Explicit cost-risk tradeoff for renewable portfolio standard constrained regional power system expansion: A case study of Guangdong Province, China

Energy 131 (2017) 125e136

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Explicit cost-risk tradeoff for renewable portfolio standard constrained regional power system expansion: A case study of Guangdong Province, China Ling Ji, Ph.D Research Assistant a, *, Guo-He Huang Professor and Canada Research Chair b, Yu-Lei Xie Research Assistant c, Dong-Xiao Niu Professor and Cheung Kong Scholar d, Yi-Hang Song e a

Research Base of Beijing Modern Manufacturing Development, College of Economics and Management, Beijing University of Technology, Beijing, 100124, China b Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Sask, S4S 0A2, Canada c School of Mechanical Engineering, University of Science & Technology, Beijing, 100083, China d School of Economics and Management, North China Electric Power University, Beijing, 102206, China e Electric Power Research Institute, CSG, Guangzhou, 510080, Guangdong Province, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 December 2016 Received in revised form 3 April 2017 Accepted 3 May 2017

In this paper, a risk explicit interval two-stage programming (REITSP) model was proposed for supporting the regional electricity generation expansion with renewable portfolio standard (RPS) constraint. It could effectively tackle multiple uncertainties expressed as interval numbers. But unlike the traditional interval two-stage programming model, the proposed REITSP model could provide an explicit trade-off information between system cost and risk for decision makers with different risk preferences. It could minimize the total system cost, as well as the decision risk according to the aspiration risk level of decision maker. The developed REITSP model was applied to the case study in Guangdong Province, China for its long-term electricity system planning. Crisp solutions under different aspiration risk levels for varying RPS targets were obtained and analyzed. The results showed that according to the current available renewable energy and affordable construction speed, the maximum RPS target for Guangzhou Province during 2016e2025 should be 17%. Higher RPS level would promote the renewable energy generation, especially solar power; meanwhile, it would reduce the CO2 emission and the imported electricity, but with greater investment cost. The obtained results and trade-off information would be valuable for the optimal long-term electricity system expansion planning when facing future uncertain situation. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Renewable portfolio standards Interval two-stage programming Risk preference Risk explicit Generation expansion planning

1. Introduction Electricity power industry is one of the main contributors of greenhouse gas emission in many countries, and serious environment issues caused by fossil-based electricity generation have raised global concern [1,2]. So far, great efforts for electricity system structure adjustment and control have been made in order to

* Corresponding author. School of Economics and Management, Beijing University of Technology, 100 Ping Le Yuan, Chaoyang District, Beijing, 100124, China. E-mail addresses: [email protected] (L. Ji), [email protected] (G.-H. Huang), [email protected] (Y.-L. Xie), [email protected] (D.-X. Niu), [email protected] (Y.-H. Song). http://dx.doi.org/10.1016/j.energy.2017.05.017 0360-5442/© 2017 Elsevier Ltd. All rights reserved.

mitigate its adverse effects. Among various measures, renewable energy is regarded as environmental friendly alternative resource to reduce the carbon emission of traditional power industry. Therefore, renewable portfolio standard (RPS), which requires a certain percentage for renewable energy generation, is a popular mandatory policy to promote greater use of renewable energy sources [3]. So far, many countries have implemented RPS at different degree to achieve their ambitious emission reduction goal. For example, in Europe, France, Germany and Britain have set the share of renewable energy in total energy consumption as 23%, 18% and 15%, respectively. In the United States, RPS program has been put forward at state level, for instance, the RPS level of California is 33% [4]. China has also declared to raise its renewable energy share

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L. Ji et al. / Energy 131 (2017) 125e136

to 20% by 2030 [5]. However, implementing such mandatory policy inevitably leads to great impacts on regional power system design and operation management. Thus, how to make a well-balanced compromise among competing power supply-security, maximum renewable energy accommodation, economic, and environmental objectives in generation expansion planning (GEP) under the regulation of environmental policy has been a major issue to be addressed in recent decades. Extensive researches on GEP problems have been carried out to search the optimal selection of technology, location, size, and operation mode with a broad range of objectives, such as maximization of project lifetime economic return, minimization of CO2 emission, minimization of total cost [6,7]. Numerous techniques, such as dynamic programming [8], linear programming [9], nonlinear programming [10], mixed integer programming [11], and evolutionary programming [12,13], have been applied to solve the problem. For example, Koltsaklis and Georgiadis [14] presented a generic mixed integer linear programming (MILP) model for longterm GEP with the consideration of both typical daily constraints and representative yearly constraints. From a policymaker’s perspective, Siddiqui et al. [15] formulated a bi-level model to investigate how RPS policy may be designed with the consideration of the energy sector’s equilibrium and market structure. In these deterministic models, the accurate estimation of technical parameters and load demand has great impact on the reliability of optimal strategies. In practice, the uncertain characteristic for regional energy system, such as the stochastic renewable energy penetration, the fluctuant fuel price, and uncertain policy regulation, is inevitable to take into account under the long-term electricity expansion planning [16]. A number of inexact optimization methods, such as fuzzy mathematical programming, stochastic mathematical programming, and interval parameter programming, have been developed to address the uncertain information. Different technologies have their unique advantages in handling the uncertainties. For instance, in the framework of fuzzy mathematical programming, fuzzy membership function is used to reflect the uncertain coefficients in the objective function and constrains, as well as the satisfying attitude of decision maker in multi-objective programming [17,18]. In scenario-based stochastic programming, based on the accurate probability distribution information of uncertain parameters, a large number of scenarios are generated by Monte Carlo simulation or other sampling approaches to formulate the uncertainties [19e21]. Repeated random samplings and computations require a lot of time and effort [22]. In addition, with more uncertainties considered in the model, the number of scenarios would grow exponentially. For instance, Koltsaklis et al. [23] presents a multiregional, multi-period MILP model with the combination of Monte Carlo simulation for the GEP of a large-scale central power system in a highly uncertain and volatile electricity industry environment. Li et al. [24] addressed the climate change impact on GEP problem by setting discrete climate scenarios to model the uncertainty. Compared with other fuzzy and stochastic mathematical programming, interval parameter programming (IPP) requires less information, and its solution processes are easy and less computational [25,26]. Due to its merits, many inexact optimization methods are integrated with interval parameter programming for reflecting various uncertain information, and the hybrid models have been obtained a wide application in generation expansion and operation dispatch of electricity system under uncertainty. For example, Ji et al. [27] presented an inexact risk-aversion optimization model for regional electricity system planning with the regard of CO2 emission cap and trade scheme, and decision maker’s risk preference. Under the framework of interval programming, Liu

