Evaluating PWM Solar Charge Regulators for Off-Grid Solar PV Street Lighting Systems Using Linear Regression Approach

Abstract

The global adoption of solar-powered streetlights has grown significantly, driven by their cost-effectiveness and potential to reduce dependence on fossil fuels associated with conventional street lighting. Battery storage represents a substantial portion of the total capital cost in solar-powered streetlight systems. Therefore, selecting an efficient charge regulator is crucial to protect battery lifespan and reduce energy losses. In this context, the choice of an appropriate charge regulator plays a vital role in enhancing system reliability and overall performance. This study presents a practical approach for evaluating three commercially available 6 A-rated Pulse Width Modulation (PWM) solar charge regulators intended for recharging lead-acid batteries in a proposed 12 V off-grid solar photovoltaic (PV) street lighting system. The regulators were evaluated concurrently in separate circuits, each experiencing similar meteorological conditions, including similar temperature and solar irradiance. The measured data for each regulator were acquired using LabVIEW-based virtual instruments. The performance comparison was conducted using the Linear Regression Algorithm (LRA) to support decision-making. Based on the analysis, the most suitable PWM charge regulator was identified as the one offering the best charging performance due to low internal losses. Hence, solar battery charge regulators with identical load current ratings do not necessarily deliver equivalent charge/discharge performance.

1. Introduction

Globally, fossil fuels have been the main source of electricity generation. Hence, the rising energy demand led to global warming because of the emission of greenhouse gases. This necessitates the global need to minimize the reliance on fossil fuels. Outdoor lighting plays an important role in ensuring the safety and security of residents at night. The conventional outdoor streetlight puts severe pressure on the national grids since it consumes around 19% of electricity consumption around the world [1]. The answer to such challenges is to utilize solar renewable energy systems to minimize the fossil fuel electricity consumption. Solar renewable energy is gaining more popularity by reducing the reliance on fossil fuels around the world. If a utility company chooses to power streetlights with solar energy, this can lead to a reduction in greenhouse gas emissions, especially in countries that depend heavily on fossil fuels for electricity generation. This will not only benefit economically but also environmentally by minimizing the amount of emitted CO₂ during electricity generation [2]. In this context, the application of small-scale solar PV systems in streetlighting systems is a solution to such environmental problems.

An off-grid solar-powered streetlight consists of several components, such as a solar PV panel, a battery storage system, a charge regulator, and a DC lighting unit. Energy from the sun is harnessed and converted into electrical energy using solar panels. Solar panels used in street lighting are typically installed at a fixed tilt angle, which is approximately equal to the latitude of the installation site [3]. The reason for not opting for a single-axis or dual-axis tracker is due to the complexity that introduces higher maintenance and capital costs. Modern DC solar-powered streetlights use light-emitting diodes (LEDs) as a source of light. The reason is due to the minimal operational costs and maximum reliability offered by LEDs compared to the conventional lamps [4]. LED lights with lower lumen output can effectively replace a conventional lamp with higher lumen output due to directionality and efficiency [5]. The LED-based solar-powered streetlight has proved to yield an energy savings capacity of around 40% compared to the traditional streetlight.

The battery is a crucial component of an off-grid solar streetlight system, representing a significant portion of the total capital investment. Therefore, the proper sizing, utilization, and management of the battery are essential strategies for minimizing system costs [6,7,8]. Lead-acid batteries remain a cost-effective choice for small-scale off-grid PV systems, offering lower upfront costs despite their shorter lifespan and maintenance requirements [9,10]. Additionally, lead acid has proved to have a low self-discharging rate and the ability to operate under variable temperatures [11]. Lead-acid batteries have proven to be a cost-effective option for budget-conscious projects, whereas lithium-ion batteries are more economical in hybrid systems involving multiple energy sources [12,13]. Under normal operating conditions, the aging of storage batteries is primarily attributed to four factors: deep discharging, overcharging, low electrolyte levels, and elevated temperatures [14,15].

Selection of a reliable battery charging strategy is important to ensure the longevity of a battery [7]. The reliability and longevity of a battery hinge on the quality of the charge regulator since the PV system and the load are primarily connected to the battery via the regulator. The charge regulator used in solar streetlights plays a critical role in charging the battery and discharging stored electricity to the load. The Pulse Width Modulation (PWM) type has been selected since it is the most cost-effective charge regulator used in small-scale solar PV systems applications as compared to the Maximum Power Point Tracker (MPPT) [16,17,18]. PWM charge controllers contain fewer electronic components than MPPT types, resulting in a longer lifespan and reduced thermal stress [19]. They are particularly well-suited for lead-acid batteries and off-grid solar PV systems. PWM technology offers an effective method for maintaining a consistent battery charging voltage [20]. These controllers support multi-stage charging—bulk, absorption, and float—which is essential for prolonging battery life [21]. In an off-grid solar PV street lighting system, the PWM charge regulator ensures safe battery charging by preventing overcharging, blocking reverse current flow during nighttime, and protecting the battery from deep discharge under load conditions.

