Modified interval‐based generator scheduling for PFR adequacy under uncertain PV generation
2019; Institution of Engineering and Technology; Volume: 13; Issue: 16 Linguagem: Inglês
10.1049/iet-gtd.2018.6391
ISSN1751-8695
AutoresVivek Prakash, Kailash Chand Sharma, Rohit Bhakar, Harpal Tiwari,
Tópico(s)Smart Grid Energy Management
ResumoIET Generation, Transmission & DistributionVolume 13, Issue 16 p. 3725-3733 Research ArticleFree Access Modified interval-based generator scheduling for PFR adequacy under uncertain PV generation Vivek Prakash, Vivek Prakash orcid.org/0000-0002-1236-0439 School of Automation, Banasthali Vidyapith, Rajasthan, IndiaSearch for more papers by this authorKailash Chand Sharma, Kailash Chand Sharma School of Automation, Banasthali Vidyapith, Rajasthan, IndiaSearch for more papers by this authorRohit Bhakar, Corresponding Author Rohit Bhakar rbhakar.ee@mnit.ac.in Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Rajasthan, IndiaSearch for more papers by this authorHarpal Tiwari, Harpal Tiwari Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Rajasthan, IndiaSearch for more papers by this author Vivek Prakash, Vivek Prakash orcid.org/0000-0002-1236-0439 School of Automation, Banasthali Vidyapith, Rajasthan, IndiaSearch for more papers by this authorKailash Chand Sharma, Kailash Chand Sharma School of Automation, Banasthali Vidyapith, Rajasthan, IndiaSearch for more papers by this authorRohit Bhakar, Corresponding Author Rohit Bhakar rbhakar.ee@mnit.ac.in Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Rajasthan, IndiaSearch for more papers by this authorHarpal Tiwari, Harpal Tiwari Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Rajasthan, IndiaSearch for more papers by this author First published: 26 July 2019 https://doi.org/10.1049/iet-gtd.2018.6391Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Large quantum of photovoltaic (PV) generation into the grid would reduce system's primary frequency response (PFR) capability. Adequate PFR is critical to provide rapid frequency stability after contingencies such as large generation outage. PFR estimation and its scheduling within acceptable operational time frames is a challenging task for system operator. Uncertain PV generation makes this problem critical. Existing models for PV uncertainty characterisation with stochastic scheduling are computationally demanding. This study proposes a computationally fast modified interval scheduling approach for operation and PFR cost minimisation. Uncertainty is modelled through interval forecasting, while hourly ramp needs are based on net load scenario. The proposed model is compared with stochastic scheduling approach for PFR performance, overall cost performance, computational time and PV curtailment. Numerical results show that the proposed model drastically reduces simulation time for similar cost performance. Nomenclature Indexes and sets index and set of time interval index and set of generator units index and set of linear segments of generator cost curve index and set of generator start-up costs Gng generator set with disabled governor pv, PV index and set of PV plants Variables output power of unit i in time interval t (MW) output power of segment b of generator i in time interval t (MW) combined start-up and shutdown cost of generator i in time interval t ($) binary variable, start-up cost matrix (1 if generator i starts up during time t for cost segment j; 0 otherwise) binary variable, generator up/down status (1 if generator i is on during hour t; 0 otherwise) binary variable, generator start-up/down status (1 if generator i starts up in time interval t; 0 otherwise) binary variable, generator headroom availability status for PFR (1 if headroom is available for generator i in time t; 0 otherwise) curtailment of pv power during hour t (MW) PFR available from generator i at nadir/steady state at time interval t (MW) total PFR from generator i at time interval t (MW) frequency deviation at nadir/steady state (Hz) governor status of generator i at time interval t (1 if enabled; 0 otherwise) System parameters and constants forecasted load in time interval t (MW) net load at time interval t (MW) PV power available from pv at time interval t (MW) minimum down/up time of generator i in initial time period (h) minimum down/up time of generator i in remaining time period (h) maximum/minimum output of generator i (MW) ramp up/down limit of generator i (MW/h) start-up cost of segment j of generator i ($) no-load cost of generator i ($) running cost of generator i, for the b th segment of the cost curve ($/MW) upper/lower limit of segment j of generator i based on generator off time (h) nominal frequency/steady-state frequency (Hz) infeed loss (MW) LD load damping rate (1/Hz) PFR delivery time (s) maximum frequency deviation (Hz) inertia constant of generator i (s) governor's frequency deadband (Hz) equivalent load inertia (s) time to reach steady-state/nadir frequency (s) nadir frequency (Hz) PFR capacity requirement, overall/at nadir/at steady state (MW) system inertia/inertia requirement (MWs) governor