Method for Improving the Performance of the Energy Management in a Nearly Zero Energy Building

Abstract

An optimal energy management method and a system that implements the method for a nearly zero energy building (nZEB) based on the genetic algorithm technique that can provide an optimal balance between the objectives of energy saving, comfort of the building residents and maximum exploitation of the generated electric energy by the renewable energy sources through the proper utilization of a battery storage system, is developed in this invention. The above can be attained by minimizing a cost function that considers the real-time electricity price, the generated/consumed electric energy by each device, the user preferences, the state-of-charge and the energy price of the battery storage system (BSS), and the weather forecast. the system that implements the optimal energy management method comprises energy and temperature sensors, controllable power switches, a battery storage system and a controller with human machine interface. The outcomes of the energy management system are control signals that regulate the operation of the power switches and the inverter of the battery storage system.

Claims

1. A method for the optimal energy management of a nearly zero energy building (nZEB) that is based on the genetic algorithm technique and it can provide an optimal balance between the objectives of energy saving, comfort of the building residents and maximum exploitation of the generated electric energy by the wind turbines and photovoltaics through the proper utilization of a battery storage system (BSS), comprising the following steps that are referred to a time period of 24-hours ahead which is divided into N discrete time intervals: a) considering the residents' selection of the acceptable starting and ending time-slots of the programmable appliances (PAs) (denoted by a.sub.PA.sup.i and b.sub.PA.sup.i, respectively for each i appliance), the energy consumption vectors for the PAs are estimated, for N time-slots, (denoted by E.sub.PA), where PAs are electric loads that their operating time can be planned (such as, the electric cooker, the washing machine, dishwasher, ironing, vacuum cleaner, etc.), b) considering the residents' selection of the acceptable minimum and maximum indoor temperature of the nZEB (denoted by T.sub.in.sup.min and T.sub.in.sup.max, respectively), the energy consumption vectors of the controllable appliances (CAs) are estimated, for N time-slots, (denoted by E.sub.CA), where CAs are electric loads that their operation is regulated by the temperature (such as, the heat pump, the air-conditioner, etc.), c) for N time-slots, the energy consumption vectors of the uncontrollable appliances (UAs) is reported (denoted by E.sub.UA), by utilizing data obtained from energy meters, where UAs are electric loads that cannot be programmed and they are switched on/off either manually by the residents (such as, the personal computers, TV, security lighting, etc.) or automatically (such as, the lights regulated by a movement control system) and also, they are appliances that the residents do not have any control action (such as, the refrigerator, water cooler, etc.), d) for N time-slots, the energy production vectors of the wind turbines and the photovoltaics (denoted by E.sub.WT and E.sub.PV, respectively) are estimated considering meteorological data obtained by a weather forecast utility, and thus, the estimated total energy generated by the renewable energy sources (wind turbine and photovoltaics) is determined by E.sub.RES=E.sub.WT+E.sub.PV, e) for N time-slots, the energy vectors of the BSS for charging and discharging modes (denoted by E′.sub.BSS.sup.ch and E′.sub.BSS.sup.dis, respectively) are estimated, f) for N time-slots, the electric energy price vectors of buying and selling is constructed (denoted by EEP.sub.buy and EEP.sub.sell, respectively), by the estimated buying and selling prices, respectively, obtained by an electric energy utility, g) the values of the acceptable starting and ending time-slots of each i appliance (a.sub.PA.sup.i and b.sub.PA.sup.i, respectively), and the acceptable minimum and maximum inside temperature (T.sub.in.sup.min and T.sub.in.sup.max, respectively) provided by the residents in the aforementioned steps a) and b), and the energy vectors E.sub.WT, E.sub.PV, E.sub.PA, E.sub.CA, E.sub.UA, E.sub.BSS.sup.ch, E.sub.BSS.sup.dis, and EEP which are calculated in the aforementioned steps b) to f), are imported to a cost function and then, by its minimization through the genetic algorithm technique, are provided the optimal values, for the N time-slots ahead, of the: control vectors of the starting time-slots of each PA, the reference indoor temperature, and the charging or discharging operating modes of the BSS, and optimal value of a parameter denoted by x, that can take values 0 and 1, and it assures that the energy generated by the RES and stored in the BSS is equal or higher the amount of energy which has been provided to the appliances by the BSS (specifically, x is equal to 1 when the BSS is active and 0 when the BSS is inactive), h) the optimal values, that are calculated in step g), of the: control vectors of the starting time-slots of each PA, the reference indoor temperatures for the N time-slots and the charging or discharging operating modes of the BSS for the N time-slots are provided as input signals to a system that realizes the optimal energy management method, while, the control variable x is used as input variable at the optimization procedure of the next time sampling, that is realized in step g).

