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Generation Expansion Planning with High Penetration of Wind Power

  • Ishan Sharan EMAIL logo and R. Balasubramanian
Published/Copyright: July 23, 2016
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International Journal of Emerging Electric Power Systems
From the journal International Journal of Emerging Electric Power Systems Volume 17 Issue 4

Abstract

Worldwide thrust is being provided in generation of electricity from wind. Planning for the developmental needs of wind based power has to be consistent with the objective and basic framework of overall resource planning. The operational issues associated with the integration of wind power must be addressed at the planning stage. Lack of co-ordinated planning of wind turbine generators, conventional generating units and expansion of the transmission system may lead to curtailment of wind power due to transmission inadequacy or operational constraints. This paper presents a generation expansion planning model taking into account fuel transportation and power transmission constraints, while addressing the operational issues associated with the high penetration of wind power. For analyzing the operational issues, security constrained unit commitment algorithm is embedded in the integrated generation and transmission expansion planning model. The integrated generation and transmission expansion planning problem has been formulated as a mixed integer linear problem involving both binary and continuous variables in GAMS. The model has been applied to the expansion planning of a real system to illustrate the proposed approach.

Keywords: generation expansion planning; fuel transportation; wind based electricity generation; transmission expansion planning

Appendix 1

Modeling heat rate of thermal generating units

A thermal generating unit operates at different levels of power output between its minimum operating limit and maximum capacity. The fuel consumed by a thermal generating unit is a non-linear function of its power output. The fuel consumed by a thermal generating unit has been modeled as a function of the heat rate of the generating unit. For different levels of power output, the heat rate and hence the fuel consumed by a thermal generating unit will be different. The heat rate at lower values of power output will be high as compared to the heat rate at higher power output. A simplified representation of power output versus heat rate for a coal based generating unit is shown in Figure 1. For any thermal generating unit, different heat rate values have been assumed for different loading conditions say, for loading between 100 %–80 % of full load, the heat rate is hr4, for loading between 80 %–60 % of full load, the heat rate is hr3, where hr3 > hr4.

To model the heat rate curve in the minimization problem, binary variables are required [24]. Otherwise to keep the cost minimal, the optimization model will always assume the lowest value of heat rate for any value of power output. This is accomplished by the following constraints. For simplicity the suffix t has been dropped in the equations.

(2.27)P1×δ1≤Pg,hr1≤P1
(2.28)(P2−P1)×δ2≤Pg,hr2≤(P2−P1)×δ1
(2.29)(P3−P2)×δ3≤Pg,hr3≤(P3−P2)×δ2
(2.30)0≤Pg,hr4≤(P4−P3)×δ3

Pg,hr1, Pg,hr2, Pg,hr3 and Pg,hr4 are positive variables and δ1,δ2,δ3 are binary variables. The above constraints have to be satisfied by each thermal generating unit in every hour.

As δ1,δ2,δ3 are binary variables (having value of 0 or 1), from equations (2.27)–(2.30) it is evident that δ1=0 will force δ2 to zero. Similarly, δ2=0 will force δ3 to zero. δ2 can be 1 only when δ1 is equal to 1. Similarly δ3 can be 1 only when δ2 is equal to 1. There can be four different cases in the present modeling scenario as discussed below.

  • Case I: δ1=0,δ2=0,δ3=0

    0≤Pg,hr1≤P1,Pg,hr2=0,Pg,hr3=0,Pg,hr4=0;

  • Case II: δ1=1,δ2=0,δ3=0

    Pg,hr1=P1,Pg,hr2≤(P2−P1),Pg,hr3=0,Pg,hr4=0;

  • Case III: δ1=1,δ2=1,δ3=0

    Pg,hr1=P1,Pg,hr2=(P2−P1),Pg,hr3≤(P3−P2),Pg,hr4=0;

  • Case IV: δ1=1,δ2=1,δ3=1

    Pg,hr1=P1,Pg,hr2=(P2−P1),Pg,hr3=(P3−P2),Pg,hr4≤(P4−P3);

Dispatch of a thermal generating unit at any hour will be given by.