deadband/maximum allowed deadband of generator i (Hz) equivalent droop/governor droop of generator i (Hz/MW) rated apparent power of generator i (VA) generated PV power (W) Ar area of solar panel (m2) panel efficiency 1 Introduction Environmental concerns and government policy target to achieve large generation share from green energy sources provide opportunity for photovoltaic (PV) integration at utility scale. However, uncertain generation characteristics of PV would create challenges of demand–supply imbalance, reduced system inertia and primary frequency response (PFR), due to displacement of conventional generation, under frequency load shedding etc. These reasons could restrict PV penetration due to system security constraints [1]. Initial frequency stability within the system security bounds, considering PV uncertainty and largest generation outage, necessitates reserve provisions that enhance overall cost [2]. PFR is a self-corrective measure by the system to stabilise system frequency, in response to frequency deviations. In scheduling framework, PFR scheduling finds weak attention because of its adequate availability with conventional generation [3]. Recent analysis by National Grid, UK reveals that PFR requirements are expected to increase significantly over the next 15 years, with increased generation share from renewable generation sources. By 2021, this would lead to an increase of 30–40% [4]. PFR scheduling is idiosyncratically challenging, as the response delivery time does not have the broad freedom, as available in tertiary regulation. This is a quick response and required to be delivered in 5–10 s [5]. Currently, markets world over have not incentivised PFR provision [6]. However, importance of PFR for system security is known widely and now interconnections are adopting it progressively. PFR market requires incentives for synchronous inertia, PFR capacity and responsive droop curves. Hence, this provision would encourage interconnections to maintain adequate PFR with penetration of renewable generation. Several approaches have been reported on selection of an economical combination of generating units, to minimise reserve requirement and overall cost [7–11]. Deterministic unit commitment is considered to schedule the reserves. However, probabilistic modelling and economic analysis of reserves requirement are not considered [7]. Stochastic UC (SUC) is used for reserve scheduling with wind generation uncertainty characterisation [8]. Probabilistic modelling and operating cost reduction objective is considered; however, SUC is computationally demanding because of a large number of scenarios [9]. Scenario-reduction methods are used to reduce the computational time [10]. However, inadequate scenarios result in inaccurate solution and may incur additional operating cost [11]. This requires a computationally fast mechanism to obtain solutions within allowable operational time frames. Frequency response constraints are modelled as mix integer linear programming in generation scheduling framework [3, 12–14]. Frequency at steady state and governor droop parameter is considered in UC formulation for determination of primary reserve adequacy [3]. However, dynamic frequency deviation modelling is not considered. This assessment is reported in security constrained UC (SCUC) and SUC framework [12, 13]. In SCUC formulation, linearised frequency constraints are formulated considering wind generation [12]. However, wind uncertainty impact and its modelling is not considered. In SUC formulation, PFR and frequency deviation at intermediate state with wind uncertainty is considered. However, the simulation process entails high computational burden [13–15]. Inertia and PFR constraints are included in modified interval unit commitment. Model with consideration of wind uncertainty [16]. However, PV uncertainty characterisation for PFR scheduling framework is given less attention in the literature. This requires wider understanding of system's frequency stability requirements with large PV penetration. In this paper, an exposition of computationally fast modified interval (MI) scheduling approach is proposed for overall cost minimisation with optimal PFR schedule. PV uncertainty is pragmatically characterised through interval forecast, while ramp requirement of each hour is considered based on net load. Time-series-based autoregressive (AR) integrated moving average model (ARIMA) is used to forecast upper and lower bounds considering suitable model parameters. The proposed approach is compared with SUC for cost and computational performance, considering largest generation outage. It is observed that the proposed MI scheduling model has similar economic performance but is able to reduce the computation burden significantly compared with SUC model. Furthermore, the proposed model could be enhanced to incorporate technologies such as energy storage and electric vehicles for PFR adequacy in future low carbon power system. In this remaining paper: Section 2 discusses problem outline and uncertainty characterisation. In Section 3, detailed formulations of the two models are presented. Simulation results are discussed in Section 4. Section 5 presents the conclusion. 