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ScienceDirect Energy Procedia 103 (2016) 117 – 122

Applied Energy Symposium and Forum, REM2016: Renewable Energy Integration with Mini/Microgrid, 19-21 April 2016, Maldives

Optimal integrated diesel grid-renewable energy system for hot water devices Evan M. Wanjiru*, Sam M. Sichilalu, Xiaohua Xia Centre of New Energy Systems, Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0002, South Africa

Abstract Many remote areas in developing countries such as Africa and island developing nations rely on expensive diesel grid even though there is a high potential for renewable sources such as wind and solar. Further, in domestic houses, water heating contributes to a huge percentage of the overall electricity consumption. Therefore, integration of renewable energy and efficient water heating systems would lower the electricity cost and greenhouse gas emissions. This paper introduces an optimal control model for a hybrid heat pump and instantaneous water heaters powered using integrated energy systems. The model can lead to 5.5% of power-not-delivered and 24% water savings. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). © 2016 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, Selection and/or peer-review under responsibility of REM2016 REM2016: Renewable Energy Integration with Mini/Microgrid.

Keywords: Optimal; Wind; Solar; Diesel; Grid.

1. Introduction Many countries in the world are steadily adopting renewable energy while reducing over-reliance on fossil fuels. However, remote areas in many developing nations, such as Africa and most islands developing nations, are still using fossil fuel generators [1]. The negative environmental effect of the fossil fuels, coupled with high fuel importation transport cost and diseconomies of scale in electricity production lead to exorbitantly high energy cost and long term financial risks for the economy [2]. Furthermore, the increasing population in these developing nations is straining the existing energy

* Corresponding author. Tel.: +27 12 420 6767; fax: +27 12 362 5000. E-mail address: [email protected].

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, REM2016: Renewable Energy Integration with Mini/Microgrid. doi:10.1016/j.egypro.2016.11.259

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Evan M. Wanjiru et al. / Energy Procedia 103 (2016) 117 – 122

infrastructure through the increasing energy demand. Renewable energy technologies are a sustainable solution to providing cheaper and cleaner energy in these areas. For instance, in Maldives islands, integrated solar and wind electricity generation systems have been proven to be financially feasible for supplementing the fossil fuel based generators [3]. Although hybrid renewable energy systems are being adopted, one of the challenges is to design an optimal energy management system that satisfies the load while considering the intermittent nature of these renewable energy sources and variations in power demand [4]. In buildings, about 23.60% and 60.51% of energy is used for water and space heating respectively. Energy and water efficient technologies are indeed necessary to reduce the consumption of these resources at buildings level [5]. Heat pump water heaters (HPWHs) can reduce the amount of energy consumed in water heating if optimally connected with distributed renewable energy resources. Unlike storage water heaters, HPWHs operate on the principle of the refrigerant cycle converting one unit of electrical energy to produce three units of thermal energy [6]. Various studies have looked at ways of efficiently using HPWHs [7][8][9]. Even though HPWHs have a high coefficient of performance than other water heating technologies, they have a slow rate of heating the water. Consequently, in instances where there is high demand for hot water, HPWHs are unable to supply it. Another drawback is the energy and water losses associated with the hot water conveyance up to the consumption point [10]. To mitigate these losses, instant water heaters placed at the consumption point can be used. This paper introduces an optimal model that minimizes both the energy and water consumption by using HPWH and instant heater to conveniently meet the hot water demand. The model uses an integrated wind, solar and diesel generator. Therefore, the use of diesel grid and instant shower is optimally minimized. Further, the excess energy from the renewable sources is fed back to the grid through an appropriate feed-in tariff.

2. Model formulation

Diesel grid

Pdg

Tois

Pp v

Pw

uis

u hp

Pl Warm air in

Cold air out

Compressor Electric instant shower

Tinis

Toh p

Heat exchangers

Tinhp Heat pump

Fig 1: Schematic layout of the energy and hot water flow

Domestic load

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Figure 1 shows the schematic diagram of the water heating model comprising of the HPWH and the instant shower. These models are powered using the diesel grid, P dg , solar, P pv and wind generator, P w . The HPWH meets the hot water demand of the whole house, including the shower. This means that the HPWH must be placed in a centralized position in the house. The instant shower is placed in the shower to act as back up whenever the water from the HPWH is not at the required temperature. Switches u hp and u is control the power flow to the HPWH and instant shower respectively. The diesel grid supplements power from the renewable sources as well as accepting excess power back. The model seeks to minimize the consumption of power from the diesel grid, P dg , and the use of the instant shower as shown in equation (1). N

N

J=ɘ ෍ ts pe Pdg (j) +(1 െ ɘ) ෍ ts Pis uis (j) j=1

(1)

j=1

where t s is the sampling interval, p e is the time-of-use (TOU) tariff, P is is the instant heater rated power, Ȧ is the weighting factor and N is the total number of samples. This objective function is subject to the following constraints; Pw (j)+Pdg (j)+Ppv (j)=Pl(j)+Php u1 (j)+Pis uis (j),

