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Scientific Reports volume 15, Article number: 19819 (2025)
1184
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Metrics details
The installation of solar photovoltaics (PV) has gained momentum due to growing concerns about global warming and the UN’s SDGs addressing environmental challenges. The primary objective of this paper is to evaluate and address the impacts of load uncertainty on Unit Commitment through the implementation of storage-based PV generation, wherein PV generation and energy storage operate in the proposed coordinated manner. To deal with uncertainty, a hybrid optimization technique is utilized, which combines stochastic and robust computations. Stochastic load uncertainty scenarios are generated via probabilistic Gaussian Probability Density function (PDF) approach that reside within the defined uncertainty set, as established by the robust optimization framework. The mean scenario of load uncertainty is applied to evaluate the day-ahead UC costs. The IEEE 39-bus, ten-generator system serves as the basis for this analysis. UC is optimized via Dynamic Programming (DP) in the presence of load uncertainty levels of up to 10% across three distinct case studies. Case 1 functions as the baseline for comparison as it does not include PV-storage or load uncertainty modeling. In Case 2, the influence of load uncertainty on day-ahead UC is examined for a network that excludes PV-storage. In Case 3, the system integrates the proposed coordination based PV-storage and solves UC while managing peak demand amid increasing levels of load uncertainty—specifically at 5%, 8%, and 10%. Additionally, contingency margins are evaluated across all three cases to validate day ahead 24 hours system performance and reliability enhancements. By juxtaposing the results of UC across these three cases, this study aims to analyze the implications of gradually increasing load uncertainty, load management, and peak load regulation utilizing PV-storage systems.
Unit Commitment (UC) is employed to evaluate the contribution of each generator to anticipated load demand, utilizing Day-Ahead (DA) UC forecasting at hourly or sub-hourly intervals for the forthcoming 24 h. The precision of DA UC outcomes is predicated on the assumption that forecasted load demand accurately reflects actual demand; however, forecasting inherently involves approximation, necessitating the consideration of load uncertainties to effectively address real-time fluctuations. Despite acknowledgment of this issue, a significant research gap persists regarding the integration of load forecast uncertainty within DA UC studies, particularly concerning peak load management and the incorporation of renewable energy. This paper identifies and addresses three critical research gaps in this domain.
The first research gap pertains to the limited investigation into the incorporation of load forecast uncertainty into DA UC for power systems. Notably, the initial quantitative analysis of load uncertainty in UC was conducted in 19941; however, subsequent studies have predominantly concentrated on modeling stochastic uncertainties related to generation, with minimal emphasis on the integration of uncertain load forecasts. The application of stochastic techniques to UC was further advanced by Ruiz et al. (2009)2, yet the inclusion of load uncertainty remains an underexplored facet of UC optimization, particularly in the context of day-ahead scheduling.
The next research gap arises from the insufficient analysis of peak load management in conjunction with DA UC. Effective management of peak loads is a vital component of system reliability, especially as variable renewable energy sources, such as solar photovoltaic (PV) and wind power, increasingly penetrate the grid. The demand for sophisticated methodologies to manage peak demand, particularly during periods of diminished renewable generation, is intensifying; nevertheless, there is a notable scarcity of focused research aimed at optimizing DA UC for peak load management.
Pandzic et al. (2016)3 modeled the uncertainty in wind farm generation, validating Stochastic UC (SUC) as a cost-effective approach, albeit with longer simulation times. Other uncertainties incorporated into UC modeling include thermal generation outages, PV and wind generation variability, as well as load demand forecasts4. Research conducted over the past two decades5,6,7,8,9,10,11,12,13,14,15,16 has extensively examined multi-objective optimization that incorporates these uncertainties, with a primary focus on achieving a balance between risk and profit in DA UC scheduling. Notable studies in this domain include the modeling of PV generation and load uncertainties in microgrid contexts6, the integration of Virtual Power Plants with PV, Electric Vehicles (EVs), and Energy Storage (ES) systems for real-time market revenue estimation7, the coordination of PV systems, ES, and demand response programs aimed at enhancing voltage stability while reducing operating costs associated with UC8. Additional contributions encompass methodologies for modeling uncertainties in distribution loads10 and examining the impact of demand response uncertainty on robust UC13. Moreover, approaches such as Artificial Neural Network-based methodologies14 and time-series analysis15 have been proposed to address forecast errors in load demand and uncertainties in customer load requirements16. However, effective management of peak loads within the context of DA UC in such scenarios requires further exploration for the enhancement of the overall 24-hour operational profile.