2 Problem description 2.1 PFR adequacy Growth in PV penetration has made situation intricate for system operator (SO) to provide inertia and PFR within acceptable time frames. In renewable rich countries such as Germany, USA, and UK, prescribed limit for rate of change of frequency (ROCOF) is 0.125 Hz/s. However, this value is not similar for all the interconnections [17]. PFR should contain frequency deviation before the minimum set point, and quasi-steady-state frequency should stabilise within 30 s. ROCOF, and are mainly considered as frequency security parameters. ROCOF is inversely related to system inertia. High ROCOF setting would violate generator protection relay settings, leading to under frequency load shedding. Hence, PFR response is required to arrest frequency before and settle above . PFR response is required to be delivered in first 10–30 s. This would depend on the deadband, available headroom, governor droop and load damping rate. Generator's governor operate in two frequency sensitive modes (FSMs): (i) over FSM and under FSM based on droop and deadband setting. It can vary its active power in the range of 1.5–10%. Response deadband range and deadband are in the range 0–500 MHz and 2–12%, respectively [18]. 2.2 PV generation uncertainty characterisation PV plant power output is estimated using time-series data of global horizontal irradiance, along with , Ar and performance factor (PF) as shown by the equation below: (1)PV power variability is modelled as a stochastic process. ARIMA is benchmark time-series-based method widely implemented for prediction of electricity and commodity prices, apart from load and power forecasting. ARIMA models are robust and efficient than complex structural models used for short-run forecasting. It is chosen for this work considering the literature that compares different time-series PV forecasting models and found ARIMA as most suitable model for PV forecasting [17]. This requires a stationary time-series PV radiation data to integrate in AR and MA models. PV power data are typically non-stationary time series, and require difference conversion technique to convert it to stationary time series, before obtaining ARIMA model parameters. After suitable difference conversion, ARIMA () parameter is obtained using the equation below: (2)In (2), is AR operator; is the d th-order difference; is the prediction limit of PV power at time interval t; is MA operator; p denotes AR order, while q is MA order; and is a normally distributed random number series having zero mean and constant variance. Operators , , , and q are linearly correlated. represents the PV time-series data that has no autocorrelation and known as white noise. Suitable order of model is identified by the plots of correlation functions, i.e. autocorrelation function (ACF) and partial ACF (PACF). A stochastic process can be represented either by continuous or discrete random variables or scenarios. Large numbers of scenarios are required to accurately model stochastic process. The algorithm for scenario generation is discussed in Fig. 1. For scenario generation, first the historical data of PV radiation for a specific location is collected. Thereafter, complete set of collected data is used to estimate the ARIMA model parameters (order and value of AR and MA coefficient and standard deviation of white noise). After parameter estimation, scenario and time counters are defined to generate desired number of scenario iteratively for a particular time interval. Time-series ARIMA model is simulated for each iteration with random white noise generates the PV radiation scenarios. Generated PV radiation scenarios are converted to PV power scenarios using (1). When required number of scenarios are generated, the equal probability (1/number of scenario) is assigned to each scenario. The sum of scenario probability is always unity. Fig. 1Open in figure viewerPowerPoint Scenario generation algorithm The computational effort for solving scenario-based optimisation models is proportional to the number of scenarios. Therefore, it is necessary to reduce the original scenario set in such a way that it has a smaller number of scenarios, while the stochastic properties do not change significantly [19, 20]. Two heuristic algorithms are developed in the literature for scenario reduction, namely backward reduction and forward selection. Forward selection is used when the number of preserved scenarios is small. As the number of scenario increases, the running time of the algorithm also increases [19]. The scenario-reduction algorithm discussed in Fig. 2 reduces and bundles of the scenarios using the backward reduction algorithm. This algorithm uses Kantorovich distance (KD) matrix, i.e. probability distance between the scenarios. It is generally used to quantify the closeness of different scenario sets. KD assures that maximum possible scenarios are reduced, without violating a given tolerance criteria [20]. Probability