Power System Economic Dispatch with Spatio-temporal Wind Forecasts

Le Xie*, Yingzhong Gu*, Xinxin Zhut, and Marc G. Gentont

*Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA Email: Lxie@ece.tamu.edu, gyzdmgqy@tamu.edu

tDepartment of Statistics, Texas A&M University, College Station, TX, USA Email: {xzhu,genton}@stat.tamu.edu

Abstract-In this paper spatio-temporal wind forecast is incor­porated in power system economic dispatch models. Compared to most existing power system dispatch models, the proposed formulation takes into account both spatial and temporal wind power correlations. This in turn leads to an overall more cost­effective scheduling of system-wide wind generation portfolios. The potential economic benefits are manifested in the system­wide generation cost savings, as well as the ancillary service cost savings. We illustrate in a modified IEEE 24 bus system that the overall generation cost can be reduced by 12.7% by using spatio­temporal wind forecasts compared with only using a persistent forecast model.

I. INTRODUCTION

This paper is motivated by the fact that renewable wind energy is increasingly being integrated into electric power systems throughout the world [1] [2]. By 2010 several regions in the US as well as around the globe have already achieved more than 10% wind installed capacity [3] [4]. Compared to conventional fossil fuel generation, wind generation exhibits limited predictability and high inter-temporal variations (i.e., ramping) [5]. In order to fully extract the environmental and economic potential of renewable energy resources, novel power system operating paradigm is needed to reduce the balancing and ancillary service burden on by fast responsive fossil fuel units [6].

The basic objective of power system scheduling is to maintain the supply and demand balance at a minimum cost subject to transmission constraints and plausible contingencies. Before high penetration of renewable energy such as wind and solar, the uncertainty in power system scheduling primarily comes from the demand side [5]. With the high presence of intermittent wind power, the uncertainty now comes from both demand and supply (wind and solar) sides. Load forecasting has been an active area of research for more than four decades. State-of-the-art load forecasts could achieve high accuracy in the day-ahead stage. In contrast to load forecasting, variable wind generation is very hard to be accurately predicted at 24-36 hours ahead, which is typically based on the physical weather model [7]. Only near term (lO-minute to 2 hours ahead) prediction is of acceptable confidence. The short-term forecast is usually based on statistical models, a good set of references can be found in [8]-[11].

The main subject of this paper is to exploit a novel economic dispatch model by leveraging short-term spatio-

978-1-4577-0776-6/11/$26.00 ©2011 IEEE

temporal wind forecast information for regions with high wind penetration. Wind generation is driven by wind patterns, which tend to follow certain geographical spatial correlations. For large regions of wind farms, the wind generation forecast in the downstream of wind could significantly benefit from the upstream wind power generation. Enabled by the technological advances in communications, spatially correlated wind data could be leveraged for higher system-wide short-term wind forecasts. This is potentially very applicable to large-scale wind farms, e.g., offshore wind generation.

Starting from our recent work on look-ahead dispatch, which utilizes inter-temporal wind forecasts in economic dispatch [15], we proposed in this paper a first attempt to incorporate both spatial and temporal wind forecasts in power system dispatch. In summary, the main contribution of this paper is twofold:

1) We propose to use a spatio-temporal correlated forecast model for short-term wind generation in a region. This forecast model takes into account both local and nearby wind farms' historical data. This method is tested with realistic wind data, and has shown improved forecast accuracy.

2) We formulate an economic dispatch model which incor­porates the spatio-temporal wind forecast information. Numerical study in a modified IEEE 24-bus test system shows the improved economic benefits compared to both static economic dispatch and look-ahead dynamic dispatch.

This paper is organized as follows. In Section II we propose an economic dispatch model which incorporates available short-term spatio-temporal wind power forecast data. The detailed wind forecast method is discussed in Section III, in which both spatial and temporal historical wind data is utilized for improved forecast accuracy. An illustrative power system economic dispatch example is presented in Section IV, which quantifies the potential savings in both generation cost and ancillary services in the proposed dispatch model. Concluding remarks and future work are discussed in Section V.

II . ECONOMIC DISPATCH MODEL WITH

SPATIO-TEMPOR AL WIND FOREC AST

In this section we formulate the power system economic dispatch problem considering both spatially and temporally

G D W T n

CGi CWi CRi pk G· pk w· pk D· pt P�Q' Fk

Fmax .6.t

pRMP •

TABLE I NOTATIONS

Set of conventional power plants

Set of inelastic loads

Set of wind farms

MPC window size (look-ahead horizon)

number of wind farms installed in system

Generation cost function of power plant i Generation cost function of wind farm i Reserve cost function of power plant i Scheduled generation of power plant i at time k Scheduled generation of wind farm i at time k Forecasted load level of bus i at time k Scheduled reserve capacity of power plant i at time k Scheduled regulation capacity of power plant i at time k Vector of branch flow at time k Vector of transmission line limits

Energy Market scheduling interval

Ramping constraints of power plant i Pa.in, Pa·ax Minimax generation limit for unit i Pwin, pwax Minimax generation limit for wind farm i

pk w· Forecasted wind availability for wind farm i at time k Pw The vector of forecasted wind availability

Pw The vector of historical wind data

correlated wind forecast. The notations are summarized in Table I. With spatio-temporal wind forecast, the economic dispatch model is presented as follows:

s.t.

