Operation cost and energy usage minimization of a

Operation cost and energy usage minimization of a hybrid solar/electrical water heating system P.A. Hohne, K. Kusakana, and B.P. Numbi 

Abstract— Approximately 40% to 60 % of the total energy consumed by a traditional household in South Africa can be allocated to the heating of water. Furthermore, most of water heating takes place during peak electricity consumption periods, where electricity costs are highest. In this paper, the optimal energy management of a hybrid solar electric water heater (HSWH) is presented. The hybrid system consists of an indirect flat plate collector coupled to an electric storage tank water heater (ESTWH). The electric resistive element inside the storage tank water heater serves only as an auxiliary heater when solar irradiance is insufficient. A typical medium density household within the Mangaung municipality area in the city of Bloemfontein, South Africa is considered. The aim is to evaluate if an optimal control approach can be used to effectively shift the energy usage profile of the system under the residential Time-of-Use (TOU) tariff enforced by the electricity supplier, while maintaining a comfortable thermal level of the hot water user. The secondary aim is to reduce the energy required to increase the thermal level of the water compared to a baseline water heater. The proposed water heating system with optimal control is modelled and simulated using Matlab OPTI-Toolbox. The control variable was successfully solved with switching taking place during off-peak periods while maintaining the desired temperature of the hot water consumer. Index Terms—Flat plate solar collector, hot water storage tank, hybrid solar/electric storage tank water heater modelling, optimization, Cost minimization. 1

INTRODUCTION

Approximately 40% to 60% of the total energy of a normal residential building can be allocated to the heating of water in major countries [1]. Traditionally, a standard electric storage tank-water heater (ESTWH) has been the main device for residential water heating. However, the increase in the population, economy and living standard has led to an energy shortage, which has resulted in a steadily increasing electricity price [2].

P.A. Hohne, Central University of Technology, Private Bag X20539, Bloemfontein 9300, South Africa (e-mail: [email protected]). K. Kusakana, Central University of Technology, Private Bag X20539, Bloemfontein 9300, South Africa (e-mail: [email protected]). B.P. Numbi, Centre for the Development of Green Technologies, Department of Electrical Engineering, Mangosuthu University of Technology, 511 Mangosuthu Highway, Umlazi, 4031, P.O. Box 12363, Jacobs, 4026 Durban, South Africa (e-mail: [email protected]).

As an attempt to solve the electricity crisis, many countries in the world have recently introduced energy management systems and activities, such as energy efficiency (EE), and the use of renewable energy (RE) schemes. On the one hand, the EE activities consist of reducing the total (overall) energy consumption during all the time periods, while load management (LM) activities aim to reduce the energy consumption during given time periods, such as peak times, when the grid cannot meet the demand [3]. During peak times, the electricity consumption is charged at higher rates to encourage customers to shift their loads to off-peak and standard periods when the electricity is cheaper. This type of tariff is referred to as time-of-use (TOU) electricity tariff. With TOU, customers can therefore reduce their electricity bills by shifting load demands away from the peak time periods [4]. On the other hand, in order to reduce larger amount of residential peak load demand, renewable energy systems, such as solar water heater systems (SWH) were introduced and implemented as a replacement to the ESTWH. However, it has been observed that SWH was not continuously meeting the thermal comfort of the users, under certain weather conditions and time of day. During winter period, for instance, the amount of thermal energy required is greater than that of summer due to the temperature difference of the water that needs to be heated [5]. As a solution to this, the coupling of the SWH with the ESTWH, referred to as hybrid solar water heating system (HSWH) is currently seen as technical and economic feasible option for water heating in countries where solar irradiance is in abundance. The system is composed of a solar collector which uses solar radiation to increase the temperature of water, and the ESTWH which stores the hot water. In the case of poor solar radiation, when the SWH fails to increase the temperature of water to the comfortable level, the required temperature is maintained by the ESTWH [6]. Several research works have been done over the past few decades using numerical methods for the system components sizing and cost optimization for the electric storage tank water heater, some researchers evaluated the operation and efficiency when these systems are joined to form a hybrid system as in [7]. However, with the emerging TOU tariff structures being implemented by electricity suppliers, not any arrangements exist that were optimized with these tariffs in mind. Unlike the previously-mentioned studies, the current paper develops a mathematical model dealing with the optimal switching of electric resistive water heating systems with forced circulation, with the aim of controlling the water temperature while maintaining the water

