPi i isisthe power fedfed into thethe battery, which has the components: power produced from the power into battery, which has following the following components: power produced sources wind and solar, PPVand , respectively, and the power transferred from the grid, . we and P P , respectively, and the power transferred fromPgs the from sources wind andPsolar, we

PV

grid, Pgs .



Po is the power extracted from the battery, equal with the sum of the consumed power into the

local network, Pl , and the power transferred into the grid, Psg .


‚

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Po is the power extracted from the battery, equal with the sum of the consumed power into the local network, Pl , and the power transferred into the grid, Psg .


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Figure 7. Scheme of the controller in Variant 1 of the control algorithm. Figure 7. Scheme of the controller in Variant 1 of the control algorithm.

Given the effect of noise amplification when performing numerical derivation, at the input V , Given the effect of noise amplification when performing numerical derivation, at the input ∆V, after the derivative element a filter with static amplification equal with 1 was inserted (see Figure 7). after the derivative element a filter with static amplification equal with 1 was inserted (see Figure 7). a a ,= with a = The 0.0005. The positive command action, The transfer transferfunction functionofof this filter The this filter is 1is , with 0.0005. positive command action, obtained 1 a ´p1´aqz´1

1  1  a  z

after scaling, with the factor ku “ 1, is used to control the energy flow from the grid to the distributed obtainedand after with the factor ku  1to , iscontrol used to energy from the grid to the system, thescaling, negative component is used thecontrol energythe flow from flow the distributed system to distributed and of thethe negative component is used to control the energy flowterms fromwith the the grid. Thesystem, fuzzification voltage input was performed considering three linguistic distributedmembership system to the grid. The fuzzification ofVthe voltage inputaswas considering triangular functions. The value of 48.5 was considered theperformed center of the linguistic three linguistic terms with triangular membership functions. The value of 48.5 V was considered as value “M” = medium. With respect to this value, the linguistic values: “S”= small and “B”= Big were the center ofFor thethe linguistic value “M” = medium. With to linguistic this value,values the linguistic values: “S”= considered. fuzzification of the inputs ∆V andrespect de p , two (“N” = negative and de  V small and “B”= Big were considered. For the fuzzification of the inputs and , two linguistic “P” = positive) with Gaussian membership functions were used. Regarding the controller output, u, p five linguistic withand singleton membership functions, positive bigfunctions (PB), positive values (“N” =values negative “P” = type positive) with Gaussian membership weremedium used. (PM), zero (Z), negative medium (NM), and negative big (NB), were adopted. The fuzzy controller rules Regarding the controller output, u, five linguistic values with singleton type membership functions, are given Tablepositive 2. Table 2 also (PM), showszero the (Z), correspondence between theand fuzzy commands andwere the positive bigin(PB), medium negative medium (NM), negative big (NB), commands from the crisp strategy. adopted. The fuzzy controller rules are given in Table 2. Table 2 also shows the correspondence between the fuzzy commands and the commands from the crisp strategy. Table 2. Fuzzy Controller Rules (Variant 1). Vb

∆V

Table 2. Fuzzy Controller Rules (Variant 1). de p u Corresponding Crisp Strategy

CorrespondingCCrisp Strategy Vb S ΔV N de p N u PB 1 P PB PM S S N N N C21 N PM PM C22 S S N P P C S P P Z C S P N PM C32 M N N PM C2 SM P N P C P Z Z C33 M M N P N N PM Z C32 P Z NM C43 MM N P P C C33 MB P N N N Z Z C B N P NM C4 MB P P P C N NM NM C44 B B N P N Z C P NB C53 B N P NM C4 B P N NM C4 (2) Variant 2 of the control algorithms is implemented using a voltage controller whose scheme is B P P NB C5 given in Figure 8. The voltage setpoint, which is explicitly provided, may be imposed either at a fixed value, for example 48.5 V, or from a signal generator, which provides a periodically (2) Variant 2 of the control algorithms is implemented using a voltage controller whose scheme is varying ramp with an average value of 48.5 V. Both controllers (Variant 1 and Variant 2) are given in Figure 8. The voltage setpoint, which is explicitly provided, may be imposed either at a equivalent to a pseudo Proportional-Derivative type control law with anticipation with respect fixed value, for example 48.5 V, or from a signal generator, which provides a periodically varying ramp with an average value of 48.5 V. Both controllers (Variant 1 and Variant 2) are equivalent to a pseudo Proportional-Derivative type control law with anticipation with respect to the disturbance deficit/surplus energy. The integrative component that is missing is not an important impediment, since in practice the system is always working in a dynamic regime and


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to the disturbance deficit/surplus energy. The integrative component that is missing is not an important impediment, since in practice the system is always working in a dynamic regime Sustainability 2016, 8, 748 voltage must be in the vicinity of a value corresponding to the “charged” regime 12 of 22 and the battery of the battery. The fuzzification of the control error was carried out considering three linguistic the battery. The fuzzification of thefunctions. control error was carried out and considering threecommand linguistic terms, with triangular membership The other two inputs the controller terms, with triangular membership functions. The other two inputs and the controller maintain the same fuzzification as in Variant 1. In addition, the rule table is similar to the command maintain the same fuzzification as in Variant 1. In addition, the rule table is similar to previous controller. the previous controller.