et al. [28] proposed an inexact two-stage chance-constrained programming model for the long-term management of coal and power in north China. Jin et al. [29] developed an inexact mixed-integer linear programming for generation capacity planning, where the uncertainties are expressed by fuzzy sets with interval-valued membership function. In addition, since the mid-long term planning horizon of electricity generation expansion usually covers 5 or 10 years. It is difficult to estimate the accurate probability distribution function of the macro social or economic parameters based on limited history data. Therefore, IPP method is more appropriate for the regional GEP problem in practice. However, bounded interval value also brings two serious limitations in real world decision making process [30]. The first thing is that the optimal solutions gained from IPP may lead to non-optimal and infeasible optimization schemes. Besides, it cannot provide the trade-off between system profit and risk representing the decision maker’s risk attitude. Risk explicit interval linear programming (REILP) approach proposed by Zou et al. [31] can overcome the above shortcomings of IPP solutions. Its effectiveness and capability have been verified in several fields of study. Under the framework of REILP, Liu et al. [32] and Zhang et al. [33] proposed REILP models for water quality management problems. Simic et al. [34,35] developed a REILP model for the end-of-life vehicle recycling in EU under uncertainty, then proposed a refined REILP model by introducing fuzzy set to reflect the decision maker’s preferences. In spite of this, only few researches about REILP approach have been carried out, especially in GEP problems. Hence, in this paper, under the framework of REILP approach, we propose a risk explicit inexact two-stage stochastic programming (REITSP) model to deal with the long-term GEP problems under uncertainties. The main contributions of this work are summarized as: (1) The optimal investment and operation strategies of mid-long term electricity system under different RPS levels is analyzed and compared at regional level; (2) Multiple uncertainties are considered to make the model more practical, but with less required information and computational complexity, which is more executable in real world decision process; (3) Unlike the traditional interval two-stage stochastic programming model, explicit solution with better system cost-risk tradeoff information could be provided according to the risk preference of decision maker. The remainder of this paper is arranged as follows. The proposed REITSP model programming model and its solution process are presented in Section 2. Detail case study for Guangzhou Province is carried out in Section 3. Sector 4 illustrates the optimal strategies under different RPS levels and compares the optimal solutions of REITSP model with ITSP model. Sector 5 outlines the main conclusions. 2. Methodologies 2.1. Inexact two-stage stochastic programming approach In the inexact two-stage stochastic programming (ITSP) approach, the parameters in objective function and constraints can be expressed as intervals with lower and upper bound, besides, the stochastic of future events can described by probability distribution function. Thus, ITSP could deal with mixed uncertain information effectively. A key feature of ITSP is the two-stage decision process, where in its first stage, the initial decision is made before the random events occur, and in the second stage, corrective actions can be taken after a random event has taken place, which aims to minimize the “extra penalties” due to recourse against any infeasibility [36]. The mathematical formulation of a typical cost minimization ITSP model is presented as the follows [37,38]:

L. Ji et al. / Energy 131 (2017) 125e136

minf ± ¼

n1 X

c± x± þ j j

n2 X N X

ps d± y± j js

(1a)

j¼1 s¼1

j¼1

n h X

s:t:

127

n2 X N   i X h   þ  þ  cþ ps dþ j xj  l0 cj  cj xj þ j  l0 dj  dj j¼1 s¼1

j¼1

i  yjs

subject to: n1 X

a± x±  b± r ; r ¼ 1; 2; …; m1 rj j

  þ þ   fopt  l0 fopt  fopt

(1b)

j¼1 n1 X j¼1

(2-b) a± x± þ ij j

n1 X

b± e± y±  w is ; i ¼ 1; 2; …; m2 ; s ¼ 1; 2; …; N ij js

(1c)

bþ  i

j¼1

n X

a ij xj 

j¼1

 0; j ¼ 1; 2; …; n1 x± j

(1d)

 0; j ¼ 1; 2; …; n1 ; s ¼ 1; 2; …; N y± js

bþ w is 

(1e)

Min x ¼ 4i 4

j¼1



lij aþ ij 2

þ4k 4



a ij



xj þ



hi bþ i



b i



3

2

5 þ 4r 4

n2 X N X j¼1 s¼1

lrj a rj yrjs 



j¼1 s¼1

n2 X N X j¼1 s¼1

!





(2-c)





 lrj aþ rj  arj yrjs þ hr

(2-d)

b w is

0  lij  1; ci; j

(2-e)

0  lj  1; cj

(2-f)

xj  0; cj

(2-g)

2.3. Solution algorithm Fig. 1 illustrates the process flow diagram of REILP model. The detailed algorithmic procedure to solve the REITSP model is summarized as below: Step 1: Formulate ITSP model (1). Step 2: Solve the ITSP model according to the two-step algo rithm, then obtain the optimal solution of two sub-models, fopt þ and fopt . Step 3: Formulate REITSP model (2), and solve it by using solutions obtained in Step 2. Adjust the value of aspiration level, obtain a serious solutions representing the optimal strategies under different risk preferences with minimum decision risk.



lrj aþ rj



a rj



yrjs þ hr

3 n1 n2 X N       X X þ  þ  þ  5 lj cj  cj xj þ ps dj  dj yjs þ l0 fopt  fopt j¼1



where, x is the risk function of the entire system violating optimization model constraints, which can be seen as the risk metric; 4i and 4k represent general arithmetic operators, such as a simple or þ weighted addition, simple or weighted arithmetic mean. fopt and  are the upper and lower bound values of traditional ILP probfopt lem. lij , lj and hi are real numbers. l0 represents the system aspiration level according to decision maker’s risk preference, ranging from 0 to 1. A higher aspiration level indicates the decision maker could tolerate higher risk. We can solve this risk optimization with different crisp aspiration level values l0 . It should be noticed that due to the introduction of some unknown variables, the REITSP model is a nonlinear programming problem.

