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Robust PV MPPT optimization via LSTM

58
recurrent neural network and condition-based
super-twisting sliding mode controller
1 1st OMAR ZEB
Electrical Engineering department, SEECS
8 National University of Sciences and Technology (NUST) Islamabad, Pakistan
ozeb.dphd18seecs@seecs.edu.pk

2nd Iftikhar Ahmad

Electrical Engineering department, SEECS
National University of Sciences and Technology (NUST) Islamabad, Pakistan
45 Corresponding author: iftikhar.rana@seecs.edu.pk

Abstract—As global energy demand rises and the environ- its abundance and sustainability, solar power significantly
mental impact of fossil fuel consumption becomes increasingly contributes to clean energy generation worldwide [1]. Over
41 concerning, the need for efficient and sustainable energy solutions recent years, the adoption of solar harvesting technologies has
has never been more urgent. Solar energy, with its immense
potential, has become a focal point in the renewable energy grown rapidly due to their environmentally friendly nature
20 sector. However, the performance of photovoltaic (PV) systems is and adaptability. Although photovoltaic panels are widely
28 significantly impacted by varying environmental conditions, such deployed, their power output remains highly sensitive to
as changes in temperature and sunlight, making it challenging to variations in ambient conditions such as temperature and
7 consistently extract maximum power. To address this, Maximum irradiance [2]. To ensure efficient power extraction under
Power Point Tracking (MPPT) techniques are used to optimize
42 changing environmental inputs, maximum power point track-
1 energy harvest. Given the nonlinear nature of PV systems,
advanced control strategies are needed for effective MPPT. While ing techniques are implemented. These strategies work by
1
52 traditional methods like Perturb and Observe (P&O) have been dynamically regulating the converter’s duty cycle to maintain
1 widely used, recent advancements in artificial intelligence offer operation at an optimal voltage corresponding to the maximum
29 more sophisticated solutions. This study introduces a Long Short- power point [3]. Modern research has emphasized the design
Term Memory (LSTM) Recurrent Neural Network (RNN) for
MPPT, which is particularly well-suited to handle the time- of advanced MPPT algorithms that ensure reliable and precise
dependent nature of PV system behavior. The LSTM’s abil- tracking, enabling PV modules to operate at peak efficiency
ity to learn long-term dependencies and adapt to fluctuating [4]. Conventional MPPT techniques like (P&O) [5], [6], In-
environmental conditions makes it ideal for tracking the PV cremental Conductance (INC) [7]–[9], and Hill Climbing [10],
15
system’s optimal power point. To further enhance its robust- [11] are extensively utilized due to their algorithmic simplicity
9 ness, we combine the LSTM controller with a condition-based
super-twisting sliding mode control (C-STSMC) strategy, which and ease of implementation. However, these methods often
3 effectively addresses nonlinearities and improves performance suffer from persistent oscillations near the MPP, which can
7 under changing conditions. This paper presents the design and lead to power loss and reduced efficiency.
12 implementation of the LSTM-based MPPT controller, comparing In recent research, efforts have been made to enhance these
its performance with traditional methods like P&O and Fuzzy classical algorithms through integration with intelligent control
Logic controllers. Experimental results from hardware-in-loop
(HIL) testing demonstrate the real-time capabilities, improved methods. For instance, [12], [13] incorporated artificial neural
accuracy, and robustness of the proposed controller. The find- networks (ANNs) into the P&O method to achieve improved
ings show that the LSTM-based MPPT algorithm significantly performance. Additionally, soft computing techniques such as
enhances PV system efficiency, offering a more reliable solution fuzzy logic [14] and hybrid PI-fuzzy systems [15] have demon-
in dynamic and unpredictable environments. strated encouraging results in enhancing MPPT performance.
Index Terms—LSTM-RNN, MPPT, Robust Nonlinear Control,
Recurrent neural networks have shown greater effectiveness
40 P&O, Fuzzy Logic control , HIL
than standard ANNs due to their ability to capture temporal
patterns in solar irradiance and temperature fluctuations [16].
I. INTRODUCTION
While PI controllers are still favored for their straightforward
Solar energy has become a promising alternative in mit- design, their inability to accommodate the nonlinear dynamics
31 igating environmental challenges, including greenhouse gas of PV systems presents a significant drawback. As a result, the
emissions and the depletion of fossil fuels. Recognized for development of robust nonlinear control strategies has gained

