The history of time-keeping started with Clock Tower in towns and cities [1]. The major change in modern history of time occurred with the need of Railway Companies of USA which found it difficult to operate with so many local times [2]. Presently, times are kept across the world based on the need of both governance and commerce [3].

Several countries across the globe, e.g. USA, UK, European Union, etc., which have substantial distance from the equator in terms of latitude, make daylight energy savings by adjusting their time-keeping systems with the availability of daylight [4]. For some countries near the equator, e.g. India, South Africa, Brazil, Australia etc., the territorial distances in terms of longitude justify multiple time-keeping systems. A few studies have been carried out in Australia, India and South Africa to quantify the savings in electrical power with multiple time-keeping systems [5,6,7,8,9,10]. If the sun takes more than an hour to move across a territory from east to west, the territory may be divided into more than one time zone. With different time-keeping systems across the territory, the electrical power demand will follow different patterns based on shifted working hours. If the territory division can be optimally done, the maximum electrical power demand in the territory can be reduced and minimum electrical power demand can be increased. This will help in flattening the electrical load curve across the territory. It will result in reduction in cycling operations of electrical power plants and associated carbon emission.

The current work makes use of electric power demand data of India for the year 2015 to demonstrate modest reductions in peak demand and cycling operations using time adjustments. In cycling operations, the efficiency of a steam power plant is lower with higher heat rate and the plant produces higher marginal carbon emission [11, 12]. The available research data are used to compute the savings in heating value and carbon emission in India for the year 2015. Based on data on estimated growth of electrical power demand in India up to the year 2050, the cumulative savings in carbon emission and cost are presented in this work.

There are three important assumptions for the current work.

  1. 1.

    With identical hours of operation, the electrical load pattern shall be similar in different load areas.

  2. 2.

    Cycling operation of thermal power plants are implemented using load following operation only.

  3. 3.

    Estimation of cycling penalty is based on 40% minimum loading of coal plants and 60% minimum loading of NGCC plants with normal ramp. Penalty figures are unpredictable for lower minimum loading.

As most of the referred work quantifies heating value in BTU, the savings in heating value have been worked out in BTU. Subsequently, this has been converted to joules and Gigajoules (1 BTU = 1055 J).

Time-Keeping and Rise of Electrical Power Demand in Peak Hour

Let us consider any geographic territory with an integrated power grid. The territory may be divided arbitrarily into two sub-areas along east–west. Let P1 and P2 be the rise in electrical power demands of sub-area1 and sub-area2 during the peak hour. Due to similar pattern of load demand, the peaks occur at the same time, say, t = Tpeak;

In the peak hour t = Tpeak, the maximum rise of electrical power demand of the territory with one uniform time-keeping system is given by Eq. (1).

$$P^{\text{MAXPEAK}} = \, P1 + P2.$$
(1)

If the time-keeping systems in sub-area1 and sub-area2 are set 1 h apart, then it is expected that the peak hours of the two sub-areas shall be 1 h apart (t1 = T1peak, t2 = T2peak, t2 − t1 = 1 h). The peak rise of electrical power demand of the territory is represented by Eq. (2).

$$P^{\prime } = P1\,\,{\text{or}}\,\, \, P2,\quad {\text{whichever}}\,{\text{is}}\,{\text{higher}} .$$
(2)

The minimum value of rise of electrical power demand at peak hour shall be obtained with the equality criteria [13] given in Eq. (3).

$$P^{{\text{MINPEAK}}} = \, P1 = P2.$$
(3)

Hence, to achieve the minimum rise of electrical power demand (PMINPEAK), a territory may be divided into sub-areas with equal rise in electrical power demand during the peak hour (P1 = P2).

