Multi-objective Energy Management Model for Stand-Alone Photovoltaic-Battery Systems: Application to Refugee Camps

Abstract

Despite the benefits of stand-alone solar photovoltaic (PV) systems in the context of refugee camps, these systems fail within the first few years of operations—typically the first three years. The leading causes of the failure of solar PV systems in refugee camps are lack of technical personnel and maintenance, lack of training and education, and demand modification leading to overconsumption of energy from lead-acid batteries. This paper proposes a multi-objective energy management model that aims to increase the longevity of lead-acid batteries while considering the Levelized Cost of Used Energy (LCUE) and user satisfaction. Scenarios incorporating different levels of demand modification are proposed to verify the effectiveness of the proposed model. A weighted sum approach was applied to solve the multi-objective optimization problem. A sensitivity analysis was performed to illustrate the effect of varying the battery objective weight, on the model’s performance. Results show that the proposed model can increase battery lifetime by up to 9 years with a 33% decrease in LCUE in some cases. The results indicate that the proposed model is likely to be useful for refugee camps that experience rapidly increasing energy demand.

9.1 Introduction

About 89% of displaced people in camps have either no or limited access to electricity [1]. Considering the vital role of electricity in camps in facilitating security, entrepreneurial activities, learning and social activities, it has become a necessary component of emergency response. Decentralized power systems, usually stand-alone diesel generator-based microgrids, have been used to power some refugee camps. However, PV-based is encouraged due to its environmental and economic benefits and suitability—70% of camps are in areas with solar irradiance of over 2000 kWh/m²/year [2]. Despite the promise, stand-alone PV systems have not managed to thrive in refugee camps. No successful implementation of solar PV systems in refugee camps has been recorded. Studies have shown that failures are mostly due to battery degradation resulting from demand modification, typical of refugee camps, since they may be characterized by fluid populations [3, 4]. Demand modification, in most cases, leads to excessive energy consumption from the battery and, subsequently, lifetime reduction. Therefore, energy management and control needs to be implemented to ensure the resilience of PV-based microgrids in refugee camps, considering that the average lifespan of refugee camps is 18 years and finances for system/component replacement are usually unavailable [3].

Several methodologies and algorithms have been proposed in the energy systems management and control literature. Matallanas et al. [5] propose a neural network-based day-ahead controller for a residential grid-tied solar PV system to reduce electricity bills by shifting energy demands based on PV generation forecast and time-of-use tariffs. Shakeri et al. [6] present a real-time home Energy Management System (EMS) for a residential grid-connected PV-battery system to minimise electricity cost—battery health or lifetime was not considered. Ahmed et al. [7] propose a home EMS which minimises energy bills by limiting or shedding demand at specific times of the day—the optimisation problem was solved using a binary backtracking search algorithm.

It should be noted that every device is acquired to offer a particular amount of comfort to the user. For example, lights are installed to give visual comfort, especially at night; preventing the use of light at night may result in user dissatisfaction. Minimising the cost of energy and energy bills may involve limiting or shedding of demand, resulting in user dissatisfaction [8]. User satisfaction is defined as ‘the degree of desirability of the user to operate an appliance at a required time instant and for a particular time duration that results in a specific comfort’ [8]. Researchers have begun to consider user satisfaction in their energy management modelling. Lin et al. [9] proposed a home EMS for grid-connected houses. The energy management problem is considered a multi-objective optimization problem of ‘electricity bills versus customer satisfaction (waiting time)’ [9]. Ogunjiyigbe et al. [10] consider user satisfaction while controlling cost in a grid-connected system. Ogunjiyigbe et al. [10] propose a load shedding-based controller to maximise user-satisfaction for predetermined user electricity bill budgets. They employ Genetic Algorithm to solve the optimisation problem. Pamulapati et al. proposed a model that considers user satisfaction while reducing energy bills [8]. Like Ogunjiyigbe et al. [10], load shedding is applied to minimise the electricity bills, and loads were shed according to preference or user satisfaction indices assigned to devices. Cho et al. [11] propose a load shifting-based methodology for energy consumption scheduling in residential stand-alone PV-battery systems. The objectives of the proposed scheduling model were to maximise the utility of the PV system while maximizing user comfort, battery lifetime was not considered.