2. Method of the optimal energy management according to claim 1, wherein the genetic algorithm seeks the optimal starting time t.sub.PA.sup.i of each i-PA, within the N time-slots, considering the constraints that t.sub.PA.sup.i should be equal-or-higher than the acceptable starting time slot a.sub.PA.sup.i which is defined by the residents for each i-PA and also, equal-or-lower than the acceptable ending time slot b.sub.PA.sup.i which is defined by the residents for each i-PA, minus the duration of the i-PA operation denoted by LoO.sub.PA.sup.i (namely, a.sub.PA.sup.i≤t.sub.PA.sup.i≤b.sub.PA.sup.i−LoO.sub.PA.sup.i).

3. Method of the optimal energy management according to claim 1, wherein the genetic algorithm seeks the optimal reference indoor temperature T.sub.in.sup.ref for each of the N time-slots considering the constraint that T.sub.in.sup.ref should be equal-or-higher than the minimum indoor temperature T.sub.in.sup.min and equal-or-lower than the maximum indoor temperature T.sub.in.sup.max, which are defined by the residents (namely, T.sub.in.sup.min≤T.sub.in.sup.ref≤T.sub.in.sup.max).

4. Method of the optimal energy management according to claim 1, wherein the availability cost of a BSS, denoted by C.sub.b, is calculated by the ratio of the replacement cost, denoted by C.sub.rep, with respect to the total lifetime cycling energy capacity of the BSS, denoted by Q.sub.bt, (namely, C.sub.b=C.sub.rep/Q.sub.bt), where the total lifetime capacity is estimated by Q.sub.bt=Q.sub.br.Math.DoD[0.9L.sub.r−0.1] where DoD is the depth-of-discharge that is the maximum discharge with respect to the rated and L.sub.r is the rated lifetime of a battery obtained by the battery datasheet.

5. Method of the optimal energy management according to claim 1, wherein the objective for high comfort of the residents is determined by that the home appliances should complete their work as soon as possible and specifically, the residents' comfort is considered in the method by defining the delay time rate (DTR) for each i programmable appliance (PA) that is given by ${\mathrm{DTR}}_{\mathrm{PA}}^{\prime }=\frac{t_{PA}^i-a_{\mathrm{PA}}^i}{b_{PA}^i-\left({\mathrm{LoO}}_{PA}^i+a_{PA}^i\right)}$ and takes values between 0 and 1, where the value 0 means high residents' comfort with respect to the priority in satisfying their preferences, while the 1 means the lower acceptable comfort level and thus, the lower acceptable priority in satisfying the residents' preferences.

6. Method of the optimal energy management according to claim 1, wherein the residents comfort level degradation with respect to the total PAs of the nZEB (denoted by CLD.sub.PA) is calculated by $CL{D}_{PA}=\underset{i=1}{\overset{M}{.Math.}}{r}^{\left(DT{R}_{PA}^i\right)},$ where M is the total number of the PAs and r is an integer greater than 1 (r>1) that is decided by the fact that, the higher r the higher importance is given to the residents' comfort at the energy management.

7. Method of the optimal energy management according to claim 1, wherein the residents comfort level degradation with respect to the heating and cooling (denoted by CLD.sub.H/C), is calculated by $CL{D}_{H/C}=\{\begin{array}{cc}\underset{k=1}{\overset{N}{.Math.}}{r}^{\left(\frac{T_{\mathrm{in}}^{\mathrm{ref}}\left(k\right)-T_{\mathrm{in}}^{\max }}{T_{\mathrm{in}}^{\max }-T_{\mathrm{in}}^{\min }}\right)}& \mathrm{for}\mathrm{heating}\mathrm{mode}\\ \underset{k=1}{\overset{N}{.Math.}}{r}^{\left(\frac{T_{\mathrm{in}}^{\mathrm{ref}}\left(k\right)-T_{\mathrm{in}}^{\min }}{T_{\mathrm{in}}^{\max }-T_{\mathrm{in}}^{\min }}\right)}& \mathrm{for}\mathrm{cooling}\mathrm{mode}\end{array},$ for any sampling cycles k, (where 1≤k≤N).

8. Method of the optimal energy management according to claim 5, wherein the total comfort level degradation of the residents (denoted by CLD.sub.tot) is calculated by CLD.sub.tot=CLD.sub.PA+CLD.sub.H/C.