of all deleted scenarios is assumed to be zero. The new probability of preserved scenarios is equal to sum of its former probability and the probability of deleted scenarios that are closest to it. Backward reduction algorithm and KD matrix discussed above is modelled in MATLAB. The key focus in the proposed work is on frequency response constrained day-ahead system operation. In short-term system operation, seasonal components have mild diurnal variations. This would have minor impact on the simulation result and hence neglected. The model can be enhanced to include such variations, wherever the impact is substantial (Fig. 3). Fig. 2Open in figure viewerPowerPoint Scenario-reduction algorithm Fig. 3Open in figure viewerPowerPoint MI forecast algorithm 3 Problem formulation This section provides detailed computational framework for MI scheduling and stochastic scheduling, with inertia and PFR constraints, and an aim to contain initial frequency deviation. 3.1 MI scheduling model This model incorporates advantageous features of computationally fast interval scheduling and economical stochastic scheduling models, to improve generation and PFR scheduling performance. In the proposed MI scheduling, PV uncertainty is characterised by considering ramp requirements for all odd and even hours over a day. These ramping scenarios are constructed between the forecasted intervals. Ramp requirements of constructed scenarios for each hour depend on net load. Therefore, it pragmatically anticipates PV output. MI scheduling is expressed as mix integer programming (MIP), to minimise operation cost for central forecast scenario of PV, i.e. npv. Objective function of (3) includes no-load cost, start-up cost and running cost of each generating unit (3) 3.2 Generator operational constraints In this section, generator operational constraints of the objective function are discussed (4) (5)Generator start-up/shutdown at time t is based on its on/off status between hours and t, expressed by (4). Constraint (5) imposes restriction on generator to avoid start-up and shutdown in the same time interval. Constraint (6) obtains the points on the start-up cost curve, where generating unit is off. Start-up cost is obtained by (7) (6) (7)In (8), power balance equation is given as total generation output equal to . Equation (9) calculates net load, which is difference of forecasted load and available PV capacity. denotes the curtailment in PV capacity. In (10), output power of each generator is shown as sum of each section's cost curve output. Equation (11) shows generating unit output limits (8) (9) (10) (11)Equations (12)–(16) are formulated for PV uncertainty modelling through ramping requirements in the proposed MI scheduling. Five ramping scenarios are considered as , , , and . Here, is central forecast scenario. Scenario is up-ramp requirement, for odd and even hours. Up-ramp requirements for even and odd hours are shown by . Down-ramp requirements, for odd and even hours is considered as , while down-ramp requirements for even and odd hours is . Up and down-ramp requirements for the central forecast scenario is given by (12). Equation (13) provides ramp up requirement for scenario . Equation (14) gives ramp requirements for . Equations (15) and (16) provides lower ramp requirement for scenarios and , between odd and even hours. These constraints are implemented using modulo function (12) (13) (14) (15) (16) 3.3 Stochastic scheduling model This model considers, each reduced scenario cost, proportionate to its probability for scenario n. Objective function (17) includes start-up cost, no-load cost and operating cost of all the generators, as considered in MI model with an aim to minimise the overall cost under PV uncertainty (17)In both the models, formulations are similar, except for the ramping constraints. Stochastic ramping scenario shown by (18) provides generator i ramp up and ramp down limits for all n reduced scenarios in time intervals t and (18) 3.4 Frequency response constraints Frequency behaviour after large imbalances such as large infeed loss could be described using the motion equation of synchronously connected rotating mass, known as swing equation, and as shown in the equation below: (19)Equation (20) could be expressed in terms of total system inertia and equivalent system frequency as (20)From (20), it could be observed that as decreases, ROCOF would increase. That would lead to a higher-frequency excursion and deeper at . Governor response during inertial response time frame is negligible, as Δf is ∼0. Hence, maximum value of ROCOF should satisfy minimum in case of maximum infeed loss, as mentioned in the equation below: (21)Constraint (22) guarantees that sufficient inertial response is available, so that does not cause instability (22)After deployment of inertial response available with the system, governor PFR is deployed with maximum ramp rate (23)Equation (23) is formulated, such that available response is greater than the required response (24) (25)Equation (24) determines , which depends on PFR delivered by generators and system inertia. Equation (25) determines the quasi-steady-state frequency value. 