Figure 8. Scheme of the controller in Variant 2 of the control algorithm. Figure 8. Scheme of the controller in Variant 2 of the control algorithm.

2.4. The Performance Criterion for the Distributed Energy System 2.4. The Performance Criterion for the Distributed Energy System Out of the scenario described above, it becomes clear that, in the distributed system, the power Out of the scenario described above, it becomes clear that, in the distributed system, the power consumption with the load (the local network) is a random variable and the two electrical energy consumption with the load (the local network) is a random variable and the two electrical energy sources (wind and solar) are also random variables. The third energy source is the grid, which is the sources (wind and solar) are also random variables. The third energy source is the grid, which is the backup source. In order to regulate the energy transfer between the sources and the load, a battery is backup source. In order to regulate the energy transfer between the sources and the load, a battery is used. Its role is to use the stored energy in such a way that the energy transfer from the grid to the used. Its role is to use the stored energy in such a way that the energy transfer from the grid to the load load to be as low as possible. So the first constraint to be imposed is to reduce the cost of the to be as low as possible. So the first constraint to be imposed is to reduce the cost of the consumed consumed electrical energy from the grid. The energy bills for the consumer in a predetermined electrical energy from the grid. The energy bills for the consumer in a predetermined interval [0 T] are interval [0 T] are represented as: represented as: żT T E  `  gs Pgs (t )   sg Psg (t ) ˘dt (11) E “ 0 α gs Pgs ptq ´ αsg Psg ptq dt (11)



0



where  sg and  gs are coefficients that represents the price for the electricity flow to and from the where αsg and α gs are coefficients that represents the price for the electricity flow to and from the grid, respectively. respectively. These These prices prices vary vary depending depending on on the the legislation legislation in in each each country. country. Our Our application application grid, considered that: .     1 gs “ 1. considered that: αsgsg “ α gs At the load level the is the the efficiency efficiency of of the the ) , where At the load level the energy energy flow flow from from the the grid grid is is  ηgs Pgsgs(tptq, where  ηgs gs ¨ P gs is transfer circuit from grid to load. Similarly, the energy energy flow transferred transferred to the grid from the the sources sources and, eventually, from the battery is is ηsg P ptq, where η is the efficiency of the transfer circuit from sg(t ) , where sg sg sg sg is the efficiency of the transfer circuit load load to to grid. grid. The The energy energy transfer transfer in in aa circuit circuit that that includes includes the the battery battery is is also also affected affected by by the the battery battery efficiency, η . b . efficiency,  b An important variable, which is not “visible” in Equation (11), is the variation of the stored energy An important variable, which is not “visible” in Equation (11), is the variation of the stored into the battery. The control system of the distributed system can influence the powers Pgs ptq or Psg ptq energy into the battery. The control system of the distributed system can influence the powers in Equation (11) by acting on such stored energy. In essence, the variable E is affected by three factors: Pgs (t ) or Psg (t ) in Equation (11) by acting on such stored energy. In essence, the variable E is the power produced by the renewable energy sources; the load; and the command given by the control affectedwhich by three factors: the the variation power produced by the renewable energyTo sources; the the load; and the system, determines of the energy stored in the battery. exemplify evaluation command given by the control system, which determines the variation of the energy stored in the of Equation (11), a distributed system was considered with a diurnal variation given by the power battery. To exemplify thenetwork. evaluation Equation system (11), a distributed was the considered consumption in the local Theofdistributed battery has system 800 Ah and solar andwith winda diurnal variation given by the power consumption in the local network. The distributed system sources have nominal powers of 1.5 kW. It has been assumed that the wind source works with a battery has 800 Ah and the solar and wind sources have nominal powers of 1.5 kW. It has been assumed that the wind source works with a given wind speed profile and for the solar energy source a variation of the solar irradiance specific for a summer day was considered. In these conditions, the results shown in Figure 9 were obtained by numerical simulation of the distributed system: energy transferred from the grid to the distributed system, energy transferred from the distributed system


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given wind speed profile and for the solar energy source a variation of the solar irradiance specific for a summer day was considered. In these conditions, the results shown in Figure 9 were obtained by numerical simulation of the distributed system: energy transferred from the grid to the distributed system, energy transferred from the distributed system to the grid and the energy bills. Sustainability 2016, 8, 748 13 of 22

Figure Evolutionof of energy transferred to distributed system line), energy Figure 9.9.Evolution energy transferred from from grid togrid distributed system (blue line),(blue energy transferred transferred from distributed system to grid (red line), and energy bills for 24 h (green line). from distributed system to grid (red line), and energy bills for 24 h (green line).