It is evident in the literature that most works have focused on grid-connected systems and therefore aim to minimise energy bills, cost of energy and maximizing user satisfaction; although essential, little or no relevance is given to battery longevity, which is vital to refugee camps. As a result, Narayan et al. [12] have suggested that battery lifetime should be considered in the design of EMS for off-grid solar photovoltaic systems in developing countries. To the best of the authors’ knowledge, little or no work has combined energy cost, user satisfaction, and battery lifetime, all essential objectives for off-grid solar PV installations in refugee camps. By incorporating the battery lifetime objective, the effect of including battery lifetime on user satisfaction and energy cost can be investigated. Also, most works have not used real-life data, so verification may not necessarily be valid. EMS need to be verified with real data. This work proposes a multi-objective energy management model that considers the cost of user energy, user satisfaction and battery lifetime for off-grid solar PV systems in rural settings. The effectiveness of the proposed model is verified on real-life data from a refugee camp.

The rest of this paper is organised as follows: Sect. 9.2 presents the method used in this work. The proposed energy management model is formulated in Sect. 9.3, results are discussed in Sect. 9.4 followed by the conclusion in Sect. 9.5.

9.2 Method

A day-ahead energy management model was designed to achieve the aim and objectives of this work. The energy management model performs electrical load management (through load shedding) and controls the charge–discharge cycles of lead-acid batteries based on next-day PV forecast, load forecast and perceived user-satisfaction. Day-ahead PV forecast was obtained from Solcast—an online solar irradiance forecast service [13]. Load forecasting was achieved using the persistence forecast model and historical data [14]. Determination of user satisfaction was achieved with the user satisfaction model proposed by Pamulapati et al. [8].

A 2.04 kWp stand-alone PV system in Nyabiheke refugee camp in Rwanda (1°35′46″ S, 30°15′40″ E) (case study system) is selected to verify the proposed model. Possible demand modifications were modelled by adding loads to the case study system. These additional loads are actual loads connected to a diesel generator in the same refugee camp. Three scenarios were developed for consideration in this work, they are presented in Table 9.1.

Table 9.1 The Nyabiheke hall case study system under 3 scenarios. Scenario 1 is the current baseline operation. Scenarios 2 and 3 (modified scenarios) considered extended connections for powering an office block, restaurants and sewing cooperatives

The model’s performance is assessed based on LCUE, battery life, user satisfaction and capacity shortage. Capacity shortage is defined in HOMER Pro as the total annual shortfall that occurs between required operating capacity and actual operating capacity.

9.3 Model

In off-grid solar PV systems situated in refugee camps, it is essential to consider battery lifetime, user satisfaction and cost of energy. Due to the conflicting nature of these objectives, the problem is viewed as a multi-objective optimisation problem.

9.3.1 Objective Function I

The first objective is to maximise battery lifetime. Lead-acid batteries’ longevity is dependent on their State of Charge (SoC) throughout their lifetime. A battery is said to have exhausted its useful life when the cumulative throughput of the battery reaches the lifetime throughput provided by the manufacturer. SoC factor $\left( {f_{SoC} } \right)$, as proposed by Schiffer et al. [17], is a throughput multiplier representing a lead-acid battery’s actual operating conditions. To reduce the cumulative throughput of lead-acid batteries, $f_{SoC}$ must be minimized. Therefore, the first objective function is modelled as:

$$ F_{1} = \min \mathop \sum \limits_{t = 1}^{T} f_{SoC} \left( t \right) $$

(9.1)