Although ITSP model require less information and shorter computation time, in real world, it is not convenient for practical decision actions within the upper and lower bound of interval solutions due to a lack of linkage between decision risk and system cost. Besides, it has been verified that the obtained interval solutions may be infeasible and non-optimal. REILP approach developed by Zou et al. can overcome the shortcomings of infeasibility and non-optimality of the traditional IPP method, and provide explicit information on cost/profit-risk tradeoff. By introducing decision risk function and aspiration risk level, the REILP approach can provide explicit tradeoff information for decision maker with certain risk preference. The objective function of REILP model is to minimize the risk of the entire system violation. Under the framework of REILP [31], the risk explicit inexact two-stage programming (REITSP) model for the above ITSP model can be formulated as follows:

n1 X

n2 X N X

bþ w is

2.2. Risk explicit inexact two-stage stochastic programming approach

2



þ  lij aþ  a ij xj þ hi bj  bj ; ci ij

j¼1

j¼1 s¼1

where the superscript ± denotes the upper and lower boundary. The first term in the objective function represents the cost during first-stage decision, where x± is a vector of first-stage decision variables, x± ¼ x þ Dx$u, where Dx ¼ xþ  x , and u2½0; 1. The second term is the expected penalties during the second-stage, where s is a series of random events in the future, y± represents the decision variables based on the uncertain future events during the second-stage, and ps is the probability of uncertain events with P ps ¼ 1. According to the two-step algorithm proposed by Refs. [39,40], the ITSP model (1) could be decomposed into two deterministic submodels f þ and f  . For the minimized objective function, the submodel f  will be formulated firstly; conversely, for the maximized objective function, the submodel f þ will be formulated firstly. Finally, the obtained interval solutions will be ± þ þ   x± opt ¼ ½xopt ; xopt , yopt ¼ ½yopt ; yopt , and the optimized objective ± þ  value as fopt ¼ ½fopt ; fopt .

n X

bþ w is



b w is

!3 5 (2-a)

128

L. Ji et al. / Energy 131 (2017) 125e136

Uncertainties Discrete intervals

Probability distribution

Interval parameter programming

Two stage stochastic programming

Risk level Inexact two stage stochastic programming (ITSP) ITSP upper bound submodel Adjust aspiration level λ

ITSP lower bound submodel

Optimal solutions for the objective of ITSP model Risk explicit interval two-stage programming (REILP) model Optimal solutions under various risk preference Calculate normalized risk level Depict the cost-risk curve Fig. 1. The process flow chart of REILP model.

Step 4: Derive normalized risk levels (NRLs) based on solutions of REITSP, where the most pessimistic condition set the value of 0, and the most optimistic condition set the value of 1. Step 5: Depict the tradeoff curve of risk and system cost. Step 6: End. 3. System modeling 3.1. Overview of the electricity system in Guangdong Province Guangdong Province with flourishing economy and large population density is located in the South of China, as shown in Fig. 2. Its total population was 107 million, and GDP was RMB 6, 781 billion in 2014 [41]. Fast social development requires a large amount of electricity supply. In 2014, the regional total electricity consumption amount was 0.53  106 GWh, where 72.70% of the power demand was supplied by local generation, and the rest mainly relied on import from surrounding area. The total power

generation capacity in Guangdong Province was 91.64 GW, and the coal-fired power capacity was about 75% in 2014. Although the renewable energy, especially wind and solar power, have experienced significant growth since 2010, they only accounted for 2.23% of the total capacity and provided 0.89% of the total electricity generation in 2014 [42]. The fast urban development in Guangdong Province is expected to result in electricity demand incensement and generation expansion in future, that may bring more pressure on conventional energy resources and fragile environment. Limited by local resource, its thermal coal consumption is mainly relied on the imported from Shanxi, Shaanxi, West of Inner Mongolia though rail way or railway-river combination transport. According the coal yield and railway transport capacity of the above provinces, it is estimated that the supportable new capacity of thermal generation capacity will reach to 16 GW in 2020 and 27 GW in 2030 [43]. Similarly, the gas consumption also heavily relies on import, mainly from three sources, i.e. oversea imported LNG, inland natural gas

L. Ji et al. / Energy 131 (2017) 125e136

129

Fig. 2. Map of Guangdong Province.

pipeline, and offshore natural gas. Since limited by conventional resources, renewable energy resources will be an excellent choice in future to mitigate the dependence on local coal-fired electricity and imported electricity. Abundant onshore and offshore wind power has the great potential to improve the capability of selfsupply, and achieve national renewable energy generation target. However, the expensive investment cost of renewable energy generation will result high cost for the large-scale utilization. Therefore reasonable and scientific electricity generation expansion should be carried out to balance the total system cost and renewable energy penetration to achieve sustainable long-term development. For the electricity system manager, they have to make better cost-risk tradeoff to minimize the total cost while satisfy the environmental and safety constraints.

3.2. Data description The study period covered in this study is from 2016 to 2025, with each period covering 5 years. In this study, many uncertainties are considered to make the model more realistic, including the main social, economic, technological and policy parameters, i.e. capital investment cost, coal price, purchased electricity price, annual average operation time, emission cost, future power demand and annual peak load. The future electricity load demand is forecasted based on the historical data of local electricity consumption published by China Electric Power Yearbook [42]. According to the view of slow down economic development in Guangdong Province and some references [44,45], we assume there are three scenarios of power demand level (i.e. low, medium, and high) with the probability 0.25, 0.60, and 0.15 respectively. Limited by the actual data sources, the other uncertain parameters are expressed as interval value without exact probability information. The uncertainties expressed as interval value with or without probability distribution information could be effectively handled in the proposed REITSP model. Table 1 summarizes the key parameter configuration of different types of generation conversion technologies with the reference to

some existing studies [46,47]. Table 2 presents the emission factors and penalty cost for the pollutants from coal-fired power generation. In addition, the coal price is relatively low during economic depression and is predicted to growth in future. Thus, in this paper, it is natural to set coal price as interval value, i.e. [82, 90] $/tonne and [86, 95] $/tonne for the first and second periods, respectively. According the cross-region electricity exchange information, the imported electricity price is [70, 73] $/MWh and [71, 74] $/MWh for the first and second periods. 3.3. Model formulation 3.3.1. Inexact two-stage programming (ITSP) model The objective of long-term generation expansion planning model is to minimize the total cost during the planning horizon, including the investment cost of new capacity installation IC ± , system operation cost OC ± , purchased cost of imported electricity PC ± , and emission cost EC ± .