Another important criterion considered for the control of the distributed system is to increase Another important criterion considered for the control of the distributed system is to increase the the battery lifetime and thus increasing the system sustainability. The high cost of the battery and battery lifetime and thus increasing the system sustainability. The high cost of the battery and the fact the fact that its lifetime is dependent on the operating conditions justify the requirement imposed to that its lifetime is dependent on the operating conditions justify the requirement imposed to the control the control system to make sure that the battery lifetime is as long as possible. A first option can be to system to make sure that the battery lifetime is as long as possible. A first option can be to ensure ensure a cycle of charging and discharging at a nominal rate. Because the power produced by the a cycle of charging and discharging at a nominal rate. Because the power produced by the renewable renewable energy sources and the consumption in the local network are random variables, this energy sources and the consumption in the local network are random variables, this approach may approach may lead to high energy bills because of Equation (11). A second option can be to impose a lead to high energy bills because of Equation (11). A second option can be to impose a regime that regime that reduces the cost of the energy bills. However, this approach may lead to a high reduces the cost of the energy bills. However, this approach may lead to a high frequency in the frequency in the switches for charging–discharging the battery, thus negatively affecting the battery switches for charging–discharging the battery, thus negatively affecting the battery lifetime. To extend lifetime. To extend the battery lifetime, the charging/discharging rate must be at a low level. In the battery lifetime, the charging/discharging rate must be at a low level. In addition, in order to addition, in order to protect the battery, it is important to avoid deep discharges, the battery must be protect the battery, it is important to avoid deep discharges, the battery must be kept near the nominal kept near the nominalε load condition. Let NTε be the number of charge/discharge switches that take load condition. Let NT be the number of charge/discharge switches that take place in the interval [0 T], place in interval [0 T],charged while the is kept charged nominal value, a tolerance while thethe battery is kept at battery the nominal value, withatathe tolerance given bywith ε. Maintaining given by ε. Maintaining the battery voltage into a region of the nominal load state can be performed the battery voltage into a region of the nominal load state can be performed by means of a control by means of a control system which ensures the energy flows into the distributed system in the an system which ensures the energy flows into the distributed system in an adequate manner (given adequate manner theof randomness of the load and of the renewable energies), according to the randomness of the(given load and the renewable energies), according to the requirements imposed by the requirements imposed by the performance criterion. This criterion, which takes into account two performance criterion. This criterion, which takes into account two conflicting requirements, reducing conflicting requirements, energy bills, E, and the number of charge/discharge switches, the energy bills, E, and thereducing number the of charge/discharge switches, NTε , takes the form: ε NT , takes the form: żT T ` ˘ ε I “I  α gs (12)  Pgs Pptq (t )´ αsg P Psg(ptq t ) dtdt`  γN¨ εNT (12)



0

0

gs gs

sg

sg



T

where γ isisthe thefactor factorthat thatweights weightsthe thetwo twoterms termsofofthe theperformance performancecriterion. criterion. This This factor factor depends depends where on the price of the electricity flow to and from the grid, the efficiency of the transfer between the sources and the grid, and also on the properties of the storage unit. An important particularity of the energy distributed systems is given by the high frequency fluctuations in the power supplied by the wind source (due to the turbulence component of the wind speed) and sometimes in the load power consumption. These fluctuations can induce frequent switches between the charging/discharging regimes in the control loop of the battery voltage, with a negative effect on battery lifetime. Figure 10a illustrates the charge/discharge commutations within 24 h for the distributed system operation under the conditions mentioned above. The simulation model of the system has been provided with units for processing jumps of the type shown in Figure 10a. This was done so at every commutation


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wind source (due to the turbulence component of the wind speed) and sometimes in the load power consumption. These fluctuations can induce frequent switches between the charging/discharging regimes in the control loop of the battery voltage, with a negative effect on battery lifetime. Figure 10a illustrates the charge/discharge commutations within 24 h for the distributed system operation under the conditions mentioned above. The simulation model of the system has been provided with units for processing Sustainability 2016, jumps 8, 748 of the type shown in Figure 10a. This was done so at every commutation 14 of 22 charging–discharging–charging the variable NTε increases with a constant value. In these conditions, conditions, the of second term ofgiven the criterion given(12), by Equation (12), which assesses the evolutionthe of evolution the secondofterm the criterion by Equation which assesses the number of the number of charge/discharge switches, is shown charge/discharge switches, is shown in Figure 10b. in Figure 10b.