9. Method of the optimal energy management according to claim 1, wherein the optimization problem is solved through the minimization of the cost function J=w.sub.1CLD.sub.tot+w.sub.2[f.sub.1(E.sub.ep)+F.sub.2(E′.sub.BSS.sup.dis)] utilizing the genetic algorithm technique, by applying an iterative discrete calculation procedure for any sampling cycles k (where 1≤k≤N), where $F_1\left(E_{ep}\right)=\underset{k=1}{\overset{N}{.Math.}}\left[\lambda .Math.{\mathrm{EEP}}_{b\mathrm{.Math.}\mathrm{.Math.}y}\left(k\right)+\left(1-\lambda \right).Math.{\mathrm{EEP}}_{sell}\left(k\right)\right].Math.E_{ep}\left(k\right)$ $F_2\left(E_{BSS}^{\prime \mathrm{dis}}\right)=\underset{k=1}{\overset{N}{.Math.}}{C}_b{E}_{BSS}^{\prime \mathrm{dis}}\left(k\right)$ $E_{ep}=E_{RES}^T-\left(E{C}_{PA}^T+E{C}_{UA}^T+E_{CA}^T\right)-x\left(E_{BSS}^{{\prime }_{\mathrm{ch},T}}-E_{\mathrm{BSS}}^{\prime \mathrm{dis},T}\right)\mathrm{and}$ $\lambda =\{\begin{array}{cc}0& E_{ep}\left(k\right)\ge 0\\ 1& E_{ep}\left(k\right)<0\end{array}$ considering that the E.sub.RES.sup.T, EC.sub.PA.sup.T, E.sub.UA.sup.T, E.sub.CA.sup.T, E′.sub.BSS.sup.ch,T and E′.sub.BSS.sup.dis,T are the transpose of the vectors E.sub.RES, EC.sub.PA, EC.sub.UA, E.sub.CA, E′.sub.BSS.sup.ch and E′.sub.BSS.sup.dis respectively, and the EEP.sub.buy(k), EEP.sub.sell(k), E′.sub.BSS.sup.dis, and E.sub.ep(k) are the k.sub.th-values of the respective energy vectors.

10. Method of the optimal energy management according to claims 1 and 9 claim 1, wherein the parameters w.sub.1 and w.sub.2 of the cost function J are two weighted factors which represent the importance of the objectives of the comfort level and energy cost, respectively, and they provided by the residents according to their preferences, considering the constraints that w.sub.1+w.sub.2=1, 0≤w.sub.1≤1 and 0≤w.sub.2≤1.

11. System that implements the optimal energy management method of claim 1, wherein the system comprises: energy meters to measure, the consumed electric energy by the PAs and CAs, the stored or recovered electric energy in or from the BSS, respectively, the generated electric energy by the wind turbines and photovoltaics, and the electric energy that is absorbed or provided to the grid, temperature sensors to measure the indoor temperature of each room of the building, controllable power switches to regulate the operation of the PAs and CAs, according to claim optimal energy management method, inverter of the BSS that controls the charging and discharging operation of the batteries and it is regulated by control signals according to the optimal energy management method, controller configured to implement the optimal energy management method, with a human machine interface for the insertion, by the residents, of the acceptable starting and ending time-slots of the PAs, and the acceptable minimum and maximum inside indoor temperatures.

12. System according to claim 11 that implements the optimal energy management method of claim 1, wherein the controllable power switches are regulated by control signals of values 0 and 1 provided by the controller, and the charging or discharging mode of the BSS is regulated by the inverter of the BSS through a control signal provided by the controller.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] FIG. 2 shows examples of time slots.

[0017] FIG. 3 is a flow chart of the algorithm-based EMS of the present invention.

[0018] FIG. 4 illustrates the performance of the optimal EMS of the present invention.

[0019] FIG. 5 illustrates performance without the invention.