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traction to address the dynamic uncertainties and nonlinear

behavior encountered in real-world PV systems [17].
Numerous MPPT strategies are rooted in mathematical
modeling, while others like fuzzy logic depend on heuristic
design, mapping control actions based on expert knowledge
33 [13]. In this context, nonlinear control methodologies such as
sliding mode control (SMC) and backstepping have gained
attention for their robustness in tracking MPP under rapidly
changing environmental conditions [18]. Given the nonlinear
22 characteristics of PV modules and DC-DC converters, non-
linear controllers tend to offer superior disturbance rejection
and dynamic tracking performance. For instance, a Lyapunov-
based controller was introduced in [19], which utilized a non- Fig. 1: Proposed LSTM-based MPPT control structure for PV
inverting buck-boost converter topology [20], [21]. Moreover, system.
enhancements like integral backstepping were adopted in [21]
to improve precision, while further work developed robust
backstepping controllers capable of handling parameter uncer-
7 is generated for each unique combination of temperature
tainties due to temperature and irradiance changes [22]–[24].
and irradiance. A DC-DC buck-boost converter adjusts the
In contrast, linear controllers often underperform in scenarios
duty cycle accordingly. The LSTM network uses historical
with fast-changing dynamics and nonlinear behavior [25].
and current data trends to forecast the optimal voltage. Its
13 In this work, a novel MPPT optimization strategy is pre-
architecture, derived from multilayer perceptrons, incorporates
9 sented by combining a condition-based super-twisting sliding
feedback connections through memory cells, enabling it to
25 mode controller with a long short-term memory recurrent
identify temporal patterns and dependencies.
neural network. The LSTM model is employed to accu-
The LSTM model is trained using real-world PV data
57 rately predict the reference voltage corresponding to maximum
48 with temperature and solar irradiance as the input features.
power, leveraging its strength in modeling time-sequenced
The output is a predicted reference voltage VPVref , aimed at
environmental inputs. Meanwhile, the C-STSMC enhances the
enhancing energy extraction. For comparison, the reference
system’s robustness and transient performance. A buck-boost
voltage can also be estimated using a linear regression model,
18 converter is used as the interface between the PV module and
shown in Eq. 1, which is based on empirical data fitting:
the load, ensuring wide-range voltage regulation.
11 The organization of this paper is as follows: Section 1
introduces the study. Section 2 presents the proposed control Vpvref = 322−(1.2669×T emp(C))−(0.00964×Irr(W/m2 ))
scheme and LSTM-based reference voltage prediction. Section (1)
3 discusses the system modeling, while Section 4 details the
51 design of the nonlinear control laws applied to the buck-boost B. Training Procedure of LSTM-RNN Model
26 converter. Section 5 provides simulation and hardware-in-the- The LSTM-based reference voltage prediction model is
loop results, and Section 6 concludes the research. trained in MATLAB using the nonlinear time-series predic-
II. THE PROPOSED CONTROL SCHEME tion toolbox. It processes two primary environmental inputs,
55 temperature and solar irradiance to estimate the optimal PV
Accurate modeling of PV modules is essential to ensure
voltage at the MPP. To improve generalization under real-
efficient utilization of solar energy in simulations. Unlike con-
world variability, synthetic uncertainty is added to the training
60 ventional MPPT strategies that directly estimate the maximum
data, helping the model become more robust to noise and
power point (MPP), nonlinear control approaches generate
fluctuations. The network architecture, shown in Fig. 2, com-
a reference voltage corresponding to optimal operation. The
5 prises an input layer, a hidden layer with four memory units,
37 dynamic relationship between irradiance, temperature, and the
and an output layer. This configuration enables the LSTM to
maximum power point voltage (VMPP ) can be captured using
learn temporal patterns in the input data and accurately predict
36 intelligent algorithms such as fuzzy logic, regression models,
reference voltage values for the controller.
and various neural network architectures.
Regression plots generated from MATLAB R2023b are
In this study, an LSTM recurrent neural network is em-
shown in Fig. 3, demonstrating a strong correlation between
ployed to learn this relationship, providing a predicted ref-
the predicted and actual MPP voltages, indicating the LSTM
erence voltage for use in a robust nonlinear controller built
model’s high predictive accuracy.
10 around a non-inverting buck-boost converter. The overall con-
32 The training behavior of the LSTM-RNN model is depicted
10 trol approach is illustrated in Fig. 1.
in Fig. 4, where the top subplot illustrates the evolution of
3 A. Prediction of PV Reference Voltage via LSTM the root mean square error (RMSE) and the bottom subplot
To enable the controller to perform precise MPP tracking presents the loss over 500 training iterations. Both RMSE
under dynamic environmental conditions, a reference voltage and loss curves exhibit a rapid decline in the early iterations,