(a)

(b)

Figure 10. Evolution of the component corresponding to the commutation of the functioning Figure 10. Evolution of the component corresponding to the commutation of the functioning regimes: regimes: commutation charging/discharging (a); and corresponding component from(12) Equation commutation charging/discharging (a); and corresponding component from Equation (b). (12) (b).

Unlike the performance criteria of the lower level of the hierarchical control structure, which Unlike the performance criteria of the lower level of the hierarchical control structure, which is is optimized in real-time trough the automatic control systems, Equation (12) is used off-line in the optimized in real-time trough the automatic control systems, Equation (12) is used off-line in the design stage in order to establish the parameters of the control system at the higher level. This solution design stage in order to establish the parameters of the control system at the higher level. This is determined by the fact that the minimization of Equation (12) is valid only for a given profile solution is determined by the fact that the minimization of Equation (12) is valid only for a given (considered in a particular instance) of the evolution curves of power for the renewable energy sources profile (considered in a particular instance) of the evolution curves of power for the renewable and load, both variables having random evolutions. In another instance in which those variables have energy sources and load, both variables having random evolutions. In another instance in which those a different evolution the parameters of the control system that would minimize the Equation (12) variables have a different evolution the parameters of the control system that would minimize the would be different. In these conditions, establishing the parameters involved in the control algorithm Equation (12) would be different. In these conditions, establishing the parameters involved in the at the higher level of the distributed system can be performed by numerical simulation, i.e., analyzing control algorithm at the higher level of the distributed system can be performed by numerical the system performance in different situations related to the exogenous random variables. Choosing simulation, i.e., analyzing the system performance in different situations related to the exogenous the “proper” parameters based on this analysis should take into account in particular the summer random variables. Choosing the “proper” parameters based on this analysis should take into and winter regimes in the operation of the renewable energy sources. When using Equation (12) one account in particular the summer and winter regimes in the operation of the renewable energy must take into account the different nature of the two sub-criteria (a normalization of the sub-criteria sources. When using Equation (12) one must take into account the different nature of the two being necessary) and also the appropriate choice of the weighting factor, γ. If in the considered sub-criteria (a normalization of the sub-criteria being necessary) and also the appropriate choice of interval [0 T] there is a surplus of energy from the renewable sources in relation to the load, the first the weighting factor,  . If in the considered interval [0 T] there is a surplus of energy from the term in the Equation (12) results negative. In general, both the overall assessment of Equation (12), renewable sources in relation to the load, the first term in the Equation (12) results negative. In which is intended to be as low as possible, and the evaluation of each distinct term within this criterion general, both the overall assessment of Equation (12), which is intended to be as low as possible, and are useful. the evaluation of each distinct term within this criterion are useful. 3. Results and Discussion 3. Results and Discussion 3.1. The Multi-Criteria Performance Indicator Evaluation 3.1. The Multi-Criteria Performance Indicator Evaluation The objective of this subsection is to illustrate the energy flows from the considered distributed The objective of this is to illustrate the energy flows from the distributed system and, especially, to subsection make a comparative analysis of the performances ofconsidered the two implemented system and, especially, to make a comparative analysis of the performances of the two implemented variants of the control algorithm at the higher level. To enable the comparative analysis of the two variants the same powers generated by the solar and wind sources, and the same power consumed in the local network were used. Out of the multitude of possible situations regarding the renewable energy sources and the power consumption in the local network, the case considered was the total


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variants of the control algorithm at the higher level. To enable the comparative analysis of the two variants the same powers generated by the solar and wind sources, and the same power consumed in the local network were used. Out of the multitude of possible situations regarding the renewable energy sources and the power consumption in the local network, the case considered was the total energy generated by the renewable sources is larger than the energy consumed by the load during the Sustainability 748 15 of 22 adopted 2016, time 8,interval of a day (i.e., T = 86,400 s). A preliminary testing of the fuzzy controller that implements this variant of the control algorithm Sustainability 2016, 8, 15 of 22 Section 2. Figure 11748 shows the voltage, varies in the of in 48.5 V, value imposed was performed considering thebattery renewable energywhich sources and the loadvicinity described Section 2. Figure 11 byshows the fuzzification of the input V.varies The command variable generated by the fuzzy is given the battery voltage, which in the vicinity of 48.5 V, value imposed by thecontroller fuzzification of Section 2. Figure 11 shows the battery voltage, which varies in the vicinity of 48.5 V, value imposed in the Figure 12, the bluevariable color represents power distributed system input V.where The command generated the by the fuzzytransferred controller isfrom giventhe in Figure 12, where the to by the fuzzification of the input V. The command variable generated by the fuzzy controller is given theblue grid, andrepresents the red color showstransferred the transferred from thesystem grid to One color the power from power the distributed tothe thedistributed grid, and thesystem. red color in Figure 12, where the blue color represents the power transferred from the distributed system to canshows noticethe that there is always an energy transfer thesystem. grid and distributed in is one transferred power from the grid to the between distributed One can noticesystem, that there the grid, and the red color shows the transferred power from the grid to the distributed system. One always an energy transfer between the grid and distributed system, in one way or the other. way or the other. can notice that there is always an energy transfer between the grid and distributed system, in one way or the other.