Min f ± ¼ IC ± þ OC ± þ PC ± þ EC ±

(3-a)

(1) Investment cost of new capacity installation:

IC ± ¼

T X K X

± CRFk $CCk± $NCkt

(3-b)

t¼1 k¼1

CRFk ¼

r$ð1 þ rÞlk ð1 þ rÞlk  1

(3-c)

where, the subscript index t represents the planning period (t ¼ 1, 2), and k for electricity generation technology, k ¼ 1 for the coalfired plants, k ¼ 2 for the nuclear power, k ¼ 3 for the hydro po± wer, k ¼ 4 for the wind power, and k ¼ 5 for PV. NCkt is the new installed capacity of technology k during period t (MW). CCk± is the capital cost of technology k ($/MW). CRFk denotes the capital

130

L. Ji et al. / Energy 131 (2017) 125e136

Table 1 Key technical and economic parameters for various generation technologies. k

Unit type

1

Coal

2

Nuclear

3

Hydro

4

Wind

5

Solar

Planning period

t t t t t t t t t t

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

Capital investment (106 $/MW)

1 2 1 2 1 2 1 2 1 2

Fixed O&M cost ($/kW)

[0.80, 0.81]

Operating cost ($/MWh)

35.00 33.60 48.52 46.58 23.45 22.51 15.00 15.20 12.40 12.56

[1.81, 1.84] [1.30, 1.32] [1.80, 1.83] [3.50, 3.55]

V

VP

6.40 6.14 2.80 2.69 2.60 2.50 e e e e

7.17 6.88 3.14 3.01 2.91 2.80 e e e e

Average operation time (h)

Operating lifetime (years)

[5000, 5250]

40

[7600, 7980]

40

[3000, 3150]

50

[1800, 1890]

35

[1200, 1260]

30

Table 2 Emission factor and cost for the pollutants from coal-fired power generation. Type of pollutants

CO2

NOx

SO2

Emission factor (kg/MWh) Emission cost ($/ton)

882 [15,20] [20,25]

0.8 [9,12] [12,15]

0.2 [5,8] [8,11]

t¼1 t¼2

recovery factor. r is the interest rate, assumed as 6%, and lk is the lifetime of unit (years). (2) Operation cost of new and existing power plants: The total operation cost is consisted of the fixed cost, operation cost and fuel consumption cost.

OC ± ¼

T X K X

± Fkt $Ckt þ

t¼1 k¼1



T X K X H  X



± Vkt Ekt þ ph VPkt EPkth þ

t¼1 k¼1 h¼1

K X H X



± b±kt xkt ph Ekt þ EPkth

T X t¼1

 (3-d)

where, the subscript index h represents the scenarios, ph is the P probability of scenario h, with ph ¼ 1. Decision variable Ekt is the ± generation output during the first stage (MWh), and EPkth is the extra generation output during the second stage in scenario h (MWh). Fkt and Vkt represent the fixed and variable cost of generation technology k, respectively ($/MW). VPkt is the penalty cost for extra power generation ($/MWh). b± kt is the fuel price ($/tonne). xkt represents the conversion efficiency of power generation technology k during period t (tonne/MWh).

PC ¼

(3-e)

± where, IPt± and IEth are the price ($/MWh) and amount (MWh) of imported electricity, respectively.

t¼1 k¼1 h¼1

s

K X



± k±st EFks ph Ekt þ EPkth

(3-g)

± ± Ckt  ð1 þ rÞPmaxt ; ct

(3-h)

(3-i)

k¼1

where, D± represents the future electricity demand in scenario h th (MWh); Tr is the prespecified loss factor for the transmission sys± tem; Pmaxt represents the annual zonal peak demand (MW); g is ± capacity reserve margin; Ckt is the capacity of technology k during t ± (MW); IEth denotes the imported electricity (MWh).



(3-f)

(3-j)

± where, SHkt represents the average use time of generation technology k (hour).

(3) Generation expansion limitation: ± 0  NCkt  MNCkt ; ck; t

(4) Emission cost of electricity generation: T X K X H X S X

±  15%  D± ; ct; h IEth th

± ± Ekt þ EPkth  SHkt ; ck; t; h

± ph IPt± IEth

t¼1 h¼1

EC ± ¼

K  X  ± ±  D± ; ct; h Ekt þ EPkth $ð1  TrÞ þ IEth th

(2) Generation constraint:

(3) Cost of imported electricity: T X H X

(1) Satisfying electricity demand:

k¼1

k¼1 h¼1

±

where, s denotes the type of pollutants, s ¼ 1 for CO2, s ¼ 2 for SO2, and s ¼ 3 for NOX. k± st is the emission cost of pollutant s ($/tonne). EFks is the emission coefficient of technology k (tonne/MWh). The optimal value of the objective function is determined subjected to energy balance, planning reserve margin, resource availability, operational limitation and RPS policy constrains, as follows:

(3-k)

where, MNCkt is the maximum construction speed for technology k during planning period (MW). (4) Dynamic constraint on capacity addition:

L. Ji et al. / Energy 131 (2017) 125e136

± Ckt ¼



± C0k þ NCkt ± ± Ck;t1 þ NCkt

t¼1 t > 1 ; ck

(3-l)

131

could provide crisp solution with the aim of minimizing both total system cost and decision risk under certain aspiration risk level of decision maker. Under this framework, the REITSP model for longterm generation expansion planning is developed as follows:

where, C0k is the initial capacity of generation technology k (MW). (5) Renewable energy penetration limit:

" min ¼ 2l0

T X K X

T X K X H     X  CRFk $ CCkþ  CCk $NCkt þ bþ kt  bkt $xkt $ph $ðEkt þ EPkth Þ

t¼1 k¼1

þ

T P K P H P S  P t¼1 k¼1 h¼1 s

kþ st



k st



t¼1 k¼1 h¼1 T X

$EFks $ph $ðEkt þ EPkth Þ þ

H X

  ph IPtþ  IPt IEth

t h #  .   .   XX þ  þ  þ fopt þ fopt þ 2 Dþ þ fopt  fopt l1th Dth  D þ D th th th t  .  .  Xh  PP  þ  þ  þ  D þ 2 Pmax;t þ2 l2th Dþ  D þ D l3t Pmax;t  Pmax;t þ Pmax;t th th th th t h t .   PP þ  þ  CAFkt l4kt CAFkt  CAFkt þ CAFkt þ2 k

t

X X    ± ± Ekt þ EPkth  u$ Ekt þ EPkth ; ct; h k¼3;4;5

(4-a)

(3-m)

k

CRFk ¼

r$ð1 þ rÞlk ð1 þ rÞlk  1

(4-b)

Subject to

where, u represents the percentage of penetrated renewable energy. This constraint indicates that the electricity generation from renewable energy should not be lower than the certain RPS level.

