Impact of large-scale rooftop solar PV integration: An algorithm for hydrothermal-solar scheduling (HTSS)

Solar Energy 157 (2017) 988–1004

Contents lists available at ScienceDirect

Solar Energy journal homepage: www.elsevier.com/locate/solener

Impact of large-scale rooftop solar PV integration: An algorithm for hydrothermal-solar scheduling (HTSS)

MARK

⁎

Rhythm Singha,b, , Rangan Banerjeeb a b

National Institute of Construction Management and Research, Balewadi, Pune 411045, India Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

A R T I C L E I N F O

A B S T R A C T

Keywords: Hydrothermal-solar scheduling Large-scale rooftop solar PV scenarios Solar PV integration with grid Generation scheduling

Hydrothermal scheduling is a standard problem in the operation of power systems. With the integration of renewable resources, like solar and/or wind to the existing hydro-thermal system, there is a need for a dedicated approach for long-term generation scheduling of the integrated system. Long-term generation scheduling of hydro-thermal-solar systems at the grid level has not been reported so far. This paper discusses a HydrothermalSolar Scheduling (HTSS) algorithm for the same. The algorithm is a two-stage formulation using dynamic programming and linear programming techniques. This generic methodology can be used for assessing the impact of large-scale rooftop solar-PV integration with a hydrothermal system, in terms of the electricity energymix, generation schedules and the annual generation-costs of the concerned system. It has been illustrated by application to the problem of integration of a large-scale rooftop solar photovoltaic scenario with the existing Mumbai sub-system. The results show a significantly higher annual generation-cost saving, achieved by integrating the large-scale rooftop solar photovoltaic scenario via the proposed HTSS algorithm. The benefits, however, reduce with increasing penetrations of solar in the electricity energy-mix. The annual generation-cost savings have also been used for estimating the upper cap on feed-in tariffs for solar generation, and the financial viability indicators for the large-scale rooftop solar photovoltaic scenario; the corresponding internal rate of return is found to decline from 18.4% to 16.6% as the share of solar-PV in the electricity energy-mix of Mumbai increases from 2.8% to 13.9%.

1. Introduction Hydrothermal scheduling is a standard optimization problem for systems having significant generation from a mix of hydro and thermal plants. It entails finding an optimal generation dispatch schedule for the hydro and thermal plants in the system, such that a given objective function is optimized, subject to some constraints. Generally, hydrothermal scheduling problems are classified into two broad categories – (i) long-term hydrothermal scheduling, and (ii) short-term hydrothermal scheduling. The long-term scheduling problem is spread over a period spanning from one week to one year or several years. The shortterm scheduling problem typically spans from a period of one day to one week, and involves hour-by-hour scheduling of all the generation units in the system. While there is a very substantial and swiftly expanding body of knowledge on the techniques applicable to the shortterm hydrothermal scheduling problem, not many techniques have been demonstrated and applied to the domain of long-term hydrothermal scheduling problem. Majority of work pertaining to the

⁎

solution of the long-term problem uses techniques like dynamic programming, decomposition methods and stochastic models. Table 1 shows a listing of the techniques used for short-term and long-term hydrothermal scheduling problems, along with the references where they have been implemented. As far as generation scheduling of systems with significant integration of renewable generation is concerned, not much work has been done. Some work has been done on generation scheduling of hydro-thermal-wind systems, like Varkani et al. (2011), Sahin et al. (2012), Mahari and Zare (2014), Ilak et al. (2015), Banerjee et al. (2016), Dubey et al. (2016) and Xie et al. (2016); but as far as solar power generation systems are concerned, most of the work pertains only to developing better forecasts for solar radiation, like Liang and Liao (2007), Sharma et al. (2011), Qi et al. (2012), etc. Lu and Shahidehpour (2005) have presented a methodology for short-term scheduling of battery in a grid-connected hybrid PV system with storage. Generation scheduling of hydro-thermal-solar systems, focussed on integration of large-scale solar photovoltaic generation with an

Corresponding author at: National Institute of Construction Management and Research, Balewadi, Pune 411045, India. E-mail addresses: [email protected], [email protected] (R. Singh).

http://dx.doi.org/10.1016/j.solener.2017.09.021 Received 29 April 2017; Received in revised form 25 August 2017; Accepted 9 September 2017 0038-092X/ © 2017 Elsevier Ltd. All rights reserved.

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Nomenclature TRD THD n

HTSS hydrothermal-solar scheduling pHTSS-DP Preliminary Hydrothermal-Solar Scheduling – Dynamic Programming sHTSS-LP Secondary Hydrothermal-Solar Scheduling –Linear Programming t each stage of the planning period for pHTSS-DP, equal to one month Htp hydro generation allocation (Million kWh) of plant p during stage t St∗ (Htp) optimal annual allocation schedule, given the hydro allocations during the tth stage of the DP Dt total energy demand (Million kWh) in stage t Etsolar expected generation (Million kWh) from the estimated maximum capacity of solar PV scenario during stage t CFvar solar variability correction factor Rt rainfall (in m.) during stage t Itp reservoir level increment (in m.) in reservoir of hydro plant p, due to rainfall during stage t V tp reservoir level (in m.) of hydro plant p at the beginning of stage t Stp change in reservoir level (in m.) in reservoir of hydro plant p, due to spill-way discharge during stage t FRLp full reservoir level (in m.) of reservoir of hydro plant p MDDLp minimum draw down level (in m.) of reservoir of hydro plant p Hp(Vtp) maximum available hydro generation capacity (Million kWh) of plant p in stage t, when the reservoir level of the plant is at Vtp (in m.) Hp−1(Htp) decrease in the reservoir level (in m.) Of plant p during stage t due to hydro generation of Htpduring stage t n Ct (D) total generation-cost (Million INR) for meeting a demand of D units (Million kWh) in the tth stage, having ‘n’ available thermal generating units DThermal,t effective demand (Million kWh) for thermal units during stage t H yactual actual total hydro generation (Million kWh) from all hydro plants in year y k tp correlation factor between monthly rainfall during the tth stage and monthly reservoir level increment of plant p

ci cimp h dreg dhol Dhreg Dhhol ℏreg h

ℏhol h Ehsolar

Hmonth HCp TCn RRn,hour rrn,min RInfra TPC INR α β

θhreg ,i

θhhol ,i

τ

during stage t typical regular day typical holiday number of available thermal generating units in a given month cost of generation per unit (INR/kWh) of the ith thermal generating unit cost of importing a unit of electricity from the grid (INR/ kWh) each stage of the sHTSS-LP, equal to one hour number of regular days in the given month number of holidays in the given month total demand (Million kWh) in the hth hour of a regular day total demand (Million kWh) in the hth hour of a holiday hydro generation allocation (Million kWh) in the hth hour of a regular day hydro generation allocation (Million kWh) in the hth hour of a holiday expected hourly generation (Million kWh) from the estimated maximum capacity of solar PV scenario during the hth hour of the given month total hydro generation allocation (Million kWh) for a given month, from pHTSS-DP solution rated capacity (MW) of the pth hydro plant rated capacity (MW) of the nth thermal generating unit hourly energy ramp rate (Million kWh/ hour) of nth thermal unit per-minute power ramp rate (MW/min) of nth thermal unit Reliance Infrastructure Limited Tata Power Company Indian Rupees minimum share of the available hydro capacity in a stage that is to be used in that same stage share of the estimated maximum solar PV capacity that has been actually installed generation allocation (Million kWh) of the ith thermal generating unit during the hth hour of a TRD generation allocation (Million kWh) of the ith thermal generating unit during the hth hour of a THD time, in minutes

the first stage has been formulated as a dynamic programming problem, and the second as a linear programming problem. The solution to the first-stage problem gives the monthly generation dispatch of solar, hydro and thermal units, which goes as an input to the second stage. The solution to the second-stage problem gives the hourly generation schedules of all the hydro, thermal and solar units. The HTSS algorithm has been illustrated by application to the problem of integration of a large-scale rooftop solar photovoltaic scenario with the existing Mumbai hydrothermal system. The large-scale rooftop solar photovoltaic scenario has been developed for the Indian city of Mumbai by Singh and Banerjee (2015). The next section describes the HTSS algorithm in detail. All the generation and demand terms in this algorithm have the units of Million kWh.

