Introduction

The MCDM has been used over the years [1, 2], and is indeed a currently widely used tool for energy applications [3–6]. The aim of this paper is to focus on a set of sustainable and renewable factors that will be assessed through a precedence constraints evaluation. The optimal solution will be then chosen among the possible solutions for every one of the six equations, applying the Linear Programming Computation (LPC). The best compromised solution is then found among the Pareto optimal solutions [7], which will allow rejection of the solutions corresponding to any of the six optimizing equations that are found to be situated furthest from the rest of the optimal values obtained for the remaining equations. This way the dominating solutions will be softened, letting energy planners base their decisions on a solution that can not be improved without making at least one of the variables worse off.

This method’s greatest challenge is how investigators and then planners will decide to calculate the weights to be applied to every one of the six equations. This decision will require a broad consensus among a wide range of experts so that decisions are not postponed, generating conflict, wasting time and, therefore, damaging future programming.

The subjective part of the compromise programming is also a demanding issue, which has to be carefully and professionally performed. The value given to the different subjects must be thoroughly assessed, avoiding a personal opinionated view from the experts.

SRIME model

Figure 1 shows the steps that are proposed in this model, which has been specifically designed for low materially developed countries. The first stage is to carry out a thorough evaluation of the current energy demand, and subsequent future needs. Secondly, the possible renewable solutions will be assessed, taking into account the in-country possibilities, along with the international support, aiming to enunciate the first function, using the precedence constraints.Footnote 1 The third step will be to study the potentially avoidable emissions so that the corresponding three functions may be stated (F 2, F 3, F 4). Then the fifth function will come from a deep study of the possible interactions between health and education and renewable energy, according to the parameters described by the UN and other international organizations. The last phase is to enunciate the cost function (F 6).

Fig. 1
figure 1

SRIME energy model. Own construction

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The L k distances will then be minimized, according to the chosen weights, so that a compromised solution may be selected among the several obtained by the preferred optimization tool.Footnote 2

Functions

Maximization of RE potential capacity: F 1

The so-called green economy focuses on the various advantages our world shall enjoy if we were to go green [8–11]. Not only climate change is involved here but also the potential enhancement of the overall development factors, especially the health co-benefits. You may find the corresponding equation and Table 1 below, which includes a summary of the potential precedence constraints the authors have chosen to be applied [12–14].Footnote 3

Table 1 Precedence constraints
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$$ F_{1} \left( {x_{11} , \, x_{12} , \, \ldots , \, x_{ij} , \, \ldots , \, x_{\text{nm}} } \right) \, = \, A_{11} x_{11} + A_{12} x_{12} + \, \cdots + A_{\text{nm}} x_{\text{nm}} $$
(1)

Environmental impact minimization: F 2, F 3, F 4

Environmental impact has ben a major concern in the world for the past ten years. Local researchers are indeed looking into potential present and future sustainable possibilities [15, 16].

These are the three corresponding functions:

$$ F_{2} \left( {x_{11} , \, x_{12} , \, \ldots , \, x_{ij} , \, \ldots , \, x_{\text{nm}} } \right) \, = \, B_{11} x_{11} + \, B_{12} x_{12} + \, \cdots \, + \, B_{\text{nm}} x_{\text{nm}} $$
(2)
$$ F_{3} \left( {x_{11} , \, x_{12} , \, \ldots , \, x_{ij} , \, \ldots , \, x_{\text{nm}} } \right) \, = \, C_{11} x_{11} + \, C_{12} x_{12} + \, \cdots \, + \, C_{\text{nm}} x_{\text{nm}} $$
(3)
$$ F_{4} \left( {x_{11} , \, x_{12} , \, \ldots , \, x_{ij} , \, \ldots , \, x_{\text{nm}} } \right) \, = \, D_{11} x_{11} + \, D_{12} x_{12} + \, \cdots \, + \, D_{\text{nm}} x_{\text{nm}} $$
(4)

B ij /C ij /D ij : life cycle CO2/NOx/SO2 avoided emissions (ton/energy unit)

For all B ij  ≥ 0; C ij  ≥ 0; D ij  ≥ 0 ⇒ max F 2; F 3; F 4 ⇒ optimal avoided emissions maximization

Coefficients B ij , C ij , D ij are obtained from official statistics and specialized publications.