The imperative for efficient peak load management within DA UC frameworks has become increasingly critical as the penetration of renewable energy sources and the integration of ES systems continue to escalate. In recent years, optimization techniques related to UC have evolved from traditional methodologies to advanced algorithms such as DP17,18, mixed-integer linear programming (MILP), genetic algorithms, and metaheuristic strategies aimed at integrating PV and ES systems. Solar PV technology, which is characterized by its inherent intermittency and reliance on weather conditions, presents significant challenges in achieving a balance between supply and demand19,20. In contrast, ES systems offer an effective solution to mitigate these challenges by storing surplus energy generated during periods of low demand and discharging it during peak load situations. However, these are not addressed simultaneously with the above-mentioned complexities and gaps in the context of DA UC. This becomes the third significant gap which need to be addressed. Although DA UC with considerations for load uncertainty and PV generation is analyzed in21, this study does not adequately address the contributions of ES systems and the management of peak loads.
The incorporation of solar PVs and ES into UC optimization introduces additional complexities in PV modeling22,23, along with increased challenges in managing uncertainties associated with load forecasts and renewable generation patterns. Numerous studies have examined various optimization methodologies to address these challenges; however, these challenges have not been addressed simultaneously. A variety of algorithms have been employed in these analyses, including intelligent dynamic programming (DP)24, mixed-integer linear programming (MILP)-based approaches25, genetic algorithms26, evolutionary programming27, simulated annealing28, imperialistic competition algorithms29, fuzzy logic techniques30, artificial bee colony algorithms31, binary particle swarm optimization32, the shuffled frog leaping algorithm33, the BARON solver in the General Algebraic Modeling System (GAMS)34, as well as a hybrid metaheuristic search algorithm that combines the Chaotic Seagull Optimization Algorithm (CSOA) with the Sine–Cosine Optimization Algorithm (SCA)35, among others.
Despite advancements in forecasting methodologies, load uncertainties persist, driven by fluctuating consumer demand, variable renewable generation, and the increasing integration of PV systems, ES technologies, and electric vehicles (EVs). These uncertainties can result in suboptimal scheduling, elevated operating costs, and diminished system reliability. Addressing these multifaceted challenges necessitates innovative solutions that leverage emerging technologies and sophisticated optimization techniques. The coupling of ES with PV generation presents a promising solution, as these systems are capable of storing excess energy during periods of low demand or high PV output and discharging energy during peak demand or low PV output, thereby enhancing grid stability. The coordination between PV and ES is a focal point of this paper.
Finally, there exists a significant gap in the integration of variable load uncertainties with the coordination of PV and ES systems within day-ahead unit commitment (DA UC) frameworks. Research exploring the dynamic interaction between load uncertainty, renewable generation, and storage technologies remains limited. The combined impact of these technologies on peak load management under conditions of uncertain load warrants further investigation. The present article investigates optimized DA UC for managing peak loads with solar PV and ES, specifically under conditions of load uncertainty. By examining and synthesizing the contributions of various optimization methodologies, this paper aims to propose an integrated framework that enhances both economic and operational efficiency while considering the dynamic nature of PV generation and storage availability.
Three case studies demonstrate the effectiveness of PV-ES in optimizing UC during peak demand periods. The methodology and optimization techniques used in the study are outlined in Section II, followed by the formulation of UC with its constraints and PV-ES uncertainty modeling in Section III. Section IV presents the experimental data from the three case studies, and the results are summarized in the subsequent section before concluding the paper.
The methodology is divided into three case studies, with Case 1 serving as the baseline for the comparative analysis of results. The process flow diagram of the analysis conducted is illustrated in Fig. 1. A layout of the methodology of the performed analysis for Case 3 is depicted in Fig. 2. The Standard Test System (STS) is considered to perform the analysis.
Process flow diagram of applied methodology.
Methodology of the performed analysis for Case 3.
It can be observed from Fig. 1 that DP is applied for DA UC solution for the base case analysis with the original test system.
The optimization details of the DP technique with it’s mathematical formulation can be found in17,18. In the subsequent case studies 2 and 3, Hybrid load uncertainty is incorporated as specified in the next section.
The evaluated DA UC costs are represented via Eq. (1)
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where,
(:{C}_{uc}left({P}_{t}right)) = cost of UC for ‘k’ MW generation by all committed generators.
(:{C}_{n}left({P}_{n,t}right)) = UC cost of ‘(:{P}_{n,t})’ MW delivered by nth generator, at hour ‘t’.
(:{P}_{t}) = Total MW to be generated by ‘n’ units as per the required load demand, (:{D}_{t}) at hour ‘t’.
(:{P}_{2,t},::{P}_{3,t},:dots:{,P}_{n,t}) =Power generation by the specific unit ‘2’ to unit ‘n’.
(:{P}_{t}-left({P}_{2,t}+{P}_{3,t}+dots:{+P}_{n,t}right)) = Power generation by unit ‘1’.