$$ \begin{aligned} f_{{SoC}} \left( t \right) & = 1 + \left( {{\text{c}}_{{{\text{SoC}},0}} + {\text{c}}_{{{\text{SoC}},{\text{min}}}} \left( {1 - \left. {n_{3} \left( {\text{t}} \right)} \right|_{{{\text{t}}_{0} }}^{{\text{t}}} } \right)} \right) \\ & \, \times \left( {\frac{{I_{{10}} }}{{I\left( t \right)}}} \right)^{{1/2}} \cdot \left( {\exp \left( {\frac{{n_{1} \left( t \right)}}{{3.6}}} \right)} \right)^{{1/3}} \times n_{2} \left( t \right) \\ \end{aligned} $$

(9.2)

$$ n_{1} \left( {t + {\Delta }t} \right) = n_{1} \left( t \right) + \frac{{0.0025 - \left( {0.95 - SoC^{{{\text{max}}}} } \right)^{2} }}{0.0025} $$

(9.3)

where T is the total number of time slots in a day, $n_{1}$ is the number of bad charges, $n_{2}$ is the time since last full charge, $n_{3}$ least SoC since last full charge. ${\text{c}}_{{{\text{SoC}},0}}$ and ${\text{c}}_{{{\text{SoC}},{\text{min}}}}$ are constants representing the increase in $f_{SoC}$ when SoC = 0 and the impact of minimum SoC, respectively.

9.3.2 Objective Function II

The second objective, F₂, of the proposed energy management system is to maximise user satisfaction. This objective is formulated by:

$$ F_{2} = {\text{max}}\mathop \sum \limits_{t = 1}^{T} \left( {\frac{{\mathop \sum \nolimits_{n = 1}^{N} \beta_{n,t} \times P_{n,t} }}{{\mathop \sum \nolimits_{n = 1}^{N} P_{n,t} }}} \right) $$

(9.4)

where $\beta_{n,t}$ is a binary variable (equal to 1 if appliance is ON and 0 otherwise), $P_{n,t}$ is the preference/priority index of electrical load n at time slot t.

9.3.3 Objective Function III

The third objective, F₃, of the proposed energy management system, is the maximisation of the performance ratio, and is formulated as:

$$ F_{3} = \max \frac{{\left( {\mathop \sum \nolimits_{t = 1}^{T} \mathop \sum \nolimits_{n = 1}^{N} E_{n,t} \times \beta_{n,t} } \right)}}{{Y_{R} }} $$

(9.5)

$$ Y_{R} = \frac{{A \times \eta_{STC} \times \smallint G_{i} }}{{P_{o} }} $$

(9.6)

where $E_{n,t}$ is the forecasted energy demand of electric load n in time slot t and $Y_{R}$ is reference yield, $\eta_{STC}$ is the efficiency of the PV array under standard test conditions, $G_{i}$ is the solar irradiance incident on the tilted PV array (kW/m²) over a period, A is the area of the PV array, $P_{o}$ is the peak power rating of the PV array (kWp).

9.3.4 Combined Objective Function

A weighted sum approach is applied to solve the multi-objective optimisation problem. By applying the weighted sum method, a single objective is developed from the weighted sum of the three objective functions of the optimisation problem, as seen in Eq. (9.7):

$$ \begin{aligned} {\text{OBJ}} & = \max \left( { - w_{{bl}} \mathop \sum \limits_{{t = 1}}^{T} f_{{SoC}} \left( t \right) + w_{{us}} \mathop \sum \limits_{{t = 1}}^{T} \left( {\frac{{\mathop \sum \nolimits_{{n = 1}}^{N} \beta _{{n,t}} \times P_{{n,t}} }}{{\mathop \sum \nolimits_{{n = 1}}^{N} P_{{n,t}} }}} \right)} \right. \\ & \,\left. { + w_{{pr}} \frac{{\left( {\mathop \sum \nolimits_{{t = 1}}^{T} \mathop \sum \nolimits_{{n = 1}}^{N} \beta _{{n,t}} \times E_{{n,t}} } \right)}}{{Y_{R} }}} \right) \\ \end{aligned} $$

(9.7)

where $w_{bl}$, $w_{us}$ and $w_{pr}$ represent objective weights for battery lifetime, user satisfaction and performance ratio respectively.