Maximization of the most rural development friendly types of RE, aiming to improve health and education

One of the most usual indicators to estimate energy demand is the GDP growth rate. LEC and LRY commonly enjoy a high degree of causality. However, while HMDP show a bidirectional causality, LMDP only dictate a uni-directional causality from LRY to LEC [17]. As you can see below in Fig. 2, this is confirmed by the SL official data.

Fig. 2
figure 2

SL expenditure vs energy consumption. Prepared by the authors based on official data [18–23]

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This is the corresponding equation:

$$ F_{5} \left( {x_{11} , \, x_{12} , \, \ldots , \, x_{ij} , \, \ldots , \, x_{\text{nm}} } \right) \, = \, E_{11} x_{11} + E_{12} x_{12} + \, \ldots + E_{\text{nm}} x_{\text{nm}} $$
(5)

Coefficients E ij are non-dimensional and obtained through precedence constraints, where no energy or cost quantification is involved. These precedence constraints are based on:

  1. 1.

    Identified health and education ad-hoc applications.

  2. 2.

    Low overnight capital cost/unnecessary donor support for health and education enhancing applications.

  3. 3.

    Low maintenance cost.

  4. 4.

    Unnecessary maintenance contract.

  5. 5.

    Long lasting systems for health and education purposes.

  6. 6.

    Short distance from health and education centres to energy source.

  7. 7.

    Safe from being stolen in rural environment.

  8. 8.

    Low rural environmental impact.

  9. 9.

    Predictability.

  10. 10.

    Batteries not required for health and education purposes.

  11. 11.

    Alternating current.

  12. 12.

    Possible modularity/size accommodation for schools and hospitals.

  13. 13.

    Added benefits for rural development.

  14. 14.

    In-country development: manufacturing, training, etc.

  15. 15.

    Low LEC.

  16. 16.

    Hospitals and schools space efficiency for rural development.

  17. 17.

    Low or inexistent waste generation.

Cost minimization of substitution of renewable for existing conventional energy: F 6

$$ \begin{gathered} F_{6} \left( {x_{11} , \, x_{12} , \, \ldots , \, x_{ij} , \, \ldots , \, x_{\text{nm}} } \right) \, = \, G_{11} x_{11} + \, G_{12} x_{12} + \, \cdots \, + \, G_{\text{nm}} x_{\text{nm}} \hfill \\ G_{ij} = {\text{ initial investment or production cost/energy unit}} \hfill \\ G_{ij} \ge \, 0{\text{ or }}0 \, \le \, G_{ij} . \hfill \\ \end{gathered} $$
(6)

This function can also consider the renewable energy subsidies, therefore affecting the C coefficients. Another possibility can be to modify the coefficients, aiming to reach the best possible subsidy for every RE.

As per coefficients B ij , C ij and D ij , coefficients G ij are also obtained from official sources.

Restrictions

The restrictions to be applied are described below in Table 2, having in mind the following [1, 3, 12 and own construction]:

Table 2 Restrictions
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S j ::

Energy demand of application j, calculated as: S j  = p j − i j ; where p j is the energy demand corresponding to sector j and i j is the amount of fossil fuel renewable sources can not replace.

S e::

Energy demand of application i, calculated as: S e = p e − i e; where p e is the energy demand corresponding to sector e and i e. is the amount of fossil fuel renewable sources can not replace.

P i ::

Potential application of renewable source i in the corresponding sector.

R i ::

Minimum amount of conventional energy renewable sources can replace, as RE has already replaced this amount.