(:{S}_{n,t}) defines the commitment state (‘0’ or ‘1’) of the generator ‘n’ at hour ‘t’.
The power output (in MW) from all ‘n (1 to N)’ generators at each hour ‘t’ must satisfy the power balance requirement. Specifically, the total generated power at hour ‘t’ must be equal to the sum of the forecasted load demand and the system losses for that hour, as expressed in Eq. (2).
In this study, the hourly commitment of generators is analyzed to evaluate DA UC costs while addressing the increasing uncertainty in load levels through the integration of solar PV and ES systems. The respective hours, ranging from 1 to 24 in the context of the DA UC problem, are defined as spanning from 5 a.m. of the following day to 4 a.m. of the day after the next. For example, the first hour commences at 5 a.m. of the next day, the second hour begins at 6 a.m. of the next day, and this pattern continues until 4 a.m. of the day after the next. The total DA UC costs are assessed by calculating the hourly contributions of each committed generator to the electricity production necessary to meet the forecasted load demand. This evaluation is conducted subsequent to determining the commitment status of each generator, in accordance with the constraints outlined in the following sub-section.
The objective function of the problem is to minimize the total DA UC costs, which is defined as the summation of the hourly UC costs from hour 1 to hour 24 of the subsequent day. The overall UC cost (:{C}_{uc}) is evaluated for all 24 hours of the following day by aggregating the costs of ‘n’ generators committed during each respective hour, as illustrated in Eq. (3). The costs (:{C}_{n}left({P}_{n,t}right):,:{C}_{n-1}left({P}_{n-1,t}right):dots:dots:..) represented in Eq. (1) are bifurcated as depicted in Eq. (3).
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(:{S}_{n,t}) defines the commitment state (‘0’ or ‘1’) of the generator ‘n’ at hour ‘t’.
(:{C}_{n,t}^{fuel},:{C}_{n,t}^{st}{,:C}_{n,t}^{sd}) are the fuel cost, startup and shut down costs of generator ‘n’ at hour ‘t’, respectively.
Fuel Cost (FC) of individual generator ‘n’, is evaluated by its quadratic approximation equation with coefficients (:{a}_{n},:{b}_{n},:{c}_{n})
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Start-up cost (:{C}_{n,t}^{st}) comprises Turbine Start-up cost ((:{C}_{n,t}^{Tst})), Boiler Start-up cost ((:{C}_{n,t}^{Bst})) and Maintenance Start-up cost ((:{C}_{n,t}^{Mst}))
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where, (:td) = Number of hours a unit is down,
(:Bcd) = Boiler Cool Down Coefficient
Shut Down Cost ((:{C}_{n,t}^{sd})) is the cost that is required for shutting down a generating unit at time ‘t’ which is in operation till ‘t-1’.
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K is Incremental shut down cost. The shutdown constraint encapsulates the operational requirements and costs associated with activating or deactivating thermal generators. To delineate this constraint, it is essential to ascertain the initial status of each unit alongside minimum up and down times in conjunction with other parameters derived from a comparable study referenced in18.
Minimum up time: It is the number of hours the unit must be in ‘ON’ state, before it can be shut off i.e. (:{t}_{n}^{ON,min}). (:{T}_{n,(t-1)}^{ON}) is the number of hours the generating unit ‘n’ has been in ‘ON’ state prior to the considered hour i.e. (t-1)th hour and (:{S}_{n,t}) defines the commitment state (‘0’ or ‘1’) of the generator ‘n’ at hour ‘t’
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A unit must be in ‘OFF’ state for a minimum number of hours, before it can be brought online. This time is known as minimum down time. (:{T}_{n,left(t-1right)}^{OFF}) is the number of hours the generating unit ‘n’ has been in ‘OFF’ state prior to the considered hour i.e. (t-1)th hour and (:{S}_{n,t}) defines the commitment state (‘0’ or ‘1’) of the generator ‘n’ at hour ‘t’
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The active power output of each generating unit must be within the minimum (:{P}_{n}^{min}) and maximum (:{P}_{n}^{max}) operating limits, specified by the following inequality constraint,
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Ramp rate : The rate of rise of active power output of generators per minute, must not exceed the maximum specified value of ramping up the generating unit ‘n’ (:{P}_{n}^{RU,max}). Also the rate of decrease of active power output must not reduce lower than the minimum limit i.e. ramp down limit (:{P}_{n}^{RD,min}) for each generator ‘n’. The ramp rate for generator ‘n’ at hour ‘t2’ with respect to previous hour ‘t1’ (:{P}_{n,t2}^{RR}) is estimated by evaluating the ratio of change in active power to change in time duration, as represented by Eq. (10).