9.3.5 Constraints

The maximisation of the objective or fitness function seen in equation is subject to a number of constraints.

To guarantee durability of battery, the SoC should always be between a minimum $\left( {SoC^{\min } } \right)$ and maximum $\left( {SoC^{\max } } \right)$ threshold SoC.

$$ SoC^{\min } \le SoC\left( t \right) \le SoC^{\max } $$

(9.8)

Equation (9.9) ensures that charging and discharging of battery does not occur at the same time.

$$ y_{t}^{ch} + y_{t}^{dch} \le 1 $$

(9.9)

$$ y_{t}^{ch} ,y_{t}^{dch} \in \left\{ {0,1} \right\},\forall t $$

(9.10)

where $y_{t}^{ch}$ and $y_{t}^{dch}$ are binary and indicate the charge and discharge state of the battery. The energy discharged from the battery $\left( {e_{t}^{{usr_{ - } bat}} } \right)$ should not exceed the maximum discharge energy $\left( {R^{MDC} } \right)$ as specified on manufacturers’ specification sheets.

$$ e_{t}^{{usr_{ - } bat}} \le y_{t}^{dch} *R^{MDC} $$

(9.11)

Similarly, charge energy of battery $\left( {e_{t}^{chr} } \right)$ should not exceed maximum charge energy $\left( {R^{MCH} } \right)$

$$ e_{t}^{chr} \le y_{t}^{ch} *R^{MCH} $$

(9.12)

To ensure generation–demand balance and system stability, total energy consumption at time slot, $t,$ $\left( {E_{a}^{t} } \right)$ should not exceed available energy.

$$ \left\{ {\begin{array}{*{20}l} {E_{a}^{t} \le \left( {SoC\left( t \right)*C_{{bat}} } \right) + Y_{t} ;} \hfill & {{\text{if}}~y_{t}^{{ch}} = 0} \hfill \\ {E_{a}^{t} \le Y_{t} ;} \hfill & {{\text{if}}~y_{t}^{{ch}} = 1} \hfill \\ \end{array} } \right. $$

(9.13)

$$ Y_{t} = A \times \eta_{STC} \times G_{t} $$

(9.14)

where $C_{bat}$ is the nominal capacity of the battery and $Y_{t}$ is the PV generation forecast at time slot $t$. Also, energy consumption $\left( {E_{a}^{t} } \right)$ cannot exceed the rated capacity of the inverter $\left( {P_{inv} } \right)$.

$$ E_{a}^{t} \le P_{inv} $$

(9.15)

9.4 Results and Discussion

The proposed energy management model was simulated against a whole month of data (November 2019) for the three scenarios presented in Table 9.1. Data used in this work can be found at https://doi.org/10.5281/zenodo.4304799. Genetic Algorithm was applied to solve the optimisation problem. A sensitivity analysis is performed to investigate the effect of objectives weight variation on the performance of the model. To achieve the variation, the weight of the battery longevity objective (w_bl), is varied from 0.8 to 0.1 and $w_{us} = w_{pr} = \frac{{1 - w_{bl} }}{2}$.

Without any form energy management, the performance for each scenario is presented in Table 9.2. It can be observed that possible demand modifications can significantly impact the longevity of batteries—battery life reduction of up to 12 years.

Table 9.2 Baseline performance of the stand-alone PV system without energy management

The effect of the proposed model and variation of its weight on the three scenarios are discussed in the following subsections. Determination of appropriate weights can also be achieved from the sensitivity analysis.

