Hydrothermal Coordination Considering Wind and ... - IEEE Xplore

2015 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT LATAM)

Hydrothermal Coordination Considering Wind and Pumping Storage Unit in the Colombian Smart Grid Mar´ıa Victoria Ram´ırez, Antonio Hernando Escobar, Alejandro Garces Universidad Tecnol´ogica de Pereira, Colombia Email: [email protected]

Abstract—In this paper we describe an algorithm that involves linear programming (an exact optimization technique) and Monte Carlo Simulation for solving the middle-termed hydrothermal coordination. The proposed model considers uncertainties of wind and hydrology, as well as the effect of pump storage hydro-power units.

I. Introduction Contemporary power energy systems face major challenges such as providing less contaminating and more reliable and controllable mechanisms and technologies. As never before has humanity faced such a challenging outlook for energy and the planet. This can be summed up in five words: more energy, less carbon dioxide [1]. In order to tackle such challenges, renewable energy technologies like wind generators are highly increasing in the last decade, specially in countries such as China, United States, United Kingdom and Sweden [2]. Latin America should turn its eyes towards these new alternative resources as well.In order to integrate wind generation in a power grid, it is necessary to implement smart grids in the power systems. Smart grids aim to make more efficient electrical systems, to minimize costs and environmental impacts, while reliability and stability of the system are maximized. The energy storage systems are some of the components of smart grids that provide control mechanisms, as is the case of pump storage units (PSU). They represent a safeguard against shortages and rising energy cost and lessen the effect of stochastic uncertainty derived from variations of wind speed and hydrology. Maximization of wind power by using PSU is explored in [3]. Although literature on methods for solving problems of hydro generation dispatch considering energy storage as the PSU has been published, it is insufficient. Literature addresses the influence of PSU in hydrothermal systems [4] or in hydraulic and wind systems [5]. Wind and

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pumped hydro storage is studied by using knowledge gradient non-parametric estimation in [6]. In previous work, the authors present results of various wind power penetration scenarios in a hydrothermal system [7] that showed considerable reduction of operating cost of the wind-hydrothermal system; also the impact of energy reserves of water storage were explored in [8]. This paper presents an analysis of the stochastic effect of inflows and wind in the operating cost of a hydrothermal system, in a scenario of wind penetration, introducing the the PSU, as a smart grid element. What is new in this proposal is taking into account simultaneously two aspects: the uncertainty of two variables: wind speed and water inflows and the energy storage element, in a middle-termed hydrothermal dispatch, combining an exact technique with Monte Carlo simulation. The cost of fuel varies at each time period and its values are known, taking into account two technologies: coal and combined cycle gas. A test system with two thermal plants, three hydraulic (one of which will act as a pumping storage unit) and a wind farm that can operate continuously in the planning horizon of 12 months is used. Wind generation is modeled by the Weibull distribution function, while hydro generation is modeled by normal probability functions (NPF). Coal

Gas

H1

H2

H3 (PSU)

T1

T2

W

Fig. 1. Single node model for the Colombian wind-hydrothermal system.

The Colombian electrical grid is of hydrothermal type, which is highly dependent of climate phenomena such as El Ni˜ no (dry season) and La Ni˜ na (wet season). The

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hydrothermal coordination in the Colombian case is an indicative planning for being a market-based system. The wind component of generation in the country is very low (only 0.12%), but in the coming years, wind power penetration is being considered in expansion planning [10]. Therefore, changes are required that include energy storage in the dispatch, and pump storage unit is the best alternative at such levels of voltage and power. Fig. 1 condenses the Colombian wind-hydrothermal system as modeled in this research. The thermal power generation is concentrated in the Northern coast in two kinds of technology: coal plants (T1) and combined cycle gas plants (T2) that represent the 29.79%; the hydro generation, in the Andean region (H1, H2, H3), represents 69.59%, and the wind-generation in Guajira peninsula, represents 0.12%. Total power capacity installed of the country is approximately 15.48 GW , nevertheless the mean power value is about 9 GW . Behaviour of the Colombian demand is illustrated in Fig. 2. Net Declared Capacity vs Maximum Power Demand (MW), 2014

nct X

s.t.

gti,t +

i=1

(4)

ghnch,t ≤ gmaxhnch,t

(5)

ghnch,t = ρnch,t · unch,t

(6)

uminnch ≤ unch,t ≤ umaxnch

(7)

vnch,t ≤ vmaxnch

(8)

vnch,12 = vfnch

(9)

0

dt = dt − gwt

crt grt cvt snch,t

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Fig. 2. 2014.