Compromise programming

As indicated by Linares et al. [24–26], to obtain the set of compromised solutions, both the normalized Manhattan distance, L 1 or the Chebyshev distance, L ∞, may be minimized [27, 28]. Nonetheless, L k will also help us obtain the optimal solution. Equation (11) below shows the general definition for L d. Equations (12), (13) and (14) show the normalization to be carried out and Table 3 the distances that must be minimized.

Table 3 Normalized distances to be minimized
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$$ d = \left[ {\sum\nolimits_{j = 1}^{n} {\left| {x1j - x2j} \right|}^{d} } \right]^{1/d} $$
(11)

Taking into account that W i is the weight or preference assigned by the decision makers, the distances to be minimized may be found below in Table 4.

Table 4 Restrictions summary
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Case study: Sri Lanka

The authors have prepared a sectorial energy consumption forecast for 2015 (see Table 5; Fig. 3) and the estimated generation and capacity mix (see Figs. 4, 5). The global electricity data has been obtained from the Long Term Generation Expansion Plan 2013–2032, prepared by the Ceylon Electricity Board, and the rest of he energy consumption and the electricity sectorial data has been estimated by the authors based, on official and private documentation [29–50].

Table 5 2015 SL sectorial energy consumption forecast (ktoe) [29–50]
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Fig. 3
figure 3

2015 Sri Lanka sectorial energy consumption forecast [29–50]

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Fig. 4
figure 4

SL 2015 estimated capacity mix [29–50]

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Fig. 5
figure 5

SL 2015 estimated generation mix [29–51]

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The optimization equations

F1. Maximization of RE potential capacity

SL is very much dependent on petroleum, which currently accounts for approximately 24 % of SL import bill and 45 % of exports. The demand has been doubled, in value terms, during the last 3 years [52]. The geo-climatic settings are particularly conducive, though, to harnessing hydro resources. The climate is largely determined by the meteorological conditions caused in the Indian sub continent due to the tropical circulation [53]. The current hydro power stations are operated to meet both peak and base electricity generation requirements. A 400 MW potential has been identified for small hydropower projects [54], typically characterised with less than 10 MW capacities [53]. 128 projects, totalling 271 MW, have been already commissioned as of 31/12/2014 [55]. Once these projects are available for power generation, will be carefully followed-up by PUCSL [56]. In terms of wind power, GOSL would like to go from the current 5 % to reach 10 % by 2017 and 14.1 % by 2022 [56]. There are close to 500 km2 of windy areas with good-to-excellent wind resource potential. However, only a portion of this is deemed feasible to be harnessed because of technical and system limitations [57]. As of 31/12/2013, there are 10 commissioned projects, which will add 78.45 MW capacity to the grid [55] and also some possible future WPPs [58–61]. The wind potential has been estimated as 20,000 MW. In terms of biomass, Gliricidia sepium has been recently appointed as the fourth plantation crop after tea, rubber and coconut. Biomass application in electricity generation is not yet widespread, but it is gaining momentum [54]. As of 31/12/2014, 2 Agricultural and Industrial Waste Power projects have been commissioned (11 MW); and another 2 Dendro Power (5.5 MW) [55]. A 1000 MW of Dendro thermal potential has been estimated [59]. Biofuels are also planned to be developed to claim a 20 per cent share by 2020 [58, 62]. Although the village biogas power is at an early stage, as it has not been an easy task to introduce it [63, 64], there are indeed a number of projects going on. This NCRE seems to be following the increasing tendency currently shown in South Asia [59]. A 300 MW MSW biogas generation potential has been identified [65].