existing hydrothermal grid, has not been reported so far. The present paper addresses this research gap. The time-span of the problem under consideration is one year. The hydrothermal-solar scheduling (HTSS) algorithm has been developed taking into account the monthly rainfall intake at the reservoirs of the hydro plants under consideration, the variation of the reservoir levels across the year and the associated constraints, the capacity constraints on hydro generating units; the capacity constraints, ramp rate and availability constraints of the thermal plants under consideration; and solar radiation estimates and long-term solar variability across the year. Total annual hydro generation and monthly rainfall estimates have been approximated from historical data. As far as the dispatch of solar generation is concerned, this paper does not develop or use any technique for solar radiation prediction. Rather, average solar insolation, estimated from a period of record of around 30 years, has been taken as input to the generation scheduling algorithm. The short-term solar variability due to fluctuating variations, like cloud cover and motion of clouds, has been approximated by a flat capacity deduction from the total estimated capacity of the solar generating units. The problem of cascaded hydro units has not been considered; the hydro units are assumed to be stand-alone units with their independent reservoirs. The proposed HTSS algorithm is formulated as a two-stage problem:

2. Hydrothermal-solar scheduling (HTSS) algorithm formulation As the long-term scheduling problem is spread across a time-span of one year, the bifurcation of the problem into two stages helps in reducing the complexity. The time-span of the first stage is one year, and the output from this stage is the monthly allocations of the various units. The second stage has a time-span of one month, and the output from this stage is the hourly generation schedule of all the units. The 989

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

first stage of the HTSS algorithm has been designated as preliminary HTSS-Dynamic Programming (pHTSS-DP); and, the second stage has been designated as secondary HTSS-Linear Programming (sHTSS-LP). Fig. 1 shows the block diagram of the proposed HTSS algorithm.

There are three primary constraints for this pHTSS-DP formulation. The first one, corresponding to the upper and lower limits on the hydro generation allocation of each hydro-plant, in the t th stage, is given by Eq. (3).

α·Hp (Vtp) ⩽ Htp ⩽ Hp (Vtp)

2.1. Preliminary HTSS-dynamic programming (pHTSS-DP)

St∗ (Htp) = min{Ctn (Dt −β ·Etsolar . CFvar− ∑ Htp) + St∗+ 1 (Htp+ 1)} (1)

The objective function in Eq. (1) represents the minimization of the sum of the total cost of generation in the current stage of the DP problem and the next stage. It is a recursive equation, and ensures that the final monthly allocations, obtained as the solution to the pHTSS-DP problem, minimize the annual cost of generation. The decision variable is Htp , which represents the generation allocation of the pth hydro plant during the t th stage. The cost of generation in a given stage, t, of the DP problem, is given by the function Ctn (DThermal,t ) , where DThermal,t is the effective aggregate demand for the thermal units in the system, and n is the number of available thermal units in the t th stage. The effective aggregate demand for thermal units in the t th stage, DThermal,t, is given by Eq. (2).

Hp (Vtp) =

(2)

where Dt is the total demand in the t th stage, ∑p Htp is the total gen-

t th

Hp (FRL p) (Vtp−MDDL p) FRL p−MDDL p

(4)

The second constraint for the pHTSS-DP formulation comes from the maximum and minimum constraints on the reservoir level, Vtp , as shown in Eq. (5). The reservoir level, Vtp , at the beginning of the t th stage is determined by Eq. (6). This equation represents the water flow balance. The initial conditions of the problem are specified by Eq. (7).

DThermal,t = Dt −β ·Etsolar ·CFvar− ∑ Htp p

(3)

The upper limit in Eq. (3) is the hydro generation capacity of the plant available during the t th stage. The lower limit is a fixed minimum share of the available generation capacity that is to be used in the same stage. This minimum share of the available hydro capacity is denoted by α. The most optimal value of α needs to be estimated for a given HTSS formulation. The available hydro generation capacity in a given stage (month) is a direct function of the water level in the associated reservoir of the hydro plant, at the beginning of that stage. The function Hp (Vtp) gives the available hydro energy generation capacity of hydro plant p, in the stage t, when the reservoir level at the beginning of stage t is Vtp . Assuming linear hydro energy-water level operating characteristics for the hydro plant, the function Hp (Vtp) takes the form as given in Eq. (4). FRL p (Full Reservoir Level) and MDDL p (Minimum Draw-Down Level) are the maximum and minimum possible values, respectively, of the reservoir level, Vtp . Hp (FRL p) is the designed maximum generation capacity (MWh) of the pth hydro plant.

Applying the Bellman Equation for Dynamic Programming (Bellman, 1952), the optimal long-term hydrothermal schedule is given by the pHTSS-DP formulation as summarized in Eq. (1) (t indexes the stage of the dynamic programming (DP) problem, each stage being equal to one month; and p indexes the hydro plants).

p

∀ t = 1,2,…,12;α = 0.01,0.02….

MDDL p ⩽ Vtp ⩽ FRL p

Etsolar ·CFvar

eration from the p hydro plants in the stage, and β . is the total generation from the large-scale rooftop-PV scenario in the t th stage. Etsolar is the expected solar PV generation if the entire estimated potential of rooftop-PV, for the region under consideration, is installed. β is the ratio of the actual cumulative installed capacity of rooftop-PV to the estimated potential of rooftop-PV for the region. The HTSS algorithm has been run for values of β varying from 0 to 1.0, in steps of 0.2 each. CFvar is the variability correction factor to account for short-term solar variability due to fluctuating variations, like cloud cover and motion of clouds.

∀ t = 1,2,…,13;p = 1,2,…

Vtp = Vtp− 1 + Itp− 1−Hp−1 (Htp− 1)−Stp− 1

∀ t = 2,3,…,12;p = 1,2,…

V0p = I0p = Hp−1 (H0p) = 0; V1p = input

∀ p = 1,2,…

(5) (6) (7)

Long-term hydrothermal scheduling

References

Stochastic optimization Stochastic dual dynamic programming

Pereira and Pinto (1985) Pereira and Pinto (1991), Gorenstin et al. (1991), Halliburton (2004), De Matos et al. (2010) Escudero et al. (1996)

Vtp− 1 is the reservoir level at the beginning of the (t −1)th stage; Itp− 1 is the inflow in the reservoir during the (t −1)th stage; and Hp−1 (Htp− 1) is the draw-down from the reservoir during the (t −1)th stage, for generating the hydro generation allocation of the (t −1)th stage, Htp− 1. Stp− 1 is the change in reservoir level of plant p due to the spill-way discharge during the (t −1)th stage. The inflow during the (t −1)th stage, Itp− 1, is directly dependent on the rainfall during the (t −1)th stage, Rt − 1. Based on the historical data of monthly rainfall and monthly reservoir level increment, the correlation factor, ktp− 1, between the two variables can be derived, as shown in Eq. (8). The function Hp−1 (Htp) is, conceptually, the inverse of the function Hp (Vtp) . It maps the hydro generation allocation of plant p in stage t, Htp , to the corresponding draw-down from the reservoir level of plant p, required for generating that amount of electricity. Assuming linear operating characteristics, the function Hp−1 (Htp) takes the form as shown in Eq. (9).

Azevedo et al. (2009)

Itp− 1 = ktp− 1·Rt − 1

Table 1 Techniques for hydrothermal scheduling from literature.

Scenario analysis with decomposition algorithm Interior point method for solving nonlinear programming problem Sequential quadratic programming Short-term hydrothermal scheduling Gradient approach Dynamic programming/linear programming Simulated annealing Genetic algorithm Lagrangian relaxation Hybrid of Simulated annealing and Genetic algorithm Mixed integer linear programming Particle swarm optimization

Martins et al. (2009)

(8)

Hp−1 (Htp) = Vtp2−Vtp1 =

Wood and Wollenberg (1984) Wood and Wollenberg (1984)

(FRL p−MDDL p) p Ht Hp (FRL p)

(9)

The third constraint for the pHTSS-DP formulation corresponds to the fact that the total annual hydro generation allocation is constrained to a maximum value equal to the average of the actual annual hydro generation of the last five years, as shown in Eq. (10).