T P K P t¼1 k¼1

þ

CRFk $CCkþ $NCkt 

T P K P t¼1 k¼1

þ





l0 $CRFk $ CCkþ  CCk $NCkt

t¼1 k¼1

Fkt $Ckt þ

T P K P H P t¼1 k¼1 h¼1

þ

T X K X

T X K X H X

ðVkt $Ekt þ ph $VPkt $EPkth Þ

t¼1 k¼1 h¼1

bþ kt $xkt $ph $ðEkt þ EPkth Þ 

T P K P H P S P t¼1 k¼1 h¼1 s

T X K X H X t¼1 k¼1 h¼1 T X K X

kþ st $EFks $ph $ðEkt þ EPkth Þ 

H X S X

t¼1 k¼1 h¼1

T X H   X ph $IPtþ $IEth  l0 $ph $ IPtþ  IPt $IEth t¼1 h¼1   t¼1 h¼1 þ þ   fopt  l0 fopt  fopt

þ





 l0 $ bþ kt  bkt $xkt $ph $ðEkt þ EPkth Þ



(4-c)



 l0 $ kþ st  kst $EFks $ph $ðEkt þ EPkth Þ

s

T P H P

(6) Other: ± ± 0  EPkth  Ekt ; ck; t; h

(3-n)

Dþ  th

K   X ðEkt þ EPkth Þ$ð1  TrÞ  IEth  l1th Dþ  D th ; ct; h th k¼1

(4-d)

3.3.2. Risk explicit inexact two-stage stochastic programming (REITSP) model The solutions gained from ITSP are interval value with lower bound and upper bound. In practice, the decision maker may make a compromise rather than select the extreme decisions, for example, they may take the mean value of the interval solutions. By introducing risk function and aspiration level l, the REITSP model

  þ  IEth =15%  D th  l2th Dth  Dth ; ct; h

þ Pmaxt



K X k¼1

(4-e)

, Ckt

  þ  ; ct  Pmaxt ð1 þ rÞ  l3t Pmaxt

(4-f)

L. Ji et al. / Energy 131 (2017) 125e136

(4-k)

The aspiration level l0 , ranging from 0 to 1, is predetermined according to the risk attitude of decision maker. When l0 is 0, it indicates the decision maker is conservative and unwilling to take any decision risk. In this situation, the obtained solutions are the upper bound solutions of the original ITSP model. Whereas, when l0 is 1, it means the aggressive attitude of decision maker. Accordingly, the obtained solutions are the lower bound solutions of the original ITSP model. Both ITSP and REITSP models can be solved though the LINGO solver in a fairly short time period.

4. Results analysis and policy implications 4.1. Results of ITSP model The solutions of ITSP model can be obtained by solving the lower and upper bound submodels according to the two-step algorithm. The lower bound solution indicates the minimum total system cost from the most optimistic view, based on the assumption of low capital cost, low fuel price, low imported electricity

160 120

80 40 0

Without RPS

RPS=10% lower

RPS=17%

upper

Fig. 4. Imported electricity under different load demand scenarios and RPS levels.

90

Objective value (109$)

RPS=15%

high

0  lij  1; ci; j

medium

(4-j)

k

low

k¼3;4;5

high

X ðEkt þ EPkth Þ; ct; h

medium

ðEkt þ EPkth Þ  u$

(4-i)

low

t¼1 ; ck t>1

high

X

C0k þ NCkt Ck;t1 þ NCkt

medium

 Ckt ¼

low

(4-h)

high

0  NCkt  MNCkt ; ck; t

price, improved emission factor, and less load demand growth in future. While, the upper bound solution means the maximum total system cost from the most pessimistic view based on the opposite assumption. In addition, the influences of RPS policy on the electricity expansion planning in Guangdong Province are also analyzed in this sector. Under the assumption in Sector 3, the RPS target should be set within a reasonable range. Too high RPS level is unpractical due to the limitation of construction speed of renewable energy generation, while too low RPS level is invalid to improve the share of renewable energy generation. After multiple tests, the maximum available RPS target would be 17% for Guangdong Province during planning horizon. Fig. 3 illustrates the total system cost under different RPS levels. In general, with higher RPS level, the total system cost would increase due to more investment on renewable energy generation whose capital cost is relatively expensive. Too low RPS level would have no influence on the expansion planning. For instance, when RPS level set as 10%, its total system cost $ [75.77, 83.13]  109 would be the same with that in situation without RPS constraint.

medium

(4-g)

low

   þ  ; ck; t; h ðEkt þ EPkth Þ=Ckt  CAFkt  l4kt CAFkt  CAFkt

Imported electricity (106 MWh)

132

85 83.13

83.74

83.11

83.13

Table 4 Electricity output performance of local generation technologies under different RPS levels for low load demand (Unit: 106 MWh).

80

Generation technology

RPS levels

t¼1

t¼2

Coal-fired

Without RPS RPS ¼ 17% Without RPS RPS ¼ 17% Without RPS RPS ¼ 17% Without RPS RPS ¼ 17% Without RPS RPS ¼ 17%

[440, 441.91] [416, 429.20] [131, 137.34] [131, 137.34] [70, 73.17] [70, 73.17] [29, 30.32] [29, 30.32] [0.64, 1] [13, 13.35]

[444, 482.40] [431, 433.13] [192, 201.18] [192, 201.18] [100, 104.67] [100, 104.67] [59, 62.45] [59, 62.45] [0.64, 1] [13, 13.35]

76.86

75

75.77

75.87

75.77

Nuclear Hydro

70 without RPS

RPS=10%

RPS=15%

RPS=17%

Fig. 3. Total system cost under different RPS levels.