An efficient charge regulator may extend the battery’s operating time before it reaches the disconnection threshold. Therefore, when selecting a charge regulator, an appropriate method is required to analyze the discharge rate (slope) of the battery during use. The Linear Regression Algorithm (LRA) is one of the simplest and most widely used techniques in machine learning for predictive modeling [22]. In this study, LRA is employed to monitor, analyze, and compare the battery discharge rates by processing the acquired performance data. The method is used to evaluate the relationship between one or more independent variables and a dependent variable by fitting the best straight line through the data, minimizing the sum of squared errors. Once the line is fitted, it can be used to predict the system’s future behavior based on the line equation. The slope of this line, which represents the discharge rate, is determined using the gradient descent method.

In this study, three 6 A-rated solar PWM charge regulator models were identified and selected based on their suitability for the intended application in the real-world off-grid solar street lighting project. These regulators were selected based on their local availability, compliance with the required 6 A rating, and affordability compared to more expensive models capable of supporting both DC and AC loads. All three feature reverse polarity protection and are compatible with 12 V systems. The higher-end unit offers a multifunctional LED display and automatic 12/24 V voltage detection, making it more versatile for slightly advanced system configurations. However, the primary challenge lies in identifying which regulator offers the best charging performance. Therefore, the main objective of the study is to practically test and compare the performance of these three charge regulators in charging the selected lead-acid battery size. Based on the results, the most efficient regulator will be recommended for bulk procurement and use in the project. The performance data will be acquired using the LABVIEW program, and the comparison will be carried out using the LRA method. The aim is not to propose a new predictive model, but to demonstrate how a simple, practical, and interpretable technique can be effectively applied to assess charge regulator performance using the linear region of the battery and aid in making informed choices during system design.

2. Pulse Width Modulation and Battery Operation

The operation of a PWM regulator is achieved using a switching circuit, which is often made up of MOSFETs and controlled by microcontrollers or a comparator circuit, as shown in Figure 1. Unlike the linear regulator, the control is achieved by rapidly turning the power ON and OFF. The duration of the ON time (duty cycle) determines how much energy is transferred into the battery, as shown in Equation (1).

$$\%Duty Cycle=\left({\displaystyle \frac{T_{ON}}{T_{ON}+T_{OFF}}}\right)\times 100\%$$

(1)

where TON is the time the switch is ON; TOFF is the time the switch is OFF.

The PWM signal is a high-frequency square wave with a variable duty cycle, typically operating from a few kilohertz up to several hundred kilohertz [23]. During the bulk charging stage of a lead-acid battery, the duty cycle is maintained at 100% to enable rapid charging up to approximately 70–80% state of charge (SoC). In the absorption stage, the controller gradually reduces the duty cycle below 100% to limit the current as the battery approaches full charge [24]. During the float stage, the duty cycle is further decreased to supply a lower voltage and minimal current—just enough to compensate for the battery’s self-discharge. Battery protection features, such as prevention of overcharging, polarity reversal, and short-circuiting, further contribute to extending battery lifespan. Overcharge protection is achieved by gradually reducing the charging current as the battery nears full charge [19]. Optimal battery charging is maintained by rapidly switching the power on and off to modulate the output voltage according to the battery’s needs. Hence, the energy losses are minimal compared to the linear regulators, and the chances for overheating are minimal.

Although batteries inherently exhibit nonlinear charging and discharging behavior due to factors such as increasing electrolyte resistance and temperature fluctuations [25], a linear approximation can still offer valuable insights under controlled conditions. As the SoC decreases, the discharge rate increases for the given power consumption to exhibit a nonlinear behavior. However, batteries have also been shown to exhibit linear characteristics, particularly during the initial stages of discharge from full SoC to partial SoC [26,27,28]. As the discharge process progresses, nonlinearity becomes more pronounced, especially at low SoC levels, as denoted by the hyperbolic region in Figure 2. Therefore, when measurements are taken over a short duration of time and a battery supplying less current to the load, its behavior can often be reasonably approximated as linear. In this study, the batteries used are new, with an assumed state of health of 100%, meaning the onset of nonlinear behavior is delayed, especially under constant low load current before reaching the knee-point [27]. Hence, LRA is suitable for assessing and comparing the relative differences in slope, representing the rate of change in battery voltage.

Figure 1. Block diagram of a PWM charge regulator [24].

Figure 1. Block diagram of a PWM charge regulator [24].

Figure 2. Load terminal voltage versus SoC under different constant current discharge rates [28].

Figure 2. Load terminal voltage versus SoC under different constant current discharge rates [28].

Estimating the State of Charge (SoC) is a critical function in battery management systems (BMS), as it helps prevent both overcharging and over-discharging of batteries. Several techniques are used for SoC estimation, including direct measurement methods (which are not model-based), black-box estimation approaches, and state-space model-based methods [29]. Direct measurement techniques include coulomb counting, open circuit voltage (OCV) measurement, internal resistance analysis, discharge testing, and voltage change analysis (also known as the EMF prediction method) [29]. The coulomb counting method, while widely used, requires frequent calibration due to the high precision needed in current sensing, which is susceptible to sensor errors [28].