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Substituting the values of ‘t1’ and ‘t2’ as ‘t-1’ and ‘t’ respectively in Eq. (10), the ramp up and ramp down rates must follow Eqs. (11, 12)
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Must run units, nmr include those which must be online and available for commitment at hour ‘t’.
Must out units are out due to maintenance and not available for commitment. These are usually considered for long term UC problem and not considered for DA UC unless there is an unexpected contingency/fault/outage.
Spinning Reserve (SR) for optimal UC is found to be 10%18 of the operating reserve i.e. (:{(0.1*R}_{n,t})) for all generating units.
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The total active power generated by all units must supply the required load demand. Assuming dc power flow, the system losses are neglected. The total generated active power is evaluated by aggregating the generation of the committed generators over the 24 h of the next day. Similarly, the required load demand for the next day is calculated by aggregating the forecasted load demand over the 24 h horizon.
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(:{P}_{n,t}) is the power generated by generator ‘n’ at hour ‘t’, (:{S}_{n,t}) defines the commitment status of generator ‘n’ at hour ‘t’ (i.e. ‘0’ or ‘1’), (:{D}_{t}) is the forecasted load demand at hour ‘t’.
The forecasted load demand plays a critical role in load uncertainty modeling for UC. The actual DA load demand profile varies from the estimated forecasted load. This happens owing to the load uncertainty pattern.
The load uncertainty of the next day is introduced by (:{text{D}}^{text{u}text{n}text{c}}) in the forecasted load profile.
This paper applies a hybrid load dynamics uncertainty model using robust bounds from Eq. (15) to address forecasted load demand uncertainty. Probabilistic scenarios are generated using the Gaussian Normal PDF from Eq. (16), and the mean uncertainty scenario for the following day is evaluated.
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A number of random ‘s’ scenarios (:{d}_{s}) are generated for simulating the DA load uncertainty at each hour ‘t’ (:{D}_{t,s}^{unc}). Each scenario ‘s’ of load demand uncertainty is defined within lower and upper limits as per Eqs. (17,18), for making the problem robust. The upper and lower limits in scenario generation for the introduced load demand uncertainty are modelled in the context of ‘p’ percentage change in load demand.
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The actual load demand at hour ‘t’ for a particular scenario ‘s’ (:{D}_{t,s}) incorporating the uncertainty is given by Eq. (19)
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Thereafter, the mean scenario of the actual demand (:{stackrel{-}{D}}_{t,s}) is evaluated representing the central tendency over time which is near to the expected value of load demand. Thus it is represented by Eq. (20)
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Solar PVs are integrated with STS and implemented by considering a single large unit depicting a solar plant. The solar irradiance of the single entity PV is determined based on thevenin equivalent circuit approach as explained in19. The overall power output of the modelled solar PV plant for scenario ‘s’ at hour ‘t’, (:{P}_{s,t}^{pv}) is represented by Eq. (21).
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where,
(:{P}_{s,t}^{pv}) = Power generation of the solar PV for scenarios ‘s’ at hour ‘t’ (kW).
A = Area of solar PV (m2).
(:{eta:}_{s})= Efficiency of solar PV
(:{Ir}_{s,t})= Irradiance scenario ‘s’ of solar PV (kW/ m2) at hour ‘t’.
The solar irradiance scenarios are modeled using Gaussian distribution as represented by Eq. (22). Various data related to the solar generation of the examined system, such as the range of available solar irradiance, area requirements, and percentage power generation, are referenced from20. The range of modeled solar irradiance considered in this study spans from 100 W/m² to 220 W/m² for the analyzed 100 scenarios.
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(:{Ir}_{s,t}) is the solar irradiance at time ‘t’ (W/m²) for scenario ‘s’, (:sigma:) represents the standard deviation in solar irradiation from its mean value (:mu:) for ‘T’ hour observations as represented by Eqs. (23) and (24), respectively. The maximum irradiance is assumed to be 220 W/m2, at the peak sunlight hour i.e. noon.
The photovoltaic (PV) power is assessed using Eq. (21) across all these irradiance scenarios. Subsequently, the mean PV scenario is generated to evaluate the energy storage (ES) contribution for the remaining hours.
Large-scale ES is modeled with ‘q’ units using Eq. (25), where charging and discharging patterns over the time duration (:varDelta:t) introduce uncertainty due to variable dispatch availability. Power available in the battery, (:{P}_{q,t}^{bes}), is ensured to lie within the minimum ((:{P}_{q}^{bes,min})) and maximum ((:{P}_{q}^{bes,max})) limits of the battery as defined by Eq. (26). Charging ((:{P}_{q,t}^{bes,ch})) and discharging ((:{P}_{q,t}^{bes,dch})) limits are defined by Eqs. (27) and (28), for the power stored in the battery at any hour ‘t’.