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5 derived for controller design. The schematic diagram of the

converter is shown in Fig. 5.

A. Mode 1: Power Storage Phase

5 In this mode, switches S1 and S2 are ON while diode D1 is
43 reverse-biased. The inductor stores energy from the PV source.
Applying Kirchhoff’s laws yields:

diL
Vin = L + Vout
dt
The corresponding PV-side equations are:
Fig. 2: LSTM training framework using MATLAB toolbox.
iC1 = ipv − iL (2)

dvpv ipv iL
= − (3)
dt C1 C1

vL = vpv (4)

diL vpv
= (5)
dt L

−vo
iC = (6)
R

dvo −vo
= (7)
dt RC
Fig. 3: Regression plot of LSTM output vs. target.
B. Mode 2: Power Transfer Phase
Here, S1 and S2 are OFF, and D2 conducts. The inductor
discharges its energy to the load through the output diode:
followed by a smooth convergence to near-zero values. The
minimal and stable RMSE attained throughout training high- diL
lights the model’s high accuracy in learning the underlying Vout = L
dt
data patterns. This level of precision is critical for accurately
tracking the MPP under varying environmental conditions. The The system dynamics in this mode are:
smoothed curves further validate the consistency and robust-
ness of the training process, ensuring the model’s capability to iC1 = ipv (8)
generalize and effectively predict VMPP with negligible error.
While traditional MPPT algorithms rely on static rela-
tionships modeled via regression, LSTM-based approaches dvpv ipv
= (9)
dynamically adapt to nonlinear and time-varying conditions, dt C1
providing improved accuracy, adaptability, and robustness in
estimating the MPP reference voltage under fluctuating envi- vL = −vo (10)
ronmental parameters.

III. SYSTEM MODELING AND MATHEMATICAL diL −vo

= (11)
23 REPRESENTATION dt L
To regulate the PV system voltage and ensure maximum vo
59 power transfer, we employ a non-inverting buck-boost con- iC = iL − (12)
R
verter. The system operates in two distinct switching modes,
each with different electrical characteristics. These modes dvC iL vo
are modeled individually, and an average dynamic model is = − (13)
dt C RC

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Fig. 4: The training behavior of the LSTM-RNN model.