temperature comfort level. The objective function, control and state variables, and disturbances are identified and mathematically expressed in the developed model. The developed model’s decision variables can then be optimized using any suitable advanced algorithm able to solve such a problem. Furthermore, implementing optimal energy management of the HSWS can help to meet the required thermal comfort level while reducing the electricity cost, especially for buildings under TOU electricity tariff. With this taken into account, the aim of this work is to develop an optimal energy management model that will improve the operation efficiency of the HSWH. The main objective is to minimize the water heating energy cost from the grid by taking advantage of the TOU electricity tariff, meanwhile meeting the thermal comfort level of hot water users. The seasonal temperature changes will be included in the model in order to evaluate the annual energy usage in the system. The model contains binary control and continuous state and disturbance variables. In this paper, the solar collector water heater as well as the storage tank water heater is modeled, the objective function and all variables are to be outlined and discussed. Two switches exist as control variables in the system, one switch controls the flow of heated water to the electric storage tank water heater and the other switch controls the switching of the electric resistive heating element. The adjustment of the resistive element switch is optimized in order to minimize daily energy costs while meeting the users’ thermal comfort level. This will consist of switching the resistive element on when electricity is least expensive at the appropriate time to provide the required hot water at a later stage. 2.

MATHEMATICAL MODEL OF THE PROPOSED SOLAR/ELECTRIC WATER HEATING SYSTEM

The proposed hybrid system consists of an electric storage tank water heater and a flat plate solar collector. The solar collector is accompanied by a circulation pump. The layout of this system is illustrated in Fig. 1. The mathematical models of the different components in the system in terms of heat energy are presented: 2.1 Energy balance and temperature discretization Solar irradiance is the primary energy input for heating water in the hybrid solar electric storage tank water heater. The electrically supplied resistive element located inside the storage tank will serve as an auxilliary water heating device when solar irradiance is absent. Refering to Fig. 1, the cold water is supplied from the mains and enters the thermal storage tank. The thermal tank shares the cold water inlet supply with the solar collector so that heat can be exchanged to the incoming water.

Hot water rises in the collector and flows back to the thermal storage tank with the help of a circulation pump, the overall temperature of the water therefore rises and the process is repeated in order to continuously heat the water. Refering to Fig. 1, the thermal storage tank is the electric hot water storage tank where heated water is stored for use at a later stage. The tank needs to store enough hot water to meet the hot water demand. When insufficient amounts of heat is produced by the solar collector due to the absence of solar irradiance, the resistive electric element switches on in order to keep the temperature to required comfortable levels. No heat exchangers are present in the tank and only water in the liquid phase is allowed within the ESTWH. The hot water storage tank model is developed according to [8], with a fixed power demand rating, operating at full capacity when switched on. The hot water temperature distribution inside the tank is assumed to have high degrees of thermal stratification [9]. In this model, energy losses due to hot water demand, QD , and convectional standby loss ( QL ) are modeled. The standby losses, QL represent power losses owing to the casing material surface conduction. The energy gains from the solar collector, Qcoll , and the energy supplied by the electric resistive element, QEL , are energies supplied for water heating in the system. The resulting energy balance equation with the heat gains and losses in the system are given in Eq. (1): (1) Qs  Qcoll  QEL  QL  QD Where: Qs is the energy contained within the storage tank (J);

Qcoll is the energy received by the collector from the sun using the isotropic diffuse model [10] (J); QEL is the energy supplied to the electric element (J); QL is the standby losses through the storage tank surface conduction (J); QD is the energy losses due to the hot water drawn by the

user (J). The energy balance becomes a first derivative differential function, where Qs in Eq. (1) is replaced with •

M s cTs and represents the heat energy in the storage tank,

given in Eq. (2) [11]. •

M s c Ts  Qcoll  QEL  QL  QD Where: M s is the mass or capacity of the storage tank ( kg );

c

(2)

is the heat capacity of water ( 4184 J / kg / C );

•

Ts is the energy supplied to the electric element ( C ).