Maximum power demand

dt gtnct,t ghnch,t gmaxtnct,t

Declared net capacity vs Maximum power demand M W ,

gmaxhnch,t

II. Mathematical Model vnch,t unch,t

Our solution is based on an optimization linear model for hydrothermal coordination[9] that minimizes an objective function consisting of two terms: operating cost of thermal plants and non supplied load cost. Subject to a set of constraints. The mathematical formulation of the HTD is:

ρnct,t umaxnch uminnch vmaxnch anch,t vfnch gwt 0 dt

A. Hydrothermal Dispatch

M in

cost =

nct X t X i=1 j=1

costij · gti,j +

t X j=1

crj · grj (1)

(10)

Each equation orderly represents:(1)Objective function: consists of minimization of the operating cost of thermal plants and the cost of non supplied load; the constraints: (2)power balance equation; (3)water balance; (4)thermal power plant operating limits; (5)hydro power plant operating limits; (6)hydro generation; (7)hydro plant discharge limits; (8)hydro plant storage limits; (9)final reservoir storage and (10)stochastic demand [11]. Note

5,000

Net declared capacity

(2)

i=1

gtnct,t ≤ gmaxtnct,t

10,000

15,000

0

ghk,t + grt = dt

vnch,t = vnch,t−1 + anch,t − unch,t − snch,t (3)

Nomenclature: t nct nch costnct,t

20,000

nch X

Number of time periods Number of thermal plants Number of hydro plants Operation cost of thermal plant nct at period t Penalty cost for non supplied electricity at period t Fictitious generator at period t Cost of water spillage at period t Water spillage of hydro plant nch at period t Load demand at period t Thermal generation of plant nct at period t Hydro generation of plant nch at period t Maximum power of thermal plant nct at period t Maximum power of hydro plant nch at period t Volume of the hydro plant nch at period t Water discharge of hydro plant nch at period t Water discharge rate of hydro plant nch at period t Maximum water discharge of hydro plant nch Minimum water discharge of hydro plant nch Maximum volume of hydro plant nch at period t Water inflow of hydro plant nch at period t Final reservoir storage of hydro plant nch Wind generation at period t Stochastic demand at period t

that we have made the following assumptions: The PSU is included into the model as a hydraulic plant with possibility of negative and positive discharge, which means that energy stored by the pumping process is

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transformed into power, without any losses . Effect of the transmission line is neglected (single node analysis). Cost of water and wind for hydro and wind generators equals zero. B. Wind Farm Wind’s stochastic behaviour is modeled by the Weibull distribution function. The random values of wind that feed the Monte Carlo simulation are obtained from the cumulative value of this function. The density distribution function and the cumulative distribution function are defined in Equation (11) and Equation (12): x α α x (11) f (x) = ( )α−1 e−( β ) β β x α F (x) = 1 − e−( β ) (12)

calculated from Equation 14. Rated power is 5 M W and rated speed of the wind generator is 12[m/s]. Cp =

1 Pw = N ρCp Av 3 2

2 8.99 7.98 8 8.48 8.03

3 8.68 8.02 9 6.67 6.41

4 16.68 7.59 10 5.27 5.79

5 9.53 7.62 11 7.35 6.01

6 18.79 8.16 12 8.82 6.76

Fig. 3 depicts the Weibull PDF for January, April and December. The highest point of the curve for January corresponds to a density of 0.37.

(15)

The parameters of the wind farm are summarised in table II. Each term represents: N : number of turbines; ρ: air density [kg/m3 ]; Cp : rotor efficiency factor; A: turbine area [m2 ]; Pr : rated power [KW ] and D: turbine diameter [m]. Assuming N equals to 200 means that the total power TABLE II Parameters of wind farm. N 200

TABLE I Form (α) and scale (β) factors of the wind farm. 1 7.55 7.62 7 15.04 8.45

(14)

Wind power is calculated from the Equation 15:

Where α is the scale factor, β is the form factor and x is the wind speed [12]. In table I, the values for these factors, for each month of the year, are shown [13].

month α β month α β

2Pr ρAvr3

ρ 1.2

Cp 0.43

A π( D )2 2

Pr 5

D 120

capacity of wind power is 1,000 M W , signifying 18.8% of total hydrothermal capacity of the test system. C. Water Inflows The uncertainty of the water inflows in the hydro plants is modeled by normal distribution functions, according to equation (16): f (x) = √

1 x−µ 2 1 e− 2 ( λ ) 2πλ

(16)

Density

Where µ is the mean value and λ, the standard deviation. Equation (17) is the random variable (wind speed) with certain probability of occurrence [15]. x = F −1 (u) (17) Total water inflow is divided into three hydro plants H1, Wind speed [m/s]

Fig. 3.