Figure voltage. Figure 11. 11. The The battery battery voltage. Figure 11. The battery voltage.

Figure The commandvariable: variable:power powertransferred transferred from (red). Figure 12.12. The command from the the grid grid(blue) (blue)and andtotothe thegrid grid (red). Figure 12. The command variable: power transferred from the grid (blue) and to the grid (red).

first case(Variant (Variant1)1)ofofthe thecontrol control algorithm, algorithm, the byby thethe In In thethe first case the evolution evolutionofofthe thepower powerreceived received system,P Pwe  PPV  Pgs , the power transferred to the load and to the grid, Pl  Psg , and the power system, we  PPV  Pgs , the power transferred to the load and to the grid, Pl  Psg , and the power deficit/surplusare arepresented presentedininFigure Figure 13. 13. In In Figure Figure 14, deficit/surplus 14, in in correlation correlationwith withFigure Figure13, 13,it itcan canbebe noticed that there occurs a high number of charge/discharge switches for the battery. This is caused noticed that there occurs a high number of charge/discharge switches for the battery. This is caused mainly by the turbulence fluctuations of the wind speed. The evolution of the energy consumed mainly by the turbulence fluctuations of the wind speed. The evolution of the energy consumed from the grid, transferred to the grid, and the energy bills are given in Figure 15. For the evaluation from the grid, transferred to the grid, and the energy bills are given in Figure 15. For the evaluation of the multi-criteria performance indicator, given by Equation (12), it was necessary to use the  of the multi-criteria performance indicator, given by Equation (12), it was necessary to use the  factor that weights the two terms of the performance criteria in order to have the same scale for the factor that weights the two terms of the performance criteria in order to have the same scale for the two factors (energy sub-criterion relative to lifetime of the battery). The negative value of the


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In the first case (Variant 1) of the control algorithm, the evolution of the power received by the system, Pwe ` PPV ` Pgs , the power transferred to the load and to the grid, Pl ` Psg , and the power deficit/surplus are presented in Figure 13. In Figure 14, in correlation with Figure 13, it can be noticed that there occurs a high number of charge/discharge switches for the battery. This is caused mainly by the turbulence fluctuations of the wind speed. The evolution of the energy consumed from the grid, transferred to the grid, and the energy bills are given in Figure 15. For the evaluation of the multi-criteria performance indicator, given by Equation (12), it was necessary to use the γ factor that weights the two terms of the performance criteria in order to have the same scale for the two factors (energy sub-criterion relative to lifetime of the battery). The negative value of the sub-criterion energy (the same for the energy bills) shows that the energy transferred to the grid is greater than the one consumed from the grid. For the performance analysis of the distributed system, the two sub-criterions are shown in Figure Sustainability 2016, 8, 748 16, instead of the sum of the two terms (which should be as low as possible). 16 of 22 Sustainability 2016, 8, 748

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Figure 13. Evolution Evolution of the the power produced produced by the the renewable sources sources + power from the grid grid (blue); (blue); Figure power from from the the Figure 13. 13. Evolution of of the power power produced by by the renewable renewable sources + + power grid (blue); power consumed by by load ++ power power transferred to to the grid grid (red); power power deficit/surplus (green). power (green). power consumed consumed by load load + power transferred transferred to the the grid (red); (red); power deficit/surplus deficit/surplus (green). 1 1 0.5 0.5 0 0 -0.5 -0.5 -1 -1 0 0

1 1

2 2

3 3

4 5 4time [s]5 time [s]

6 6

7 7

Figure 14. Commutation discharge/charge. Figure 14. Commutation discharge/charge. Figure 14. Commutation discharge/charge.

8 8

9 9 4 x 104 x 10

-0.5 -1 0

1

2

3

4 5 time [s]

6

7


8

9 4

x 10

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Figure 14. Commutation discharge/charge.