Wong and Wong (1994) Orero and Irving (1998), Wu et al. (2000), Gil et al. (2003) Redondo and Conejo (1999) Wong (2001)

Y −1

∑∑ t

Chang et al. (2001) Yu et al. (2007), Rasoulzadeh-akhijahani and Mohammadi-ivatloo (2015)

p

Htp ⩽ (1/5) ×

∑ y=Y −5

H yactual (10)

The pHTSS-DP problem has been solved using the Gurobi Solver v6.5.0.0 optimization solver engine (Gurobi Optimization, Inc., 2016). 990

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 1. Block Diagram of the proposed HTSS algorithm.

regular day, whose all-day energy consumption is closest to the mean daily energy consumption of the regular days of that particular month. Similarly, a typical holiday in a given month is the holiday whose allday energy consumption is closest to the mean daily energy consumption of the holidays of that particular month. In the representative synthetic year, each month is composed of as many TRDs as the number of regular days in the corresponding month in the original year; and as many THDs as the number of holidays in the corresponding month in the original year. The actual observed hourly demand data for the TRDs and THDs of each month (as detailed in Section 3.4) has been used for the analysis. Historical data has been used for illustrating the algorithm. The algorithm can also work with predicted time series data, which, in combination with a machine learning tool, can make the proposed HTSS algorithm usable for predicting future generation schedules.

2.2. Secondary HTSS-linear programming (sHTSS-LP) Secondary Hydrothermal-Solar Scheduling-Linear Programming (sHTSS-LP) is the secondary stage of the algorithm, which can be solved with different heuristic approaches, having a suitable objective function. The choice of a heuristic scheme depends on the efficacy of the solution on pre-defined performance criteria. The heuristic approach implemented in this paper corresponds to minimizing the total monthly generation cost. The sHTSS-LP algorithm can be solved with the hourly data of a full year; but the use of a representative synthetic year considerably reduces the complexity of the problem, while retaining sufficient detail about the load profile of each month. 2.2.1. Concept and design of a representative synthetic year It’s a common observation that the daily energy consumption of a given region/city is significantly different on holidays (Sundays and other major holidays) as compared to regular working days. For constructing a representative synthetic year, a typical regular day (TRD) and a typical holiday (THD) has been identified in each month of the year. That day from a particular month has been chosen as a typical n

Minimize reg

reg

hol ℏh ,ℏhol h ,θh,i ,θh,i

2.2.2. Problem formulation The objective function for the sHTSS-LP formulation, aimed at minimizing the monthly generation cost, is given in Eq. (11). This problem formulation spans over a period of one month, and has a time resolution of one hour.

24

24

n

⎡ ⎛ reg ⎞ ⎤ reg reg reg solar ⎢ dreg × ⎜∑ (ci × ∑ θh,i ) + cimp × ∑ (Dh −(ℏh + β ·Eh ·CFvar + ∑ θh,i )) ⎟+⎥ i=1 h=1 h=1 ⎢ ⎝ i=1 ⎠ ⎥ ⎢ ⎥ n n 24 24 ⎢d ×⎛ hol hol hol solar hol ⎞ ⎥ ⎢ hol ⎜∑ (ci × ∑ θh,i ) + cimp × ∑ (Dh −(ℏh + β ·Eh ·CFvar + ∑ θh,i )) ⎟ ⎥ h=1 h=1 i=1 ⎝ i=1 ⎠⎦ ⎣ 991

(11)

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 2. Location of Mumbai city and the designated generating units.

from the grid. The generation allocation of the ith thermal unit in the hth th hour of a regular day is θhreg ,i (Million kWh), and that in the h hour of a (Million kWh). The hydro generation allocation for the holiday is θhhol ,i hth hour of the TRD is ℏreg (Million kWh), and the corresponding value h solar ·CFvar (Million for the hth hour of the THD is ℏhol h (Million kWh). β . Eh kWh) is the total solar generation during the hth hour. The HTSS algorithm has been run for values of β varying from 0 to 1.0, in steps of 0.2 each. The balance of the hourly demand and the total internal

The month under consideration has dreg number of regular days and dhol number of holidays. The number of thermal power-plant units available for generation in the given month is n; ci is the cost (INR/ kWh) of generating a unit of electricity from the ith thermal unit. Dhreg and Dhhol are the demand (in Million kWh) during the hth hour of the TRD and the THD, respectively, of the given month. This hourly demand is to be met by either the internal generation of the system (thermal plants, hydro plants or the solar generation) or by the import 992

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Table 2 Priority List of Fossil-Fuel Based Generating Units for Mumbai. S.No.

Unit name

Annual Average Energy Cost per Unit (INR/kWh)

Rated capacity (MW)

Fuel

Ramp rate (MW/min)

1 2 3 4 5 6 7 8

TPC-Unit 7 RInfra Unit 1 RInfra Unit 2 TPC-Unit 8 TPC-Unit 5 TPC-Unit 6 Grid Import TPC-Unit 4

2.81 2.88 2.88 4.06 4.15 10.76 Variable 14.18

180 250 250 250 500 500 Varies 150

Gas Coal Coal Coal Coal Gas – Oil

8–12 1–3 1–3 1–3 1–3 8–12 –

The pair of constraints in Eqs. (15) and (16) constrain the hourly generation allocation of the nth thermal unit to be lower than the maximum installed capacity of the nth thermal unit, and higher than the minimum generation level, in order to honor the unit minimum shutdown-time constraint. TCn is the installed capacity (MW) of the nth thermal plant.

Table 3 Details of the Hydro plants. Name of Hydro Unit

Khopoli

Bhivpuri

Bhira

Location Name of Main Reservoir Design Capacity (MWe) Annual Design Energy (Million kWh) Capacity Factor (%) Full Reservoir Level (m) Minimum Draw Down Level (m) Gross Storage Capacity (MCM)

18.8°N, 73.4°E Walwan Lake 72 293

18.9°N, 73.5°E Andhra Lake 75 339

18.5°N, 73.4°E Mulshi Lake 300 1217

V1p (m) (as in Eq. (6))

46.45 635.2 619.4

51.6 668 646

46.31 607.1 590.1

72.5

363.7

747

627.3

657

598.6

0.1·TCn/1000 ⩽ θhreg ,n ⩽ TCn /1000

0.1·TCn/1000 ⩽

dreg ×

∑ h=1

+ dhol ×

∑

ℏhol h

=

(12)

HCp/1000

0 ⩽ ℏhol h ⩽

∑

Monthly Rainfall (mm.)

(14)

1800

5.0

1600

4.5

1400

4.0 3.5

1200

3.0

1000

2.5 800

2.0

600

1.5

400

1.0

200

0.5

0

∀ h = 1,2,…,24;n = 1,2,3…

(18)

n

⎛ Dhreg −⎜ℏreg h + ⎝

∑

⎛ Dhhol−⎜ℏhol h + ⎝

∑

i=1 n i=1

⎞ θhreg ,i ⎟ ⩾ 0 ⎠

∀ h = 1,2,…,24

⎞ θhhol ,i ⎟ ⩾ 0 ⎠

∀ h = 1,2,…,24

(19)

(20)

τ=1

60 × 103

∀ n = 1,2,3…

(21)

The sHTSS-LP problem has been solved using the open-source optimization solver, OpenSolver 2.8.4, which is based on the COIN-OR CBC optimization engine (Mason, 2012).

∀ h = 1,2,…,24

p

hol −RRn,hour ⩽ θhhol ,n −θh − 1,n ⩽ RRn,hour

RRn,hour =

(13)

HCp/1000

(17)

60

∀ h = 1,2,…,24

p

∀ h = 1,2,…,24;n = 1,2,3…

rrn,min ∑ τ

Fig. 3. Average monthly rainfall and Reservoir levelRainfall Correlation Factors.