IV. DESIGN OF NONLINEAR CONTROLLER : C - STSMC

39 The main objective of the control strategy is to ensure
accurate tracking of the reference PV voltage, g1ref , generated
14 by the LSTM-based RNN described earlier. To achieve this,
14 a robust nonlinear controller C-STSMC is developed. The
voltage tracking error is defined as:

e1 = g1 − g1ref (17)

Taking the time derivative and substituting from the aver-

aged system model (equation 11):
ipv g2
Fig. 5: Buck-boost (Noninverting) converter topology ė1 = − u − ġ1ref (18)
C1 C1
To design the sliding manifold, a first-order sliding surface
is defined as:
C. Averaged System Model S1 = a1 e1 (19)
To design a continuous-time controller, we derive the aver-
where a1 > 0 is a design gain. The derivative of the sliding
aged model over one switching cycle using duty cycle u. Let
surface is:
g1 = vpv , g2 = iL , and g3 = vo denote the average states:  
ipv g2
Ṡ1 = a1 − u − ġ1ref (20)
ipv g2 C1 C1
ġ1 = − u (14)
49 C1 C1 To ensure robust convergence of the sliding variable to zero,
a conditioned reaching law is defined as:
 
g3 g1 + g3 R1  
S1
ġ2 = − + u− g2 (15) Ṡ1 = −k1 |S1 |α sign − v1 (21)
L L L ϕ1
where: k1 > 0 is a control gain, α ∈ (0, 1) ensures
g2 g3 g2
ġ3 = − − u (16) finite-time convergence, ϕ1 is a boundary layer thickness that
C RC C
mitigates chattering, v1 is a smooth compensator term to
21 D. Modeling Remarks handle actuator saturation. The Lyapunov candidate function
is selected as:
This state-space model encapsulates the averaged behavior 1
V = S12 (22)
10 of the buck-boost converter using volt-second and charge 2
balance principles. It forms the basis for designing a nonlinear Taking the derivative:
44 control strategy for maximum power point tracking (MPPT)
under dynamic load and irradiation conditions. V̇ = S1 Ṡ1 (23)

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Substituting equation (12) and the reaching law (14) into TABLE II: Electrical Design Parameters of Buck-Boost Con-
the Lyapunov derivative: verter
    Electrical Component Specified Value
S1 Capacitors C1 , C2 27 × 10−4 F
V̇ = S1 −k1 |S1 |α sign − v1 (24) Load Resistance RL 12 Ω
ϕ1
Inductance L 4.5 × 10−6 H
Switching Frequency 95 kHz
This ensures V̇ < 0, guaranteeing asymptotic stability under
the Lyapunov criterion. To address actuator limits and smooth
transitions, v1 is defined using an integral action term: A. PV Voltage Response under Varying Irradiance
17 The irradiance was modified from 1000 W/m2 to 800 W/m2 ,
Z
v1 = p1 sign(usat − v1 ) dt (25) and then to 500 W/m2 , with transitions every 0.05 seconds
30 while maintaining a constant temperature of 25°C. As shown
where p1 > 0 is a design constant, and usat is the saturated in Figure 6, the LSTM-RNN-based controller maintains volt-
control input: age tracking with minor steady-state errors during transitions,
( indicating strong adaptability to irradiance variability.
u, |u| ≤ R
usat = (26)
R sign(u), |u| > R

By equating equations (13) and (14), the closed-form control

input u is derived:
   
α S1 ipv g2
−k1 |S1 | sign − v1 = a1 − u − ġ1ref (27)
ϕ1 C1 C1

46 Solving for u, we obtain the final nonlinear control law:

   
C1 a1 ipv α S1
u= − a1 ġ1ref + k1 |S1 | sign + v1 Fig. 6: PV voltage response with changing irradiance using
a1 g2 C1 ϕ1 LSTM-RNN based controller
(28)
This control input ensures fast convergence, robustness to
parameter uncertainty, and smooth operation in the presence B. PV Voltage Response under Variable Temperatures
19
of actuator constraints. The designed C-STSMC controller Temperature is increased from 25°C to 30°C and finally to
12 ensures accurate tracking of the PV reference voltage g1ref 35°C over intervals from 0.5s to 2.5s, while irradiance remains
47
generated by the LSTM-RNN. It offers improved dynamic at 1000 W/m2 . As seen in Figure 7, the controller tracks
response and robustness by incorporating finite-time conver- the voltage reference accurately with negligible overshoot,
gence and adaptive compensation for chattering and saturation. showcasing effective temperature compensation.