DETAILED DESCRIPTION

[0020] In FIG. 1, a typical schematic of the microgrid and the EMS of the present invention for a nZEB is illustrated. It consists of the main grid (1), energy meters (2), temperature sensors (15), RES (3), BSS (10), programmable appliances (12), controllable appliances (14), unschedulable appliances (16) and a controller that houses the energy management software and has the capability to obtain input data through a human machine interface (17), i.e. acceptable starting and ending time-slots of the programmable appliances (18), real time buying and selling electric energy prices (19) obtained by an electric energy provider utility, and weather forecast (20) obtained by a weather forecast utility. The RES comprises the PVs (4), the WTs (5) and the corresponding power converters to connect them with the grid i.e. the AC/DC and DC/AC converters (6) and (8), respectively, for the WT, and the DC/AC converter (7) for the PV. The BSS consists of the battery pack (11) and the DC/AC power inverter to connect the batteries with the grid (9). The programmable appliances (PAs) are electric loads that their operating time can be planned (such as, the electric cooker, the washing machine, dishwasher, ironing, vacuum cleaner, etc.) and controlled by a system of power switches (13). The controllable appliances (CAs) are electric loads that their operation is regulated by one or more variables (such as, the heat pump, the air-conditioner, etc. where control variable is the temperature). The unschedulable appliances (UAs) are electric loads that cannot be programmed and they are switched on/off either manually by the residents (such as, the personal computers, TV, security lighting, etc.) or automatically (such as, the lights regulated by a movement control system) and also, they are appliances that the residents do not have any control action (such as, the refrigerator, water cooler, etc.).

[0021] The concept of the present invention that can attain an appropriate balance between the nZEB performance and the comfort of the residents is based on the following operations: [0022] 1) time scheduling of the operation of each PA, [0023] 2) proper regulation of the operation of each CA, so as the value of the reference variable is within the upper and lower limits set by the residents, and [0024] 3) decision for the proper operating mode (i.e. charging or discharging) and the level of the current of the BSS.

[0025] The above are realized by: [0026] i) constructing a prediction plan for the estimated energy demand by the loads, the energy that can be stored and recovered by the BSS, and the expected generated energy by the RES, [0027] ii) properly controlling the operation of the PAs, CAs and BSS through the energy management method by considering: [0028] the consumed or generated or stored electric energy at several devices of the nZEB microgrid (i.e. PAs, CAs, UAs, RES, ad BSS), as well as the absorbed or provided energy to the grid, and the SoC of the BSS, and [0029] the real time electricity price, the residents' preferences for the acceptable starting and ending time of the PAs and acceptable minimum and maximum indoor temperature, and the weather forecast.

[0030] The EMS of the present invention is implemented by employing the GAT where the daily operation of each appliance is divided into N discrete time intervals, as shown in FIG. 2. The solution of a genetic algorithm is represented in binary mode as strings of 0/1, where each time-slot k denotes a time interval Δt.sub.k that the energy sources and appliances activation or deactivation is represented by the binary 1 or 0, respectively. This means that, at every Δt.sub.k, the EMS is informed for the new electricity price and can take action on scheduling and controlling the operation of the nZEB's devices. The selection of the sampling rate Δt.sub.k is based on the desired accuracy, the computational capability of the controller and the frequency regime of modifying the electricity price by the energy provider. Due to the discrete control in the energy management procedure, the length of the operation of an appliance or an energy source, as that is considered by the EMS, is a rounded integer multiple of the predefined time interval and thus, equal or slightly greater than the actual length of the operation.

[0031] The optimal operation of the EMS is accomplished with the following five control sectors.

[0032] a) The output power of the wind generator is calculated by the following formula:

[00001]$\begin{array}{cc}{P}_{\mathrm{WT}}=\{\begin{array}{cc}a.Math.u^3-b.Math.P_N& u_{\mathrm{ci}}<u<u_N\\ P_N& u_N\le u\le u_{\mathrm{co}}\end{array}& \left(1\right)\end{array}$

[0033] where u is the wind speed,

[00002]$\begin{array}{cc}a=\frac{P_N}{u_N^3-u_{\mathrm{ci}}^3}\mathrm{\kappa \alpha .Math.}b=\frac{u_{\mathrm{ci}}^3}{u_N^3-u_{\mathrm{ci}}^3}& \left(2\right)\end{array}$

[0034] u.sub.ci, u.sub.co and u.sub.N are the cut-in, the cut-out and the nominal wind speeds, respectively, and P.sub.N is the rated power of wind turbine. Thus, for each sampling cycle k that has time duration Δt.sub.k, the generated electric energy is given by

e.sub.WT(k)=∫.sub.0.sup.Δt.sup.kP.sub.WTdt  (3)

[0035] and the energy generation vector for the N time-slots is

E.sub.WT=[e.sub.WT(1)e.sub.WT(2) . . . e.sub.WT(N)]  (4)