Reservoir Level Increment-Rainfall orrelaƟon (mm./mm.)

∑

reg −RRn,hour ⩽ θhreg ,n −θh − 1,n ⩽ RRn,hour

Eq. (21) relates the hourly ramp-rate (Million-kWh/hour) of the nth thermal unit, RRn,hour , to the per-minute ramp-rate (MW/min) of the nth thermal unit, rrn,min .

The pair of constraints in Eqs. (13), (14) limit the hydro generation allocations of each hour to be within the limits of the total hydro generation capacity; HCp is the installed capacity (MW) of the pth hydro plant.

0 ⩽ ℏreg h ⩽

(16)

Eqs. (19) and (20) constrain the grid import during the hour to be non-negative, implying power can only be purchased from the grid, and not sold to the grid.

H month

h=1

∀ h = 1,2,…,24;n = 1,2,3…

hth

24

ℏreg h

⩽ TCn/1000

(15)

The constraints in Eqs. (17), (18) limit the change in thermal generation of the nth thermal unit, from previous hour to the current hour, to be within the limits of the hourly ramp-rate of the thermal unit.

generation of the system is imported from the grid at a cost of cimp (INR/ reg hol hol kWh) per unit of electricity. θhreg ,i , θh,i , ℏh and ℏh ( ∀ h,i ) are the decision variables for this sHTSS-LP formulation. The first constraint for the sHTSS-LP formulation constrains the summation of all the hourly hydro generation allocations, during the month, to be equal to the monthly hydro generation allocation of the given month, which is obtained from the solution to the pHTSS-DP problem, as shown in Eq. (12). 24

θhhol ,n

∀ h = 1,2,…,24;n = 1,2,3…

0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

993

Monthly Rainfall k1 k2 k3

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

generation facilities allocated to meet the power requirements of Mumbai city. The location of Mumbai city and its designated generating units is shown in Fig. 2. The power from these generation facilities is shared by the three distribution licensees in accordance with their mutually agreed power purchase agreements and regulations set by the Maharashtra Electricity Regulation Commission (MERC). In case the demand from the city of Mumbai exceeds the generation from the designated facilities, it is met either through i) bilateral intra-state agreements with the generation utilities of Maharashtra State Power Generation Corporation Ltd., or ii) bilateral inter-state agreements with the utilities in other states, known as Inter-State Generating Stations (ISGS) or iii) through power transfer from dynamically allocated Power Exchange. Usually, the per unit cost of electricity acquired through any of these exchange mechanisms is much higher than the cost incurred for generating a unit of electricity at the designated utilities for Mumbai. Amongst the designated utilities for supplying power to Mumbai city, the majority is coal-based thermal power, along with some quota of gasbased thermal power and hydro power. The details of these generation units are given in the following sub-sections.

Table 4 Details of the large-scale solar PV scenario for HTSS algorithm. Theoretical Maximum Rated Capacity (MW) Values of β considered for the analysis Orientation and Tilt of solar PV panels Transposition Model for estimating Plane-of-Array irradiance Rated Solar Cell Efficiency (%) Efficiency of the Power Conditioning Unit (%) Power Temperature Coefficient (%/°C) Nominal Operating Cell Temperature (°C) Solar Variability Correction Factor

2190 0–1.0, in steps of 0.2 each S-facing, Fixed tilt @ 19° Liu-Jordan Model 14.5 85 −0.4383 47 0.9

2.3. Comparison of the HTSS algorithm with existing hydrothermal algorithms Since no hydrothermal-solar scheduling algorithms have been reported in the literature, the performance of the proposed HTSS algorithm, as described in Sections 2.1 and 2.2 above, has been compared with one of the classic hydrothermal algorithms, as described by Pereira and Pinto (1985). Pereira and Pinto (1985) have illustrated their stochastic optimization algorithm for hydrothermal scheduling by application to a sample hydrothermal system. The system consists of four hydro plants, one thermal unit and one “load-shedding” dummy unit (which can also be thought of as the grid, for supplying any unmet demand from the units in the system). The optimization interval spans over three stages. The minimum cost found by the stochastic algorithm by Pereira and Pinto (1985) is 298.45 units. This same problem has been solved with the HTSS algorithm proposed in this present paper. The minimum generation-cost for the three stage problem has been found to be 274 units with the HTSS algorithm, i.e. 8.2% less than that found by Pereira and Pinto (1985).

3.1. Thermal units: priority list The details of the thermal units of Reliance Infrastructure Limited (RInfra) and Tata Power (TPC) are obtained from the annual performance and revenue reports of the respective company (Raja and Sonavane, 2013; Tata Power-Generation, 2013). These have been analysed to prepare a priority list of the available units. A priority list is a list of generating options, arranged in the ascending order of their energy cost per unit; it is a standard tool used for solving generation dispatch and unit commitment problems. The priority list of the thermal units for the hydrothermal-solar scheduling problem for the Mumbai system has been shown in Table 2. The currency unit used in this paper is Indian Rupees (INR). The exchange rate of INR to US Dollars (USD), as of 1st January 2016, is given in Eq. (22). The availability constraints of the concerned thermal units have been taken from the System Performance Reports produced by the State Load Dispatch Centre, Airoli, Maharashtra (Maharashtra State Load Dispatch Centre, 2013).

3. Sample system for illustrating the HTSS Algorithm: Mumbai sub-system Mumbai is a part of the Indian state of Maharashtra. It has mainly three distribution licensees operating in the city for supplying electricity to the consumers. These companies are Reliance Infrastructure Limited (RInfra), Tata Power (TPC-D) and Brihanmumbai Electricity Supply and Transport Undertaking (BEST). These three distribution utilities get their power supply mainly from the thermal and hydro generation units of Tata Power (TPC) in and around Mumbai, and the Dahanu Thermal Power station of Reliance Infrastructure Limited (RInfra). Thus, there is some designated quota of hydro-thermal

3.2. Details of the hydro units The details of the three hydro units supplying electricity to the Mumbai system are given in Table 3 (Hydro Electric Projects in Fig. 4. Daily Energy Demand of Mumbai city: January and July 2013.

60 50

Demand (Million kWh)

(22)

1 INR = 0.015 USD

40 30 20 10 0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Jan

Jul

1 - Daily Demand

1 - Regular Day Average

1 - Holiday Average

2 - Daily Demand

2 - Regular Day Average

2 - Holiday Average

994

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 5. Variation in daily demand in the Synthetic Year.

Typical Daily Energy Demand (Million kWh)

60

50

40 Typical Regular Day

30

Typical Holiday 20

10

0

Jan Feb Mar Apr May Jun

Jul Aug Sep Oct Nov Dec

Fig. 6. Monthly demand variation: 2013 Actual and Synthetic Year.

1700

1600

1500

2013 Actual SyntheƟc Year

1400

Dec

Oct

Nov

Sep

Jun

May

Apr

Mar

Jan

Min. Annual 'eneraƟon ost (Million INR)

Feb

1200

Aug

1300

Jul

Monthly Demand (Million kWh)

1800

Fig. 7. Variation of minimized annual generation cost with α: pHTSS-DP result.

105000 100000 95000 90000 85000

ɴ=0 80000

ɴ = 0.4

75000

ɴ=1

70000 65000 60000 0

0.02

0.04

0.06

0.08

0.1

0.12

Min. share of Available Hydro to be used in a month (ɲ)

3.3. Details of the solar generation scenario

Maharashtra, 2016). The average monthly rainfall data, initial reservoir level data and the reservoir level increment-rainfall correlation factors for the three hydro plants have been obtained from the Central Water and Power Research Station (2017). Fig. 3 shows the average monthly rainfall in the vicinity of the three hydro plants, averaged over the years 2000–2014, and the reservoir level increment-rainfall correlation factors (k1, k2 and k3) for the three hydro plants.

