Development of a New Support Mechanism to Calculate Feed-in Tariffs for Electricity Generation from Renewable Energy Sources in Turkey

Abstract

Turkish government agencies support capital investments in electricity generation from renewable energy sources. When making support decisions related with renewable electrical energy sources, the government agencies should consider various issues such as renewability, cleanliness, origin of the source, supply security, cost per kilowatt hour (kWh), and total electricity generation capacity. The tariff mechanism being used in Turkey provides constant rates per kWh of electricity generated from renewable energy sources. The levels of the rates are determined to stimulate renewable energy sources’ usage. In this paper, instead of a constant rate, a feed-in tariff is calculated for each individual electricity generation project using renewable energy source and its level is increased according to the source’s desirability with respect to other renewable energy sources. Various criteria are taken into account in determination of electrical energy sources’ desirability. Furthermore, a combination of two multi-criteria decision-making (MCDM) approaches (the fuzzy versions of the analytic hierarchy process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)) is used in obtaining a ranking among alternative renewable electrical energy sources. The developed support model’s applicability is illustrated in this paper. The new model developed in this paper has many key benefits. For example, for an individual renewable electrical energy project, final cost per kWh can be calculated and multiplied by new Support Constant to calculate feed-in tariff purchase price per kWh. In another key benefit of the developed model, only local instead of state-wide renewable electrical energy projects can be compared within the AHP-TOPSIS decision hierarchy.

Appendices

Appendix. Calculation for wind energy

Project life (year) = 20

Installed power (MW) = 1

Investment cost (Capex) = 1,100,000 $

Annual Cost (Opex) = Annual Profit*0.15 = 191,884*0.15 = 28,776.6$

Energy Output (MWh) = 1*24*365*0.3 = 2628

Equivalent Uniform Annual Cost = Annual Cost+(Investment Cost*(A/P)) = 117,043.45$

Cost/kWh = Equivalent Uniform Annual Cost/Energy Output/1000 = 0.04 $cent/kWh

State (Fixed) Feed-in Tariff (FIT) = 7.3/100 = 0.07 $cent/kWh

Annual Revenue = Energy Output*1000* State (Fixed) Feed-in Tariff (FET) = 191,884$

Payback Period = Investment cost/(Annual Revenue/Annual Cost) = 6.75 year

Present Value= Investment cost+(Annual Revenue-Annual Cost)*(1/A/P) = 932,180.24$

Interest rate = %5

(A/P, i%, 20) = [i*(1 + i)²⁰]/[(1 + i)²⁰–1) = [0.05*(+0.05)²⁰]/[(1 + 0.05)²⁰–1)] = 0.0802

Steps of the fuzzy AHP and fuzzy TOPSIS methods

Description of fuzzy AHP

(i) The arithmetic operations performed on triangular fuzzy numbers are presented below (Ic et al. 2013; Chen and Hwang 1992)

Let $\tilde{A}=$ (l₁, m₁, u₁) and $\tilde{B}=$ (l₂, m₂, u₂) be any two positive triangular fuzzy numbers. Then, the fuzzy number operations {⊕, ⊗, ⊘} are defined by

$$ \tilde{A}\oplus \tilde{B}=\left({l}_1+{l}_2,{m}_1+{m}_2,{u}_1+{u}_2\right) $$

(2)

$$ \tilde{A}\oplus \tilde{B}=\left({l}_1\times {l}_2,{m}_1\times {m}_2,{u}_{1\times }{u}_2\right) $$

(3)

$$ \tilde{A}\oslash \tilde{B}=\left({l}_1/{u}_2,{m}_1/{m}_2,{u}_1/{l}_2\right) $$

(4)

(ii) Geometric mean method (Ic et al. 2013; Chen and Hwang 1992)

• Step 1. Form the pairwise comparison matrix “$\overset{\sim }{A}$” whose elements are triangular fuzzy numbers ((${\overset{\sim }{a}}_{ij}$=(l_ij, m_ij, u_ij) and (i and j = 1,…, n), where n is the number of attribute.

$$ \overset{\sim }{A}=\left[\begin{array}{cccc}{\overset{\sim }{a}}_{11}& {\overset{\sim }{a}}_{12}& \dots & {\overset{\sim }{a}}_{1n}\\ {}{\overset{\sim }{a}}_{21}& {\overset{\sim }{a}}_{22}& \dots & {\overset{\sim }{a}}_{2n}\\ {}\vdots & \vdots & \dots & \vdots \\ {}{\overset{\sim }{a}}_{n1}& {\overset{\sim }{a}}_{n2}& \dots & {\overset{\sim }{a}}_{nn}\end{array}\right] $$

(5)

In assigning the values to the pairwise comparisons, Saaty’s fuzzy scale and reverse fuzzy scale (last two columns in Table 1) are used.

• Step 1. The fuzzy weight (${\tilde{w}}_i$) of each attribute (i = 1,…, n) can be calculated as follows:

First, the geometric mean for each pertinent attribute (i) is determined as:

$$ {l}_i={\left[\underset{j=1}{\overset{n}{\varPi }}{l}_{ij}\right]}^{1/n}\kern0.5em \mathrm{and}\kern0.5em l=\sum \limits_{i=1}^n{l}_i $$

(6)

$$ {m}_i={\left[\underset{j=1}{\overset{n}{\varPi }}{m}_{ij}\right]}^{1/n}\kern0.5em \mathrm{and}\kern0.5em m=\sum \limits_{i=1}^n{m}_i $$

(7)

$$ {u}_i={\left[\underset{j=1}{\overset{n}{\varPi }}{u}_{ij}\right]}^{1/n}\kern0.5em \mathrm{and}\kern0.5em u=\sum \limits_{i=1}^n{u}_i $$

(8)

Second, the fuzzy weight of each attribute i is determined as:

$$ {\tilde{w}}_i=\left(\frac{l_i}{u},\frac{m_i}{m},\frac{u_i}{l}\right),\kern0.5em {\forall}_i $$

(9)

In the application of the fuzzy AHP approach, a fuzzy version of the Saaty’s 1–9 scale (Table 15) (Saaty 2006) is used to assign values for pairwise comparison of the decision criteria.