[0036] In a similar way, by having as inputs the irradiance level R.sub.irr and the average temperature of the cells T.sub.cell.sup.AV that are estimated by the weather forecast, the output power of a PV system for each sampling cycle k is given by

e.sub.PV(k)=∫.sub.0.sup.Δt.sup.kP.sub.PVdt  (5)

where

[00003]$\begin{array}{cc}{P}_{PV}=N_{PV}\left\{P_{{\mathrm{PV}}_{\max }}\frac{R_{\mathrm{irr}}}{1000}\left[1-a_T\left(T_{cell}^{AV}-25\right)\right]\right\}& \left(6\right)\end{array}$

[0037] and N.sub.pv is the number of PV modules, P.sub.PVmax is the peak output power of a PV module and a.sub.T is the temperature effect coefficient. The predicted generated electric energy by a PV system for each sampling cycle k is given by

E.sub.PV=[e.sub.PV(1)e.sub.PV(2) . . . e.sub.PV(N)]  (7)

[0038] Thus, by using the eq. (4) and (7), the total energy production vector by the RES is

E.sub.RES=E.sub.WT+E.sub.PV  (8)

[0039] b) The energy consumption vector N×M for the appliances of the building is:

[00004]$\begin{array}{cc}{E}_A=\left[\begin{array}{cccc}{e}_A^1\left(1\right)& e_A^1\left(2\right)& \mathrm{.Math.}& e_A^1\left(N\right)\\ e_A^2\left(1\right)& e_A^2\left(2\right)& \mathrm{.Math.}& e_A^2\left(N\right)\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ e_A^M\left(1\right)& e_A^M\left(2\right)& \mathrm{.Math.}& e_A^M\left(N\right)\end{array}\right]& \left(9\right)\end{array}$

[0040] where, in any e.sub.A.sup.i(k) of the above vector, k is the number of the sampling cycle that each one has time duration Δt.sub.k and i is the number of the appliance A, where A={PA, CA, UA}. The N is the number of time-slots per day and M is the maximum number of the appliances in the above three types.

[0041] For each i PA, additionally to the energy consumption e.sub.PA.sup.i, three parameters are introduced that their values are provided by the residents, i.e, the a.sub.PA.sup.i and b.sub.PA.sup.i that denote the acceptable starting and ending time-slot, and the LoO.sub.PA.sup.i that represents the duration of the operation of the i PA.

[0042] In order to improve the performance of the nZEB, the genetic algorithm seeks the optimal starting time t.sub.PA.sup.i of each i PA with the following constraint

t.sub.PA.sup.i∈[a.sub.PA.sup.i(b.sub.PA.sup.i−LoO.sub.PA.sup.i)]  (10)

[0043] and defines the optimal operation starting time vector for the PAs

t.sub.PA=[t.sub.PA.sup.1t.sub.PA.sup.2 . . . t.sub.PA.sup.M]  (11)

[0044] The optimal operating starting time matrix for the PAs is

[00005]$\begin{array}{cc}{T}_{PA}=\left[\begin{array}{cccc}{t}_{PA}^{\prime 1}\left(1\right)& t_{PA}^{\prime 1}\left(2\right)& \mathrm{.Math.}& t_{PA}^{\prime 1}\left(N\right)\\ t_{PA}^{\prime 2}\left(1\right)& t_{PA}^{\prime 2}\left(2\right)& \mathrm{.Math.}& t_{PA}^{\prime 2}\left(N\right)\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ t_{PA}^{\prime M}\left(1\right)& t_{PA}^{\prime M}\left(2\right)& \mathrm{.Math.}& t_{PA}^{\prime M}\left(N\right)\end{array}\right]& \left(12\right)\\ t_{PA}^{\prime i}\left(k\right)=\{\begin{array}{cc}1& k\in \left[t_{\mathrm{PA}}^i{t}_{\mathrm{PA}}^i+{\mathrm{LoO}}_{\mathrm{PA}}^i\right)\\ 0& k.Math.\left[t_{\mathrm{PA}}^i{t}_{\mathrm{PA}}^i+{\mathrm{LoO}}_{\mathrm{PA}}^i\right)\end{array}\forall i\in \left[1M\right],k\in \left[1N\right]& \left(13\right)\end{array}$