The large-scale rooftop solar PV scenario developed by Singh and Banerjee (2015) has been taken as the solar generation unit for illustrating the HTSS algorithm. The land resource for this large-scale rooftop solar PV scenario had been estimated by combining high-resolution land-use data from the Municipal Corporation of Greater Mumbai (Existing Land Use Survey for Development Plan for Greater Mumbai (2014–2034), 2013) with image analysis of GIS maps of sample areas and micro-level building simulations of sample buildings 995

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 8. Optimal Monthly Hydro Allocation: pHTSS-DP result.

Monthly Hydro AllocaƟon (Million kWh)

200 180 160 140 120 100 80 60 40 20 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0

ɴ=0

ɴ = 0.4

ɴ=1 Fig. 9. Monthly Solar Allocations at the end of the pHTSS-DP algorithm.

Monthly Solar AllocaƟon (Million kWh)

300.0

250.0

200.0

ɴ=0 150.0

ɴ = 0.4 ɴ = 1.0

100.0

50.0

0.0 Jan

Feb Mar Apr May Jun

Jul

Aug Sep

Oct Nov Dec

Fig. 10. Monthly Thermal Allocations at the end of the pHTSS-DP algorithm.

Monthly Thermal AllocaƟon (Million kWh)

1800 1600 1400 1200

ɴ=0

1000

ɴ = 0.4

800

ɴ=1 600 400 200 0

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

hydrothermal system has been studied, by varying the proportion of installed capacity out of the estimated maximum capacity of rooftop solar PV for Mumbai. This ratio of total installed capacity of solar PV to the theoretical maximum capacity is denoted by β, as discussed before. The details of this large-scale solar PV scenario have been summarized in Table 4.

in PVSyst. The solar resource for this large-scale rooftop solar PV scenario had been estimated by combining 30 years’ average hourly solar insolation (GHI, DNI and DHI) data for Mumbai (ASHRAE, 2009) into hourly average plane-of-array insolation data using the Liu-Jordan Transposition model. The impact of integration of this large-scale solar PV scenario on the electricity energy-mix and generation dispatch of the Mumbai 996

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Hourly AllocaƟon (x 1000 MW)

3.0

Import

2.5

Fig. 11. Hourly generation dispatch for typical regular day of January 2013.

Hydro 2.0

SolarPV

1.5

TPC-U6 TPC-Unit 5

1.0

TPC-Unit 8 0.5

RInfra Unit 2 RInfra-Unit 1

0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

TPC-Unit 7

(a) ȕ V+766/3UHVXOW

Hourly AllocaƟon (x 1000 MW)

3.0

Import 2.5

Hydro

2.0

SolarPV

1.5

TPC-U6 TPC-Unit 5

1.0

TPC-Unit 8 0.5

RInfra Unit 2

0.0

RInfra-Unit 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

TPC-Unit 7

(b) ȕ V+766/3UHVXOW Hourly AllocaƟon (x 1000 MW)

3.0

Import

2.5

Hydro 2.0

SolarPV

1.5

TPC-U6 TPC-Unit 5

1.0

TPC-Unit 8 0.5

RInfra Unit 2 RInfra-Unit 1

0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

TPC-Unit 7

(c) ȕ V+766/3UHVXOW 4. Results from the HTSS algorithm

3.4. Demand data for Mumbai and representative synthetic year formulation

4.1. Results from the pHTSS-DP algorithm The hourly demand data for Mumbai for all the typical regular days and the typical holidays (Office Holidays, 2015), used for constructing the synthetic year, has been obtained from the respective Combined Daily Reports and System Performance Reports produced by the State Load Dispatch Centre, Airoli, Maharashtra (Maharashtra State Load Dispatch Centre, 2013). This data has been used to construct a synthetic year demand profile, as discussed above. Fig. 4 shows the dichotomy between the average daily energy demand of a regular day and a holiday, for the case of Mumbai city. The variation in daily demand of the typical regular days and typical holidays which constitute the synthetic year is shown in Fig. 5. The monthly demand variation in the synthetic year and the 2013 actual has been compared in Fig. 6.

The very first thing to be determined in the pHTSS-DP algorithm is the value of the parameter α, as this is the only unknown input parameter in the pHTSS-DP problem formulation. The underlying concept behind α is described in Section 2.1 and in Eq. (2); α is an operational constraint. For determining the best value of α, different formulations of the pHTSS-DP problem are solved with (i) value of β = 0, (ii) value of β = 0.4, and (iii) value of β = 1.0, and values of α varying in steps of 0.01 in each formulation, starting from α = 0. The value of α which gives the minimum value for the minimized annual generation-cost estimate is taken as the best value of α. For the present problem, it is found that the pHTSS-DP optimization problem has no feasible solution for values of α greater than 0.1. It is not a limitation of the algorithm, 997

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Hourly AllocaƟon (x 1000 MW)

3.0

Import

2.5

Fig. 12. Hourly generation dispatch for typical holiday of January 2013.

Hydro SolarPV

2.0

TPC-U6 1.5

TPC-Unit 5

1.0

TPC-Unit 8 RInfra Unit 2

0.5

RInfra-Unit 1 0.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

TPC-Unit 7

Hour of Day

(a) ȕ V+766/3UHVXOW Hourly AllocaƟon (x 1000 MW)

3.0

Import

2.5

Hydro SolarPV

2.0

TPC-U6 1.5

TPC-Unit 5

1.0

TPC-Unit 8 RInfra Unit 2

0.5

RInfra-Unit 1 0.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

TPC-Unit 7

Hour of Day

(b) ȕ V+766/3UHVXOW

Hourly AllocaƟon (x 1000 MW)

3.0

Import

2.5

Hydro SolarPV

2.0

TPC-U6 1.5

TPC-Unit 5

1.0

TPC-Unit 8 RInfra Unit 2

0.5

RInfra-Unit 1 0.0

TPC-Unit 7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

(c) ȕ V+766/3UHVXOW to September) and the electricity demand profile of Mumbai (significantly higher demand from March to October). The monthly allocations of solar and thermal units for different values of β, as a result of the pHTSS-DP solution, are shown in Figs. 9-10.

rather a constraint imposed due to the physical realities of the system under consideration. A larger value of α will indicate an unsustainably high draw-down from the reservoirs during some of the months, since the region receives rainfall for only four months during the year. The best value of α has been found to be 0.1, for all the three cases, (i) β = 0, (ii) β = 0.4, and (iii) β = 1.0, as shown in Fig. 7. Thus α = 0.1 has been used for all the pHTSS-DP and sHTSS-LP formulations. This implies that minimum 10% of the total available hydro generation capacity in a month must be used in the same month. The optimal monthly hydro allocation for different values of β, found from the solution of the pHTSS-DP algorithm, is shown in Fig. 8. The particular shape of these curves is a result of the interplay of the rainfall profile of the region (almost all the rainfall in the four-month window from June

4.2. Results from the sHTSS-LP algorithm The results for the typical regular day and typical holiday of a sample month, January, are shown in Figs. 11 and 12. In each of these figures, figure (a) shows the HTSS output for β = 0; figure (b) shows the HTSS output for β = 0.4; and figure (c) shows the HTSS output for β = 1.0. The β = 0 output from the HTSS is very similar to the original 998

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Table 5 Comparison of Original dispatch schedule with the β = 0 solution from HTSS for TRD of January 2013. Generation Allocation (Million kWh)

TPC-Unit 7 RInfra Unit-1 RInfra Unit-2 TPC Unit-8 TPC Unit-5 Import

Hourly Solar 'eneraƟon (x 1000 MW)

Hydro

β=0 Original β=0 Original β=0 Original β=0 Original β=0 Original β=0 Original β=0 Original

Morning Partial Peak

Morning Peak

Afternoon Partial Peak

Evening Peak

Off Peak

Daily Total

0.54 0.53 0.75 0.72 0.75 0.71 0.75 0.66 1.50 1.21 0.65 0.86 0.00 0.27

0.54 0.53 0.75 0.72 0.75 0.72 0.75 0.69 1.50 1.42 1.49 1.36 0.89 1.25

1.08 1.05 1.50 1.44 1.50 1.40 1.50 1.35 3.00 2.63 3.69 3.31 0.87 1.97

0.72 0.70 1.00 0.92 1.00 0.90 1.00 0.86 2.00 1.47 0.98 2.48 1.79 1.17

1.44 1.40 1.96 1.52 1.98 1.47 1.59 1.47 3.27 2.08 0.42 2.70 0.00 0.02

4.32 4.20 5.96 5.32 5.98 5.19 5.59 5.02 11.27 8.80 7.22 10.69 3.56 4.67

Fig. 13. Annual average daily solar generation schedule.