9.4.1 Scenario 1

Scenario 1 can be classified as an oversized system since its average daily consumption is 1729 Wh, which is significantly less than the system’s generation and storage capacities—2.05 kWp and 10,560 Wh, respectively. The application of the model increases the battery life significantly for scenario 1. A corresponding decrease in LCUE is expected. However, the reverse is the case due to the dependence of LCUE on the trade-off between energy consumption and system lifetime. Since the system is originally oversized, an increase in $w_{bl}$ which implies an increase in capacity shortage, will have a negative impact on the LCUE, as seen in Fig. 9.1a. For every increase in $w_{bl}$ beyond $w_{bl}$ = 0.1, user satisfaction decreases significantly. Increasing $w_{bl}$ between 0.1 and 0.3 can decrease user satisfaction by up to 15%, as illustrated in Fig. 9.1b. Further increment of $w_{bl}$ will lead to unnecessarily high user dissatisfaction.

Fig. 9.1

Plots for scenario 1—a effect of proposed EMS on battery lifetime and cost of energy b the effect of battery lifetime weight on absolute satisfaction

For an oversized system such as scenario 1, the application of the proposed model may not be helpful since the battery life with energy management is satisfactory (13.8 years in the case of scenario 1), considering that the average lifetime of a refugee camp is about 17 years. Also, the energy management model has a significantly negative impact on user satisfaction and LCUE.

9.4.2 Scenario 2

The application of the proposed energy management model to scenario 2 can increase the battery life by up to 9 years as seen in Fig. 9.2a. The battery life increment is accompanied by increase in capacity shortage and an increase and subsequent decrease in LCUE. The initial unexpected increase for values of $w_{bl}$ between 0.1 and 0.3 is due to a relatively small increase in battery life (from 4.5 to 4.99 years) accompanied by a relatively high increase in capacity shortage of approximately 85.9 kWh. Beyond w_bl = 0.3, there is a significant increase in battery life and a decrease in LCUE.

Fig. 9.2

Plots for scenario 2—a effect of proposed EMS on battery lifetime and cost of energy b the effect of battery lifetime weight on absolute satisfaction

Selecting a value of w_bl equal to or greater than 0.6 may be a good point to operate. There needs to be a balance between battery lifetime and user satisfaction. LCUE may be ignored because it constantly decreases in this region $\left( {w_{bl} \ge 0.6} \right)$. Increasing the value of w_bl from 0.1 to 0.8 results in a decrement in user satisfaction from 91% to about 65%. The mid-point is approximately 77.5%, corresponding to w_bl = 0.5 (battery life of 6.5). However, Fig. 9.2b depicts that sacrificing 10% more satisfaction corresponds to a w_bl of 0.8, which further increases the battery life by an additional 7 years. w_bl = 0.8 may be considered the best option.

9.4.3 Scenario 3

Scenario 3 has the highest level of demand modification of all the scenarios considered. This demand modification can reduce the battery to 1.4 years. Due to high demand, there is a default capacity shortage of approximately 45%. Application of the energy management model can increase the battery life by up to 2.3 years with minimal impact on user satisfaction, as seen in Fig. 9.3a and b. The user satisfaction decreases by only 3%, varying the value of w_bl from 0.1 to 0.8. For this scenario, the proposed energy management model is beneficial since it can improve battery life by up to 2.3 years with an LCUE reduction of about 25% and minimal impact on user satisfaction.

Fig. 9.3

Plots for scenario 3—a effect of proposed EMS on battery lifetime and cost of energy b the effect of battery lifetime weight on absolute satisfaction

9.5 Conclusion

Our findings show that the proposed load-shedding-based energy management model is unsuitable for oversized systems, even though it can significantly increase the system's lifetime. The significant increase in battery life is accompanied by an increase in LCUE and unnecessarily high user dissatisfaction. However, applying the proposed model to modified systems (as seen in scenarios 2 and 3) can increase the battery life and reduce LCUE with reasonable impact on user satisfaction. Therefore, the proposed model is suitable for refugee camps that experience a constant influx of refugees because it can protect standalone solar PV-Battery systems against informal demand modification typical of refugee camps.