A robust approach for the interdependency analysis of integrated energy systems considering wind power uncertainty

Transcription

1 1 A robust approach for the interdependency analysis of integrated energy systems considering wind power uncertainty Martinez-Mares A. and Fuerte-Esquivel C.R. IEEE Transactions on Power Systems, vol. 28, no.4, November 2013, pp

2 Hydro Gas or CC Coal This paper reports a multi-energy network model suitable to assess how wind power uncertainties affect the economic and secure operation of a multi-energy system composed of natural gas, coal and electricity infrastructures, which are coupled at multiple nodes of the electricity network through thermal power plants.

3 ROBUST OPTIMIZATION A Robust Optimization Model is also proposed to generate an optimal solution that is immunized against the effect of wind power production uncertainty The approach assumes that the values of uncertainty parameters are known for a finite number of scenarios, each with its own probability of occurrence The discrete probability distribution Scenarios Wind Speed Probability 10% 10% 20% 50% 10% The key idea is to define the problem data, both deterministic and uncertain data, by a finite number of scenarios, each of which is a deterministic set containing one of the possible values for the uncertain data.

4 4 MULTI-ENERGY SYSTEM MODELING The state of each infrastructure is formulated for a time horizon corresponding to a single time period (snapshot) based on the nodal energy flows mismatch equations COAL SYSTEM Coal mass flow through railways from k to m Coal supplied by a mine-mouth at bus k Coal extracted by loads at bus k MC MC MC MC MC 0; k N km k k k, i co k r source load load mk MC MC MC kmin k kmax source source source

5 5 MULTI-ENERGY SYSTEM MODELING The locomotives energy consumption is computed based on the distance, weight and average train speed COAL SYSTEM The locomotives energy consumption EC l MC C K 1 r km 2 V km km km km km r r r r r r km km ln lr Diesel required by locomotives DR km r EC km r GHV d

6 6 MULTI-ENERGY SYSTEM MODELING The natural gas system is modeled as a nonlinear network composed of pipelines, compressors, sources and loads. GAS SYSTEM Gas flow in a pipeline from k to m Gas extracted by a compressor Gas extracted by load at bus k MG MG k m MG MG MG MG k N km km km k k k, i ng k p sgn c(, ) C C source load load 0 ; mk mk mk Gas flow in a compressor Gas supplied by from k to m a source at bus k MG MG MG kmin k kmax source source source

7 7 MULTI-ENERGY SYSTEM MODELING kv ELECTRICITY kv SYSTEM G G G 9 33 kv 2 G 3 1 kv kv G kv P P P P L 0, i N i i i km, i el i gen load cal comp Q Q Q Q 0, i N N i i i el el i gen load cal PV S S, S, S, S i i i i i gen gen, ng gen, co gen, hy gen, w

8 8 COUPLING BETWEEN INFRASTRUCTURES The coupling of infrastructures is modeled through the Heat Rate Curve, related to the conversion process of the thermal energy contained in the natural gas (or coal) into electrical energy supplied by each generator to the electric power system. HR P P k, i k k i k i gen gen P P, P i i i gen gen, ng gen, co 2 The fossil fuel quantity required for the energy demanded in the conversion process MG ki, load HR GHV ki, ng Typically 1015 BTU/SCF of natural gas 27.5 MBTU/ton of coal 33.4 MJ/litter of diesel Gross Heating Value MC ki, load HR GHV ki, co

9 Power Output COUPLING BETWEEN INFRASTRUCTURES Nominal water gross head for basin (m) h WR P P i rate i i i i i i gen, hy gen, hy h i Water gross head for basin (m) 2 The water resources available in each basin are delimited WR WR WR min max i i i P rate w s < w s rated P wind w s 3 w s > w s rated P wind = P rated Wind speed (m/s) wind p air rotor s Pwind aw bw ws cw ws dw ws ew ws P C A w 2 f w g w h w i w w s w s w s w s

10 ROBUST OPTIMIZATION min. f( x, ) s. t. h( x, ) 0 ; g ( x, ) 0 ; x x x The robust optimization counterpart is formulated by introducing a set of scenarios ={1,2,,S} over the wind speed uncertainty, and each scenario is a deterministic set with the probability of occurrence p s, p 1 s s The optimal solution is robust with respect to optimality if it remains close to the optimal solution of any scenario of the input data. feasibility if all constraints are satisfied for all possible values associated with the uncertain parameters. It is unlikely that the solution remains near optimal and feasible for all possible scenarios, such that a trade-off between solution and model robustness must be defined We introduce a function to control the variability in the optimal solution for all realizations of s

11 11 min ps s ps s p ' ' s s s s ' s 2 RO MODEL Robust objective function. The expected value of the objective function over all possible scenarios The variance of the objective function, weighted by a constant. A measure of the solution robustness, i.e. value of the objective function and its variance, is obtained by varying the penalty parameter s s s. t. h x,, 0; g x,, 0; x x x s s d u s d u x co MC r sr ng ng sources C x, BHP, MG ng s N N s N s N C C el el el el el sngen Ngen, w sn NPV sn 1 x P, V, el gen