1.20 1.00 0.80 0.60

ɴ=1 ɴ=0

0.40 0.20 0.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

Fig. 14. Annual average daily hydro generation schedule.

Hourly Hydro 'eneraƟon (x 1000 MW)

0.45 0.40 0.35 0.30 0.25 0.20

ɴ=1

0.15

ɴ=0

0.10 0.05 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day

base load throughout the year and the peaks are met through either solar or hydro or import from the grid, as the case may be. Thus there is an interplay between solar and hydro/grid import. This can be understood by Figs. 13–15, which show the annual average daily generation schedule for solar, hydro and grid import, for β = 0 and β = 1. The average values shown in these figures (Figs. 13–15) are estimated by taking the weighted average of the hourly generation schedules for the regular days and holidays of all the months in the synthetic year. It’s clear from Figs. 13–15 that as the solar generation kicks in during the sunshine hours, it (i) replaces the grid import, (ii) displaces the hydro to the evening peak hours (leading to reduction in grid import in evening peak hours as well), and (iii) if demand during the sunshine hours is low, it might necessitate backing-down of the thermal plants (as in Figs. 11(c) and 12(b), (c)).

dispatch. The comparison between the two, for a sample day (TRD of January 2013), has been shown in Table 5. The marginal difference between the two can be explained by two underlying factors. First, the monthly allocations of hydro generation are different in the two cases because the HTSS algorithm tends to optimize the monthly hydro generation allocations over the year. Second, the hourly generation allocations of some of the thermal units and the hydro units are different in the two cases because the HTSS algorithm doesn't have access to many operational constraints of these power-plants and the overall system, like fuel availability constraints, area protection and transmission network congestion constraints, labour rules and crew scheduling policies, etc. Due to unavailability of these operational details, the HTSS output for β = 0 case is taken as the base case for the analysis of large-scale solar-PV integration presented in this paper. To summarize the sHTSS-LP results, the thermal-units supply the 999

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 15. Annual average daily grid import schedule.

Hourly Grid Import (x 1000 MW)

0.80 0.70 0.60 0.50 0.40 ɴ=1 0.30

ɴ=0

0.20 0.10 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of Day Fig. 16. Monthly generation-cost estimates for β = 0, 0.4 and 1.0.

Monthly GeneraƟon-Cost (Million INR)

12000

10000

8000

ɴ=0 6000

ɴ = 0.4 ɴ = 1.0

4000

2000

0 Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

import from grid reduces from 17.1% to 6.3%, as solar increases from 0% to 13.9%. This shows that β = 1, corresponding to the estimated rooftop solar photovoltaic potential of Mumbai, would amount to solar generation equal to only 13.9% of the total annual electricity consumption of Mumbai.

Table 6 Annual Generation-Cost Estimates from sHTSS-LP. Case

β β β β β β

= = = = = =

0 0.2 0.4 0.6 0.8 1.0

Annual Generation-Cost Estimate from sHTSS-LP (Million INR)

% change from β = 0 case

97,530 91,449 85,469 79,672 74,313 69,610

0 −6.2 −12.4 −18.3 −23.8 −28.6

5. Analysis of the results and inferences The efficacy of this whole exercise of generation scheduling using a dedicated Hydrothermal-Solar Scheduling (HTSS) algorithm, for minimization of the annual generation-cost, can be assessed as follows. Let us consider, as base case, the scenario that there is no dedicated HTSS algorithm; and whatever generation from rooftop solar photovoltaic systems is there, is simply superimposed on the existing generation schedule. In such a scenario, the estimated annual generation-cost saving by solar photovoltaic generation would be equal to the product of the number of units generated annually from the solar photovoltaic systems and the prevailing average cost of one unit of electricity, before the commissioning of the solar photovoltaic systems. This would be the ad-hoc expected annual generation-cost saving, without a dedicated HTSS algorithm. Contrary to this, the annual generation-cost saving with the implementation of a HTSS algorithm is the difference between the annual generation-cost before the commissioning of the solar photovoltaic systems (“β = 0” result from sHTSS-LP) and the estimated annual generation-cost with the HTSS algorithm, as indicated in Table 6. The results of this comparison have been summarized in Table 7. Table 7 shows that, for β = 0.2, the integration of the solar photovoltaic generation via the proposed HTSS algorithm yields 123.5% higher annual

4.3. Annual generation-cost estimates The monthly generation-cost estimates, estimated from the hourly dispatch schedules derived from the sHTSS-LP solution, are shown in Fig. 16. Table 6 shows the annual generation-cost estimates for the six cases from β = 0 to β = 1.0. 4.4. Energy-mix of the electricity supply There are five types of energy sources for meeting the energy demand of Mumbai – solar, hydro, coal, gas and import from the grid. The energy-mix of the generation dispatch, for the three sample cases of β = 0, 0.4 and 1.0, as determined by sHTSS-LP, is shown in Fig. 17. The comparison of the percentage share of the various energy sources in the supply mix, for the six cases from β = 0 to β = 1.0, is shown in Fig. 18. It can be seen that for change of β from 0 to 1, the share of coal and gas in the supply mix decreases marginally from 59.6% to 58.0% and from 16.3% to 14.6% respectively; hydro remains constant at 7.1%; and 1000

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 17. Annual energy supply mix by source type.

Monthly GeneraƟon Dispatch by source (Million kWh)

2000 1800 1600 1400

Import

1200

Solar

1000

Hydro

800

Gas

600

Coal

400 200 0

Jan

Feb Mar Apr May Jun

Jul

Aug Sep Oct Nov Dec

(a) ȕ  Monthly GeneraƟon Dispatch by source (Million kWh)

2000 1800 1600 1400

Import

1200

Solar

1000

Hydro

800

Gas

600

Coal

400 200 0 Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

(b) ȕ 

Monthly GeneraƟon Dispatch by source (Million kWh)

2000 1800 1600 1400

Import

1200

Solar

1000

Hydro

800

Gas

600

Coal

400 200 0

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

(c) ȕ 

goes on increasing, the rescheduling by the HTSS algorithm replaces progressively lesser costlier sources of generation. Thus, the incremental generation-cost savings for incrementally higher penetrations of solar are progressively smaller in magnitude. This effect can be observed even in the present paper. From Table 7 it can be observed that the generation-cost saving per unit of solar photovoltaic generation, obtained by the HTSS algorithm for the case of β = 0.2 (corresponding to 2.79% share of solar in the electricity energy-mix), is 11.91 INR/ kWh; whereas the corresponding value for the case of β = 1.0 (corresponding to 13.9% share of solar in the electricity energy-mix) is 10.94 INR/kWh. If one considers the tariff of solar generation, the above observation very aptly corroborates the common notion and practice of having feedin tariff mechanism at lower penetrations of solar photovoltaic generation, and net metering scheme for higher penetrations, above some threshold penetration level. The idea is that at lower penetration levels,

generation-cost saving than the ad-hoc average generation-cost saving expected. This is attributable to the fact that, with the HTSS algorithm, the hydro generation and grid import are rescheduled to take care of the evening peak, as the solar generation takes care of the morning/ afternoon peak. This rescheduling tends to offer significantly higher generation-cost savings than the ad-hoc expected savings. However, for β = 0.4, the corresponding difference between annual generation-cost saving via the HTSS algorithm and the ad-hoc average generation-cost saving expected is 121.6%, which further reduces to 118.7% for β = 0.6; and onwards to 105.2% for β = 1.0. The reason is that when the share of solar generation in the overall electricity energymix is small (2.79% for β = 0.2; 5.58% for β = 0.4), the rescheduling by the HTSS algorithm replaces expensive options like costlier thermal units and/or costly power import from external grid; thus leading to significantly higher generation-cost savings for every unit of solar generation. However, as the share of solar in the overall generation mix

1001

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Fig. 18. Percentage share of the various supply options in different scenarios.