Pg,t=Pg,t,hr1+Pg,t,hr2+Pg,t,hr3+Pg,t,hr4

Additional constraint δ3≤δ2≤δ1 has also been added to the optimization model.

Appendix 2

Data of system considered for expansion planning

Table 14:

Data of generating units.

Generating unitLocated at busMaximum capacity (MW)Minimum operating limit (MW)Existing/ProposedFull load heat rate (kCal/kWh)Normative cost (million $/MW)Auxiliary power consumption (%)
coal11200120Existing2,5008
coal21200120Existing2,5008
coal31200120Existing2,5008
coal41500300Existing2,4258
coal51500300Existing2,4258
coal61500300Existing2,4258
coal71500300Existing2,4258
coal813500300Existing2,4258
coal913500300Existing2,4258
coal1017200120Existing2,5008
coal1117200120Existing2,5008
coal1217200120Existing2,5008
coal1317200120Existing2,5008
coal1445500300Existing2,4258
coal1556800400Proposed2,3000.86257.5
coal1656800400Proposed2,3000.86257.5
coal1717600300Proposed2,4250.757.5
coal1854800400Proposed2,3000.86257.5
coal1949800400Proposed2,3000.86257.5
coal2057500300Proposed2,4250.757.5
coal2157500300Proposed2,4250.757.5
coal2243500300Proposed2,4250.757.5
coal238500300Proposed2,4250.757.5
coal2410500300Proposed2,4250.757.5
coal2510500300Proposed2,4250.757.5
coal2658660330Proposed2,3000.86257.5
coal2758660330Proposed2,3000.86257.5
coal2858660330Proposed2,3000.86257.5
coal2958660330Proposed2,3000.86257.5
coal3058660330Proposed2,3000.86257.5
coal3154800400Proposed2,3000.86257.5
lignite132200120Existing2,7508
lignite232200120Existing2,7508
lignite332200120Existing2,7508
lignite432200120Existing2,7508
lignite540200120Existing2,7508
lignite640200120Existing2,7508
nuclear121200190Existing10
nuclear221200190Existing10
import151,000500Existing
import2302,000500Existing8
gast1–gast16gast29–gast45(gas engines)71,650 MW(each of 50 MW)Proposed2,0000.501
gast17–gast28(gas engines)55600 MW(each of 50 MW)Proposed2,0000.501
wind1412,000Existing
wind2372,000Existing
hydro116900Existing1
hydro259390Existing1
hydro359180Existing1
hydro460517Existing1
psp1 (pumped storage plant)37400Existing1
[1]

  1. Nuclear units have been treated as must run units with the cost of electricity generation as $ 8.4/MWh.

  2. The ramp rate of coal and lignite based generating units has been considered as 1 % (of its maximum capacity) per minute between minimum operating limit and maximum capacity. However, for the purpose of providing spinning reserve (USR/DSR), the ramp rate of 200 MW class of units has been considered as 2 MW/min, for 500 MW class of units it has been considered as 3 MW/min, for 600 MW class of units it has been considered as 3.6 MW/min, for 660 MW class of units it has been considered as 4 MW/min and for 800 MW class of units it has been considered as 4.8 MW/min. Hence, the maximum contribution towards USR/DSR from 200 MW class, 500 MW class, 600 MW class, 660 MW class and 800 MW class of coal based generating units would be 20 MW, 30 MW, 36 MW, 40 MW and 48 MW respectively.

Table 15:

Distance of coal and lignite based generating units from fuel source (km).

Generating unitf1 (Lignite Mine)f2 (Coal Mine)f3 (Coal Mine)f4 (Imported Coal)
coal150
coal250
coal350
coal450
coal550
coal650
coal750
coal8612
coal9612
coal105001,600
coal115001,600
coal125001,600
coal135001,600
coal14800
coal151,10020
coal161,10020
coal171,600
coal181,600
coal191,600
coal2020
cosl2120
coal22500
coal23900
coal241,300
coal251,300
coal2620
coal2720
coal2820
coal2920
coal3020
coal311,600
lignite140
lignite240
lignite340
lignite440
lignite540
lignite640
Table 16:

Fuel characteristics.