[0045] The energy consumption matrix by the PAs is

[00006]$\begin{array}{cc}{E}_{PA}=\left[\begin{array}{cccc}{e}_{PA}^1\left(1\right)t_{PA}^{\prime 1}\left(1\right)& e_{PA}^1\left(2\right)t_{PA}^{\prime 1}\left(2\right)& \mathrm{.Math.}& e_{PA}^1\left(N\right)t_{PA}^{\prime 1}\left(N\right)\\ e_{PA}^2\left(1\right)t_{PA}^{\prime 2}\left(1\right)& e_{PA}^2\left(2\right)t_{PA}^{\prime 2}\left(2\right)& \mathrm{.Math.}& e_{PA}^2\left(N\right)t_{PA}^{\prime 2}\left(N\right)\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ e_{PA}^M\left(1\right)t_{PA}^{\prime M}\left(1\right)& e_{PA}^M\left(2\right)t_{PA}^{\prime M}\left(2\right)& \mathrm{.Math.}& e_{PA}^M\left(N\right)t_{PA}^{\prime M}\left(N\right)\end{array}\right]& \left(14\right)\end{array}$

[0046] and thus, the total energy consumption by the PAs is given by

[00007]$\begin{array}{cc}E{C}_{PA}=\underset{i=1}{\overset{M}{.Math.}}{e}_{PA}^i\left(k\right)t_{PA}^{\prime i}\left(k\right)=\left[e{c}_{PA}^{1}e{c}_{PA}^2\mathrm{.Math.}{\mathrm{ec}}_{PA}^N\right]\forall k\in \left[1,N\right]& \left(15\right)\end{array}$

[0047] Finally, the energy consumption of the UAs can be calculated in a week basis by

[00008]$\begin{array}{cc}E{C}_{UA}=\underset{i=1}{\overset{M}{.Math.}}{e}_{UA}^i\left(k\right)=\left[e{c}_{UA}^{1}e{c}_{UA}^2\mathrm{.Math.}{\mathrm{ec}}_{UA}^N\right]\forall k\in \left[1,N\right]& \left(16\right)\end{array}$

[0048] c) One of the goals of the EMS is to manipulate the energy generated by the RES and to decide if it is beneficial to be consumed by the appliances of the building, stored in the batteries or sold to the energy provider. The energy battery storage system vector for the charging and discharging modes of the BSS, respectively, for the N time-slots, are

E.sub.BSS.sup.ch=[e.sub.BSS.sup.ch(1)e.sub.BSS.sup.ch(2) . . . e.sub.BSS.sup.ch(N)]  (17)

E.sub.BSS.sup.dis=[e.sub.BSS.sup.dis(1)e.sub.BSS.sup.dis(2) . . . e.sub.BSS.sup.dis(N)]  (18)

[0049] In addition, the genetic algorithm defines the optimal operating time vectors for the charging and discharging modes of the BSS, respectively, as

T.sub.ch=[t.sub.ch(1)t.sub.ch(2) . . . t.sub.ch(N)]  (19)

T.sub.dis=[t.sub.dis(1)t.sub.dis(2) . . . t.sub.dis(N)]  (20)

[0050] where the t.sub.ch(k) and the t.sub.dis(k) denote if the BSS is in the charging and discharging modes, respectively, and they can take values of 1 or 0 if the BSS is in operation or not, respectively.

[0051] Thus, considering the eq. (17)-(20), the final energy battery storage system vectors for the charging and discharging modes of the BSS, respectively, for the N time-slots, are

E′.sub.BSS.sup.ch=[e.sub.BSS.sup.ch(1)t.sub.ch(1)e.sub.BSS.sup.ch(2)t.sub.ch(2) . . . e.sub.BSS.sup.ch(N)t.sub.ch(N)]  (21)

E′.sub.BSS.sup.dis=[e.sub.BSS.sup.dis(1)t.sub.dis(1)e.sub.BSS.sup.dis(2)t.sub.dis(2) . . . e.sub.BSS.sup.dis(N)t.sub.dis(N)]  (22)

[0052] Since the batteries are charged by the RES, the main cost is the availability cost C.sub.b that is defined as the replacement cost C.sub.rep with respect to the total lifetime cycling energy capacity of the battery Q.sub.bt and it is calculated by

[00009]$\begin{array}{cc}{C}_b=\frac{C_{rep}}{Q_{\mathrm{bt}}}& \left(23\right)\end{array}$

[0053] The total lifetime capacity is estimated by Q.sub.bt=Q.sub.br.Math.DoD [0.9L.sub.r−−0.1], where DoD is the depth-of-discharge that is the maximum discharge with respect to the rated and L.sub.r is the rated lifetime of a battery obtained by the battery datasheet.