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Here the efficiency of battery charging is mentioned as (:{eta:}^{ch}) whereas the discharging efficiency is indicated by (:{eta:}^{dch}) in Eq. (25).
The 24-hour horizon of the DA UC problem is defined from 5 AM of the subsequent day to 5 AM of the following day. Within this framework, solar photovoltaic (PV) generation is assumed to be available for ten hours, specifically from 7 AM to 5 PM on the next day, in order to align with the DA UC schedule of thermal generators. Consequently, ES is coordinated to charge during these ten hours when solar generation is actively occurring.
Following 5 PM, when PV generation ceases, the ES begins to discharge to support the load. The duration for which the ES provides energy to the load depends on the quantity of stored energy available and the hourly load demand. The hours during which the ES charges to its maximum capacity are evaluated according to Eq. (25) which considers the charging and discharging efficiencies of the battery. After being charged during the ten hours in which PV power is available, the discharging duration will vary based on the power discharged each hour, as determined by load requirements, discharging efficiency, and the battery’s ability to meet the load demands while remaining within its minimum state-of-charge constraints as defined by Eq. (25) to (28).
The contingency margin (CM) is conventionally articulated as a percentage of the total load or installed capacity and denotes the reserve capacity that can be activated promptly to address unanticipated events. In this study, CM at hour ‘t’, (:{CM}_{t}) is assessed with consideration of the contributions from spinning reserve of thermal generators (:{SR}_{t}), PV generation, and ES as expressed by Eq. (29).
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(:{P}_{t}^{pv})is the generated PV power at hour ‘t’, (:{D}_{t}^{pv}) is the load demand fulfilled by PV generation, (:{P}_{t}^{bes}) is the charging/discharging power absorbed/delivered to load by ES at hour ‘t’.
(:{SR}_{t}) is the spinning reserve at hour ‘t’ which is evaluated by subtracting the total generated power by ‘n’ thermal generators at hour ‘t’ from the toal installed capacity of thermal generators for STS, (:{TIC}_{th}) as shown in Eq. (30)
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Solar PV generation is projected to be available for the presumed duration of ten hours the following day, thereby contributing to CM at a specific hour. ES systems absorb excess energy during the charging phase utilizing the power generated by PV systems and subsequently inject power during discharging, rendering them valuable assets for sustaining CM.
This section provides a summary of the test system description, followed by the experimental data for the three case studies. The test system serves as a representative example in this study to illustrate the findings; however, the methodology may also be applied to other systems. It is important to note that the simulation time and computational complexity increase with the scaling of the system (i.e., an increased number of generators, larger capacity generators, extensive PV installations and ES systems, among others).
The Single Line Diagram (SLD) of STS IEEE 39 bus, ten generator system18 is shown in Fig. 3. Original system is analyzed in Case 1. The generating unit data with the fuel cost coefficients, minimum & maximum active power generation limits, minimum up-time, down-time etc. are referred from17,18.
SLD of standard IEEE 39 bus, ten generator system.
Three cases are analyzed to explicitly highlight the contribution of photovoltaic energy storage (PV-ES) in managing peak loads in the presence of load uncertainties, as presented in Table 1.
The forecasted demand of the next day is represented graphically in Fig. 4. It can be observed from Fig. 4 that the peak load demand of the system is 1500 MW at 12th hour. The next subsequent peak of 1400 MW is observed at 20th hour of the next day.
In this case study, load uncertainty is introduced on the maximum side, with the upper bound established as mentioned in Eq. (18), in the absence of PV-ES. This configuration yields the maximum deviation from peak demand in comparison to that in Case 1.
The impacts of increasing levels of induced load uncertainty are analyzed in this section, focusing on their management through the inclusion of PV-ES systems and the coordination between these systems & thermal generators.
The test system Total Installed capacity of thermal generation (TICth) is 1662 MW. A large-scale PV-storage penetration with an installed capacity of 30% of TICth is considered, which approximates to 500 MVA. Solar PVs are assumed to have an efficiency of 20%. The maximum achievable output for the maximum illumination at right angle on solar panels is considered to be 100 MVA for lower solar irradiance levels. The battery storage capacity is considered to be 60% of PV efficient output amounting to a capacity of approximately 60 MVA. The battery Depth of Discharge (DoD) is assumed to be 10%, with SoC of 90% corresponding to a maximum discharging energy of 54 MVAh.
In Case 2, a load uncertainty of 10% is introduced into the system. The resultant excess demand attributed to this load uncertainty must be met exclusively by the thermal generators. In the analysis of Case 3, the load uncertainty is incrementally increased by 5%, 8%, and ultimately to 10%, as delineated by the limits established in the load uncertainty formulation described through Eq. (15) to (20). The peak load demand in Case 3 will be addressed through the coordinated operation of thermal UC and PV-storage systems.