As previously discussed, the battery voltage curve can be divided into two regions: a linear region, corresponding to full-to-partial SoC, and a hyperbolic region, representing partial-to-low SoC. The impedance-based method has limitations, as battery impedance is affected by both temperature and aging. However, this method becomes more suitable at lower SoC levels, where the battery operates in the nonlinear region [28]. In contrast, during the linear region of operation, the terminal voltage is approximately proportional to the EMF. Therefore, under a constant load current, the terminal voltage can be used to estimate the EMF voltage without relying on impedance measurements. This predicted EMF voltage can then be used to estimate the SoC of the battery. Unlike lithium-ion batteries, lead-acid batteries exhibit a linear relationship between EMF voltage and SoC, particularly from full to partial SoC. As a result, the EMF prediction method can provide accurate SoC estimations during constant current discharge conditions [28,30]. Thus, in the full-to-partial SoC range, terminal voltage can be effectively used to track the battery’s discharge rate, as the battery operates within the linear region of its voltage curve. In such a context, the terminal voltage slope determined using LRA acts as a performance indicator of the discharging rate, not a battery model. The LRA has proved to be capable of monitoring and predicting the battery power as well as the battery state of health [27,31,32].

3. Materials and Methods

The planning of solar PV streetlight encompasses various aspects such as appropriate solar PV panel size, optimal tilt angle, energy storage size, and a suitable charge regulator. The study area of Bloemfontein, South Africa, is situated within Latitudes 29°7′6.06″ South and Longitude 26°13′29.71″ East. The average annual solar radiation is about 5.86 kWh/m²/day, which ranges from a minimum of 3.75 kWh/m²/day in winter to a maximum of 8.03 kWh/m²/day in summer [33]. The electrical power output of a solar PV panel is directly dependent on the level of solar irradiance at the installation site, as described by Equation (2) [34].

$$P_{PV}={\eta }_{PV}\times A_{PV}\times G\left(t\right)$$

(2)

where ɳ_pv is the efficiency of the solar PV panel; A_pv is the panel surface area (m²); G(t) is the solar irradiance (kW/m²).

3.1. Material

In this study, an 80 W solar PV panel with an open circuit voltage (Voc) of 21.6 V and short circuit current (Isc) of 4.76 A has been used, as shown in

Table 1. System components to be connected to the charge regulators.

Components	Specifications
Photovoltaic module	Wp = 80 W, Vmp = 18 V, Imp = 4.44 A Voc = 21.6 V, Isc = 4.44 A, 780 × 670 × 30 mm
Battery	100 Ah, 12 V
LED light unit	44 W, 12 V

. At normal operating cell temperature (NOCT), the solar PV panel’s maximum power voltage (Vmp) and maximum power current (Imp) are 18 V and 4.44 A, respectively. The dimensions of the solar PV panel are 780 × 670 × 30 mm.

In this study, a 44 W LED lamp is selected for each streetlight since a 36 W LED has proved to offer the required luminance flux at an installation height of 4–7 m [35]. Hence, the total daily energy consumption of each streetlight is determined to be 528 Wh for a total cumulative illumination time of 12 h. For a 12 V battery system, the total current consumption of each streetlight is 3.76 A (44 W/12 V).

Energy storage process is achieved using a charge regulator since it regulates the flow of energy to the battery and to the load. The charge regulators to be used in this study are a series of PWM types, as shown in

Table 2. Solar PWM charge regulators.

Charge Regulators	Sunsaver SS-6L (Regulator A)	Sunguard SK-6 (Regulator B)	Solsum 6.6F (Regulator C)
System voltage	12 V	12 V	12 V or 24 V
Battery voltage range	6–15 V	0–15 V	0–15 V
Max. solar voltage	30 V	30 V	<47 V
Max. solar current	6 A	6 A	6 A
Max. load current	6 A	6 A	6 A
End of charge voltage	15.3 V	15.3 V	13.9 V
Reconnection voltage	12.6 V	13.7 V	12.4 V
Operating Temperature Range	−40 °C to +60 °C	−40 °C to +70 °C	−25 °C to +50 °C

. PWM has proved to be cost-effective for smaller solar arrays and offers high conversion efficiency [16]. To ensure proper sizing of the PWM, the voltage rating of the charger should not exceed or match the system voltage of the array. The amperage rating should be sufficient to handle the maximum current produced by the solar panel. Hence, to ensure that the current rating is sufficient to handle the maximum current produced by the solar PV panel and to incorporate a 25% safety margin, the required amperage rating is then calculated as follows [36]:

$$I_{Charge}=I_{SC}\times 1.25$$

(3)

Given that the short-circuit current (I_sc) of the selected solar PV panel is 4.76 A, the charge regulator should have a current rating of approximately 5.95 A (rounded up to 6 A) to accommodate potential power fluctuations and surges. The three cost-effective (cheaper to buy) and suitable 6 A 4-stage PWM charge regulators were identified for this purpose, namely, Charge regulator A: Morningstar Sunsaver (SS-6L-12 V 6 A) is manufactured by Morningstar Corporation, located at Newtown, PA, USA, Charge regulator B: Morningstar Sunguard (SK-6 6 A/12 V) is manufactured by Morningstar Corporation, located at Newtown, PA, USA, Charge regulator C: Steca Solar charge regulator (Solsum 6.6F 12/24 V, 6 A) is manufactured by Steca GmbH, located at Memmingen, Bavaria, Germany and are as shown in Table 2. All three charge regulators can handle a maximum voltage of 30 V, which exceeds the solar panel’s open-circuit voltage, as detailed in Table 1, below. The selected PWM batteries are all compatible with lead-acid or NiCd batteries.