Fuel sourceCostHeat value
f1 (Lignite)$ 18/Ton2,700 kcal/kg
f2 (Domestic Coal)$ 22/Ton3,500 kcal/kg
f3 (Domestic Coal)$ 22/Ton3,500 kcal/kg
f4 (Imported Coal)$ 75/Ton5,300 kcal/kg
f5 (Natural Gas-Domestic)$ 238/thousand m39,000 kcal/m3
f6 (Natural Gas-Imported)$ 555/thousand m39,000 kcal/m3

  1. Fuel source f1 represents lignite mine. Fuel source f2 and f3 represent domestic coal mines. Fuel source f4 represents port at which imported coal is brought in the country. f5 represents domestic gas source and f6 represents LNG terminal.

  2. Cost of domestic coal and lignite given in Table 16 is the cost of fuel at mine (excluding transportation cost). Cost of imported coal is the landed cost at port. Cost of coal transportation through railways has been assumed to be $ 0.02/km/Ton.

  3. Cost of natural gas is the delivered cost, including the cost of transportation in pipeline.

  4. Coal to group of coal based units coal10–coal13 from coal mine f2 (which is closer to the generating units) has been restricted to 1.6 million tonnes per annum. Coal based units coal15 and coal 16 can get upto 70 % coal from coal mine f3 and balance 30 % coal has to be imported coal.

  5. Minimum up-time of coal and lignite based generating units has been considered as 10 hours and minimum down time has been considered as 2 hours.