Substituting all variables and coefficients (parameters) associated with the system described and illustrated in Fig. 2 to Fig. 7, and Table I in Eq. (2) will result in Eq. (3). In the equation, the temperature of the water inside the storage tank is isolated as the state variable and made the subject of the formula. Fig. 1 Hybrid Solar/Electric water heater

•

Ts 

cW (t )T (t ) AsU s t( h )Ta (t ) Y (t ) SeQEL cWD (t )  AsU s t( h )   (Ts (t ))  D m  M sc M sc M sc M sc M sc

(3)

A state space equation is formulated using the energy balance in Eq. (3) after isolating the control and state variables in the system. In order to visualize the variation in temperature of the water inside the storage tank, the • continuous temperature function ( T ) needs to be s

transferred into a general discrete formulation resulting in Eq. (4): k

k

k

k

k

j 0

j 0

i  j 1

j 0

j i 1

T( k 1)  T0  (1  ts Aj )  ts B Se j  (1  ts Ai )  ts   j  (1  ts Ai ) (4)

3.3. Proposed algorithm The objective function has been modeled as a sum of the linear and non-linear functions of the hybrid solar water heater. This combination of linear and non-linear optimization problem can be solved using “SCIP” solver in the Matlab interface OPTI-Toolbox [13]. Then modified which canonical form of MINLP suited to the specific developed model can be expresses as:

min f ( x) x

3. OPTIMIZATION CONTROL MODEL 3.1. Objective function The objective is to minimize energy costs and thermal discomfort of the user while maintaining fixed final state conditions for repeated implementation. Therefore, the developed model has the following primary, secondary and tertiary objective functions which can be mathematically modelled, adapted from [12]: min J p  ts

N

P k 1

EL

pk Sek +

tf

min J s  (Ts (t )  F (t )) 2 dt + 

(5)

t0 tf

min J t  (Ts (t f )  Ts (t0 )) 2  t0

Where: • N is the number of sampling intervals within the operation range or period of the system; PEL is the rated power supplied to the electric resistive • • •

element (kW); k is the kth sampling interval; pk is the TOU tariff function (ZAR/kWh);

•

Sek is the optimized switching function;

• •

t s is the sampling interval; Ts (t ) is the variable temperature of the water inside

•

the storage tank and the state variable (°C); F (t ) is the desired temperature level of the user (°C);

•

Ts (t f ) is the temperature of the water at the end of the

•

specified control horizon (°C); Ts (t0 ) is the initial temperature of the water inside the

storage tank (°C). 3.2. Constraints The developed objective function is subjected to the variable limits. This constraint represents the switching status of the electric element inside the storage tank so that only a single binary value can be taken as the control output variable:

Sek  {0,1}

Subject to:

lb  x  ub

(7)

Where: • x, lb, and ub are vectors; • and f(x) is a combination of linear and non-linear functions that returns a scalar. 4. SIMULATION INPUT PARAMETERS 4.1. Exogenous variables The case study represents a medium density household located in Bloemfontein, South Africa. Winter and summer solar irradiance as well as the ambient air temperature data obtained from the University of the Free state weather station for the Bloemfontein area is illustrated in Figs. 2-3 and Figs. 4-5, respectively [14]. From Figs. 2 and 3, clear differences in solar output from the sun can be seen. Most winter months in Bloemfontein have clear skies whereas during the summer, overcast or cloudy skies have significant effect on solar radiation reaching earth’s surface. The ambient air temperatures for the two seasons follow a similar trend, however as can be expected for the winter case, much lower temperatures are apparent. Inlet water temperatures are adapted from [15] and plotted on the same chart area as the ambient temperature in Figs. 4 and 5. The inlet water temperature fluctuations can be seen as near constant when compared to the ambient air temperature. The proposed daily hot water consumption profile for winter and summer periods are shown in Fig. 3 and 4, respectively. The profiles of the household of three occupants that prefers showering rather than bathing are used for the case study. The times at which the occupants usually take showers are 06:30, 07:00 and 20:00, additional hot water is consumed at 11:00 by a dishwasher or washing machine. From these figures, it can be observed that the demand in winter is much higher than that of the summer. This is due to the temperature difference between the coldwater inlet and hot water supply to the user that needs to be diminished by means of thermal mixing in order to reach the desired thermal level of the user.