As showed on Table 6 above, the use of SHSs has been spreading fast in the rural areas of Sri Lanka, mainly because of the financial incentives provided by the donor agencies, and also due to the aggressive marketing strategies of the SHS dealers in rural areas [66, 67]. As of 31/12/2013, 4 solar projects have been commissioned, totalling 1,4 MW. As of 31/12/2012, the installed PV capacity was 10.10 MWp [68]. Concerning geothermal energy resources, SL is still at a preliminary stage, although a 700–1300 MWe potential has been recently estimated. As a first step in the development, a USD 10 M investment would cover a site selection study, surface exploration at the most promising site followed by deep drilling, and commissioning of a 2 MW binary power plant if the wells are successful [69]. Regarding off-grid schemes, a pilot project was recently conducted to connect two village micro hydro power plants (10 and 20 kW) to the national grid. This pilot project has become instrumental in removing the technical, social, and legal barriers for grid interconnection. It is necessary, though, to review these fees structure and try to reduce them, taking into account the capacity of the project [70] and the potential funding [71–73]. The overall target for NCRE is to reach 10 % by 2016 and 20 % by 2020 [63]. Some authors are praising SLs NCRE implementation [64], while others believe that lack of financing instruments, along with high initial cost and lack of assurance of resource supply or availability are the main barriers for renewable technologies expansion in SL [65, 66]. Reaching the above mentioned targets is not just an environmental matter, but are related in one way or another to at least five other MDG [67, 74]:

Table 6 2012 status of Sri Lanka off-grid energy technologies
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  1. 1.

    Eradicate extreme poverty and hunger.

  2. 2.

    Achieve universal primary education.

  3. 3.

    Gender equality and empowering women.

  4. 4.

    Reduce child mortality.

  5. 5.

    Improve maternal health.

Taking into account all of the above, the authors have estimated that the following energy is considered to be substitutable in 2015 (see below Table 7).

Table 7 Substitutable energy in 2015 (ktoe)
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The authors have defined the following variables:

  • BTI: biomass thermal, industrial.

  • BTH: biomass thermal, household.

  • BTHE: biomass thermal, health.

  • BTC: biomass thermal, commercial.

  • LBFA: liquid biofuel, agriculture.

  • LBFT: liquid biofuel, transport.

  • SH: small hydro.

  • WPP: wind power plant.

  • BEG: biomass for electricity generation.

  • PV: photovoltaic electricity generation.

  • MSW: municipal solid waste.

The restrictions for this case study have been established by the authors as per below:

A: Based on energy demand and RE real potential (in ktoe):

  1. 1.

    LBFA ≤ 1.8

  2. 2.

    BTI ≤  2148.9

  3. 3.

    LBFT ≤  436.3

  4. 4.

    BTH ≤ 1.2

  5. 5.

    BTHE ≤  0.4

  6. 6.

    BTC ≤ 432.1

  7. 7.

    ElectricityFootnote 4:

$$ {\text{SH }} + {\text{ PV }} + {\text{ WPP }} + {\text{ MSW }} + {\text{ BEG}} \, \le \,\, 2 1 9. 8 $$
(22)
  1. 8.

    SH ≤ 150

  2. 9.

    PV ≤ 30

  3. 10.

    WPP ≤ 100

  4. 11.

    MSW ≤ 100

  5. 12.

    BEG ≤ 60

B: Based on the already existing RE (in ktoe):

  1. 1.

    LBFA, LBFT ≥ 0

  2. 2.

    BTI ≥ 2109Footnote 5

  3. 3.

    BTH ≥ 0

  4. 4.

    BTHE ≥ 0

  5. 5.

    BTC ≥ 427.8

  6. 6.

    SH ≥ 47.3

  7. 7.

    PV ≥ 3.6

  8. 8.

    WPP ≥ 8.6

  9. 9.

    MSW ≥ 0

  10. 10.

    BEG ≥ 15.1

To determine the coefficients corresponding to function F 1, the authors have established the precedence constraints included below in Table 8.