To size the lead acid battery to be used (in Ah unit), the total energy consumption of the load, the desired autonomy days, as well as the Depth of Discharge (DoD) needs to be considered. Hence, the size of the required battery can be determined as follows [37,38]:

$$Battery \left(\mathrm{A}\mathrm{h} unit\right)={\displaystyle \frac{Load \left(\mathrm{A}\mathrm{h} unit\right)\times {Days}_{Autonomous}}{DoD}}$$

(4)

The efficiency of the lead-acid battery is assumed to be 85% at a DoD of 50% [38,39]. In this study, a 12 V, 100 Ah sealed lead acid battery has been selected to meet the lighting demand at an autonomy of 1 day since the conventional outdoor streetlight will be used as back-up during insufficient solar radiation (e.g., during rainy or cloudy days). Installing streetlights without removing the existing conventional grid-powered streetlights can reduce battery costs. Hence, better economic returns are ensured because of backup reliability and reduced street lighting grid consumption during sunny days.

3.2. Method

The experimental setup of the off-grid, solar-powered LED lighting system is illustrated in Figure 3. The objective is to assess the combined charging and discharging performance of each charge regulator operating in an independent circuit. Three 12 V, 100 Ah sealed lead-acid batteries are used to assess the performance of three different PWM charge regulators rated 6 A, as listed in Table 2. The aim is to select the best charge regulator to be used for the solar-powered streetlight. The tests are conducted simultaneously under uniform meteorological conditions, such as the same temperature and solar irradiance. This methodology enhances the reliability of the results and supports the validation of simulation findings. The experiment was carried out during the winter season, representing a worst-case scenario due to reduced solar irradiance. Three identical 80 Wp solar PV panels have been used to generate electricity for each circuit. Given that the study site is located at a latitude of 29°7′6.06″ South and a longitude of 26°13′29.71″ East, the panels are installed at an optimal tilt angle of 30° facing true North, closely aligned with the site’s latitude (≈29.118°). This is a rule of thumb for fixed solar panels in order to ensure optimal year-round performance during solar energy capturing [40]. All three batteries were verified to be in a fully charged state prior to connecting the 44 W LED lighting load. To confirm this, the no-load terminal voltage of each battery was measured using a multimeter and found to be approximately 12.7 V, revealing a fully charged condition.

In this study, the LabVIEW real-time interface program has been used to measure the real-time output voltage of the solar PV panel, battery voltage, as well as the load current, as shown in Figure 3. LabVIEW uses graphical blocks to represent the source code of a program, as shown in Figure 4. The sample has been measured in a time step of 1.5 min (90,000 ms) for a 2 h snapshot using a virtual instrument Data Acquisition (DAQ). Hence, 82 data points were collected for each charge regulator circuit.

As illustrated in Figure 4, the LabVIEW DAQ system was developed to measure the battery and PV voltage as well as the current consumed by a 44 W LED load via the NI ELVIS prototype board. During voltage measurements, two external voltmeters were used to verify the voltage measurements obtained from the LabVIEW DAQ system. During verification, the battery and PV voltages were adjusted using a calibration scaling factor of 1.196 to align with the actual measured values. The applied calibration scaling factor ensured close agreement between the acquired data and the measured values. To measure the load current, a simple 741 non-inverting op-amp circuit with a gain of 3.2 (Gain = R2/R1 + 1) on an NI ELVIS prototype board was used, as shown in Figure 5.

The op-amp circuit was employed to amplify the low-voltage signal developed across a series 1 Ω resistor, as illustrated in Figure 3. This voltage signal represents the load current in accordance with Ohm’s Law, given the known resistance value of 1 Ω. An external ammeter was used to verify the accuracy of the current measured by the LabVIEW DAQ system. To obtain the actual load current, the amplified signal was divided by a calibration scaling factor approximately equal to the amplifier gain (3.35), as shown in Figure 4. The results demonstrated a close agreement between the externally measured current and the current acquired by the DAQ system.

4. Results and Discussion

The comparison process began by selecting three commercially available 6 A-rated solar charge regulators to be applied to recharge the lead-acid battery of a 12 V off-grid solar photovoltaic (PV) street lighting system. The experiment was conducted during the winter season as a worst-case scenario. The minimum average solar irradiation at the installation site is approximately 3.75 kWh/m²/day during the winter season. The indoor ambient temperature was recorded to be around 15.1 °C, which falls within the specified operating temperature range for all three charge regulators. LabVIEW real-time interface program was then used to acquire the real-time output voltage of the solar PV panel, battery voltage as well as the load current. The acquired data was validated through practical measurements, which confirmed consistency between the measured and acquired values through the calibration process. After acquiring 2 h of data in a sample of 1.5 min (as shown in

Table A1. Data points of voltages and current measurement.