(6)

Fig. 2: Winter solar irradiance

Fig. 3: Summer solar irradiance

Fig. 8: Time-of-Use periods [17]

4.3. System parameters Table I - [18-22]: Component sizes and parameters of the hybrid solar electric water heater Item

Fig. 4: Winter ambient air ( Ta ) and inlet water ( Tm ) temperature

Effective absorbance area of the collector ( m )

As

Storage tank area ( m ) Tilted angle of the collector array (°)

coll

M

Storage tank capacity (kg)

QEL

g

Td

Ts ,max

Ttstat

Fig. 6: Winter hot water demand profile ( WD )

Fig. 7: Summer hot water demand profile ( WD )

4.2. TOU tariff structure The time-based pricing structure implemented by Eskom, provides electricity tariffs for a high demand season (winter) and a low demand season (summer). Illustrated in Fig. 8, each day is divided into segments representing an off-peak, peak and standard pricing period [16].

30

Heat capacity of water (J/kg.°C) Heat removal factor (-) Collector flow rate (kg/s.

2 1.1

2

mc (t ) PEL

temperature

Value 2

Acoll

C FR

Fig. 5: Summer ambient air ( Ta ) and inlet water ( Tm )

Description

4184 0.665

2

m )

0.011 150

Rated power of electric resistive element (W)

3000

Energy delivered to resistive element (MJ/h)

10.8

Ground reflectance factor (-)

0.2

Desired hot water temperature (°C)

60

Default thermostat switch-off temperature (°C)

65

Thermostat switch-on temperature (°C)

60

  ,s

Summer incidence angle on tilted surface (°)

  ,w

Winter Incidence angle on titled surface (°)



Transmittance absorbance product (-)

109 67.6 1.12

UL

Collector overall heat transfer coefficient (W/ m .°C)

Us

Storage tank heat loss coefficient (W/ m )

2

2

7.28 0.3

4.4 Electric storage tank water heater (baseline) In this case, an electric storage tank water heater with a bi-metal thermostat to control the temperature of the water inside the storage tank is used as a baseline. The electric resistive element is rated at 3 kW. The default thermostat temperature of the thermostat is set at 65 °C [23]. The tank has a capacity of 150 L. The simulation parameters are given in Table II. The switching function of the thermostat is represented for the winter and summer cases in Figs. 9 and 11, respectively. In Figs. 10 and 12, the temperature of the water inside the ESTWH associated with the thermostat switching functions are shown. For both the summer and winter cases, the switchingon of the resistive element occurs during the peak and

standard periods, unnecessarily increasing costs to the consumer. Table II - Simulation parameters Item Simulation horizon time Sampling time Comfortable thermal level range

Value 24 hrs 15 min 55 °C  Ts  65 °C

tank water temperatures shown in Figs. 14 and 16 for the two respective seasons. From the graphs, it can clearly be observed that switching only takes place during off-peak periods with an added benefit of saving cost due to the reduction of switch on time of the resistive element. Further observations prove that it is not necessary to switch the element on during or after hot water is drawn to maintain the desired temperature level of the water.

Fig. 9: ESTWH thermostat switching function: Winter case Fig. 13: Optimally controlled HSWH switching function: Winter case

Fig. 10: ESTWH storage tank water temperature ( Ts ): Winter case Fig. 14: Optimally controlled HSWH storage tank temperature: Winter case

Fig. 11: ESTWH thermostat switching function: Summer case

Fig. 15: Optimally controlled HSWH switching function: Summer case

Fig. 12: ESTWH storage tank water temperature ( Ts ): Summer case

4.4. Proposed hybrid solar water heater with optimal control In this case, a flat plate solar collector is coupled to the ESTWH. The same simulation parameters used for the baseline, are used to simulate the operation of the HSWH with optimal control. The optimal control model replaces the decision-making ability of the thermostat. Figs. 13 and 15 shows the optimal switching of the resistive element while maintaining the desired storage