4 Case study In this paper, one area IEEE RTS is considered [21]. Test system includes 24 buses including 17 load buses and 32 generators. In this system, there are 11 oil/steam, 9 coal/steam, 6 hydro, 4 oil/combustion and 2 nuclear units (Table 1). Table 1. Test system generator parameters [21] Unit , MW , s , pu , MHz U12 12 2.6 0.05 15 U20 20 2.8 0.05 15 U50 50 3.5 0.05 15 U76 76 3.0 0.05 15 U100 100 2.8 0.05 15 U155 155 3.0 0.05 15 U197 197 2.8 0.05 15 U350 350 3.0 0.05 15 U400 400 5.0 0.05 15 Total installed capacity of one area system is 3405 MW. Peak load of system is 2850 MW. In this paper, PV generation and its penetration are considered based on the percentage of load served. For each penetration, net load is estimated, i.e. load minus available PV power at time interval t, as given by (9). System parameters such as f0 = 50 Hz, = 5%, LD = 1% Hz and = 10 s are considered. There are two nuclear units of 400 MW with highest capacity, and outage of one of the unit is considered. ROCOF limit for this paper is considered to be limited to 1.2 Hz/s. However, this value may vary for different interconnections [17]. PFR should be deployed in a manner that Δfmax is not more than 49.5 Hz. Maximum is considered as 30% of total generation capacity and for governor is considered as 100 MHz. 4.1 PV uncertainty modelling In ARIMA model, collected historical data is first analysed for non-stationarity. On that basis, suitable differentiation degree and order is determined. Non-stationary PV power time-series data is differentiated, to obtain stationary time series. From Figs. 4a and b, it could be observed that suitable parameter for PV power scenario representation is ARIMA (3, 0, 0). The estimated values of AR1, AR2 and AR3 are 1.820, −1.031 and 0.383 while value of variance is 0.23. Root-mean-square error of the ARIMA model on forecasted PV radiation data is 6.19%. ARIMA model is having minimum forecast error compared with models such as unobserved components, regression, neural network, transfer function and hybrid model [22]. Fig. 4Open in figure viewerPowerPoint PACF and ACF plots of PV power data(a) PACF plot, (b) ACF plot PV irradiation time-series data of 1 year from Chicago, USA is used in this paper for the durations 01.01.2016–31.12.2016 [23]. Ar, and PF are 3.5 km2, 15 and 75%, respectively. Fig. 5a demonstrates fan plot for probabilistic normalised PV power with prediction intervals from 10 to 90%, in a step of 10%. This consideration accurately captures the expected PV output. In stochastic model, 1000 scenarios are generated and reduced to obtain 10 representative scenarios, as shown in Figs. 5b and c, so that quality of actual scenario is maintained. Table 2 provides the obtained reduced PV power scenarios with their corresponding probabilities. Fig. 5Open in figure viewerPowerPoint PV power scenario and interval forecast(a) Fan plot of probabilistic normalised PV power with different intervals, (b) PV power scenario generation (grey solid), mean scenario (red dashed) and forecasted PV power (black dotted), (c) Reduced PV power scenario (grey solid), mean scenario (red dashed) and forecasted PV power (black dotted), (d) Interval forecast with upper and lower bounds and central forecast at 95% confidence interval Table 2. Reduced PV power scenarios, probabilities and KD of first hour Scenario index PV power, kW Probability KD 1 37.900 0.071 0.392301 2 46.931 0.104 0.378336 3 78.635 0.013 1.153745 4 73.352 0.087 1.35347 5 61.099 0.392 0.557562 6 39.280 0.024 1.831448 7 47.989 0.031 3.395021 8 87.220 0.053 0.221976 9 78.851 0.028 0.374087 10 52.276 0.197 0.973555 These reduced scenario probabilities are incorporated in stochastic model for PV uncertainty representation. Scenario reduction is required to reduce the computational burden of modelling. In MI scheduling model, uncertainty is represented by forecasted PV power with upper and lower bounds, as shown in Fig. 5d. Mean value of generated and reduced scenarios vary with 95% confidence interval. PV power output shown in Fig. 5 is normalised in percentage with installed capacity of 200 MW. 4.2 PFR performance In this section, comparative assessment of both the models for PFR schedules is discussed. Stochastic formulation considered is a two-stage optimisation problem. First here-and-now decisions are made on the binary status of generators. Wait-and-see decisions on the dispatch of each generator committed at the first stage are then made separately for each of the reduced scenario. Stochastic formulation is modified to incorporate frequency response constraints and results of Tables 3 and 4 are obtained for each reduced scenario and compared with the proposed MI method. Equations (4), (5) and (8) give generator status and power balance constraints for the calculation of available PFR. Maximum PFR is 30% of the generator maximum capacity. Equation (23) denotes the minimum PFR availability constraints. Available PFR response from each unit is shown in Table 3. It could be observed that both the