Model of Time-Keeping Systems for Minimum Peak Demand

As the longitudinal distance of the extreme points of a geographic territory is constant, the number of solar hours between these two points shall also be a constant (N). Sub-areas between these two points from east to west may be assigned separate time-keeping systems with 1-h time difference between adjacent sub-areas.

$$\begin{aligned} & {\text{Maximum}}\,{\text{number}}\,{\text{of}}\,{\text{sub-areas}}\,{\text{in}}\,{\text{the}}\,{\text{territory}} \\ & = {\text{Number}}\,{\text{of}}\,{\text{Time-keeping}}\,{\text{systems}}\,{\text{with}}\,{\text{one}}\,{\text{hour}}\,{\text{time}}\,{\text{interval}} \\ & = \, N + 1. \\ \end{aligned}$$

Let ‘A’ represent a territory with ‘m’ physically demarcated unit-areas and ‘ai’ represent the ‘i’th unit-area between east and west. The relationship between the territory and unit-areas is given in Eq. (4).

$$A = a_{1} U\,a_{2} U\,a_{3} \ldots \, Ua_{m - 1} Ua_{m} .$$
(4)

Let Ei be the longitude of eastern edge of ‘i’th unit-area in degrees. Let Wi be the longitude of Western edge of ‘i’th unit-area in degrees. The mean geographical position in longitude of ‘i’th unit-area in degrees is given by Eq. (5).

$$M_{i} = \left( {E_{i} + W_{i} } \right)/2.$$
(5)

Let us index the unit-areas such that, M1 > M2 > ··· Mm−1 > Mm.

Number of hours between time-keeping systems for the territory is given by Eq. (6).

$$N = \left( {E_{1} - \, W_{m} } \right)/15.$$
(6)

where in terms of solar position, distance in longitude for 1 h is = 15° (360°/24 h).

Let Pj be the rise in electrical power demand in MW (Megawatts) during peak hour for ‘j’th unit-area. To achieve minimum peak electrical demand as per Eq. (3), the rise in electrical power demand during peak hour of each sub-area is given by Eq. (7).

$$P^{{\text{MINPEAK}}} = \varSigma P_{j} /( {N + 1} ),\quad {\text{for all}}\, {\text{`}}{j}{\text{'}}\; {\text{unit-areas within the territory}} .$$
(7)

It may not be physically possible to divide a territory according to our choice. However, a territory such as a country is divided into states. The states are further subdivided into districts or counties. A cluster of such unit-areas may form a sub-area of one uniform time-keeping system. The equal rise in power demand among sub-areas during peak hour may be achieved with the constraint equations given in (8), (9) and (10).

$$\begin{aligned} & {\text{Sub-area 1 is represented as}}\,A_{1} ( {P_{j} , \, M_{j} , \, N} ) = a_{1} Ua_{2} Ua_{3} \ldots Ua_{j} , \\ & {\text{where}}\, (P_{1} + P_{2} + \cdots + P_{j} ) \approx \varSigma P_{i} /( {N + 1} ),\, {\text{for all}}\,{\text{`}}i{\text{'}} \quad {\text{such that}}\,M_{k} < M_{j} \quad {\text{for all}}\,k > j. \end{aligned}$$
(8)
$$\begin{aligned} & {\text{Sub-area 2 is represented as}}\,A_{2} ( {P_{j + x} , \, M_{j + x} ,N} ) = a_{j + 1} U \, a_{j + 2} U \, a_{j + 3} \ldots \, Ua_{j + x} , \\ & {\text{where }}( {P_{j + 1} + \, P_{j + 2} + \cdots + P_{j + x} } ) \approx \varSigma P_{i} /( {N + 1} ),\quad {\text{ for all}}\,{\text{`}}i{\text{'}}\, {\text{such that}}\,M_{k} < M_{j + x} \quad {\text{for all}}\,k > ( {j + x} ). \end{aligned}$$
(9)
$$\begin{aligned} & {\text{Sub-area }} ( {N + 1} )\,{\text{is represented as}}\,A_{N + 1} ( {P_{m} , \, M_{m} , \, N} ) = a_{m - n + 1} U \, a_{m - n + 2} U \cdots \, U \, a_{m} , \\ & {\text{where }}( {P_{m - n + 1} + P_{m - n + 2} + \cdots + P_{m} } )\, \approx \varSigma P_{i} /( {N + 1} ),\quad {\text{for all}}\,{\text{`}}i{\text{'}}\, {\text{such that}}\,M_{k} > M_{m - n + 1} \quad {\text{for all}}\,k < ( {m - n + 1} ). \end{aligned}$$
(10)

In Eqs. (8), (9) and (10), each sub-area with a separate time-keeping system is represented by a mathematical function of electrical power demand and mean geographical position in longitude. As time adjustments are related to governance, it is necessary that each sub-area consists of distinct unit-areas of governance.