60.0 Import

50.0

Solar 40.0

Hydro Gas

30.0

Coal

20.0 10.0 0.0 ɴ=0

ɴ = 0.2

ɴ = 0.4

ɴ = 0.6

ɴ = 0.8

ɴ = 1.0

whereas at a penetration level of 13.94% (β = 1.0), the maximum feedin tariff justified is 10.94 INR/kWh. One can also estimate the financial viability indicators for the rooftop solar PV installation by taking the annual generation-cost savings as the return from the rooftop solar PV installation. The inputs for capital cost of solar PV projects have been taken from Pradhan et al. (2014). As per this report, the benchmark project cost for rooftop solar PV projects in India, as of 2014–15, is around 65.5 Million Rupees/MW. This includes the cost components of module cost, civil and general works, mounting structures, power conditioning units, cables and transformers, and preliminary expenses. The capital cost break-up is shown in Fig. 19. The annual generation-cost saving with sHTSS-LP has been taken as given in Table 7. The discount rate for future cash flows in the calculation of the financial viability indicators has been taken as 10%. Useful life of the rooftop solar-PV installations has been taken as 25 years; operation and maintenance (O & M) costs have been taken as 1.3 Million INR/MW/year (Pradhan et al., 2015). Assuming 50% of the rooftop solar-PV modules to be of monocrystalline-Si technology, and the remaining 50% to be of multicrystalline-Si, the average annual degradation rate of the modules has been taken as 0.5%/year (Jordan and Kurtz, 2013). The results for the financial viability indicators are shown in Table 8, and the standard formulae used for this analysis have been given in Appendix A, for reference.

Table 7 Annual Generation-Cost: with and without HTSS algorithm. Total Annual Consumption (Million kWh) Total Annual Generation-Cost without Solar PV (Million INR) Ave. Cost of Electricity without Solar PV (INR/kWh)

18300 97530 5.33

β

Annual Solar PV Generation (Million kWh)

% Share of SolarPV in EnergyMix

Ad-hoc Annual GenerationCost Saving Expected with Solar PV (Million INR)

Annual GenerationCost Saving with Solar PV, with HTSS (Million INR)

GenerationCost Saving per unit SolarPV Generation with HTSS (Rs./kWh)

0.2 0.4 0.6 0.8 1.0

511 1021 1532 2042 2553

2.79 5.58 8.37 11.16 13.94

2721 5442 8163 10884 13605

6081 12061 17858 23217 27920

11.91 11.81 11.66 11.37 10.94

each unit of solar generation effectively adds more value to the overall grid operation, and hence a higher feed-in tariff might be justified. However, as the penetration of solar in the electricity energy-mix goes on increasing, the incremental benefits to the grid operations are progressively diminishing; and hence it makes sense to treat solar gen-

6. Conclusion Cables and Transformers 9% Power CondiƟoning Unit 8%

Preliminary expenses 10%

The paper discusses a proposed Hydrothermal-Solar Scheduling (HTSS) algorithm for integrating solar photovoltaic generation with an existing hydrothermal system at grid level. The proposed algorithm has been illustrated by integrating a large-scale rooftop solar PV scenario with the existing hydrothermal system of the city of Mumbai in India. The analysis is carried out in terms of the proportion of the estimated rooftop solar PV potential of Mumbai that has been installed (β). The results show that, for β = 0.2 (corresponding to 2.79% share of solar in the electricity energy-mix), the annual generation-cost saving achieved by integrating the large-scale rooftop solar PV scenario via the proposed HTSS algorithm is 123.5% higher than the ad hoc generationcost saving expected. However, for β = 1.0 (corresponding to 13.9% share of solar in the electricity energy-mix), the corresponding increase in annual generation-cost saving is 105.2%. This shows that the benefit of integrating the solar generation via the HTSS algorithm is progressively reducing with increasing penetration level of solar in the electricity energy-mix. At a given penetration level, the generation-cost saving, achieved by integrating a unit of solar generation through the HTSS algorithm, can be used to decide the upper limit on the feed-in tariff for solar at that level. In the sample case of Mumbai, for a 2.79%

Module Cost 56%

MounƟng Structure 8% Civil & General Works 9% Fig. 19. Break-up of capital cost of rooftop solar-PV installations.

eration at par with the generation from other sources, beyond some threshold penetration level of solar. In the present paper, it can be seen that for a 2.79% penetration of solar in the electricity energy-mix (β = 0.2), a feed-in tariff for solar up to 11.91 INR/kWh might be justified; 1002

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

tariff for solar up to 11.91 INR/kWh might be justified; whereas at a penetration level of 13.94% (β = 1.0), the maximum feed-in tariff justified is 10.94 INR/kWh. The annual generation-cost saving has also been used for estimating the financial viability indicators for the large-scale rooftop solar-PV scenario. The discounted payback period, at a discount rate of 10%, has been found to be 7.9 years for β = 0.2, and 9.2 years for β = 1.0; the corresponding values for the internal rate of return are 18.4% and 16.6% respectively. The proposed methodology can be used to determine the actual benefit of solar generation integration at a given penetration level. The impact of this integration depends upon the dynamics of the demand, solar generation profile, hydro generation allocation, characteristics of the available thermal units and power purchase from the external grid.

Table 8 Financial viability indicators for Rooftop Solar-PV. Capital cost for 1 MW (Million INR) (Pradhan et al., 2014)

Total Solar PV Capacity (MW) % Share of Solar-PV in Electricity Energy-mix Total Capital Cost (Million INR) Annual Generation-Cost Saving (Million INR) Discounted Payback Period (years) Net Present Value (Million INR) Internal Rate of Return (%)

65.5

β = 0.2

β = 0.6

β = 1.0

438 2.79 28,680 6081 7.9 19,350 18.4

1314 8.37 86,041 17858 8.2 54,682 18.0

2190 13.94 143,401 27,920 9.2 75,010 16.6

penetration of solar in the electricity energy-mix (β = 0.2), a feed-in Appendix A

If C0 is the capital cost, d is the discount rate, nmax is the useful life of the project in years, and Bi is the monetary value of the net benefit accrued at the end of the ith year, then the discounted payback period ndp is given by Eq. (23), net present value (NPV) is given by Eq. (24), and the internal rate of return (IRR) is given by Eq. (25).

Bndp B1 B2 + + …+ = C0 (1 + d ) (1 + d )2 (1 + d )ndp nmax

Bi )−C0 (1 + d )i

(24)

Bi ⎛ ⎞−C0 = 0 + (1 IRR)i ⎠ ⎝

(25)

NPV =

∑ i=1

nmax

∑ i=1

(23)