Fig. 16: Optimally controlled HSWH storage tank temperature (

Ts ): Summer case 4.5. Daily energy consumption and savings analysis The cumulative energy consumed after each simulation of the baseline and optimal control strategy are shown and compared in Table III and IV. The percentage in savings can be calculated from these tables. A 60% saving of the

energy in the winter season is observed, while a 50% saving during summer is noted. With switching taking place (optimal control strategy) in the low-cost regions of the TOU tariff function, a saving of 75.2% in cost can be observed for winter season while in summer a total saving in cost of 60.5% can be made. The results of this comparison highlight the importance of avoiding the use of electricity during high demand periods.

[2]

[3]

[4]

[5]

Table III - Winter daily energy savings System ESTWH Optimal controlled HSWH Savings

Energy used 3.75 kWh 1.50 kWh 2.25 kWh

Table IV - Summer daily energy savings System ESTWH Optimal controlled HSWH Savings

5.

Energy used 1.5 kWh 0.75 kWh 0.75 kWh

CONCLUSION AND RECOMMENDATION

Recent years have encouraged consumers to improve their energy efficiency activities, such as the retro-fitment of the electric storage tank water heater with a solar collector water heater. Energy consumers soon realized that these types of activities have the potential to shave off significant costs from energy bills. Further improvement to these hybrid systems are possible and required in order to operate at optimal efficiency. In response to this requirement, a mathematical model has been developed to determine the optimal operation control of the hybrid water heating setup. The aim of this paper is to provide a model so that researchers interested in the field can adapt or design a similar configuration where some of the parameters (i.e. number of collectors, size of storage tank, demand profile, etc.). can be changed to suit any water heating setup that needs to be optimized. The constraints on operation have been set and outlined according to the hot water users’ specific thermal comfort level while attaining the maximum savings possible. By shifting the load profile maximum energy usage times to time intervals where energy is charged at off-peak tariffs increases savings in cost. The developed optimal control model in this paper effectively improved the energy usage of the proposed hybrid systems, while maintaining the desired temperature of the user. For further studies, the developed model can be integrated to obtain the hybrid system’s total life cycling cost and be compared to the baseline cost to assess the economic feasibility of the system. REFERENCES [1]

N. Qase, 2015. State of Renewable Energy in South Africa. 1st ed. Matimba House, 192 Visagie Str, Pretoria, South Africa: Department of Energy, 2015.

[6]