Framework of Time-Keeping Systems for Indian Power Grid

Time-Keeping Systems with Equal Rise in Peak Demand

Across India, there is an interconnected power grid connecting all states and union territories except Lakshadweep and Andaman and Nicobar Islands. The daily peak demand for the entire nation in 2017 and 2018 was 160 GW and 175 GW with a base demand of 141 GW and 149 GW, respectively. The configuration of three time-keeping systems for Indian states based on the hourly demand data of different dates spread over the year 2015 [13, 14] and longitude positions is presented in Fig. 1.

Fig. 1
figure 1

Geographical configuration of proposed three time-keeping systems with equal power demand in Indian power grid

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The estimated reduction in daily peak demand and cycling operation for Indian power grid has been worked out for the year 2015 with the three time-keeping systems.

The variation in actual demand data with single uniform time-keeping system and projected demand data with three time-keeping systems is presented in Table 1 and Fig. 2.

Table 1 Cycling operation reduction in Indian power grid—computed data set January to December 2015
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Fig. 2
figure 2

Variation in power demand with three time-keeping systems for Indian power grid during January to December, 2015

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The rate of reduction in terms of peak demand for the year 2015 is calculated based on the data set in the daily operation reports of January to December 2015 [14] and calculations based on Eqs. (11)–(14).

$${\text{Differential}}\,{\text{Peak}}\,{\text{Demand}}\,\left( {\text{MW}} \right),\quad {\mathbf{DD}} = {\mathbf{PD1}}{-}{\mathbf{BD1}}{\mathbf{.}}$$
(11)
$${\text{Load}}\,{\text{Cycling}}\,{\text{Rate}}\,\left( \% \right),\quad {\text{LCR}} = \left[ {{\mathbf{DD}}\,*\,{\mathbf{100/PD1}}} \right].$$
(12)
$${\text{Rate}}\,{\text{of}}\,{\text{Reduction}}\,{\text{of}}\,{\text{Peak}}\,{\text{Demand}}\,\left( \% \right)\,{\text{PRR}} = \left[ {{\mathbf{PR*100/PD1}}} \right].$$
(13)
$${\text{Rate}}\,{\text{of}}\,{\text{Reduction}}\,{\text{in}}\,{\text{Cycling}}\,{\text{Operation}}\,\left( \% \right)\,{\text{CRR}} = \left[ {{\mathbf{CR*100/PD1}}} \right].$$
(14)

The reduction in peak demand and rate of reduction in cycling operation for the year 2015 is estimated as 6% and 9%, respectively, and demonstrated in Table 1.

Availability of Hourly Demand Data of Indian Power Grid

The peak hour and off-peak hour power demand values of each state in the Indian power grid for a 24-h period are obtained from the daily operation reports [14]. For many states, power demand data for all the hours are available. For some states, the power demand data for intermediate hours are not available. In such cases, linear extrapolation has been used to estimate the hourly power demand data at the intermediate hours [13]. All hourly data and linear extrapolations used in this paper are available in [15].

Estimation of Rate of Reduction in Cycling Operation

The variation in CRR against variation in peak demand and load cycling is presented in Fig. 3.

Fig. 3
figure 3

Cycling reduction rate for Indian power grid—January to December 2015

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It is observed from the demand data of developed countries that with development and growth, the differential between peak demand and base demand increases to 40% [16]. It is estimated that India will enter the league of developed countries around the year 2030 [17]. Penetration of renewable energy power plants shall induce additional cycling operations with deep load following [18].