TABLE III Colombian water inflow montly-added, 2012, in %

Weibull Probability Distribution Functions. January December April

The cumulative distribution function has values between zero and one. A random value in this range corresponds to a value of the cumulative function u. The wind value is derived from Equation 13, from known values of α and β for the correspondent month. 1 1 x = β( )α (13) ln u The wind value generated is used to calculate the wind power to install [14], where Cp is the rotor efficiency

P eriod a P eriod a

1 60.48 7 65.34

2 51.87 8 66.23

3 44.07 9 69.22

4 46.23 10 71.8

5 51.69 11 80.63

6 57.21 12 79.21

H2 and H3 in percentages of 48.32%, 24.16% y 27.52%, respectively, as seen in table IV. Table V shows the parameters of the Normal Distribution Function (NDF) for each of the hydro generation plants and Fig. 4, their Density Distribution Functions.

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TABLE IV Water inflow values of hydro plants in [m3 /s]. Period 1 2 3 4 5 6 7 8 9 10 11 12

aH1 466.08 399.73 399.62 356.26 398.34 404.88 503.53 510.39 533.43 553.31 621.36 610.42

aH2 233.04 199.86 169.81 178.73 199.17 220.44 251.76 255.19 266.72 276.66 310.68 305.21

aH3 265.54 227.74 193.49 202.98 226.95 287.18 286.88 290.79 303.91 315.24 354.01 347.77

TABLE V Parameters of the NDF. Plant µ λ

H1 479.78 89.147

H2 238.94 46.76

H3 275.21 53.081

TABLE VI Monthly average demand, 2012, in [M W ]. Per d Per d

1

2

3

4

5

6

4800.91

4631.42

5033.86

4724.69

5032.71

4893.7

7

8

9

10

11

12

5033.98

5104.31

5024.61

5069.53

4979.62

5034.27

F. Modeling of fuel cost The operating costs of thermal plants is given in M U (Monetary Units) per megawatt-month, are based on stock market prices of fuels (gas and coal), published by UPME (Unidad de Planeamiento Minero Energ´etica de Colombia) - The Mining and Energy Planning Unit of Colombia). For purposes of study in this work, the rationing costs cr are calculated by multiplying rationing penalty cost of the more expensive thermal plant in each period, by a factor of 10. In the current case, the cost of water (hydro-turbines) and the cost of wind (wind-turbines) are assumed equal to zero. Data are summarized (in months) in table VII. TABLE VII Costs of fuel and rationing in [M U ] .

Density

Period 1 2 3 4 5 6 7 8 9 10 11 12

Water inflows [m³/s] H1

Fig. 4.

H2

H3

Probability density functions of water inflows.

costT 1 54.22 78.47 119.82 57.5 47.02 87.38 78.83 139.28 183.64 200.21 166.29 181.39

costT 2 109.125 110.69 114.54 150 113.58 113.325 113.1 115.65 111.625 103.825 101.85 98.575

cr 1091.25 1106.9 1198.2 1500 1135.8 1133.25 1131 1392.8 1836.4 2002.1 1662.9 1813.9

D. Monte Carlo Simulation This method consists of performing multiple experiments with the mathematical model, ie evaluate different values of the random variables of the real problem under consideration [16]. The steps of the algorithm are: a) selecting the random input variables (wind speed and inflows), b) generating a probability value xij , defined by its inverse transfer function, c) evaluating the output variable d) evaluating the convergence criterion, which in this case is the maximum iteration number (10,000).

G. Parameters of the system Parameters of the reservoirs such as initial volume, final volume and maximum volume of hydro plants are shown in table VIII. In table IX the discharge factor TABLE VIII Initial volume, final reservoir storage and hydro plants’ maximum storage limits, in [Hm3 ] . P lant H1 H2 H3

vo 2416 1208 1376

vf 2415.955 1207.9765 1375.99

vmax 4848.39 2424.20 2761.33

E. Modeling of demand The average demand in each period of time is based on UPME’s projections for 2012, shown in table VI.

and maximum discharge values for each hydroplant are presented.