Hourly DA forecasted load demand.
The generation from PVs is modeled as per Eq. (21). PV generation is based on the assumption that the solar irradiance is available for ten hours from 7 am to 5 pm of the next day increasing from 7 am till noon, decreasing thereafter till 5 pm.
The power generation from PVs correspondingly rises upto noon and reduces thereafter. The temperature effects on the PV power output are neglected. A consolidated model of overall PVs is simulated under standard test conditions (STCs). STCs are globally recognized with irradiance of 1000 W/m2 under a temperature of 250C in air mass of 1.5 corresponding to solar zenith angle of 48.19°, Angstrom turbidity (base e) at 500 nm of 0.084c, total column water vapor equivalent of 1.42 cm and total column ozone equivalent of 0.34 cm. Solar data is procured from20 and verified from NREL.
The irradiance scenarios generated as per the formulation discussed in Sect. 3.2 are represented in Fig. 5. The PV generation is assessed using Eq. (21), incorporating the modeled solar irradiance and a plant performance factor of 0.7. The resulting 100 scenarios of PV generation are illustrated in Fig. 6. The mean scenario of the PV generated output is represented by the bold black line in Fig. 6.
Solar Irradiance (100 scenarios) for the considered ten hours.
PV generation (100 scenarios) with mean scenario for the considered ten hours.
The cumulative hourly costs of UC, for the next day are evaluated and compiled for the three case studies. The results for the three cases are discussed and analyzed in this section.
This section discusses DA UC optimization utilizing DP. The cumulative hourly UC costs corresponding to the forecasted load demand, as illustrated in Fig. 4, are presented in Table 2. A comparative analysis of the results from the proposed study for Case 1 is provided in Table 3, alongside findings from other recent studies cited in the literature. It is evident that the DA UC costs associated with the proposed method (Case 1) are lower than those obtained through alternative methods for the same ten-generator test system. This comparison underscores the effectiveness of our approach in cost optimization relative to existing methodologies, thereby facilitating further analysis that incorporates load uncertainties.
The load uncertainty if managed without PV-storage leads to high demands at peak hours i.e. 12th and 20th hour (Fig. 4). The generated load uncertainty scenario profiles lie between upper and lower limits depicted in Fig. 7.
Overall load demand limits with uncertainty.
The maximum uncertainty is modeled in Case 2 with the upper limit incorporated in the system as 10% increase in load demand. The effective load demand of system after adding this uncertainty is graphically represented in Fig. 8. It can be observed that the peaks at 12th and 20th hours increase. The peak demand to be fulfilled rises to 1650 MW from 1500 MW (at 12th hour). The next peak rises to 1550 MW from 1400 MW to (at 20th hour).
DA load demand profile for Case 2.
In the absence of PV-storage this escalated demand is to be fulfilled by the thermal units with a TICth of 1662 MW. This will overload the generators reducing spinning reserve to zero, thus leaving no room for handling any other simultaneous uncertainty/contingency. This gives increased cumulative hourly DA UC costs of the next day, as compiled in Table 4. Column 2 and 3 give the cumulative UC costs obtained in Case 1 and Case 2 respectively. The percentage increase of UC costs in Case 2 w.r.t. Case 1 is listed in column 4. The maximum rise in UC costs is observed as 19.59% at the 13th hour. The rise at 12th and 20th hour is 19.34% and 16.84% respectively.
Thus, for fulfilling a high demand, more units are committed resulting in high electricity production costs as observed from Table 4. Without any PV-storage installation this cost has to be borne by the thermal generators, with the additional costs of generator overloading leading to overheating, at the expense of their lifetime reduction.
In Case 3, the test system is incorporated with PV-ES as per the assumptions and modeling mentioned in previous sections. The system induced load uncertainty in this case is gradually increased from 5 to 8% and then to 10%. This rise in load uncertainty leads to a proportionate increase in load demand as shown in Figs. 9, 10 and 11.
In presence of PV-storage, inclusion of 5% load uncertainty leads to reduction in peak load demand. The 12th hour peak is reduced to 1485 MW, and the 20th hour peak also comes down to 1450 MW as shown in Fig. 9.
Load demand profile with 5% load uncertainty for Case 3.
When induced load uncertainty is increased to 8% only one peak is managed by PV-storage contribution in the system. The peak demand at 12th hour is reduced to 1525 MW but still exists above 1500 MW. The other subsequent peak at 20th hour is reduced to 1490 MW as shown in Fig. 10.