Wind Solar

Table 3 New installed capacity of generation technologies (Unit: 103 MW). Technologies

Period

Coal

t t t t t t t t t t

Nuclear Hydro Wind Solar

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

1 2 1 2 1 2 1 2 1 2

Without RPS

RPS ¼ 10%

RPS ¼ 15%

RPS ¼ 17%

[20.17, 25.34] e 10.00 8.00 10.00 10.00 14.00 17.00 e e

[20.17, 25.34] e 10.00 8.00 10.00 10.00 14.00 17.00 e e

17.61 [0, 2.56] 10.00 8.00 10.00 10.00 14.00 17.00 e e

[13.87, 14.49] [0, 3.13] 10.00 8.00 10.00 10.00 14.00 17.00 [10.09, 10.62]

L. Ji et al. / Energy 131 (2017) 125e136

When the RPS level is set as the maximum, the total system cost would increase to $ [76.86, 83.74]  109. Table 3 shows the capacity investment portfolio during the planning horizon under different RPS levels. Since the forecasted incensement of load demand slow down, the new installed capacity during the second period would be far less than that in the first period. Especially, if without RPS policy, there would be no capacity investment of coal-fired power plant during the second period. With the RPS increasing, the expansion scale of coal-fired power during the first period would decrease, and some investment on coal-fired power would be postponed to the second period. For instance, without RPS constraint, the new installed capacity for coal-fired power would be [20.17, 25.34]  103 MW, and 0 MW during the first and second period, respectively. In addition, as the RPS level fixed as 17%, the new installed capacity for coal-fired power would be [13.87, 14.49]  103 MW, and [0, 3.13]  103 MW during the first and second period. The future development of nuclear and hydro would mainly follow the government approval. Among renewable energy, wind power would gain the priority to develop with its maximum available construction speed. Extremely high RPS level would promote the solar power development. When RPS is 17%, during the first period, the new installed capacity of coal-fired power would be [13.87, 14.49]  103 MW, and the new installed capacity for solar power would be [10.09, 10.62]  103 MW. According to the solutions, the load demand change would be satisfied by imported electricity, and have little influence on local power system operation. Fig. 4 presents the imported electricity under different load demand scenarios and RPS levels during the second period. With the higher load demand and RPS level, the amount of imported electricity would increase accordingly. For instance, under medium load demand scenario, without RPS, RPS as 10%, 15% and 17%, the amount of imported electricity would be [33.18, 81.55]  106 MWh, [33.18, 81.55]  106 MWh, [72.96, 81.55]  106 MWh, and [79.74, 81.55]  106 MWh, respectively. Besides, when RPS is set as 17%, the imported electricity would be [35.83, 38.50]  106 MWh, [79.74, 81.55]  106 MWh, and [136.86, 137.55]  106 MWh for low, medium and high load demand scenarios, respectively. In addition, Table 4 illustrates the electricity output performance of local generation technologies under different RPS levels for low load demand scenario. In general, the electricity output during the second period would be greater than that in the first

133

period, due to the incensement of load demand. The generation output of nuclear, hydro and wind power would be their maximum available amount, while not affected by the changes of RPS level. With the higher RPS level, the electricity output of coal-fired power would decrease. At the same time, the supply of solar power generation and imported electricity would increase. During the first period, when without the constraint of RPS, the electricity output of coal-fired power would be [440, 441.91]  106 MWh, and the solar power generation output would be [0.64, 1.00]  106 MWh. While if RPS level is set as 17%, the electricity output of coal-fired power and solar power would be [416.00, 429.20]  106 MWh and [13, 13.35]  106 MWh, accordingly. Therefore, the CO2 emission amount would also decrease when RPS level is higher. As shown in Fig. 5, under the scenario of without RPS, RPS set as 15% and 17%, the total CO2 emission during the first period would be [391.60, 435.13]  106 tonne, [380.32, 399.33]  106 tonne and [366.56, 382.02]  106 tonne, respectively. 4.2. Results of REITSP model For brief explanation, in this sector, we set the RPS level as 17%, and then compare the results of REITSP model with that of ITSP model. Unlike the interval solution of traditional TSP model, by introducing the risk function and aspiration level, REITSP model could offer sufficient insight into the trade-offs between economic and system risk, and provide the accurate solutions under various aspiration levels from 0 to 1 with 0.1 step. Fig. 6 depicts the risk-cost tradeoff curve according to the solutions from the REILP model. It shows that the pessimistic decision maker with lower aspiration level leads to more system cost and smaller value of risk function. On the other hand, the optimistic decision maker with higher aspiration level leads to less system cost and greater value of risk function. The linear relationship between aspiration level and total system cost indicates with the increment of 0.1 aspiration level, the total system cost would reduce $ 0.69  106. And the slope of linear relationship between aspiration level and risk function level is 1. In addition, compared with the results of ITSP, it is found that the total system cost when aspiration level set as 0 would be equal to the lower bound solution of ITSP, and that the total system cost when aspiration level as 1 would be the same with the upper bound solution of ITSP. At a certain aspiration risk level, the REITSP model can provide

CO2 emission (106 ton)

450

400

350

300 without RPS=10% RPS=15% RPS=17% without RPS=10% RPS=15% RPS=17% RPS RPS t=1

t=2 Lower

Upper

Fig. 5. CO2 emission under different RPS levels for high load demand scenario.

134

L. Ji et al. / Energy 131 (2017) 125e136

Total cost

Risk level

86

1 0.9 0.8

82

0.7

80

0.6 0.5

78

0.4

76

0.3 0.2

74

normalized risk level

Total cost (109 $)

84

0.1 0

72 0

0.1

0.2

0.3

0.4 0.5 0.6 Aspiration level

0.7

0.8

0.9

1

Fig. 6. Relationship between aspiration level, risk function and system cost.