[0054] d) The objective for high comfort of the residents is determined by the approach that the home appliances should complete their work as soon as possible. This means that, for any i PA, it is aimed to reduce the delay between the starting time that is preferred by the residents and is expressed by the a.sub.PA.sup.i and the starting time t.sub.PA.sup.i that has been programmed by the control algorithm of the EMS.

[0055] Thus, a variable which can be used to consider the residents' comfort is the delay time rate (DTR), that for each i PA is defined by the following formula

[00010]$\begin{array}{cc}{\mathrm{DTR}}_{PA}^i=\frac{t_{PA}^i-a_{\mathrm{PA}}^i}{b_{PA}^i-\left({\mathrm{LoO}}_{PA}^i+a_{PA}^i\right)}& \left(24\right)\end{array}$

[0056] The DTR takes values between 0 and 1 and specifically, the value 0 means high residents' comfort with respect to the priority in satisfying their preferences, while the 1 means the lower acceptable comfort level and thus, the lower acceptable priority in satisfying the residents' preferences.

[0057] Based on the above, the residents' comfort level degradation (CLD) is introduced that is determined by the expression

[00011]$\begin{array}{cc}CL{D}_{PA}=\underset{i=1}{\overset{M}{.Math.}}{r}^{\left({\mathrm{DTR}}_{PA}^i\right)}& \left(25\right)\end{array}$

[0058] where the r can be any integer greater than 1 (r>1). The above parameter is used to consider the residents' comfort level in the cost function of the EMS optimization problem.

[0059] Another parameter that affects the residents' comfort is the proper heating/cooling of the building premises with respect to their preferences. The residents are allowed to determine the acceptable temperature range of the building indoor temperature T.sub.in.sup.min≤T.sub.in≤T.sub.in.sup.max and the EMS controls the reference temperature T.sub.in.sup.ref in order to both improve the performance of the nZEB and reduce the residents' CLD with respect to heating/cooling. For any sampling cycles k, the latter is defined as

[00012]$\begin{array}{cc}CL{D}_{H/C}=\{\begin{array}{cc}\underset{i=1}{\overset{N}{.Math.}}{r}^{\left(\frac{T_{\mathrm{in}}^{\mathrm{ref}}\left(k\right)-T_{\mathrm{in}}^{\max }}{T_{\mathrm{in}}^{\max }-T_{\mathrm{in}}^{\min }}\right)}& \mathrm{for}\mathrm{heating}\\ \underset{i=1}{\overset{N}{.Math.}}{r}^{\left(\frac{T_{\mathrm{in}}^{\mathrm{ref}}\left(k\right)-T_{\mathrm{in}}^{\min }}{T_{\mathrm{in}}^{\max }-T_{\mathrm{in}}^{\min }}\right)}& \mathrm{for}\mathrm{cooling}\end{array}& \left(26\right)\end{array}$

[0060] Thus, from eqs. (25) and (26), the total comfort level degradation is

CLD.sub.tot=CLD.sub.PA+CLD.sub.H/C  (27)

[0061] Therefore, the regulation of the reference indoor temperature affects the electric energy consumption of the heat pump and thus the energy consumption vector for the heating/cooling system is

E.sub.CA=E.sub.H/C=[e.sub.H/C(1)e.sub.H/C(2) . . . e.sub.H/C(N)]  (28)

[0062] where e.sub.H/C(k) is the electric energy consumption by the heating/cooling system, for each sampling step k.

[0063] e) The buying and selling electric energy price vectors are defined, respectively, by

EEP.sub.buy=[EEP.sub.buy(1)EEP.sub.buy(2) . . . EEP.sub.buy(N)]  (29)

EEP.sub.sell=[EEP.sub.sell(1)EEP.sub.sell(2) . . . EEP.sub.sell(N)]  (30)

[0064] where EEP.sub.buy(k) and EEP.sub.sell(k) are the buying and selling electric energy price, respectively, for any k sampling cycle (1≤k≤N).

[0065] By using the eqs. (1)-(29), the optimization problem that involves the energy generation, consumption and storage options, can be solved by minimizing the following cost/fitness function