Figure 15. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and Figure 15. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and energy bills (green). (green). energy bills


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Figure 16. 16. Evolution Evolution of of sub-criterions: sub-criterions: energy energy (blue) (blue) and and battery battery lifetime lifetime (red). (red). Figure

The results obtained showed that the adopted structure of the fuzzy controller has one The results obtained showed that the adopted structure of the fuzzy controller has one disadvantage, disadvantage, namely it does not allow obtaining the regime in which the charge and discharge namely it does not allow obtaining the regime in which the charge and discharge cycles take place, cycles take place, during the normal operation of the distributed system. To ensure the operation of during the normal operation of the distributed system. To ensure the operation of the distributed the distributed system with fuzzy controller both in a buffer regime and in charge–discharge cycles system with fuzzy controller both in a buffer regime and in charge–discharge cycles the controller in the controller in Variant 2 was used. Variant 2 was used. The performances of the control algorithm when the setpoint is set at 48.5 V are similar to those The performances of the control algorithm when the setpoint is set at 48.5 V are similar to those illustrated in Figures 11 and 12. Although the battery works most of the time in the “buffer” regime, illustrated in Figures 11 and 12. Although the battery works most of the time in the “buffer” regime, it is often recommended for the system to work, even for short time periods, in a charging– it is often recommended for the system to work, even for short time periods, in a charging–discharging discharging regime. When the battery voltage controller setpoint is constant, the performances of regime. When the battery voltage controller setpoint is constant, the performances of Variant 2 control Variant 2 control algorithm are similar to those of the previous case. For the regime that ensures a algorithm are similar to those of the previous case. For the regime that ensures a periodic charging and periodic charging and discharging of the battery while normally supplying the local network, the discharging of the battery while normally supplying the local network, the performance indicators are performance indicators are now given in Figures 17 and 18. In this case, the transferred powers in now given in Figures 17 and 18. In this case, the transferred powers in one direction or the other in the one direction or the other in the charging–discharging regimes are much higher than those from the charging–discharging regimes are much higher than those from the renewable sources powers and renewable sources powers and of the load. Obviously, taking into account the efficiency of the of the load. Obviously, taking into account the efficiency of the transfer circuits, the intense energy transfer circuits, the intense energy transfer is accompanied by significant losses in the system. transfer is accompanied by significant losses in the system. Instead, the charge–discharge switches Instead, the charge–discharge switches are rarely influenced by the evolution of the renewable are rarely influenced by the evolution of the renewable sources powers or by the load. Most often, sources powers or by the load. Most often, these switches are virtually equal to those imposed these switches are virtually equal to those imposed through the voltage loop setpoint. Consequently, through the voltage loop setpoint. Consequently, the evolution of the two sub-criterions, shown in Figure 18, indicates a very low energy performance and a good performance in terms of the battery regime. We must mention that this regime is for a short period of time and it is part of the maintenance program of the battery.

performance indicators are now given in Figures 17 and 18. In this case, the transferred powers in one direction or the other in the charging–discharging regimes are much higher than those from the renewable sources powers and of the load. Obviously, taking into account the efficiency of the transfer circuits, the intense energy transfer is accompanied by significant losses in the system. Instead, the charge–discharge switches are rarely influenced by the evolution of the renewable Sustainability 2016, 8, 748 18 of 23 sources powers or by the load. Most often, these switches are virtually equal to those imposed through the voltage loop setpoint. Consequently, the evolution of the two sub-criterions, shown in Figure 18, indicates a very low energy performance and18, a good performance in energy terms ofperformance the battery the evolution of the two sub-criterions, shown in Figure indicates a very low regime. Weperformance must mention that of this is for aWe short period of that timethis and it is ispart the and a good in terms theregime battery regime. must mention regime for aofshort maintenance program of the battery. period of time and it is part of the maintenance program of the battery.

Figure 17. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and Figure 17. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and energy bills (green). energy bills2016, (green). Sustainability 8, 748 18 of 22

Figure 18. Evolution of sub-criterions: energy (blue) and battery lifetime (red).

Figure 18. Evolution of sub-criterions: energy (blue) and battery lifetime (red).

3.2. An Improved Intelligent Control Algorithm for the Distributed Energy System

3.2. An Improved Intelligent Control Algorithm for the Distributed Energy System

The fuzzy controllers from Variant 1 and Variant 2 are constantly generating non-zero The fuzzy controllers from Variant and Variant 2 are the constantly non-zero commands commands to transfer energy in either1 direction between grid andgenerating the distributed system. The permanent variations of the controller command have and the effect of maintaining, with The reasonable to transfer energy in either direction between the grid the distributed system. permanent precision, the controller battery voltage around have the setpoint. However, in reality, this not variations of the command the effect of maintaining, withperformance reasonableisprecision, necessarily required. The battery voltage can fluctuate within a range of width ε, which can the battery voltage around the setpoint. However, in reality, this performance is not necessarily correspond to the linguistic value for “battery charged”, as it is in the recommendations for ensuring required. The battery voltage can fluctuate within a range of width ε, which can correspond to the a long lifetime of the battery. Instead, the parameter ε greatly influences the number of linguistic value for “battery charged”, as it is in the recommendations for ensuring a long lifetime of charge/discharge switches, NTε , which appears in the performance criterion given by Equation (12). ε