As the load uncertainty is further heightened to 10%, though both the peak loads reduce due to the contribution of PV-storage, the load demand to be fulfilled by conventional generation still exist above 1500 MW. The peak load demand at 12th hour reduces to 1555 MW compared to 1650 MW in Case 2. At 20th hour this reduction is quite less, the peak decreased to 1520 MW compared to 1550 MW in Case 2, as shown in Fig. 11. These peak demands are then fulfilled by the conventional thermal generation.
The contribution of PV generation and storage is depicted in Fig. 12 where PV generation is available for ten hours of the next day with storage contribution at the peak demands i.e. at 12th hour and 20th hour. The PV- ES contribution for the three load uncertainty patterns of Case 3, namely 5%, 8%, and 10% are graphically represented in Figs. 13, 14 and 15 with respect to the thermal generation. Comparing Figs. 9, 10 and 11 with Figs. 13, 14 and 15, it is evident that the PV-ES contribution is significant for the three modeled load uncertainty levels.
Load demand profile with 8% load uncertainty for Case 3.
Load demand profile with 10% load uncertainty for Case 3.
PV-storage contribution for Case 3.
PV-storage contribution w.r.t. thermal generation for Case 3 with 5% load uncertainty.
The PV-ES contribution clearly reduces the UC costs and the burden on the thermal generators. It can be observed that the percentage reduction in UC costs vary in the range (2.01–10.32)%. The contribution of PV-ES is significant in reducing the load demand profile throughout the 24 h of the next day. Also, the peak load management becomes better when PV-ES is implemented in the system. The percentage reduction in peak load at the 12th and 20th hour are 10.32% and 7.28%, respectively.
PV-storage contribution w.r.t. thermal generation for Case 3 with 8% load uncertainty.
PV-storage contribution w.r.t. thermal generation for Case 3 with 10% load uncertainty.
This section offers a comprehensive comparative analysis of hourly cumulative DA UC costs across three simulated case studies, each exemplifying distinct methodologies. For clarity, the various components and total DA UC costs associated with the three case studies are presented in Table 5.
The hourly cumulative DA UC costs for Case 1, Case 2, and Case 3, corresponding to load uncertainties of 5%, 8%, and 10% induced in the system with PV-storage, are compiled in Table 6. The first column represents the hours from 1 to 24 of the subsequent day. The hourly DA UC costs for the deterministic base case (Case 1) are detailed in Column 2, with total DA UC costs amounting to $538,920. The total DA UC costs associated with maximum load uncertainty (Case 2) are $622,809, as presented in Column 3, reflecting a 15.57% increase compared to Case 1. The hourly DA UC costs for Case 3, which considers various levels of load uncertainty, are specified in Columns 4 to 6.
The total DA UC costs for Case 3 at a 5% load uncertainty are $563,904, indicating a reduction of 10.44% in comparison to Case 2, while also demonstrating an increase of 4.6% relative to Case 1. The total DA UC costs for Case 3 at an 8% load uncertainty are $574,201, showing a reduction of 7.8% compared to Case 2, alongside an increase of 6.5% relative to Case 1. The total DA UC costs for Case 3 at a 10% load uncertainty amount to $587,016, representing a reduction of 5.74% in relation to Case 2, while exhibiting an increase of 8.9% compared to Case 1.
This analysis indicates that the total DA UC costs rise by 15.57% when load uncertainty is introduced in the system without PV-storage. However, following the installation of PV-storage in the system, the increase in costs associated with load uncertainty is comparatively lower.
Although the comprehensive assessment of DA UC costs is elucidated for the three cases in the preceding sub-section, a comparative analysis of Case 2 and Case 3 (which includes 10% load uncertainty) is essential for a more nuanced understanding of the cost reductions associated with the installation of photovoltaic energy storage (PV-ES) systems within the framework. The findings of this comparative analysis are summarized in Table 7, which illustrates the percentage reduction in cumulative UC costs resulting from the implementation of PV-storage under a 10% load uncertainty (Case 3) compared to the scenario devoid of PV-storage (Case 2).
The data presented in the table indicate that a reduction in DA UC costs is observed in nearly every hour analyzed. The maximum reduction of 10.32% occurs during hour 12, while the minimum reduction of 2.01% is noted during hour 2. Specifically, during peak hours, reductions in DA UC costs are recorded at 10.32% for hour 12 and 7.28% for hour 20. These results clearly demonstrate that the integration of photovoltaic and energy storage systems into the grid yields a substantial decrease in DA UC costs, even in the context of up to 10% load uncertainty within the system.
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This section presents a discussion on the CMs for all Cases to address system robustness under uncertain conditions. The contribution of PV-storage to enhance the power generation profile, managing peak load, and maintaining scheduling margins is substantiated through an evaluation of CMs for the two identified peak hours, thereby facilitating a comparative analysis of Cases 2 and 3. CM for the two peak loads in Case 2 is illustrated graphically in Fig. 16, while the CM for Case 3 is represented in Fig. 17. These findings are comparatively analyzed with respect to the CMs for Case 1, thereby providing a clearer understanding of the increase in CM observed in Case 3.