Installed capacity (103 MW)

18

coal-fired

wind

14

10 0

0.1

0.2

0.3

0.4 0.5 0.6 Aspiration level

0.7

0.8

0.9

1

Fig. 7. New installed capacity of coal-fired and wind power units under different aspiration levels.

specific and executable strategies for capacity investment and electricity supply arrangement as shown in Figs. 7 and 8. In general, the pessimistic oriented decision making would require more local electricity generation. As the aspiration level increasing, the power generation capacity of traditional and renewable technologies would increase, such as the coal-fired and wind power units, in order to keep the regional electric power system secure operation and improve the ability of unknown risk prevention and control (Fig. 7). For example, the new installed capacity of coal-fired and wind power units would be 15.80  103 MW and 11.73  103 MW under the aspiration level fixed as 0, and 16.27  103 MW and 12.00  103 MW as the aspiration level increasing to 1.0. In addition, electricity generation performance and imported electricity under different aspiration levels are shown in Fig. 8. The purchased electricity would reduce with the increment of aspiration level. For instance, when the aspiration level is set as 0.1 and 0.9, the imported electricity would be 52.91  106 MWh and 51.27  106 MWh, respectively. While the power output of coal-

fired and solar power would increase with the increment of aspiration level. When the aspiration level is 0.1, the electricity output of coal-fired and solar power would be 422.33  106 MWh and 14.73  106 MWh. When it rises to 0.9, the corresponding output would be 423.72  106 MWh and 15.01  106 MWh, respectively. The performance of other generation units would not be affected by the risk preferences. The power output of nuclear, hydro and wind power would be 130.80  106 MWh, 69.69  106 MWh, and 28.87  106 MWh, respectively. With economic and social development slowing down, the generation expansion planning in Guangdong Province would be much less aggressive. Coal-fired power plant would still play a significant and dominant role in the power industry in near future. However, according to the forecasted future power demand growth, the capacity of coal-fired power plant would reach a temporary peak level by the end of 2020, and no extra coal-fired power plant construction would be required during the period of 2021e2025. Limited by local resources and construction speed, the

L. Ji et al. / Energy 131 (2017) 125e136

135

800 14.85

14.89

14.94

14.98

15.01

15.01

15.01

423.72

14.81

423.72

14.77

423.14

14.73

422.93

14.69

106 MWh

600

400 423.72

423.57 0.7

0.8

hydro

wind

solar

51.27

0.6

51.27

51.27

51.45

coal-fired

0.5 λ nuclear

51.71

0.4

423.35

imported

0.3

51.96

0.2

52.21

52.45

0.1

52.68

0

52.91

53.14

0

422.72

422.52

422.33

422.14

200

0.9

1

Fig. 8. Electricity generation performance and imported electricity under various aspiration levels.

maximum available RPS level could be set as 17%, which would promote the renewable energy generation, increase the imported electricity requirement, and postpone the coal-fired power plant construction. During the planning horizon, the maximum CO2 emission reduction by implementing RPS policy could reach [25.04, 53.11]  106 tonne at the expense of total system cost. Compared the optimal results of ITSP model and REITSP model, it can be found that the optimal solutions of REITSP model with l as 0 and 1 are equal to the lower bound and upper bound of the interval solutions obtained from ITSP model, respectively. By adjusting the value of l from 0 to 1, the decision maker would gain less convention conservative planning strategy with less system cost but higher risk. The decision maker could fully make use of the depicted cost-risk curve to gain desired cost-risk tradeoff.

5. Conclusions This study developed a risk explicit interval two-stage stochastic programming model for long-term generation expansion planning with RPS target, and applied it in the electricity system of Guangdong Province, China. The results indicated that the maximum reasonable RPS for Guangdong Province during 2016e2025 should be 17% within the limitation of the environment resource exploiting speed. Wind power will have great potential for development in future. Higher RPS target could facilitate the development of solar power. As consequence, more aggressive RPS target could reduce the total CO2 emission and the reliance of imported electricity, but at greater system cost. In addition, the REILP framework provides the tradeoff between system cost and risk for decision maker when considering complex uncertain factors. It aims to provide the optimal strategy with both minimum system cost and risk according the risk tolerance of decision maker. During the practical decision making process, the crisp solutions provide by REITSP model are more explicit, efficient and enforceable. Therefore, it is a valuable and meaningful practice tool for long-term regional generation expansion planning with multiple complex uncertainties.

Acknowledgement The work is financial supported by National Natural Science Foundation of China (Grand No. 71603016 and 51609003) and Beijing Postdoctoral Research Foundation (Grand No. 2016ZZ-21). The authors would also like to thank the reviewers and editors for their constructive feedback on improving the manuscript. References [1] Ding N, Liu J, Yang J, Yang D. Comparative life cycle assessment of regional electricity supplies in China. Resour Conserv Recycl 2017;119:47e59. [2] Li FGN, Trutnevyte E. Investment appraisal of cost-optimal and near-optimal pathways for the UK electricity sector transition to 2050. Appl Energy 2017;189:89e109. [3] Farooq MK, Kumar S, Shrestha M. Energy, environmental and economic effects of renewable portfolio standards (RPS) in a developing country. Energy policy 2013;62:989e1001. [4] Walmsley MRW, Walmsley TG, Atkins MJ. Achieving 33% renewable electricity generation by 2020 in California. Energy 2015;92:260e9. [5] Wang T, Gong Y, Jiang C. A review on promoting share of renewable energy by green-trading mechanism in power system. Renew Sustain Energy Rev 2014;40:923e9. [6] Gitizadeh M, Kaji M, Aghaei J. Risk based multiobjective generation expansion planning considering renewable energy sources. Energy 2013;50:74e82. [7] Das I, Bhattacharya K, Canizares C. Optimal incentive design for targeted penetration of renewable energy sources. IEEE Trans Sustain Energy 2014;5(4):1213e25. [8] Xie K, Dong J, Singh C, Hu B. Optimal capacity and type planning of generating units in a bundled wind-thermal generation system. Appl Energy 2016;164: 200e10. [9] Qiu J, Yang H, Dong Z, Zhao JH, Meng K, Luo FJ, et al. A linear programming approach to expansion co-planning in gas and electricity markets. IEEE Trans Power Syst 2016;31(5):3594e606. [10] Jalali M, Zare K, Hagh MT. A multi-stage MINLP-based model for subtransmission system expansion planning considering the placement of DG units. Int J Electr Power & Energy Syst 2014;63:8e16. [11] Wierzbowski M, Lyzwa W, Musial I. MILP model for long-term energy mix planning with consideration of power system reserves. Appl Energy 2016;169:93e111. [12] Hemmati R, Saboori H, Jirdehi MA. Multistage generation expansion planning incorporating large scale energy storage systems and environmental pollution. Renew Energy 2016;97:636e45. [13] Aghaei J, Muttaqi KM, Azizivahed A, Gitizadeh M. Distribution expansion planning considering reliability and security of energy using modified PSO