Solsum 6.6F				Sunguard SK-6			Sunsaver SS-6L
Time	Battery	PV	Load	Battery	PV	Load	Battery	PV	Load
H: Min: S	Voltage	Voltage	Current	Voltage	Voltage	Current	Voltage	Voltage	Current
	(V)	(V)	(A)	(V)	(V)	(A)	(V)	(V)	(A)
10:26:01 a.m.	12.474614	20.457887	0.000161	12.482836	20.214258	0.000180	12.488137	20.324011	0.000090
10:27:24 a.m.	12.401295	12.882287	3.510339	12.325702	12.447423	3.528563	12.479800	13.000150	3.679366
10:28:54 a.m.	12.473582	12.723818	3.577161	12.397549	12.346145	3.324453	12.502662	13.016042	3.779010
10:30:24 a.m.	12.337040	12.801710	3.596600	12.261839	12.309397	3.742393	12.435035	13.095684	3.841944
10:31:54 a.m.	12.365597	12.665259	3.662206	12.290222	12.295954	3.737533	12.463819	12.956063	3.831454
10:33:24 a.m.	12.370952	12.698255	3.645197	12.295544	12.293264	3.681646	12.469217	12.989793	3.805233
10:34:54 a.m.	12.382554	12.707446	3.675571	12.307075	12.277132	3.744822	12.480910	12.999159	3.844566
10:36:24 a.m.	12.355780	12.723051	3.634263	12.280465	12.294161	3.448377	12.453924	13.015093	3.873410
10:37:54 a.m.	12.402187	12.699225	3.786130	12.326589	12.269066	3.733888	12.500699	12.990689	3.743611
10:39:24 a.m.	12.369168	12.750624	3.708374	12.293771	12.298643	3.797065	12.467418	13.043230	3.777699
10:40:54 a.m.	12.358458	12.720364	3.678001	12.283126	12.289680	3.668281	12.456623	13.012244	3.730499
10:42:24 a.m.	12.404864	12.713032	3.633048	12.329250	12.269066	3.755757	12.503398	13.004715	3.752789
10:43:54 a.m.	12.356673	12.764471	3.688935	12.281352	12.269962	3.714449	12.454824	13.057298	3.772455
10:45:24 a.m.	12.362028	12.718566	3.718094	12.286675	12.304916	3.679216	12.460222	13.010309	3.819654
10:46:54 a.m.	12.391240	12.740369	3.693795	12.315709	12.254725	3.676786	12.477312	13.032577	3.843255
10:48:24 a.m.	12.371588	12.761540	3.645197	12.296176	12.260103	3.701085	12.482191	13.054199	3.785565
10:49:54 a.m.	12.375161	12.744990	3.824729	12.299727	12.265480	3.845662	12.485796	13.037235	3.917987
10:51:24 a.m.	12.366228	12.752360	3.716879	12.290848	12.282510	3.668281	12.476783	13.044743	3.796055
10:52:54 a.m.	12.401067	12.746840	3.798280	12.325475	12.268169	3.618469	12.511934	13.039065	3.866854
10:54:24 a.m.	12.373374	12.786451	3.695010	12.297951	12.277132	3.579591	12.483994	13.079551	3.797366
10:55:54 a.m.	12.346575	12.761580	3.660992	12.271316	12.258310	3.741178	12.456955	13.054084	3.814410
10:57:24 a.m.	12.442160	12.737629	3.664636	12.366318	12.269962	3.597815	12.553394	13.029544	3.832765
10:58:54 a.m.	12.343001	12.839953	3.720524	12.267764	12.261896	3.718094	12.453349	13.134179	3.765899
11:00:24 a.m.	12.353722	12.741299	3.697440	12.278419	12.226045	3.653702	12.464165	13.033237	3.831454
11:01:54 a.m.	12.368014	12.756050	3.681646	12.292624	12.269962	3.654917	12.478585	13.048293	3.739677
11:03:24 a.m.	12.393920	12.774491	3.669496	12.318372	12.281613	3.658562	12.504723	13.067128	3.769833
11:04:54 a.m.	12.322455	12.804952	3.736318	12.247343	12.277132	3.612394	12.432619	13.098247	3.794744
11:06:24 a.m.	12.351042	12.734789	3.780056	12.275755	12.259206	3.522488	12.461461	13.026447	3.878654
11:07:54 a.m.	12.357754	12.780639	3.628188	12.286120	12.337182	3.551177	12.459659	13.073320	3.836699
11:09:24 a.m.	12.346133	12.782481	3.692580	12.274566	12.254725	3.592297	12.447942	13.075167	3.902254
11:10:54 a.m.	12.332723	12.774142	3.682860	12.261234	12.236800	3.551177	12.434422	13.066605	3.789500
11:12:24 a.m.	12.322891	12.763941	3.656132	12.251459	12.236800	3.551177	12.424508	13.056143	3.759344
11:13:54 a.m.	12.427481	12.757444	3.676786	12.355442	12.257415	3.551177	12.519961	13.049461	3.739677
11:15:24 a.m.	12.333618	12.869432	3.680431	12.262123	12.206327	3.551177	12.435323	13.163977	3.817032
11:16:54 a.m.	12.321102	12.775903	3.769121	12.249680	12.243970	3.471351	12.422705	13.068282	3.831454
11:18:24 a.m.	12.312163	12.766613	3.747252	12.240793	12.243970	3.676072	12.413692	13.058747	3.784254
11:19:54 a.m.	12.314845	12.761027	3.705944	12.243460	12.239489	3.548679	12.416396	13.052997	3.620367
11:21:24 a.m.	12.442677	12.767483	3.718094	12.370551	12.237696	3.622367	12.515282	13.059566	3.588900
11:22:54 a.m.	12.327360	12.903719	3.741178	12.255902	12.217082	3.629861	12.429015	13.198892	3.956009
11:24:24 a.m.	12.313951	12.787804	3.746037	12.242570	12.229629	3.663582	12.415494	13.080295	3.925855