Explanation of symbols used in the text

t: index for time period; g: index for thermal generating units; w: index for wind farms; c: index for thermal and hydro generating units; b: index for base load thermal generating units; q: index for fast response thermal and hydro generating units; ps: index for pumped storage plant; nuc: index for nuclear generating units; i−j,n: index for transmission line n between nodes i and j; ∗−j,n: index for transmission line n ending at node j; j−∗,n: index for transmission line n originating from node j; f: index for fuel source; f−g: index for fuel transportation route from fuel source f to thermal generating unit g; hr: index for heat rate of thermal generating unit; T: time period of study; NGE/NGN: set of existing/proposed thermal and hydro generating units in the system; NG: set of thermal and hydro generating units in the system (NGE+NGN); NGj: thermal and hydro generating units at node j; NB: set of base load thermal generating units in the system; NQ: set of fast response generating units (thermal+hydro) in the system; NT: set of thermal generating units in the system (base load+fast response); NW: set of wind farms in the system; NWj: wind farms located at node j; NS: set of pumped storage plants in the system; NSj: pumped storage plants located at node j; TLE/TLN: set of existing/proposed transmission lines; TL: set of transmission lines (TLE+TLN); FG: set of fuel transportation routes; NNUC: set of existing nuclear generating units in the system; NNUCj: nuclear generating units at node j; Cc: annualized cost of proposed generating unit c; Ci−j,n: annualized cost of proposed transmission line n between nodes i and j; Cf: per unit cost of fuel at source f; CFTf−g: per unit cost for unit distance fuel transportation from fuel source f to thermal generating unit g (in units of $/Ton/km for coal); df−g: distance of thermal generating unit g from fuel source f; calf: calorific value of fuel from fuel source f; SUCg: start-up cost of thermal generating unit g; SDCg: shut-down cost of thermal generating unit g; FAf: fuel availability at fuel source f (per annum); capf−g: fuel transportation limit (per annum) from fuel source f to thermal generating unit g; Pw,tforecast: forecasted wind power at time t; Pcmax: maximum capacity of generating unit c; Pcmin: minimum operating limit of generating unit c; aux(c): auxiliary power consumption (%) of generating unit c; RUc/RDc: ramp up/down rate of generating unit c for normal operation; RUcs/RDcs: ramp up/down rate of generating unit c for providing spinning reserve; SUb/SDb: start-up/shut-down ramp limit of base load thermal generating unit; τbup/τbdown: minimum up/down time of base load thermal generating unit; rq: percentage of fast response generating unit’s capacity available for reserve; hr1−hr4: heat rate of a thermal generating unit corresponding to different power output levels; Pd,j,t: electricity demand (forecasted value) at node j at time t; T10/T60: 10 minutes/60 minutes; Pi−j,nmax: limit on power flow in transmission line n between nodes i and j; γi−j,n: susceptance of transmission line n between nodes i and j; wu/wd: coefficients of up/down spinning reserve due to wind power uncertainty; Mi−j,n: “big M” value for proposed transmission line n between nodes i and j; K: penalty factor for curtailment of wind power (big number); K1: penalty factor for curtailment of electricity demand (big number);Er: electrical energy requirement; ℜ: discount rate; n′: operational life of generation/transmission schemes (years); Cnuc: electricity generation cost from nuclear generating units ($/MWh); Epsmax: maximum amount of energy (MWh) that can be stored in the upper reservoir of pumped storage plant; Ppsmax: maximum capacity of pumped storage plant; Pnucmax/Pnucmin: maximum/minimum operating limit of nuclear generating unit nuc; ηps: efficiency of the pumping cycle of the pumped storage plant. It is the ratio of energy put into storage (upper reservoir) to the energy taken from the power system; Eps0,Eps,1: energy available initially in the upper reservoir of pumped storage plant; Pw,t: wind power that can be absorbed in the system at time t; Pc,t: dispatch of generating unit c at time t; Pg,t,hr: dispatch of thermal generating unit g at time t corresponding to heat rate hr; Pc,tusr/Pc,tdsr: USR/DSR provided by generating unit c at time t; u(c,t): binary unit commitment variable for generating unit c at time t; y(c,t)/z(c,t): start-up/shut-down binary variable for generating unit c at time t; vc:binary decision variable for proposed (new) generating unit c; xi−j,n: binary decision variable for proposed transmission line n between nodes i and j; Pi−j,n,t: power flow in transmission line n between nodes i and j at time t; θi.t: voltage angle at node i at time t (in radians); USRt/DSRt: up/down spinning reserve requirement at time t; SRt: spinning reserve requirement at time t without considering wind generators; Pj,tlc: load curtailed at node j at time t; FTf−g,t,hr: fuel transported from fuel source f to thermal generating unit g at time t corresponding to heat rate hr; Pnuc,t: dispatch of nuclear generating unit nuc at time t; Eps,T: energy available in the upper reservoir of pumped storage plant at the end of optimization period; Eps,t: energy available during period t for electricity generation by the pumped storage plant; pum(ps,t): binary variable indicating whether the pumped storage plant is pumping water (1: pumping; 0: not pumping); Pps,tg: power generated (dispatch) by the pumped storage plant at time t; Pps,tp: power consumed by the pumped storage plant in pumping mode operation at time t.

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Published Online: 2016-7-23
Published in Print: 2016-8-1

©2016 by De Gruyter

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https://doi.org/10.1515/ijeeps-2015-0186
Keywords for this article
generation expansion planning; fuel transportation; wind based electricity generation; transmission expansion planning

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Control of Grid Connected Photovoltaic System Using Three-Level T-Type Inverter
  4. A New Method for Setting Calculation Sequence of Directional Relay Protection in Multi-Loop Networks
  5. Performance Analysis of SISFCL with the Variation of Circuit Parameters using Jiles Atherton Hysteresis Model
  6. Generation Expansion Planning with High Penetration of Wind Power
  7. Grid Integration of Single Stage Solar PV System using Three-level Voltage Source Converter
  8. Extraction and Analysis of Inter-area Oscillation Using Improved Multi-signal Matrix Pencil Algorithm Based on Data Reduction in Power System
  9. A New Control Method to Mitigate Power Fluctuations for Grid Integrated PV/Wind Hybrid Power System Using Ultracapacitors
  10. Comparative Analysis of Instruments Measuring Time Varying Harmonics
  11. Application of Energy Function as a Measure of Error in the Numerical Solution for Online Transient Stability Assessment
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