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TABLE IX Discharge factor and maximum discharge of hydrogenerators. P lant H1 H2 H3(PSU)

f to

umax

M W/[m3 /s]

[m3 /s]

1 1 1

2,000 1,000 1,376(-1,376)

capacity. Table X contains the outputs of the five power plants, without the effects of: wind penetration, the PSU and incertanties of hydrology , at each period of time (month). The cost in this deterministic case is 1,648,350 U M . When only stochastic wind effect is taken into TABLE X Hydro and thermal generation without wind nor PSU effects, in [M W ].

III. Solution Technique

Period 1 2 3 4 5 6 7 8 9 10 11 12

Dispatch Parameters

Probabilistic model

Water Inflows

Linear programming CPLEX

Histograms

• Cost • Hydro power • Thermal power

Fig. 5.

gh1 2000.00 2000.00 1612.25 1446.21 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00

gh2 1000.00 969.02 964.01 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00

gh3 138.51 0.00 795.20 1139.47 370.31 231.30 441.91 167.70 1139.47 1139.47 1139.47 1139.47

gt1 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 222.74 267.66 177.75 232.40

gt2 662.40 662.40 662.40 139.01 662.40 662.40 662.40 662.40 662.40 662.40 662.40 662.40

account (hydrology remains fixed and no PSU effect is introduced) the histogram of cost is as shown in Fig. 6.

Implementation of the interface AMPL-Matlab.

Our solution is a hybrid methodology that combines an exact optimization technique (linear programming) to solve the hydrothermal dispatch and a stochastic algorithm that includes the effect of two random variables: wind power served and water inflows. In each iteration, the stochastic algorithm obtains the random value o both water inflow (hydrology) and wind power for every period of the planning term (12 months). The wind power is subtracted from the demand (negative demand) that is treated as a parameter of the system. Subsequently, the PL algorithm calculates the values of the output variables: hydro and thermal generation as well as the operating cost. This is done by the Monte Carlo Simulation along 10,000 iterations. Results are summarized and presented in histograms of cost. The implementation of the algorithm was done through an interface between Matlab and AMPL. The probabilistic part of the algorithm is run in Matlab that generates values of wind power and water inflows that enter the exact technique as parameters. Matlab calls AMPL’s routine to run the linear programming by using the solver CPLEX. The process is illustrated in Fig. 5. IV. Results The total hydrothermal capacity in the test system is 5,501.81 M W . A wind power penetration of 1,000 M W is assumed, that represents 18.18 % of the hydrothermal

Fig. 6.

Histogram of cost with wind effect.

In this case, the cost is located in the range between 1,200,000 and 1,230,000, in the 72.8% of the Monte Carlo iterations. For the highest frequency this means a cost drop of 27%. Table XI shows the results for power generation of the five plants H1, H2, H3(PSU), T1 and T2, at each period of time (month) in one specific iteration, with the purpose of illustrating the effect of the PSU, that is not perceptible in the histogram. The negative values (periods 1 and 7 of H3(PSU)) correspond to the periods in which the PSU is pumping water from the reservoir located at a lower altitude to the reservoir at a higher altitude. This water is stored as gravitational energy to be fed into the grid during periods of peak demand. Note that negative values only appeared in H3, since this is the PSU and accomplishes two functions: pumping(negative generation) and storage (positive generation). The total cost of power is 950,742

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M U . Fig. 7 shows the cost of energy, including the TABLE XI Hydro and thermal generation including wind and PSU effects, in [M W ]. Period 1 2 3 4 5 6 7 8 9 10 11 12

gh1 0.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00 2000.00

gh2 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00

gh3−P SU -26.27 51.56 1139.47 612.00 632.94 662.24 -63.85 1135.47 867.04 940.96 895.58 1138.51

gt1 0.00 1000.00 0.00 1000.00 1000.00 1000.00 1000.00 0.00 0.00 0.00 0.00 0.00

gt2 662.40 662.40 537.59 0.00 246.21 662.40 662.40 662.40 662.40 662.40 662.40 662.40

effects of wind energy and the PSU. The highest level of occurrence is at the cost of 935,000 M U . The cost reduction compared to the deterministic case is up to 43.47%. It should be kept in mind that this result could occur in the highest frequency of occurance, 29.2% of the times. Moreover, the cost could be in a range between 905,000 and 965,000 U M with frequency of occurance of 73.5%.