models have similar PFR performance. Stochastic approach results in 2–3% higher PFR than MI approach. Table 3. Comparative assessment of PFR performance Generator PFR, MW MI Stochastic U-12 2.5 3.8 U-20 16 18 U-50 3 4.8 U-76 28.5 30 U-100 44.6 46.5 U-155 6.8 9.4 U-197 56.7 59.1 U-350 47.8 50.2 Table 4. Cost performance variation with PV penetration PV, % 10% 20% 30% proposed techniques→ stochastic MI stochastic MI stochastic MI operation cost×105, $ 9.200 9.247 9.002 9.182 8.790 8.974 PFR cost, $ 2625 2703 2665 2742 2732 2802 Units U-12 and U-155 commitments are less in the scheduling horizon. Hence, there are negligible PFR contributions from these units. Peak load plants such as U-197 and U-350 provide better response. This reduces the requirement of spinning reserve and provides an opportunity for more PV integration, which results in reduced overall cost. 4.3 Cost performance Figs. 6a and b show the operation and PFR cost with increased PV penetration level in both the models. It could be observed that the proposed MI model has similar operation and PFR cost, compared with stochastic model. Fig. 6Open in figure viewerPowerPoint Cost comparison with variation in PV penetration(a) Operation cost, (b) PFR payments Modelling of PFR constraints with PV penetration reduces the online units at any given instant. This is because units with high operation cost get displaced, as operation cost of PV generation is zero. In this work, inertial response cost is considered zero. This is because system has adequate commitment of inherent inertial response. PV uncertainty effect on inertial response reduction is considered; this would help in accurate estimation of PFR service requirement. This would avoid the over and under estimations of reserve requirement and result in overall cost reduction. Table 4 compares the cost performance of both the scenarios with varying PV penetration. At low penetration level (10%), MI operating cost and PFR cost are higher (about 0.5%) than the stochastic formulation (Figs. 6a and b). For higher penetration levels (20 and 30%), there is increase in cost difference (<2%). However, there is reduction in overall cost with increasing PV penetration. 4.4 Computational performance GAMS 24.2.3 with linear solver CPLEX is used to solve MIP-based scheduling problem on Intel Core i5, 1.7 GHz processor, with 8 GB RAM. It is observed that simulation time of the proposed MI model is less than half, as compared with the stochastic model. This is because, MI approach has reduced number of ramping scenarios compared with number of actual scenarios of stochastic process. Hence, simulation time of MI approach is reduced for similar performance. It is observed from Table 5 that stochastic model with and without PFR constraints have computational CPU times 885 and 692 s, respectively, as compared with MI model with and without PFR constraints as 430 and 348 s, respectively. Table 5. Comparison of computational performance of stochastic and MI model Scheduling model Time elapsed, s stochastic without PFR 692 stochastic with PFR 885 MI without PFR 348 MI with PFR 430 5 PV curtailment based on frequency security criteria In this section, impacts of system frequency security components such as ROCOF and frequency deviations on operation cost and PV power curtailment are investigated. ROCOF depends on the system inertia condition and increasing this setting leads to significant PV disconnection. It could be observed from Figs. 7a and b, ROCOF setting variation from 1.176 to 0.869 Hz/s would result in increased operation cost (20%) and PV curtailment (22%). Similarly in Fig. 7c, frequency deviation from 49.87 to 49.79 Hz results in increased PV curtailment and decrease in operation cost of about 18%. This is because of reduction in number of committed conventional generators, and hence reduced operation cost. This paper would be helpful to frame the system frequency security requirements such as ROCOF setting, with increment in PV generation share. Fig. 7Open in figure viewerPowerPoint Operation cost with frequency security criteria(a) Operation cost with variation in ROCOF and frequency deviation, (b) Operation cost and PV curtailment with variation in ROCOF setting, (c) Operation cost and PV curtailment with variation in frequency deviation 6 Conclusion This paper proposes a novel MI scheduling approach for PFR schedules considering PV uncertainty. ARIMA model is used to characterise uncertainty of MI forecast, while scenario generation and reduction approach is used for stochastic model. Furthermore, the proposed approach is compared with widely known stochastic scheduling model for overall cost, computational time and PFR availability. It is observed that MI approach performs similar for PV uncertainty handling with reduction in cost and PFR availability. There is a marginal difference in operation cost, PFR cost (<2%), PFR schedule and PV curtailment, as compared with stochastic model. However, computational burden of the proposed model is less than half of stochastic model. 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