136

L. Ji et al. / Energy 131 (2017) 125e136

(Particle Swarm Optimization) algorithm. Energy 2014;65:398e411. [14] Koltsaklis NE, Georgiadis MC. A multi-period, multi-regional generation expansion planning model incorporating unit commitment constraints. Appl Energy 2015;158:310e31. [15] Siddiqui AS, Tanaka M, Chen Y. Are targets for renewable portfolio standards too low? The impact of market structure on energy policy. Eur J Oper Res 2016;250:328e41. [16] Lu Z, Qi J, Wen B, Li X. A dynamic model for generation expansion planning based on conditional value-at-risk theory under low-carbon economy. Electr Power Syst Res 2016;141:363e71. [17] Soroudi A, Ehsan M. A distribution network expansion planning model considering distributed generation options and techo-economical issues. Energy 2010;35(8):3364e74. [18] Ganguly S, Sahoo NC, Das D. Multi-objective particle swarm optimization based on fuzzy-Pareto-dominance for possibilistic planning of electrical distribution systems incorporating distributed generation. Fuzzy Sets Syst 2013;213:47e73. €hndorf N. An empirical analysis of scenario generation methods for sto[19] Lo chastic optimization. Eur J Oper Res 2016;225(1):121e32. [20] Santos MJ, Ferreira P, Araújo M. A methodology to incorporate risk and uncertainty in electricity power planning. Energy 2016;115:1400e11. [21] Zhang X, Shahidehpour M, Alabdulwahab A, Abusorrah A. Hourly electricity demand response in the stochastic day-ahead scheduling of coordinated electricity and natural gas networks. IEEE Trans Power Syst 2016;31(1): 592e601. [22] Li CZ, Shi YM, Liu S, Zheng Z, Liu Y. Uncertain programming of building cooling heating and power (BCHP) system based on Monte-Carlo method. Energy Build 2010;42(9):1369e75. [23] Koltsaklis NE, Liu P, Georgiadis MC. An integrated stochastic multi-regional long-term energy planning model incorporating autonomous power systems and demand response. Energy 2015;82:865e88. [24] Li S, Coit DW, Felder F. Stochastic optimization for electric power generation expansion planning with discrete climate change scenarios. Electr Power Syst Res 2016;140:401e12. [25] Huang H, Li F, Mishra Y. Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation. IEEE Trans Smart Grid 2015;6(6):2704e13. [26] Bai L, Li F, Cui H, Jiang T, Sun H, Zhu J. Interval optimization based operating strategy for gas-electricity integrated energy systems considering demand response and wind uncertainty. Appl Energy 2016;167:270e9. [27] Ji L, Zhang XP, Huang GH, Yin JG. Development of an inexact risk-aversion optimization model for regional carbon constrained electricity system planning under uncertainty. Energy Convers Manag 2015;94:353e64. [28] Liu Y, Cai YP, Yang ZF, Tan Q, Lin X. Identification of optimal recourse strategies for power generation under a government-guided coal-pricing mechanism in north China. Int J Electr Power & Energy Syst 2016;79:210e27. [29] Jin SW, Li YP, Huang GH, Zhang K. Inexact mixed-integer programming with interval-valued membership function for sustainable power-generation

capacity planning. J Clean Prod 2016;122:52e66. [30] Zhou F, Huang GH, Chen GX, Guo HC. Enhanced interval linear programming. Eur J Oper Res 2009;199:323e33. [31] Zou R, Liu Y, Liu L, Guo H. REILP approach for uncertainty-based decision making in civil engineering. J Comput Civ Eng 2010;24(4):357e64. [32] Liu Y, Zou R, Guo H. Risk explicit interval linear programming model for uncertainty-based reduction optimization for the lake Qionghai watershed. J Water Resour Plan Manag 2010;137(1):83e91. [33] Zhang X, Huang K, Zou R, Liu Y, Yu Y. A risk explicit interval linear programming model for uncertainty-based environmental economic optimization in the Lake Fuxian Watershed, China. Sci World J 2013;2013(9):160e9. [34] Simic V, Dimitrijevic B. Risk explicit interval linear programming model for long-term planning of vehicle recycling in the EU legislative context under uncertainty. Resour Conserv Recycl 2013;73:197e210. [35] Simic V. Fuzzy risk explicit interval linear programming model for end-of-life vehicle recycling planning in the EU. Waste Manag 2015;35:265e82. [36] Ji L, Niu DX, Huang GH. An inexact two-stage stochastic robust programming for residential micro-gird management based on random demand. Energy 2014;67:186e99. [37] Huang GH, Loucks DP. An inexact two-stage stochastic programming model for water resources management under uncertainty. Civ Eng Environ Syst 2000;2(17):95e118. [38] Li YP, Huang GH. An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina. J Environ Manag 2006;3(81):188e209. [39] Huang GH, Beatz BW, Patry GG. A grey linear programming approach for municipal solid waste management planning under uncertainty. Civ Eng Syst 1992;9:319e35. [40] Huang GH, Beatz BW, Patry GG. Grey integer programming: an application to waste management planning under uncertainty. Eur J Oper Res 1995;83: 594e620. [41] Guangdong Provincial Statistic Bureau. Guangdong statistic yearbook 2014. 2015. [42] China electric power yearbook. China Electric Power Press; 2015. [43] Guangdong Power Grid Company. The 13th five year and mid-long term planning of power industry in Guangdong Province. 2014. [44] Li YF, Li YP, Huang GH, Chen X. Energy and environmental systems planning under uncertainty-an inexact fuzzy-stochastic programming approach. Appl Energy 2010;87(10):3189e211. [45] Ji L, Zhang XP, Huang GH, Yin JG. Development of an inexact risk-aversion optimization model for regional carbon constrained electricity system planning under uncertainty. Energy Convers Manag 2015;94:353e64. [46] Krishna Priya GS, Bandyopadhyay Santanu, Tan Raymand R. Power system planning with emission constraints: effects of CCS retrofitting. Process Saf Environ Prot 2014;92:447e55. [47] Lee MY, Hashim H. Modelling and optimization of CO2 abatement strategies. J Clean Prod 2014;71:40e7.