Fig. 7.

Histogram of cost with wind and PSU effects.

V. Conclusions A methodology suitable for solving the hydrothermal coordination that considers stochastic effects was developed. Two stochastic variables were considered: wind speed and water inflows. A test system that takes into account some particular features of the Colombian power system was designed. The proposed methodology which combines Monte Carlo simulation and mathematical optimization proved to be proper to solve the hydrothermal coordination under uncertainties. Simulation results on a equivalent model of the Colombian system show that operating cost decreases up to 27% of the total cost, when considering the effect the stochastic model for wind power and water inflows.

The Colombian electric power system requires storage elements such PSU, if wind power is integrated to the grid. Smart grids planning in Colombia should include wind generation. Comparison between a deterministic model and our methodology (that adds the effects of wind power penetration (18.8%), uncertainties in wind generation and hydrology, as well as the PSU) may lead to cost savings up to 43.27%. References [1] Shell, Shell energy sceneries to 2050. Shell International B.V., 2008. [2] Global Wind Energy Council, Global Wind Report. Annual market update 2012. pg. 8, 2013. [3] M. A. Hozouri, M. Fotuhi-Firuzabad and M. Moeini-Aghtaie, On the use of pumped storage for wind energy maximization in transmission-constrained power systems. Transactions on Power Systems,vol.30, pp. 1017–1025, 2015. [4] A. E. Neshad, M. S. Javadi and E. Rahimi, Applying augmented e-constraint approach and lexicographic optimization to solve multi-objective hydrothermal generation scheduling considering the impacts of pumped-storage units. Elsevier. Electrical Power and Energy Systems, vol. 55, pp. 195-204, 2013. [5] T. Malakar, S. K. Goswami and A. K. Sinha, Optimum scheduling of micro grid connected wind-pumped storage hydro plant in a frequency based pricing environment. Elsevier. Electrical Power and Energy Systems, vol. 54, pp. 341-351, 2013. [6] C. Schoppe, Wind and pumped-hydro power storage: determining optimal commitment policies with knowledge gradient non-parametric estimation. MS. thesis, 2010. [7] S. Ramos, M. V. Ram´ırez and A. Garc´ es, Impact of wind power in middle termed hydrothermal dispatch. Rev. Fac. Ing. Univ. Antioquia, no.73 , pp. 214-224, 2014. [8] A. M. Mart´ınez, M. V. Ram´ırez, S. Botero and A. H. Escobar, Impact of aspects related to hydrology and storage in the annual ´ hydrothermal dispatch. Rev. Epsilon. Univ. de La Salle, no.73, pp. 59-81, 2013. [9] R. W. Jim´ enez and V. L. Paucar, Long term hydrothermal scheduling linear programming model for large scale power systems. Power Engineering , Large Engineering Systems Conference, pp. 96-10, 2007. [10] Unidad de Planeamiento Minero Energ´ etica, Plan de expansi´ on de referencia. Generaci´ on Transmisi´ on 2014-2028. pp. 139–410, 2014. [11] I. A. Isaac, J. M. Areiza, J. W. Gonzalez and H. Biechl, Long-term energetic analysis for electric expansion planning under high wind power penetration scenarios in Colombia and neighboring countries. Energy Market (EEM), 2010 7th International Conference on the European, pp.1–7, June 2010. [12] J. F. Manwell, J. G. McGowan and A. L. Rogers, Wind energy explained: theory, design and application. University of Massachusetts, John Willey & Sons. England, pp. 57-59, 2002. [13] Ministerio de Minas y Energ´ıa de Colombia, Atlas del viento y energ´ıa e´ olica de Colombia. pp. 146, 2006. [14] M.R. Patel, Wind and solar power systems: Design, analysis and operation. Taylor & Francis Group, 1999. [15] J. C. Canavos, Probabilidad y estad´ıstica. Aplicaciones y m´ etodos. pp. 111–130, 1998. [16] A. Garc´ es and O. G´ omez, Soluci´ on del problema del despacho hidrot´ ermico mediante simulaci´ on de Monte Carlo y punto interior. Revista Facultad de Ingenier´ıa de la Universidad de Antioquia, no.45, pp. 132-147, 2008.

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