the battery. Instead, the parameter ε greatly influences the number of charge/discharge switches, NT , In these conditions it is useful to have a dead zone in the static characteristic of the controller, which which appears in the performance criterion given by Equation (12). In these conditions it is useful ensures the battery voltage fluctuates in a predetermined area. An improved variant of the controller to have a dead zone in basis. the static characteristic of the controller, which ensures the battery voltage is established on this fluctuatesVariant in a predetermined area. Anuses improved of the on this 3 of the control algorithms a specialvariant controller withcontroller dead zone,isofestablished a tri-positional typebasis. Variant 3 of the control algorithms uses a special controller with dead zone, of a tri-positional block implemented by fuzzy techniques. Unlike the tri-positional controller the command from type the dead zone, techniques. either positive or negative, is proportional to the the command control error. blockoutside implemented by fuzzy Unlike the tri-positional controller fromLet outside D   p

p  be the dead zone imposed on the variation domain of control error ε. The control

algorithm performed by the controller can be summarized as:

0 if ε(t )  D u (t )    K  ε(t )  sign  ε(t )  if ε(t )  D

(13)

a long lifetime of the battery. Instead, the parameter ε greatly influences the number of charge/discharge switches, NTε , which appears in the performance criterion given by Equation (12). In these conditions it is useful to have a dead zone in the static characteristic of the controller, which ensures the battery voltage fluctuates in a predetermined area. An improved variant of the controller Sustainability 2016, 8,on 748 19 of 23 is established this basis. Variant 3 of the control algorithms uses a special controller with dead zone, of a tri-positional type ” ı block implemented by fuzzy techniques. Unlike the tri-positional controller the command from theoutside dead zone, either zone, positive or negative, the control error. D “ error. ´p pLet be the dead either positive isorproportional negative, istoproportional to theLetcontrol

theDdead on thezone variation domain of control error ε. Theofcontrol performed be the dead imposed on the variation domain controlalgorithm error ε. The control by    pzone p imposed thealgorithm controllerperformed can be summarized as: by the controller can be summarized as: # 0if ε ptq D 0 if ε(t )PD uptq “ u (t )   (13)(13) K ¨K|ε ε( ptq| sign ε( pεt )ptqq t ) ¨ sign  if ε(iftε) ptqDR D  The schemeofofthe thecontroller controllerininthis thisvariant variant is given in operation with thethe The scheme in Figure Figure19. 19.The Thesystem system operation with parameters k1 2,  2K, =K1000 = 1000 and p =0.2, 0.2,when whenthe thesetpoint setpointisisconstant, constant,isisillustrated illustratedin inFigures Figures20 20 and and 21. parameters k1 “ and p= 21.noticeable It is noticeable that the energy transfer commanded the controller is much the of It is that the energy transfer commanded by thebycontroller is much lowerlower than than in theincase case of1 Variant 1 or2.Variant 2. Variant or Variant

Figure 19. Scheme of the controller in Variant 3 of the control algorithm.

Figure 19. Scheme of the controller in Variant 3 of the control algorithm. Sustainability 2016, 8, 748 Sustainability 2016, 8, 748

19 of 22 19 of 22

Figure 20. The battery voltage. Figure Figure 20. 20. The Thebattery battery voltage. voltage.

Figure 21. The command variable: power transferred from the grid (blue) and to the grid (red). Figure 21. The command variable: power transferred from the grid (blue) and to the grid (red). Figure 21. The command variable: power transferred from the grid (blue) and to the grid (red).

Variant 3 of the control algorithm leads to noticeably different results as compared to the Variant 3 of the control algorithm leads to noticeably different results as compared to the previous cases. The variables represented in Figures 13–16, have now the evolution given by Figures previous cases. The variables represented in Figures 13–16, have now the evolution given by Figures 22–25. One can see a very important reduction in the number of charge/discharge switches of the 22–25. One can see a very important reduction in the number of charge/discharge switches of the battery. When using the algorithm given by Equation (13), the energy sub-criterion has an evolution battery. When using the algorithm given by Equation (13), the energy sub-criterion has an evolution close to that of Variant 1, but the sub-criterion regarding the battery regime shows a considerable close to that of Variant 1, but the sub-criterion regarding the battery regime shows a considerable

Sustainability 2016, 8, 748 Figure 21. The command variable: power transferred from the grid (blue) and to the grid (red).