For estimation of savings in carbon emission and expenditure for India up to the year 2050, the rate of reduction with three time-keeping systems has been restricted at 6% in peak demand and 9% in cycling operation.

Savings in Cycling Operations

Efficiencies of Steam Power Plants with Cycling Operations

The costs and damages in cycling operations to serve peak demand have been quantified in the reports of National Energy Technology Laboratory, USA [19], National Renewable Energy Laboratory, USA [20] and the TME working paper of University of Leuven, Belgium [21]. The research on estimation of cycling costs based on 20 years of operational data has been summarized for all kinds of cycling operations, i.e. cold start, warm start and load following operations [22]. An analysis of the historical cycling data shows that 99% of the cycling operations are load following operations and the rest are mostly warm start operations [23]. An analysis of load following operations for coal plants in Ireland shows that efficiency of the power plant may come down by 11% and carbon emission may increase by 65% [24]. The cycling operation also leads to accelerated component failures and creep–fatigue [25].

The drop in efficiency due to partial load operation and load following of steam power plants can be certainly estimated from characteristic equations of individual plants. The steam power plant technologies under consideration are:

  • Natural Gas Single-Cycle or Open-Cycle Combustion Turbine technology—NGSC

  • Natural Gas Combined Cycle technology—NGCC

  • Sub-critical Coal with Rankine Cycle technology

  • Super-critical Coal with Rankine Cycle technology

  • Integrated Gasification Combined Cycle technology using Coal—IGCC

The heat rate penalties for the above steam power plant technologies are summarized in Table 2 [19].

Table 2 Heat rate penalties for partial loading with available steam power plant technologies
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The decrease in efficiency due to cycling operation results in carbon emission at a higher rate [26].

Requirement of Centrally Coordinated Cycling Operation and Additional Transmission Loss

If the requirement of rise in power demand in a sub-area is addressed locally, different sets of power plants will be used for rise in power demand in different areas. Hence, without central pool of cycling power plants, there will be no savings in cycling operation. To coordinate cycling operations with central pool of power plants, the additional transmission loss must be taken into consideration. The percentage power loss in a transmission line depends on conductor resistance (r), the positive sequence reactance (x) and the phase angle (δ). It is given by Eq. (15).

$$P_{\text{LOSS}} \left( \% \right) = 100*{ \sin }\delta *\left( {r/x} \right)$$
(15)

A large number of super thermal power plants are located in central India. These plants are suitable for both base load and cycling operations. Based on the hourly data of 2015 in Table 3, the average cycling power required to be transferred from these central pool of power plants to the adjacent sub-area is presented in Eq. (16).

$${\text{CP}} = 4385\,{\text{MW}}$$
(16)
Table 3 Savings in heating value and fuel cost for Indian power grid—January to December 2015
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The percentage power loss for 1200 kV power line is taken as 0.584% from Eq. (15). The power loss per day for transfer to two adjacent sub-areas from the central sub-area at 1200 kV for 2 h is estimated in Eq. (17).

$$\begin{aligned} P_{\text{LOSS}} & = 2*{\text{CP}}*0.00584 \\ & = 2*4385*0.00584 = 51\,{\text{MWh}} \\ \end{aligned}$$
(17)

The additional power loss and related penalties for central coordination of cycling operation for average peak demand in 2015 are included in Table 3.

Based on the estimated transmission losses for Indian power grid for the year 2015 with a transmission backbone at 1200 kV level, the additional heating value is approximately 0.2% of the savings from reduction in cycling operation. Also, savings are achieved towards non-fuel expenditure.