Table 8 Precedence constraints [54, 75–103]
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The following values are then calculated (see Table 9 below):

Table 9 Calculation of N and M factors
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$$ M_{ij} = \varPi^{n}_{i = 1} a_{ij} $$
(23)
$$ N_{ij} = \varPi^{n}_{i = 1} \left( {6 - a_{ij} } \right) $$
(24)

Once the coefficients are applied, this is the final equation for F 1:

F 1 = 2.5 SH + 2.5 WPP + 2 PV + 2 BTI + 2 BTH + 2 BTHE + 2 BTC + 2 MSW + 1.5 BEG + LBFA + LBFT

Environmental impact minimization

CEB expected generation system for 2015 [20] has been taken into account (see below Table 10) to establish the potentially avoided emissions. According to the different types of fuel and their corresponding GWh in 2015, a 9.9 tCO2/toe weighted average will be considered as the amount of avoided emission as well as 0.028 tNOx/toe and 0.041 tSO2/toe [20, 104–114].

Table 10 Generation forecast data from the Long Term Generation Expansion Plan 2013–2032, prepared by the CEB [20]
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You can find below Table 11, which includes a summary of the life cycle emissions corresponding to the different types of renewable energy, based on the below mentioned references.

Table 11 RE life cycle CO2 emissions; tCO2/toe, tNOx/toe, tSO2/toe [109, 112–121]
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In terms of LBF, 90 % of the CO2 emissions are considered to be potentially avoided [122–124] that is, approximately 2.7 tCO2/toe. When biofuel replaces gasoline and diesel in the transport sector, SO2 emissions are reduced, but changes in NOx emissions depend on the substitution pattern and technology. The effects of replacing gasoline with ethanol and biodiesel also depend on engine features. Biodiesel can have higher NOx emissions than petroleum diesel in traditional direct-injected diesel engines that are not equipped with NOx control catalysts [125]. This is why no NOx avoided emissions have been taken into account. A 50 % average SO2 emissions reduction is however considered, as the avoided emissions will depend very much on the blend.

Please find below de corresponding functions:

F 2 = 9.78 SH + 9.78 WPP + 9.44 PV + 9.27 BTI + 9.27 BTH + 9.27 BTHE + 9.27 BTC + 8.9 MSW + 9.38 BEG + 2.7 LBFA + 2.7 LBFT

F 3 = 0.028 SH + 0.028 WPP + 0.026 PV + 0.02 BTI + 0.02 BTH + 0.02 BTHE + 0.02 BTC + 0.028 MSW + 0.02 BEG

F 4 = 0.04126 SH + 0.0407 WPP + 0.038 PV + 0.041 BTI + 0.041 BTH + 0.041 BTHE + 0.041 BTC + 0.04128 MSW + 0.041 BEG + 0.0058 LBFA + 0.0058 LBFT

F5: Cost minimization of substitution of RE for existing conventional energy

Based on the typical capital cost ranges for RE power generation technologies, USD/kW [49, 137–139], the overnight capital cost is calculated (USD/toe) so that the appropriate coefficients can be applied:

F 5 = 0.08 SH + 0.32 WPP + 0.3 PV + 0.18 BTI + 0.14 BTH + 0.18 BTHE + 0.14 BTC + 0.48 MSW + 0.55 BEG + 0.94 LBFA + 0.94 LBFT

It must be noted that a CHP use has been assumed for MSW biogas plants and LBF production.

F6: Maximization of the most rural development friendly types of RE, aiming to improve health and education

See below Table 12, where the precedence constraints have been evaluated by the authors as per the below mentioned subjects, based on the indicated references.

Table 12 Precedence constraints [126–136]
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M and N are then calculated as per Eqs. (23) and (24) (see Table 13 below):

Table 13 Calculation of N and M factors
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Once the coefficients are applied, this is the final equation for F6:

F 6 = 2.5 SH + 2.5 WPP + 2 PV + 2 BTI + 2 BTH + 2 BTHE + 2 BTC + MSW + 2 BEG + 1.5 LBFA + 1.5 LBFT

Results and discussion

Please find below Table 14 and Figs. 6, 7, 8, 9, 10 and 11, which include the results obtained (in ktoe), using the Chebyshev distance, L∞, following the Anti-Ideal Compromise Programming as previously defined in chapter 2.3; taking into account the below mentioned weights.