20 of 23

Variant 3 ofcontrol the control algorithm to noticeably different results as compared to previous the Variant 3 of the algorithm leadsleads to noticeably different results as compared to the cases. The variables represented in 13–16, Figureshave 13–16,now havethe nowevolution the evolution given Figures22–25. cases.previous The variables represented in Figures given byby Figures can see a very important reduction in the number of charge/discharge switches of the One 22–25. can seeOne a very important reduction in the number of charge/discharge switches of the battery. battery. When using the algorithm given by Equation (13), the energy sub-criterion has an evolution When using the algorithm given by Equation (13), the energy sub-criterion has an evolution close to close to that of Variant 1, but the sub-criterion regarding the battery regime shows a considerable that of Variant 1, but the sub-criterion regarding the battery regime shows a considerable improvement. improvement. One of the goals of the simulation based performance analysis is the choice of the One of the goals of the simulation analysis is the choice the p. controller parameter p. This is based chosenperformance within a predetermined domain [0 of pmax ], controller where pmaxparameter is the This tolerance is chosenofwithin a predetermined domain [0 p ], where p is the tolerance of the nominal max can be considered max the nominal voltage, for which the battery in the regime “charged voltage, for which the battery can be considered in the regime “charged battery”. battery”.


20 of 22

Sustainability 2016, 8, 748of the power produced by the renewable sources + power from the grid 20 of 22 Figure 22. Evolution (blue); Figure 22. Evolution of the power produced by the renewable sources + power from the grid (blue); power consumed by load + power transferred to the grid (red); and power deficit/surplus (green). power consumed by load + power transferred to the grid (red); and power deficit/surplus (green).

Figure 22. Evolution of the power produced by the renewable sources + power from the grid (blue); power consumed by load + power transferred to the grid (red); and power deficit/surplus (green). 1 1 0.5 0.5 0 0 -0.5 -0.5 -1 -10 0

1 1

2 2

3 3

4 5 time [s] 4 5 time [s]

6

7

8

9 4

6

7

Figure 23. Commutation discharge/charge.

8

x 10

9 4

x 10

Figure 23. Commutation discharge/charge. Figure 23. Commutation discharge/charge.

Figure 24. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and energy (green). of the consumed energy from the grid (blue), transferred to the grid (red) and Figure bills 24. Evolution Figure 24. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and energy bills (green).

energy bills (green).

Figure2016, 24. Evolution of the consumed energy from the grid (blue), transferred to the grid (red) and Sustainability 8, 748 21 of 23 energy bills (green).

Figure 25. Evolution of sub-criterions: energy (blue) and battery lifetime (red). Figure 25. Evolution of sub-criterions: energy (blue) and battery lifetime (red).

In the future we, intend to use the performance indicator given by Equation (12) as a criterion in In the future we,problem. intend to We use the indicator given by Equation as apaper criterion a predictive control willperformance also implement the proposed solution (12) in this onina a predictive control problem. We will also implement the proposed solution in this paper on a Hardware. In the Loop platform, the renewable energy simulators being replaced by hardware emulators. 4. Conclusions Firstly the paper describes the models used to simulate the distributed system components, thus allowing designing and evaluating different control solutions for the system considered. All the renewable energy sources and the load where modeled, and a performance criterion was considered. This criterion takes into account the two important factors that ensure the system sustainability: the cost of electricity supplied to local consumers, and the lifetime of the battery. In this paper, three variants for the algorithm to control the energy transfer in the system, implemented using fuzzy techniques, have been proposed. This is done in order to evaluate the distributed energy system behavior when different control algorithms are chosen. The first two variants use a deficit/surplus prediction of energy in the system, and the third variant imposes a dead zone at low values of the control error. It was shown that the three variants offer similar results regarding the cost of electricity supplied to local consumers when the setpoint is chosen to be constant. Variant 3 of the control algorithm offers the best results, thus increasing the system sustainability. This evaluation takes into account that although the energy sub-criterion has an evolution close to the one from the first two variants, the sub-criterion regarding the battery regime has a radical improvement. Although the battery works most of the time in a “buffer” regime, the maintenance program of the battery often recommends its operation, for short periods, in a charging–discharging regime in order to increase its lifetime. This option was implemented in Variants 2 and 3 of the control algorithm and the results obtained showed that the energy sub-criterion was not affected. Acknowledgments: This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-1761. Ramon Vilanova acknowledges the support by Spanish CICYT program under grant DPI2013-47825-C3-1-R. Author Contributions: Authors contributed equally to this paper. Conflicts of Interest: The authors declare no conflict of interest.


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