[00013]$\begin{array}{cc}J=w_{1}CL{D}_{tot}+w_2\left[F_1\left(E_{ep}\right)+F_2\left(E_{BSS}^{\prime \mathrm{dis}}\right)\right]\mathrm{where}& \left(31\right)\\ F_1\left(E_{ep}\right)=\underset{k=1}{\overset{N}{.Math.}}\left[\lambda .Math.{\mathrm{EEP}}_{b\mathrm{.Math.}\mathrm{.Math.}y}\left(k\right)+\left(1-\lambda \right).Math.{\mathrm{EEP}}_{sell}\left(k\right)\right].Math.E_{ep}\left(k\right)& \left(32\right)\\ F_2\left(E_{BSS}^{\prime \mathrm{dis}}\right)=\underset{k=1}{\overset{N}{.Math.}}{C}_b{E}_{BSS}^{\prime \mathrm{dis}}\left(k\right)& \left(33\right)\\ E_{ep}=E_{RES}^T-\left(E{C}_{PA}^T+E{C}_{UA}^T+E_{CA}^T\right)-x\left(E_{BSS}^{{\prime }_{\mathrm{ch},T}}-E_{\mathrm{BSS}}^{\prime \mathrm{dis},T}\right)& \left(34\right)\\ \lambda =\{\begin{array}{cc}0& E_{ep}\left(k\right)\ge 0\\ 1& E_{ep}\left(k\right)<0\end{array}& \left(35\right)\end{array}$

[0066] The parameters w.sub.1 and w.sub.2 are the weighting factors that represent the importance of the objectives of the comfort level and energy cost respectively (w.sub.1+w.sub.2=1, where 0≤w.sub.1≤1 and 0≤w.sub.2≤1).

[0067] The parameter x takes values 0 and 1, and it is used to assure in the eq. (34) that the energy which has been generated by the RES and stored in the BSS is equal or higher the amount of energy which has been provided to the appliances by the BSS. The x is equal to 1 when the BSS is active and 0 when it is inactive. This constraint is imposed by the fact that, the BSS should operate as uninterruptible power supply (UPS) in case of electric power outage and the RES could not provide the required amount of electric energy to the appliances.

[0068] The optimal starting time t.sub.PA of the PAs as defined by the eq. (11) and the reference indoor temperature of the building T.sub.in.sup.ref considering the residents' comfort level as defined by the eq. (27), as well as the optimal time vectors T.sub.ch and T.sub.dis for the charging and discharging operation of the battery storage system are determined by the EMS that is realized by utilizing the GAT.

[0069] The flow chart of the genetic algorithm-based EMS of the present invention is illustrated in FIG. 3. The genetic algorithm is initiated by creating a certain number of random “chromosomes” which are sets of possible solutions of the optimization problem [initial population, step (21)]. Then, the RES energy vector is calculated [step (22)], by considering the weather forecasting data (23) and data from energy meters (24). Then, the buying and selling electric energy price vectors are calculated [step (25)], by the predicted electric energy prices (26). The outcomes of the above steps are utilized to calculate the energy demand by the PAs, CAs, and UAs [step (27)], considering data with respect to the residents' preferences (28) and data obtained from sensors (29). Then, the energy vectors of the BSS are calculated [step (30)], considering data obtained from the inverter of the BSS (31). The outcomes of the above steps are imported to a cost/fitness function [step (32)] and the genetic algorithm evaluates the exported fitness values [step (33)]. Then, the best chromosomes are selected and via crossover and mutation, the new solutions are created that include both old and new sets of solutions. Finally, the genetic algorithm evaluates if the expected generation number has been satisfied or not [step (34)] and thus, new sets of solutions are provided as the new generation or the GAT converges to the final solution, by following an iterative procedure that includes the steps (27) to (34). When, the GAT converges and the best solution for the cost function is attained [step (35)], control signals of ON/OFF (digital signals of 1 and 0) are provided to power switches to regulate the operation of PAs and CAs, and control signal to the inverter of the BSS to regulate the operation of the battery (charging or discharging modes).

[0070] FIG. 4 illustrates the performance of the optimal EMS of the present invention, in a nZEB over a 24-hours period, and is compared with the case that the electric loads are operated according to the residents' selection without applying an energy management method. As can be seen, lower electric energy is absorbed from the grid in FIG. 4 compared to FIG. 5, due to the proper scheduling of the electric loads that considers the residents' preferences. Specifically, 2.7 kWh is absorbed by the grid, in the examined day, with the optimal EMS of FIG. 4, compared to the 9.8 kWh that is absorbed by the grid, in the examined day for the case of FIG. 5. This is attained because the optimal energy management provides an optimal balance, through the minimization of a properly configured cost function, between the residents' comfort (since the electric loads operate within the acceptable time intervals and the indoor temperature is within the acceptable maximum and minimum temperature range) and the maximum exploitation of the generated electric energy by RES through the proper utilization of the BSS. Moreover, due to the above goals and since the real time energy price is considered, reduction of the total energy cost is attained.