CM is evaluated within the framework of the specified system in relation to TICth. CMs for Case 1 and various levels of load uncertainty in Case 3 are illustrated in Fig. 16. CMs corresponding to the two peak load hours of Case 1 are represented as(::{CM}_{base}^{p1}) and (:{CM}_{base}^{p2}). The CMs corresponding to the two peak load hours across various levels of load uncertainty (specifically 5%, 8%, and 10%) are indicated as (:{CM}_{Lu}^{p1}) and (:{CM}_{Lu}^{p2}). For a 5% load uncertainty considering the contribution of photovoltaic energy storage (PV-ES) during the two peak load hours, the available CMs are represented as (:{CM}_{5}^{p1}) and (:{CM}_{5}^{p2}). Similarly, (:{CM}_{8}^{p1}) and (:{CM}_{8}^{p2}) represent the CMs for the two peak load hours under an 8% load uncertainty level, while (:{CM}_{10}^{p1}) and (:{CM}_{10}^{p2}) correspond to the 10% load uncertainty level. The contribution of PV storage enhances the contingency margin of the system. The influence of PV-ES on the system is emphasized through the evaluation of CMs of thermal generators, thereby illustrating the management of peak load while simultaneously improving the overall system profile, as depicted in Fig. 17. It is evident that the CM is highest at a 5% load uncertainty level and decreases for the 8% and 10% load uncertainty levels; however, it does not diminish to the level of Case 2 due to the contribution of PV-ES. It can be observed that the CMs for the two peak hours of Case 3 at various uncertainty levels are comparatively lower than those of Case 1, which serves as the baseline for comparison. Nevertheless, owing to the contribution of PV-ES, the CMs for Case 3 for all load uncertainty levels are greater than those for Case 2 as can be observed from Figs. 16 and 17.
Contingency margin for Case 2 compared to Case 1.
Contingency margin for various load uncertainty levels of Case 3 compared to Case 1.
This paper incorporates a load uncertainty model to account for errors in forecasted load demand resulting from the dynamic nature of load over time, specifically in addressing the problem of Day-Ahead Unit Commitment in the context of the dynamics associated with solar PV systems and ES. The levels of uncertainty are incrementally increased from 5 to 8% and subsequently to 10%. The contribution of PV-ES systems is analyzed concerning peak load management under the simulated load uncertainty levels.
The DA UC costs obtained through DP exhibit a reduction compared to other referenced techniques for the assessed system under Case 1. This finding validates the efficacy of the applied technique, which is subsequently applied to analyze Cases 2 and 3 for evaluating the contribution of PV-ES in optimizing total DA UC costs, managing peak loads during peak hours and improving the overall load profile across the 24-hour period, under various levels of load uncertainties.
The percentage increase in costs is highest at 19.59%, 19.34%, and 16.84% for hours 13, 12, and 20, respectively, for Case 2. This indicates that in the presence of 10% load uncertainty, without PV-ES, DA UC costs escalate significantly. However, these costs are reduced in Case 3 when PV-ES are employed. In Case 2, CM at the two peak hours are very low, indicating improper peak load management, while for Case 3, the CMs increase, showing proper peak load management. DA UC costs are reduced at the two peaks despite the load uncertainties in Case 3 by 10% and 7.28%. The overall power generation profiles improve with increasing uncertainty levels in the presence of PV-ES for all 24 h of the next day.
The results indicate that PV storage systems effectively mitigate system peak loads, thereby enabling conventional generators to fulfill the requisite energy demand for DA UC while maintaining the minimum contingency margin and preventing overload. Additionally, PV storage systems play a significant role in peak load management when employed in conjunction with the commitment of conventional generation by the system operator. Consequently, the reliance on peaking plants within the power system has been reduced since CMs of conventional generators increase by the proposed approach, thereby enhancing overall system reliability.
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Open access funding provided by Manipal University Jaipur.
Department of Electrical Engineering, Manipal University Jaipur, Jaipur, India
Smriti Jain & Neeraj Kanwar
Department of Electrical Engineering, Swami Keshvanand Institute of Technology, Management & Gramothan, Jaipur, India
Smriti Jain
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Original draft is prepared by S.J. and N.K. All authors are equally contributed for data curation, validation and formal analysis, writing—review and editing of manuscript.
Correspondence to Neeraj Kanwar.
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Jain, S., Kanwar, N. Optimized unit commitment for peak load management with solar PV and storage under load uncertainty. Sci Rep 15, 19819 (2025). https://doi.org/10.1038/s41598-025-04341-5
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