11:25:54 a.m.	12.305012	12.777573	3.653702	12.233683	12.230526	3.678571	12.406481	13.069791	3.803922
11:27:24 a.m.	12.292497	12.771966	3.736318	12.221241	12.242178	3.589894	12.393864	13.064025	3.664945
11:28:54 a.m.	12.273725	12.762646	3.730243	12.202577	12.332701	3.589894	12.374936	13.054457	3.743611
11:30:24 a.m.	12.318421	12.746808	3.743607	12.247015	12.211705	3.618621	12.420002	13.038233	3.898321
11:31:54 a.m.	12.274618	12.796902	3.704729	12.203465	12.232319	3.777238	12.375837	13.089440	3.883899
11:33:24 a.m.	12.368481	12.755066	3.696225	12.296785	12.211705	3.683566	12.470474	13.046608	3.929788
11:34:54 a.m.	12.296072	12.856286	3.695010	12.224796	12.176750	3.573658	12.399919	13.163109	3.883899
11:36:24 a.m.	12.296072	12.784687	3.708374	12.224796	12.262792	3.704798	12.399919	13.089771	3.793433
11:37:54 a.m.	12.254058	12.788361	3.713234	12.183024	12.209015	3.724781	12.357549	13.093495	3.567923
11:39:24 a.m.	12.218301	12.748316	3.519309	12.147475	12.203638	3.509190	12.321490	13.052465	3.444679
11:40:54 a.m.	12.271043	12.714758	3.738748	12.199911	12.219771	3.673574	12.374677	13.018078	3.844566
11:42:24 a.m.	12.304796	12.773302	3.664636	12.231017	12.200949	3.661085	12.406229	13.077987	3.914054
11:43:54 a.m.	12.300325	12.809542	3.703514	12.226573	12.211705	3.629861	12.401721	13.115057	3.906187
11:45:24 a.m.	12.285126	12.808560	3.804354	12.211465	12.203638	3.626114	12.386397	13.114015	3.858988
11:46:54 a.m.	12.394207	12.796396	3.730243	12.319892	12.195571	3.606130	12.496377	13.101529	3.893077
11:48:24 a.m.	12.263667	12.913707	3.704729	12.190134	12.180335	3.747263	12.364761	13.221611	3.889143
11:49:54 a.m.	12.239527	12.781358	3.752112	12.166139	12.192883	3.741018	12.340422	13.086069	3.784254
11:51:24 a.m.	12.252044	12.759842	3.753327	12.178581	12.265480	3.594890	12.353042	13.064015	3.855054
11:52:54 a.m.	12.378113	12.776551	3.726598	12.303895	12.182128	3.642350	12.480151	13.081084	3.873410
11:54:24 a.m.	12.249361	12.911703	3.763047	12.175914	12.191987	3.636106	12.350337	13.219431	3.903565
11:55:54 a.m.	12.273336	12.781054	3.763047	12.199139	12.214394	3.702301	12.375324	13.085636	3.824899
11:57:24 a.m.	12.244891	12.809097	3.722953	12.171471	12.165099	3.676072	12.345830	13.115827	3.852432
11:58:54 a.m.	12.236844	12.783695	3.730243	12.163472	12.186610	3.713541	12.337717	13.088274	3.928477
12:00:24 p.m.	12.277575	12.791576	3.693795	12.167817	12.190194	3.794723	12.366564	13.096293	3.835388
12:01:54 p.m.	12.275785	12.825137	3.767906	12.166043	12.163306	3.790976	12.364761	13.130630	3.925855
12:03:24 p.m.	12.248936	12.826930	3.744822	12.139434	12.163306	3.733524	12.337717	13.132432	3.820966
12:04:54 p.m.	12.249830	12.802527	3.731458	12.140320	12.162410	3.747263	12.338618	13.107416	3.841944
12:06:24 p.m.	12.249830	12.807116	3.671926	12.140320	12.153447	3.765997	12.338618	13.112082	3.883899
12:07:54 p.m.	12.269521	12.810773	3.863887	12.159835	12.156136	3.736022	12.358451	13.115790	3.891766
12:09:24 p.m.	12.240880	12.835024	3.769121	12.131451	12.154343	3.661085	12.329603	13.140586	3.911432
12:10:54 p.m.	12.237301	12.808706	3.713234	12.127903	12.153447	3.853424	12.325998	13.113618	3.709522
12:12:24 p.m.	12.214926	12.808615	3.647627	12.105728	12.132833	3.711043	12.303460	13.113488	3.806544
12:13:54 p.m.	12.231931	12.788841	3.693795	12.122581	12.141796	3.716039	12.320588	13.093208	3.883899
12:15:24 p.m.	12.229246	12.810287	3.697440	12.119920	12.130144	3.789727	12.317884	13.115139	3.870787
12:16:54 p.m.	12.270416	12.811127	3.834728	12.160722	12.164203	3.733524	12.359353	13.115961	3.845877
12:18:24 p.m.	12.191668	12.857908	3.696225	12.105728	12.130144	3.813457	12.303460	13.163831	3.879966
12:19:54 p.m.	12.205068	12.803408	3.714449	12.119033	12.115804	3.737271	12.316983	13.107998	3.889143
12:21:24 p.m.	12.273851	12.821126	3.696225	12.187331	12.169580	3.642350	12.386397	13.126107	3.788189
12:22:54 p.m.	12.206855	12.897050	3.727813	12.120807	12.139107	3.662623	12.318786	13.203803	3.895699
12:24:24 p.m.	12.244373	12.830293	3.787345	12.158061	12.139107	3.672325	12.356648	13.135433	3.899632
12:25:54 p.m.	12.189882	12.873386	3.701085	12.103954	12.216186	3.639853	12.301657	13.179519	3.849810
12:27:24 p.m.	12.178269	12.819738	3.770336	12.092423	12.110426	3.650806	12.289938	13.124563	3.827521