12 12 Energy (gas, coal, electric power) flow mismatch equations s MC 0 ; k N k s MG 0 ; k N k co ng s P 0 ; k N k Q 0 ; k N N s el el k PV el Compressor s energy consumption and its compression ratio HP BHP Z ck 1 s, km s ck s, km s, km MGC T k c k m C C C N a 1 0 s ng EC C ck 1 k k N ng s m N s, km m RC Rkm 0 k m s k Inequality constraints to variables MC MC MC ; k N k, min s, k k, max co source source source sources MG MG MG ; k N k, min s, k k, max ng source source source sources

13 13 The energy system is composed of 15 nodes gas, 4 nodes coal and 118-nodes electricity networks STUDY CASE 1 The objective function for each scenario is defined as the total cost of fossil fuels injected by all natural gas and coal sources. NGsources CO N sources Railways k1 k1 k2 k2 k3 NG MG cost x source CO MC cost x source + DI cost x DRr k1=1 SCFH k2=1 Ton litter k3=1 The discrete probability distribution Scenarios Wind Speed Probability 10% 10% 20% 50% 10% The prices are : Diesel is 1 USD/liter, Natural gas is 4 USD/MSCF Coal is USD/Ton 13

14 Generated active power [pu] Cost [K USD] 14 OPF Cost Coal Wind Natural Gas Hydro An optimal power flow study is carried out for each wind speed scenario S1 S2 S3 S4 S5 Scenarios Cost per Scenario S 1 S 2 S 3 S 4 S 5 Expected Value Cost The cost and generation dispatch are in bars and solid lines, respectively The increment of active power produced by wind generators has a major impact on the total generation associated with coal-fired power plants There exists a dispersion of the operation cost between scenarios, which is about 30 KUSD between the first and last scenarios. The expected cost value was calculated considering the result of each scenario and its corresponding probability of occurrence

15 15 RO approach The study case is repeated considering different penalty factors, 0 Lambda 1, on the operation cost variance Robust Cost per Scenario s Total RO S Cost 1 S 2 S 3 S 4 S , , , , , , , , ,780 The robust operation cost of each scenario s and the total RO cost tend toward the same value as the penalization factor increases its value, which is the most expensive cost An uncertainty-immunized solution is obtained for all scenarios of wind speeds.

16 Active power in hydro-generators [pu] Std. deviation of hydro-power [pu] Active power in coal-generators [pu] Std. deviation of coal-fired power [pu] Active power in gas-generators [pu] Std. deviation of gas-fired power [pu] CO-S1 CO-S2 CO-S3 CO-S4 CO-S5 StdDev CO NG-S1 NG-S2 NG-S3 NG-S4 NG-S5 StdDev NG E+00 1.E-05 1.E-03 1.E-01 5.E-01 9.E E+00 1.E-05 1.E-03 1.E-01 5.E-01 9.E Active power and standard deviation of coal-fired units. Active power and standard deviation of gas-fired units HY-S1 HY-S2 HY-S3 HY-S4 HY-S5 StdDev HY When we select a low value for the penalization factor, thereby putting more weight on the total expected cost while we are less concerned about the cost variance, the balance in load-generation is attained through the most economic power generating schedule, which implies lower coal consumption E+00 1.E-05 1.E-03 1.E-01 5.E-01 9.E-01 Active power and standard deviation of hydroelectric units A higher value of lambda results in an increase in the active power dispatch of the most expensive generators, which means higher coal consumption

17 Active power in hydro-generators [pu] Std. deviation of hydro-power [pu] Active power in coal-generators [pu] Std. deviation of coal-fired power [pu] Active power in gas-generators [pu] Std. deviation of gas-fired power [pu] CO-S1 CO-S2 CO-S3 CO-S4 CO-S5 StdDev CO NG-S1 NG-S2 NG-S3 NG-S4 NG-S5 StdDev NG E+00 1.E-05 1.E-03 1.E-01 5.E-01 9.E E+00 1.E-05 1.E-03 1.E-01 5.E-01 9.E Active power and standard deviation of coal-fired units. Active power and standard deviation of gas-fired units HY-S1 HY-S2 HY-S3 HY-S4 HY-S5 StdDev HY The increment in the participation of coal-fired units provokes a reduction in the amount of active power supplied by the hydro and natural gas generation units E+00 1.E-05 1.E-03 1.E-01 5.E-01 9.E-01 Active power and standard deviation of hydroelectric units The higher penalty factor, the smaller dispersion in the operation cost and total coal-based power generation associated with the set of scenarios for wind speed.

18 18 STUDY CASE 2 The aim of this experiment is to attain a similar operation conditions for the natural gas system independently of the wind power generation Penalizing the variance in the natural gas consumed by gas-fired generators. The objective function is to minimize the cost fossil-fuel consumption by thermal power plants ip k k, i k k, i NG MGload CO MCload cost x cost x SCFH Ton gen, ng ipgen, co MG ki, load P GHV P 2 gen k k i k i gen ng min ip s p s s p NG MG p NG MG k s, k, i k s ', k, i s load s ' load cost x cost x i s SCFH s' SCFH gen, ng 2 Robust objective function.

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21 21 Nodal Pressure (PSI) λ=0.0 λ=0.001 λ=10 Node S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S Active power dispatch in gas-fired plants (pu) Electric Node S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S

22 22 CONCLUSIONS The RO formulation has been implemented to attain an optimal operating condition of the overall multi-energy system taking into account the uncertainties associated with the wind power generation. Numerical examples have been reported to illustrate how the economic and secure operation of the multi-energy system is optimized over all wind power scenarios.