Table 14 Optimization results using Matlab® programming tools
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Fig. 6
figure 6

SH, WP, MSW and LBFT variation as per the weights assigned to function 1. Source: own construction

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Fig. 7
figure 7

SH, WP, MSW and LBFT variation as per the weights assigned to function 2. Source: own construction

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Fig. 8
figure 8

SH, WP, MSW and LBFT variation as per the weights assigned to function 3. Source: own construction

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Fig. 9
figure 9

SH, WP, MSW and LBFT variation as per the weights assigned to function 4. Source: own construction

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Fig. 10
figure 10

SH, WP, MSW and LBFT variation as per the weights assigned to function 5. Source: own construction

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Fig. 11
figure 11

SH, WP, MSW and LBFT Variation as per the weights assigned to function 6. Source: own construction

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The authors have aimed to compare the solution obtained given no special weight to any of the functions: (1,1,1,1,1,1); with the obtained values when only one of the functions is taken into account: for example (1,0,0,0,0,0); and finally with the outcome solution when a special weight has been given to a particular function: for example (5,1,1,1,1,1). This way, the different solutions will clearly show the tendency the variables follow, when a particular function is given more importance than the others. The authors have added two more cases to this list, one giving special importance to the three emissions functions (F 2, F 3, F 4), and another one targeting the maximum renewable energy substitution and rural health and education development (F 1 and F 6).

The nominal weights (1,1,1,1,1,1) are considered as the baseline. Once this baseline is obtained, then the other cases will be taken into account to give some special relative importance to any of the six functions or even to address some different weights to be applied if necessary [15, 16, 23, 24]. The results show that PV and BEG stay at their minimum potential value independently of the chosen weights, while the four biomass variables (BTI, BTH, BTHE and BTC) reach approximately their maximum potential value, except for the two cases where the economic factor is given a certain weight versus the other functions. This exception is totally expected, as function F 5 will always look for the cheapest solution, i.e., the one implementing less renewable energy substitution. The rest of the variables, SH, WP, MSW LBFA and LBFT do vary, depending on the chosen weights. The first three variables are linked together as per Eq. (22). This means that any variation in one of them, will therefore affect the other. As can be seen in Figs. 6, 7, 8, 9, 10 and 11 above, when only one function is optimized, a maximum polarized value is obtained for the different variables. Once all six functions are taking into account, even if a weight 5 is applied to a particular one, the difference from the nominal results [the ones obtained as per (1,1,1,1,1,1)] is less acute, flattening this way the value given to the different variables.

If the individual optimizations [for example: (1,0,0,0,0,0)] are not considered, and the last two cases or also not taken into account, the maximization of the above mentioned variables may be summarized as per Table 15 below.

Table 15 Maximization of SH, WP, MSW, LBFA and LBFT
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The authors have summarized below in Table 16 the advantages of applying this energy planning model to Sri Lanka, and also the potential improvements in Table 17.

Table 16 Advantages of SRIME application in Sri Lanka
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Table 17 Potential Improvements for SRIME application in Sri Lanka
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Conclusions

This paper shows the possibility of using MCDM methods, focusing on a sustainable and renewable energy approach. The resulting energy models give a great level of importance to the human environmental development factors, avoiding, therefore, the purely economic reasoning. These type of models are becoming a common way of choosing global energy plans [139] or some independent power plants, such as wind farms [140]. This work has aimed at establishing a potential energy model implementation methodology that may be applicable for developing countries. The Case Study shows that if SRIME was implemented in Sri Lanka, SH, WP, MSW and LBFT would be specially benefited from the Pareto optimization, while PV and BEG would stay at their official future expected value [20], having no growth at all. The SRIME model could be relatively easily interpolated to other Asian tropical countries, due to the similar circumstances in terms of health an education low overall parameters, high biomass consumption, monsoon special weather characteristics, low GDP and extremely high petroleum imports dependency.