), the snapshots of regulators’ performances are analyzed and compared. The comparison results are shown in Figure 6, Figure 7 and Figure 8 below. As previously mentioned, when measurements are taken over a short time window starting from a 100% SoC, battery behavior can often be approximated as linear. This is because the most significant nonlinear effects typically arise at lower SoC levels. Furthermore, since new batteries were used in this study, their state of health is assumed to be 100%, which delays the onset of nonlinear behavior. Another contributing factor is the low discharge current drawn from the batteries, as the solar PV panels also contribute to supplying current to the load. This further reduces the rate at which the battery transitions into nonlinear response regions. Given these conditions, the use of the Linear Regression Algorithm (LRA) is appropriate for comparing the relative slope differences in battery voltage across the charge regulators (i.e., the rate of change in battery voltage). In this context, the slope derived from LRA serves as a performance indicator for each charge regulator rather than a detailed model of battery behavior. It is also important to note that using new batteries is critical when comparing charge regulator performance. Previous studies [41,42] have shown that as batteries age, nonlinearity becomes more pronounced due to capacity loss and increased internal impedance from repeated charge–discharge cycles.

Solar PV module receives sunlight and converts it into electricity. The generated current will then be supplied to the battery and load via the PWM solar charge regulator, which has proved to be cost-effective for smaller solar array projects [16,17,18]. The charge regulator is designed to control the DC voltage and current from the solar panel to the battery to ensure safe charging and discharge.

Figure 6, Figure 7 and Figure 8 present the battery voltage, solar PV voltage, and load current data as acquired simultaneously via LabVIEW for each PWM charge regulator. Prior to switching on the LED lighting load, battery voltages were measured at 10:26:01 a.m. to verify that all batteries are in a fully charged state, as shown in Figure 6. Hence, the open-circuit battery voltage in each circuit was approximately 12.48 V since they are in a fully charged state. The corresponding open-circuit voltage across each solar panel was around 20 V, namely 20.21425808 V, 20.033674 V, and 20.166225 V, respectively, as shown in Table A1 and Figure 7, since no load was connected. Following confirmation of the batteries’ fully charged condition, all three charge regulator circuits were simultaneously activated to supply power to their respective loads for a duration of two hours, during which data was recorded.

As shown in Figure 6, when the load is connected, the battery voltage fluctuates to represent charging and discharging activity as a result of a change in solar irradiance due to partly cloudy conditions. During the winter season, when solar radiation is limited, the observed decline in battery voltage indicates that the solar PV panel is unable to meet the full load demand on its own. Hence, the batteries discharge to compensate for the energy deficit. This discharging process occurs under all three charge regulators. To compare their discharge performance, the Linear Regression Analysis (LRA) method is applied to analyze the gradients of the battery voltage curves. The linear line (trendline) for each regulator is shown by the dashed lines as determined from data series. In this context, a steeper slope corresponds to a more rapid discharge rate, thereby providing a quantitative basis for performance comparison. The comparison indicates that regulator A exhibits a more favorable gradient of −2.2355, suggesting a slower battery discharge rate compared to the other two charge regulators. Such performance is attributed to lower internal losses, likely due to reduced idle current consumption. This represents that regulator A offers the best charging performance as compared to the other two charge regulators.

As shown in Figure 8, all three charge regulators consistently supply current to the lighting load at levels approaching the full-load current of 3.76 A. Minor fluctuations in the supplied current are attributed to variations in solar irradiance. Regulator A delivers a slightly higher current to the load, attributed to its superior conversion efficiency. Figure 7 illustrates the solar PV voltage for each charge regulator circuit. Since solar module voltage is directly proportional to solar irradiance, an increase in irradiance is observed as the day progresses from 10:26 a.m. to 12:27 p.m. [43]. Fluctuations in irradiance due to intermittent cloud cover are also noted. Despite these variations, Figure 7 shows that the solar PV voltage remains relatively stable, which is characteristic of PWM charge regulators. Unlike the MPPT type, the PWM regulators regulate the PV module voltage to remain close to the battery voltage [44].

To evaluate if regulator A consistently offers the best charging performance throughout all 82 data points (10:26 a.m. to 12:27 p.m.), the slopes are determined in steps of 10 samples, as shown in

Table 3. Slope and Coefficient of Determination in steps of 10 data points.