Savings in Capital & Maintenance Cost for super-critical coal plants in India in 2015(@ US$ 1.96/MW capacity for 30% ramp operation) [22, 23, 27, 28] are given by Eqs. (18) and (19),

$${\text{CM}}1\left( {{\text{US}}\$ } \right) = {\text{PD}}1*{\text{US}}\$ 1.96\,{\text{par}}\,{\text{MW}}\,{\text{Capacity}} = 152,512*1.96 = 298,924.$$
(18)

Savings in Capital and Maintenance Cost for NGCC plants in India in 2015 (@ US$ 0.64/MW capacity for 20% ramp operation) [22, 23, 27, 28] are given by Eq. (19),

$${\text{CM}}2\left( {{\text{US}}\$ } \right) = {\text{PD}}1*{\text{US}}\$ 0.64\,{\text{ per}}\,{\text{MW}}\,{\text{Capacity}} = 152,512*0.64 = 97,608.$$
(19)

Estimation of Growth in Peak Demand in Indian Power Grid

Assessment of the growth of electrical power demand in India is available in research work carried out by government reports, peer reviewed journals, reports of international agencies and international conferences [17, 29,30,31,32,33,34,35,36,37]. The published research work of a project taken up by The Grantham Institute of Climate Change, The Imperial College, London [29,30,31], is close to the projections of Central Electricity Authority, Government of India [32, 33].

The SPSS PASW Statistics 18 with exponential growth model is used to estimate curve Eq. (20) for electricity generation from 2005 to 2050.

$$Y = 2.291*e^{0.05241 \, * \, t}$$
(20)

where Y = electrical energy generation in exajoules (EJ) and t = 0–45 for the years from 2005 to 2050.

In the annual report of the planning commission, 2014 [32], the minimum rate of growth is observed in the year 2012–2013 with a peak demand of 135, 453 MW. This value is fitted with the estimated curve Eq. (20) to obtain the exponential growth Eq. (21) for peak demand.

$$Z = 93,855* \, e^{0.05241 \, * \, t}$$
(21)

where Z = peak demand in MW; t = 0–45 for the years from 2005 to 2050;

Based on Eq. (21), the estimated peak demand is calculated for the years from 2020 to 2050.

The peak demand of 185,505 MW projected for 2018 as per the exponential growth model is very close to the peak demand of 180,682 MW anticipated in CEA Load Generation Balance Report 2018–19 [33] and the actual data of 174,682 MW [14].

Cumulative Savings in Carbon Emission and Expenditure Up to the Year 2050

The estimated savings in carbon emission are presented in Table 4. The cumulative savings in capital expenditure and cost of cycling operation are presented in Table 5 based on published data [38,39,40,41].

Table 4 Estimated carbon savings with three time zones
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Table 5 Cumulative savings in capital expenditure, cycling operation expenditure and social cost of carbon from year 2020 to 2050
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Conclusion

Calculations for sub-critical coal plants, open-cycle gas turbine plants and IGCC plants have not been included in this work. For these types of plants, the cost of cycling operation is substantially higher. Between the coal plants and NGCC plants, the operation cost of NGCC plants is higher due to fuel cost. Naturally, the NGCC plants are avoided for base load operations and are used in case of higher demand. Hence, the NGCC plants have become the convenient choice for cycling operations. Also, overall carbon emission of coal plants is higher and they are expected to be gradually replaced by IGCC plants with substantially lower carbon emission with the same fuel. With the existing built-up capacity, the coal plants will continue to be an option for cycling for many years. In spite of high penalty for cycling operations of NGCC plants, the life-cycle savings are marginally lower than coal-based plants.

As time is in the domain of public interest, all adjustments of time have to be implemented through legislation. The major technical challenge of implementation of time adjustments across India shall be to adjust the transmitter and receiver end-equipments of Standard Time & Frequency Systems under National Physical Laboratory (NPL) [13]. To minimize the cost of these changes, it is possible to restrict the modifications to software and firmware without replacing the hardware.

The load consumption pattern across the geography of a country is not expected to change within a decade. Hence, the Standard Time and Frequency Systems will not need frequent adjustments. Given that several countries are adjusting their time systems every year for daylight savings [4], it is expected that the proposed time adjustments can be implemented across the states of India.

Adjusting the time-keeping systems in other countries should result in similar benefits. With the availability of a precise model, the application can be replicated for any large country where the territory is suitable for more than one time-keeping system.