Description of Fuzzy TOPSIS

The steps of fuzzy TOPSIS approach to rank alternatives are as follows (Chen and Hwang 1992; Torabzadeh and Khorasani 2018; Dhull and Narwal 2018):

• Step 1. A fuzzy decision matrix ($\overset{\sim }{D}$) is built by taking the triangular fuzzy performance values of feasible energy sources at attributes. In $\overset{\sim }{D}$, which is shown in Eq. (10), $\overset{\sim }{x}$_ki denotes the fuzzy performance value of feasible energy sources k (k = 1,2,…,number of feasible energy sources (n_es)) at attribute i (i = 1,2,…. number of attributes (n)).

$$ \overset{\sim }{D}=\left[\begin{array}{ccc}{\overset{\sim }{x}}_{11}& {\overset{\sim }{x}}_{12}\dots & {\overset{\sim }{x}}_{1n}\\ {}{\overset{\sim }{x}}_{21}& {\overset{\sim }{x}}_{22}\dots & {\overset{\sim }{x}}_{2n}\\ {}{\overset{\sim }{x}}_{n_{es}1}& {\overset{\sim }{x}}_{n_{es}2}\dots & {\overset{\sim }{x}}_{n_{es}n}\end{array}\right] $$

(10)

In the application of the fuzzy TOPSIS approach, the crisp numbers in the Hwang and Yoon’s Crisp Scale is converted to fuzzy numbers (Table 16) to use as performance values of the renewable electrical energy sources at decision criteria.

Table 16 Fuzzy numbers to be used as performance values of alternative electrical energy sources at decision criteria

• Step 2. Calculate normalized ratings by the vector normalization:

$$ k= 1,\dots, {n}_{es}\ \mathrm{and}\ i= 1,\dots n $$

(11)

• Step 3. Calculate fuzzy weighted normalized ratings: The fuzzy weighted normalized value ${\tilde{v}}_{ki}$ is calculated by Eq. (12).

$$ {\tilde{v}}_{ki}={\tilde{w}}_i{\tilde{r}}_{ki}\kern0.48em i=1,...,n;\kern0.6em k=1,...,{n}_{es} $$

(12)

where ${\tilde{w}}_i$ is the weight of the i^th attribute obtained by the fuzzy-AHP.

• Step 4. Defuzzification: Fuzzy performance values are converted to crisp values by calculating the means of the fuzzy numbers. Given a fuzzy number $\tilde{A}$, its generalized mean value is calculated using Eq. 13. When $\overset{\sim }{A}$ is a triangular fuzzy number (l, m, u), Eq. (13) can be simplified into Eq. (14) (Ic et al. 2013; Chen and Hwang 1992):

$$ \overset{\_}{x}\left(\tilde{A}\right)=\frac{\int x{\mu}_{\tilde{A}}(x) dx}{\int {\mu}_{\tilde{A}}(x) dx} $$

(13)

$$ \overset{\_}{x}\left(\overset{\sim }{A}\right)=\frac{\left(l+m+u\right)}{3} $$

(14)

The fuzzy weighted normalized values (${\tilde{v}}_{ki}$) provided in Eq. (12) is defuzzified using Eq. (14) and the crisp weighted normalized values (v_ki) is obtained.

• Step 5. Identify positive ideal and negative ideal solutions: The A* and A− are defined in terms of the weighted normalized values, as shown in Eqs. (15) and (16):

$$ {A}^{\ast }=\left\{\underset{k}{\Big(\max }{v}_{ki}\mid i\in I\right),\left(\underset{k}{\min }{v}_{ki}\mid i\in {I}^{\hbox{'}}\right\}\kern9.599993em $$

(15)

$$ {A}^{-}=\left\{\underset{k}{\Big(\min }{v}_{ki}\mid i\in I\right),\left(\underset{k}{\max }{v}_{ki}\mid i\in {I}^{\hbox{'}}\right\}\kern12.59999em $$

(16)

where I is the set of benefit type measures and I′ is the set of cost type attribute.

• Step 6. Calculation of separation measures: The separation between scenarios can be measured by the n-dimensional Euclidean distance. The separation of each scenario from the positive ideal solution, A*, and the negative ideal solution, A−, is then given by Eqs. (17) and (18) respectively:

$$ {D}_k^{+}=\sqrt{\sum \limits_{i=1}^n{\left({v}_{ki}-{v}_i^{\ast}\right)}^2} $$

(17)

$$ {D}_k^{-}=\sqrt{\sum \limits_{i=1}^n{\left({v}_{ki}-{v}_i^{-}\right)}^2} $$

(18)

where v_i^* is the positive-ideal value for i^th attribute, and v_i⁻ is the negative-ideal value for the i^th attribute.

• Step 7. Calculation of ranking scores of feasible energy sources:

$$ {C}_k^{\ast }=\frac{D_k^{-}}{D_k^{-}+{D}_k^{+}}\kern0.5em k=1,\dots, {n}_{es} $$

(19)