V. SIMULATION - BASED PERFORMANCE EVALUATION

54 This section presents the simulation-based analysis of the

35 proposed LSTM-RNN-based nonlinear controller applied to a
PV system integrated with a buck-boost converter. The perfor-
38 mance is evaluated under dynamic environmental conditions
such as variations in solar irradiance and ambient temperature.
56 MATLAB/Simulink was used to validate the system response.
Key control and converter parameters are provided in Tables
I and II respectively.
Fig. 7: PV voltage tracking under different temperature levels
TABLE I: Control Parameters for LSTM-RNN based C-
STSMC Controller
9 Control Parameter Assigned Value C. Hardware-in-the-Loop (HIL) Validation
k1 , k 2 1200, 1380 The controller implementation was validated using a Texas
a1 1.45
p1 0.0105 Instruments TMS320F28379D DSP through HIL testing. The
α 0.91 controller generates duty ratios in real-time by interfacing
φ1 0.61 with dual LaunchPad modules. HIL test results closely match
simulated performance under both irradiance and temperature

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13 fluctuations, as shown in Figures 8 and 9, with only minor VI. CONCLUSION AND FUTURE W ORK
acceptable voltage spikes, confirming real-time feasibility.
This work presented a novel LSTM-RNN-based C-STSMC
53 robust controller for efficient MPPT in PV systems using
a buck-boost converter. Through extensive simulations and
(HIL) validation, the proposed controller demonstrated su-
perior dynamic tracking performance under varying envi-
ronmental conditions, including fluctuations in solar irradi-
24 ance and temperature. Compared to conventional techniques
such as Perturb and Observe (P&O) and intelligent methods
like Fuzzy Logic, the LSTM-RNN-based C-STSMC achieved
3 faster convergence to the MPP, reduced steady-state oscilla-
tions, and enhanced stability. The integration of the recurrent
neural architecture enabled the controller to learn temporal
Fig. 8: Simulated vs. HIL response during irradiance variations
dependencies in system behavior, thereby improving real-time
adaptability.
The HIL results confirmed the feasibility of implementing
the proposed control strategy on low-cost embedded platforms
such as TI’s TMS320F28379D DSP. The consistency between
simulation and HIL outcomes further validates the robustness
34 and real-time applicability of the developed controller.
Future research will focus on the following directions:
• Integration with Energy Storage Systems (ESS): Ex-
panding the controller framework to manage hybrid PV-
battery systems, enabling coordinated control for both
power generation and storage.
Fig. 9: Simulated vs. HIL response during temperature varia- • Grid-Tied Operation: Extending the model to support
tions grid-connected PV configurations while ensuring compli-
ance with power quality and grid-code requirements.
• Real-Time Machine Learning Optimization: Incor-
D. Comparative Analysis with Classical and Intelligent Con- porating adaptive learning mechanisms that allow the
trollers controller to self-tune its parameters based on real-time
A comparative assessment was conducted between the pro- operating data for improved long-term performance.
27 posed LSTM-RNN-based C-STSMC, classical Perturb and • Multi-Objective Optimization: Designing the controller

63 Observe (P&O), and Fuzzy Logic-based MPPT algorithms. As to balance competing objectives such as power efficiency,
shown in Figure 10, the proposed controller achieved quicker thermal constraints, and converter stress.
3 convergence to the Maximum Power Point (MPP) with sig- • FPGA Implementation: Porting the controller to FPGA

nificantly lower oscillations. While the Fuzzy Logic controller platforms for ultra-fast, parallel execution, which may
performed relatively well, it suffered from greater instability enhance response speed and scalability for large PV
50 near the MPP. The P&O method demonstrated the slowest arrays.
tracking and was more sensitive to sudden environmental These extensions aim to make the proposed LSTM-RNN
changes. controller a versatile and scalable solution for modern renew-
1 able energy systems.

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