[7] [8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

Koko, Sandile Phillip, Kanzumba Kusakana, and Herman Jacobus Vermaak. "Micro-hydrokinetic river system modelling and analysis as compared to wind system for remote rural electrification." Electric Power Systems Research 126 (2015): 38-44. Vine, E.; Hamrin, J.; Eyre, N “Public policy analysis of energy efficiency and load management in changing electricity businesses” Energy Policy 31 (2003), 405-430 Kusakana K. "Energy management of a grid-connected hydrokinetic system under Time of Use tariff." Renewable Energy 101 (2017): 1325-1333. Kalogirou, Soteris. "Thermal performance, economic and environmental life cycle analysis of thermosiphon solar water heaters." Solar energy 83, no. 1 (2009): 39-48. Ko, M.J. “Multi-Objective Optimization Design for Indirect ForcedCirculation Solar water heating system Using NSGA-II”, Energies, (2015) pp. 13138 -13134 Hohne, PA, (2017). A survey of water heating technologies in SouthAfrica. In SAUPEC 2017. Stellenbosch, 2017. South Africa, 1-8. Ko, Myeong Jin. "Multi-objective optimization design for indirect forced-circulation solar water heating system using NSGAII." Energies 8, no. 11 (2015): 13137-13161. Ntsaluba, Sula, Bing Zhu, and Xiaohua Xia. "Optimal flow control of a forced circulation solar water heating system with energy storage units and connecting pipes." Renewable Energy 89 (2016): 108-124. Numbi, B. P., and S. J. Malinga. "Optimal energy cost and economic analysis of a residential grid-interactive solar PV system-case of eThekwini municipality in South Africa." Applied Energy 186 (2017): 28-45. Sichilalu, Sam M., and Xiaohua Xia. "Optimal power dispatch of a grid tied-battery-photovoltaic system supplying heat pump water heaters." Energy conversion and management 102 (2015): 81-91. Zhang, Jiangfeng, and Xiaohua Xia. "Best switching time of hot water cylinder-switched optimal control approach." In AFRICON 2007, pp. 1-7. IEEE, 2007. Wanjiru, Evan M., Sam M. Sichilalu, and Xiaohua Xia. "Optimal control of heat pump water heater-instantaneous shower using integrated renewable-grid energy systems." Applied Energy 201 (2017): 332-342. Sauran.net. (2017). Station Details - Southern African Universities Radiometric Network. [online] Available at: http://www.sauran.net/ShowStation.aspx?station=7 [Accessed 8 Dec. 2017]. Ratikane, Mosepeli. "Quality of drinking water sources in the Bloemfontein area of the Mangaung Metropolitan Municipality." PhD diss., Bloemfontein: Central University of Technology, Free State, 2013 EE Publishers. (2017). Energy management systems save money EE Publishers. [online] Available at: http://www.ee.co.za/article/energy-management systems-savemoney.html [Accessed 8 Dec. 2017]. Meyer, J. P., and M. Tshimankinda. "Domestic hot-water consumption in South African apartments." Energy 23, no. 1 (1998): 61-66. Ko, Myeong Jin. "Multi-Objective Optimization Design for Indirect Forced-Circulation Solar Water Heating System Using NSGAII." Energies 8, no. 11 (2015): 13137-13161. Eskom Rebates For Solar Water Heating Systems | GeoSolar | Geo Group", Geogroup.co.za, 2017. [Online]. Available at: http://www.geogroup.co.za/solar-heating/solar-water-heatingsystems/eskom-solar-heating-rebates. [Accessed: 08- Dec- 2017]. 150L GAP ECO ELECTRIC GEYSERS", Solar Advice, 2017. [Online]. Available: https://solaradvice.co.za/product/150l-gap-ecoelectric-geyser/. [Accessed: 08- Dec- 2017]. Sun & moon times today, Bloemfontein, South Africa", Timeanddate.com, 2017. [Online]. Available: https://www.timeanddate.com/astronomy/southafrica/bloemfontein. [Accessed: 08- Dec- 2017]. Solar Radiation on a Tilted Surface PVEducation", Pveducation.org, 2017. [Online]. Available: http://www.pveducation.org/pvcdrom/properties-sunlight/solarradiation-tilted-surface. [Accessed: 08- Dec- 2017]. Harris, A., M. Kilfoil, and E. A. Uken. "Domestic energy savings with geyser blankets." (2007).

AUTHORS BIOS AND PHOTOGRAPHS P.A. Hohne obtained his B.Tech degree in Electrical Engineering in 2016 and his M.Eng degree in 2018 from the Central University of Technology. Since 2016, he has been working at the Central University of Technology as a lecturer’s assistant and plans to enrol for the D.Eng degree in Electrical Engineering. His area of interest is energy management and renewable energy systems. K. Kusakana (DTech, Pr.Eng, CEM) is a NRF rated researcher. His research interests are power and energy systems, energy management, renewable and alternative energies. He is currently an Associate Professor and Head of the Electrical, Electronic and Computer Engineering Department at CUT. B.P. Numbi obtained his PhD from the University of Pretoria (UP) in 2015. From 2010 to 2012, he was a teaching assistant at TUT. From 2014 to 2015, he worked as a project engineer on mining energy efficiency projects in the Centre of New Energy Systems (CNES) at UP. From 2015 to 2016, Dr Numbi worked as a postdoctoral research fellow within the Centre for the Development of Green Technologies (CDGT) at the Mangosuthu University of Technology (MUT). Since 2016, he has been a lecturer in the Department of Electrical Engineering at the MUT. Presenting author: The paper will be presented by P.A. Hohne