(2)

hp Tmin Thp o M Tmax ,

(3)

Tismin Tiso M Tmax ,

(4)

uhp M ,

(5)

uis M ,

(6)

-Pdg M ,

(7) hp

where P hp is the HPWH rated power,Tmin and Tismin are the HPWH and instant shower minimum allowable temperature while Tmax is the maximum allowable temperature which is the same for both HPWH and is instant shower. Thp o (j) and To (j) are the state variables representing the HPWH and instant shower water temperature respectively, while u hp (j), u is (j) and P dg (j) are the control variables. In order to develop the model, it is assumed that the temperature of water in the HPWH is even throughout the storage. The temperature of water getting into the instant shower is assumed to be 90% of the temperature leaving the HPWH. Both the HPWH and the instant shower experience same temperature losses, namely the stand by losses and the losses caused by the inlet of cold water. The temperature variation in either of the two is therefore modeled as, ܿmt Tሶ (j)=Qo (j)-Qs (j)-Qd (j) (8) where, c is the specific heat capacity of water, m t is the mass of water inside the HPWH or the instant shower, Q o (j) is the total power output from either of the two devices, Q s (j) is the standby losses and Q D (j) is the loss associated with the inlet of cold water into the device. A case study was conducted in a house in Gauteng province, South Africa, having the hot water demand profile as shown in Figure 2.

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Fig 2: Hot water demand

3. Results and discussions This is a linear optimization problem solved in MATLAB using OPTI toolbox preferred for its high speed. Sampling interval, t s =30 min is chosen over a 24-hour horizon leading total samples, N=48. The optimal schedules for the HPWH and the instant shower are shown in Figure 3. Both devices are operating in the cheaper off-peak period in response to the household hot water demand. This effectively shifts the peak power demand in response to hot water demand.

Fig 3: Optimal switching schedule for the HPWH and instant shower.


Fig 4: Optimal diesel grid power consumption.

The optimal power consumption from the grid is shown in Figure 4. It can be seen that most grid power is consumed during the day when the demand for hot water is high. The availability of renewable energy is also available during the day and when there is more renewable energy than needed to power both devices, the excess energy is fed back to the grid as is the case between 08:00-08:30 and 11:30 and 14:00. Through selling the power to the grid, the cost of power to the consumer would lower even further. The power to the grid appears intermittent as the model assumes that there is no energy storage, through a battery. Therefore, whenever the renewable energy is in excess, it is immediately sold to the grid to be used by others. Figure 5 shows the variation of the temperature of water using the HPWH and the instant shower. Since the HPWH is supplying hot water to the whole house, where the water temperature is allowed to go as low as 45oC, it is unable to always meet the temperature required for the shower.

Fig 5: Hot water temperature variation resulting from HPWH and instant shower.

The temperature of the hot water in the HPWH rises at 00:05 when the HPWH is switched first switched on as seen in Figure 2(a) as the optimal controller predicts the rise in hot water demand. Thereafter the temperature gradually falls due to the stand by losses and the losses due to the incoming water temperature in the HPWH. In order for the HPWH to overcome these losses, it switches on, increasing the water temperature between 04:30 and 06:30. The temperature thereafter decreases rapidly as the demand for water is higher up to 09:30. The cycle continues until the end of the control period. It

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can be noted that the HPWH doesn’t always meet the minimum required temperature of 47 oC in the shower, for example between 08:30 and 16:30. It is in such period that the instant shower switches on as seen in Figure 2(b). When the HPWH meets the required water temperature in the shower, for instance, before 08:00, the instant shower is not switched on, in order to minimize the cost of power, while ensuring the convenience required while showering. The optimal model saves about 5.5% of power-not-delivered from the diesel grid in one day. This model, when adopted by many end-users within the grid would lead to significant savings over a long period greatly lowering the operational cost of the diesel generator. Further, about 5.05 kWh is sold back to the diesel grid in 24-h. This helps to lower the diesel grid operation further on fuel leading to greener and cleaner energy generation. Furthermore, instant showers have been compared to the normal shower heads they lead to lead to about 24% water savings [11]. The instant showers lead to less water being heated through lower demand, leading to more energy savings. 4. Conclusion This paper introduces an optimal model for controlling a HPWH connected with an instant shower leading to significant savings of both energy and water. The model offers novel solutions that will lead to increased market penetration in developing nations, like South Africa. The instant shower leads to water conservation through heating the water that cools inside the pipes. Such water is normally allowed to drain until hot water reaches the shower. However, this paper shows that the instant heaters consume higher energy due to their low storage capacity and high power rating while HPWHs lower the cost of power due to their high storage capacity and coefficient of performance. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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