Number of Data Points (n) Time: H: Min: S	Charge Regulator	Coefficient of Determination (R2)	Slope (m)
n = 10 From: 10:26:01 a.m. To: 10:39:24 a.m.	Regulator A	0.0150	−0.814
	Regulator B	0.2937	−8.081
	Regulator C	0.3461	−12.412
n = 20 From: 10:26:01 a.m. To: 10:54:24 a.m.	Regulator A	0.0396	0.632
	Regulator B	0.1345	−2.113
	Regulator C	0.1674	−3.250
n = 30 From: 10:26:01 a.m. To: 11:09:24 a.m.	Regulator A	0.0059	−0.210
	Regulator B	0.1902	−1.706
	Regulator C	0.1927	−2.172
n = 40 From: 10:26:01 a.m. To: 11:24:24 a.m.	Regulator A	0.1370	−0.980
	Regulator B	0.2256	−1.606
	Regulator C	0.2085	−1.780
n = 50 From: 10:26:01 a.m. To: 11:39:24 a.m.	Regulator A	0.4198	−1.921
	Regulator B	0.4685	−2.329
	Regulator C	0.4306	−2.401
n = 60 From: 10:26:01 a.m. To: 11:54:24 a.m.	Regulator A	0.4503	−1.871
	Regulator B	0.4839	−2.146
	Regulator C	0.4591	−2.207
n = 70 From: 10:26:01 a.m. To: 12:09:24 p.m.	Regulator A	0.6127	−2.124
	Regulator B	0.6095	−2.227
	Regulator C	0.6266	−2.546
n = 80 From: 10:26:01 a.m. To: 12:24:24 p.m.	Regulator A	0.6944	−2.189
	Regulator B	0.6943	−2.282
	Regulator C	0.7157	−2.661
n = 82 From: 10:26:01 a.m. To: 12:27:24 p.m.	Regulator A	0.7155	−2.235
	Regulator B	0.7159	−2.344
	Regulator C	0.7351	−2.708

. The slope (m) and Pearson correlation coefficient (R²) are determined using the relationship between the scalar variable (Y) and explanatory variables denoted by (X) using Equations (5) and (6) [45]. To represent a strong linear relationship, the golden rule is to allow the coefficient of determination, R², to lie between 0.7 and 1 [46]. Hence, the more the data points, the R² increases until it reaches a value of above 0.7 to represent a strong linear relationship for all the charge regulators.

$$m={\displaystyle \frac{n\sum \left(XY\right)-\sum X\cdot \sum Y}{n\sum \left(X^2\right)-{\left(\sum X\right)}^2}}$$

(5)

$$R={\displaystyle \frac{n\sum \left(XY\right)-\sum X\cdot \sum Y}{\sqrt{\left[n\sum \left(X^2\right)-{\left(\sum X\right)}^2\right]\hspace{0.33em}\left[n\sum \left(Y^2\right)-{\left(\sum Y\right)}^2\right]}}}$$

(6)

As shown in Table 3, the absolute value of the slope (m) for regulator A (Sunsaver SS-6L) is consistently lower than that of the other two regulators across all data points. As the number of data points increases, R² also increases until it rises above 0.7 (70%), indicating a strong linear relationship and thereby strengthening the validity of the comparison. Hence, charge regulator A has been determined to be the most suitable 6 A PWM charge regulator for the proposed project and is therefore recommended for bulk procurement, owing to its best charging performance compared to the other regulators evaluated.

5. Conclusions

This study presents a practical and data-driven methodology for selecting an efficient PWM solar charge regulator for use in a real-world off-grid solar PV streetlight configuration. The primary objective was to address the challenge of identifying the most suitable regulator among the three commercially available selected units with identical load current ratings, particularly when manufacturers do not provide efficiency specifications in the data sheets. Data acquisition was performed using LabVIEW-based virtual instrumentation to analyze battery charge/discharge behavior over time. Linear Regression Algorithm (LRA) has proved to be suitable to analyze battery discharge performance only in the linear SoC region of the voltage curve.

All three charge regulators consistently delivered current to the lighting load at levels nearing the full-load current of 3.76 A as tests were conducted simultaneously under similar environmental conditions to minimize comparative measurement errors. However, their battery discharge rates varied significantly. The discharge slope reflects the rate of battery voltage decline under constant load, providing a useful indication of how much current is drawn from the battery relative to the charging contribution from the regulator. This is a reasonable proxy for internal losses and voltage drop. A steeper slope suggests higher net discharge, while a flatter slope indicates more effective energy retention. This LRA resulted in the identification of the best charge regulator, characterized by low internal losses. This regulator demonstrated the slowest discharge rate (i.e., the least negative voltage gradient of −2.235 as compared to −2.344 and −2.708 offered by other charge regulators) as a result of the lowest voltage drop. These characteristics make it the most suitable option for enhancing the performance and reliability of small-scale off-grid solar PV systems.

The study has identified the following future gaps:

1.

For long-term systems optimization, a more comprehensive efficiency analysis that incorporates coulombic efficiency, energy balance over time, and idle current measurement should be undertaken to study the nonlinear behavior.

2.

Incorporating a full GUM-based analysis for uncertainty in future extended studies, particularly those involving long-term field data or model-based performance extrapolation.

3.

While this study focuses on PWM regulators, the results should not be generalized to all types of charge regulators. Hence, future work will include benchmarking other regulator types, such as MPPT regulators, for further validation.

4.

Additionally, further testing using various battery chemistries—such as Lithium-ion, Nickel-Cadmium (Ni-Cd), and Nickel-Metal Hydride (Ni-MH)—is recommended to study optimal compatibility and system performance in a small-scale solar project.

5.

A future study will be conducted to study the impact of seasonal variations on the performance of the PWM charge regulators.