⎜

(

⎟

on the hydro generation water shadow price. Appl. Energy 154, 197–208. Jordan, D.C., Kurtz, S.R., 2013. Photovoltaic degradation rates—an analytical review. Prog. Photovolt. Res. Appl. 21 (1), 12–29. Liang, R.H., Liao, J.H., 2007. A fuzzy-optimization approach for generation scheduling with wind and solar energy systems. IEEE Trans. Power Syst. 22 (4), 1665–1674. Lu, B., Shahidehpour, M., 2005. Short-term scheduling of battery in a grid-connected PV/ battery system. IEEE Trans. Power Syst. 20 (2), 1053–1061. Maharashtra State Load Dispatch Centre, Airoli, 2013. Combined Daily Reports and System Performance Reports. Retrieved from Maharashtra State Electricity Transmission Company Ltd. Website: < http://mahasldc.in/reports > . Mahari, A., Zare, K., 2014. A solution to the generation scheduling problem in power systems with large-scale wind farms using MICA. Int. J. Electr. Power Energy Syst. 54, 1–9. Martins, L.S., Soares, S., Azevedo, A.T., 2009. A nonlinear model for the long-term hydrothermal generation scheduling problem over multiple areas with transmission constraints. In: Power Systems Conference and Exposition, 2009. PSCE'09. IEEE/PES. IEEE, pp. 1–7. Mason, A.J., 2012. OpenSolver-An Open Source Add-in to Solve Linear and Integer Progammes in Excel. In: Operations Research Proceedings 2011. Springer, Berlin Heidelberg, pp. 401–406. Office Holidays, 2015. Public Holidays in India in 2013 [online] Available at: < http:// www.officeholidays.com/countries/india/2013.php > (Accessed: July 1, 2015). Orero, S.O., Irving, M.R., 1998. A genetic algorithm modelling framework and solution technique for short term optimal hydrothermal scheduling. IEEE Trans. Power Syst. 13 (2), 501–518. Pereira, M.V.F., Pinto, L.M.V.G., 1985. Stochastic optimization of a multireservoir hydroelectric system: a decomposition approach. Water Resour. Res. 21 (6), 779–792. Pereira, M.V., Pinto, L.M., 1991. Multi-stage stochastic optimization applied to energy planning. Math. Program. 52 (1–3), 359–375. Pradhan, G.B., Dayalan, M.D., Singhal, A.K., Mathur, N., 2014. Determination of Benchmark Capital Cost Norm for Solar PV power projects and Solar Thermal power projects applicable during FY 2014–15 (Petition No. SM/353/2013). Central Electricity Regulatory Commission, New Delhi. Pradhan, G.B., Singhal, A.K., Bakshi, A.S., 2015. Determination of generic levellised generation tariff for the FY 2015–16 under Regulation 8 of the Central Electricity Regulatory Commission (Petition No. SM/004/2015). Central Electricity Regulatory Commission, New Delhi. Qi, W., Liu, J., Christofides, P.D., 2012. Supervisory predictive control for long-term scheduling of an integrated wind/solar energy generation and water desalination system. IEEE Trans. Control Syst. Technol. 20 (2), 504–512. Raja, V.P., Sonavane, V.L., 2013. Order for Approval of ARR and Determination of Tariff for Second Control Period (Case No. 1 of 2013). Maharashtra Electricity Regulatory Commission, Mumbai, Maharashtra. Rasoulzadeh-akhijahani, A., Mohammadi-ivatloo, B., 2015. Short-term hydrothermal generation scheduling by a modified dynamic neighbourhood learning based particle

References American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE), 2009. Climate Design Data 2009 ASHRAE Handbook. Azevedo, A.T., Oliveira, A.R.L., Soares, S., 2009. Interior point method for long-term generation scheduling of large-scale hydrothermal systems. Ann. Oper. Res. 169 (1), 55–80. Banerjee, S., Dasgupta, K., Chanda, C.K., 2016. Short term hydro–wind–thermal scheduling based on particle swarm optimization technique. Int. J. Electr. Power Energy Syst. 81, 275–288. Bellman, R., 1952. On the theory of dynamic programming. Proc. Natl. Acad. Sci. 38 (8), 716–719. Central Water and Power Research Station, 2017. Personal Discussion with the Authorities. Pune, India. Chang, G.W., Aganagic, M., Waight, J.G., Medina, J., Burton, T., Reeves, S., Christoforidis, M., 2001. Experiences with mixed integer linear programming based approaches on short-term hydro scheduling. IEEE Trans. Power Syst. 16 (4), 743–749. De Matos, V., Philpott, A. B., Finardi, E. C., Guan, Z., 2010. Solving long-term hydrothermal scheduling problems. Technical report, Electric Power Optimization Centre, University of Auckland. Dubey, H.M., Pandit, M., Panigrahi, B.K., 2016. Ant lion optimization for short-term wind integrated hydrothermal power generation scheduling. Int. J. Electr. Power Energy Syst. 83, 158–174. Escudero, L.F., De la Fuente, J.L., Garcia, C., Prieto, F.J., 1996. Hydropower generation management under uncertainty via scenario analysis and parallel computation. IEEE Trans. Power Syst. 11 (2), 683–689. Existing Land Use Survey for Development Plan for Greater Mumbai (2014–2034), 2013 < http://www.mcgm.gov.in/irj/portal/anonymous/ qlELUSurveyData > (Accessed: 21.09.13). Gil, E., Bustos, J., Rudnick, H., 2003. Short-term hydrothermal generation scheduling model using a genetic algorithm. IEEE Trans. Power Syst. 18 (4), 1256–1264. Gorenstin, B.G., Campodonico, N.M., Costa, J.P., Pereira, M.V.F., 1991. Stochastic optimization of a hydro-thermal system including network constraints. In: Power Industry Computer Application Conference, 1991. Conference Proceedings. IEEE, pp. 127–133. Gurobi Optimization, Inc., 2016. Gurobi Optimizer Reference Manual. < http://www. gurobi.com > . Halliburton, T.S., 2004. An optimal hydrothermal planning model for the New Zealand power system. Austral. J. Electr. Electron. Eng. 1 (3), 193–198. Hydro Electric Projects in Maharashtra. (2016, March 3). Retrieved from < http://indiawris.nrsc.gov.in/wrpinfo/index.php?title=Hydro_Electric_Projects_in_ Maharashtra > . Ilak, P., Rajšl, I., Krajcar, S., Delimar, M., 2015. The impact of a wind variable generation

1003

Solar Energy 157 (2017) 988–1004

R. Singh, R. Banerjee

Wong, K.P., Wong, Y.W., 1994. Short-term hydrothermal scheduling part. I. Simulated annealing approach. IEE Proceedings-Generation. Transmiss. Distrib. 141 (5), 497–501. Wong, S.Y.W., 2001. Hybrid simulated annealing/genetic algorithm approach to shortterm hydro-thermal scheduling with multiple thermal plants. Int. J. Electr. Power Energy Syst. 23 (7), 565–575. Wood, A.J., Wollenberg, B.F., 1984. Power system generation, operation and control. John Wiley, New York. Wu, Y.G., Ho, C.Y., Wang, D.Y., 2000. A diploid genetic approach to short-term scheduling of hydro-thermal system. IEEE Trans. Power Syst. 15 (4), 1268–1274. Xie, K., Dong, J., Singh, C., Hu, B., 2016. Optimal capacity and type planning of generating units in a bundled wind–thermal generation system. Appl. Energy 164, 200–210. Yu, B., Yuan, X., Wang, J., 2007. Short-term hydro-thermal scheduling using particle swarm optimization method. Energy Convers. Manage. 48 (7), 1902–1908.

swarm optimization. Int. J. Electr. Power Energy Syst. 67, 350–367. Redondo, N.J., Conejo, A.J., 1999. Short-term hydro-thermal coordination by Lagrangian relaxation: solution of the dual problem. IEEE Trans. Power Syst. 14 (1), 89–95. Sahin, C., Shahidehpour, M., Erkmen, I., 2012. Generation risk assessment in volatile conditions with wind, hydro, and natural gas units. Appl. Energy 96, 4–11. Sharma, N., Sharma, P., Irwin, D., Shenoy, P., 2011. Predicting solar generation from weather forecasts using machine learning. In: 2011 IEEE International Conference on Smart Grid Communications (SmartGridComm). IEEE, pp. 528–533. Singh, R., Banerjee, R., 2015. Estimation of rooftop solar photovoltaic potential of a city. Sol. Energy 115, 589–602. Tata Power-Generation. (2013). True up Petition for FY 2011–12 as well as MYT Petition for FY 2012–13 to FY 2015–16.Mumbai, Maharashtra: Tata Power. Varkani, A.K., Daraeepour, A., Monsef, H., 2011. A new self-scheduling strategy for integrated operation of wind and pumped-storage power plants in power markets. Appl. Energy 88 (12), 5002–5012.

1004