T

min: L [ LCGi(P8J + L CWi(P�J

iEG

k=ko iEG iEW + L CR8i(P�8J + CR9i(P�9J]

iEG

iEW iED

iEG LP�9i � Rg(aD,aw,PLS) (3) iEG

IFkl � Fmax, k = ko, ... , T (4)

1P8i - p��ll � piRD..T, i E G U W, k = ko, ... , T (5)

pe;in � P8i � Pe;ax, k = ko, ... , T (6)

o � pti � Pe;ax, k = ko, ... , T (7)

o � P�9i � Pe;ax, k = ko, ... , T (8)

pe;in � P8i + pti + P�9i � Pe;ax, k = ko, ... , T (9)

Pwiin � P�i � PWiax, k = ko, ... , T (10) k Ak PWi � PWi' k = ko, ... , T (11)

Pw = f(Pw). (12) In the proposed formulation, the objective function is to

mInImIZe the power system operating costs which include costs of generation and costs of providing reserve services. Constraints of this problem are system and individual units operating constraints for security and reliability purposes. (1) is the energy balance equations, requiring the generated energy to be always equal to the energy consumed in steady state. (2) is the system reserve requirement. (3) is the system regulation requirement balancing equation. Given the system reliability requirement, the wind forecast accuracy and load forecast ac­curacy, the functions used to determine the reserve requirement and regulation requirement of the system are assumed to be linear. (4) is the transmission line capacity limitation, which contributes to network transmission congestion. (5) is the ramping constraints of units. (6) is the upper bound and lower bound of conventional generators' output. (7) is the available reserve capacity constraints. (8) is the available regulation capacity. (9) is the capacity constraints of each generator for providing energy reserve and regulation services. (10) is the mechanical upper and lower constraints of wind farms' output. In our study, wind resources are assumed to not participate into ancillary services market such as reserve and regulation markets. (11) is the wind forecast for each wind farm, which is regarded as the nature availability for each wind farm at specific times. (12) is the spatial and temporal correlation between historical wind data and wind forecast data, which will be explained in detail in section III.

III. SPATIO-TEMPOR AL WIND SPEED FORECASTING

In this section, we focus on wind speed forecasting, which is a hot topic due to the large scale penetration of wind energy. In [11], some statistical models for short-term wind speed forecasting were reviewed, including conventional time series forecasting models and spatio-temporal forecasting models. In our case, we illustrate equation (12) in detail with a wind speed dataset from three locations in the northwest of the U.S .. Based on the dataset, the short-term future wind speed at each location is forecast with two models: persistent forecasting (PSS) and a trigonometric direction diurnal (TDD) model [9] which takes the spatio-temporal information into the forecasting model. And then wind forecasts are converted into wind power with a certain power curve.

Specifically, 10 minutes average wind speed and wind direction data from 2002 and 2003 were collected from three meteorological towers along the Columbia River Gorge at the boundary of Washington (WA) to the south and Oregon (OR) to the north in Northwest U.S.: Vansycle (OR), Kennewick (WA) and Goodnoe Hills (WA). Vansycle is close to the Stateline wind energy center; Kennewick is 39 kIn northwest of Vansycle; and Goodnoe Hills is located 146 km west of Vansycle. Missing data were imputed with the method mentioned in [17].

Wind speed in this area mainly blows from west or east due to its special geographic features. The Columbia River Gorge runs from east to west passaging through the Cascade Mountains, with high terrain in the north and south and this condition results in west wind or east wind. Therefore, wind

speed at these three locations are correlated with each other, and to predict near future wind speed at one of the three locations, spatial correlation should be considered in addition to correlation with historical wind speed observations of itself. This can be seen in Fig. I in which auto-correlations and cross-correlations or spatial correlations of the three locations up to time lag 40 min. with 2003 data are displayed. Auto­correlations at each location are strong. Auto-correlation co­efficients are larger than 0.7 up to 40 min. lag. And cross­correlation coefficients are also significantly large. All the values are around 0.6 up to 40 min. lag.

First, we aim at forecasting k min. ahead wind speed at Vansycie, Kennewick and Goodnoe Hills respectively, based on the 10 min. average wind speed and wind direction data, with k = 10, ... ,120, or 10 min. to 2 hours, and a time horizon 24 hours is of interest. In the following, persistent forecasting and a most recent space-time forecasting model will be applied after being briefly introduced.

�

��

.; 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

Lag Lag Lag K , V K , G

.; ,q , .

� -40 -30 -20 -10 0 0 10 20 30 40 0 10 20 30 40

Lag Lag Lag

G , K

�

��

.; -40 -30 -20 -10 0 -40 -30 -20 -10 0 0 10 20 30 40

Lag Lag Lag

Fig. I. Auto-correlations and cross-correlations of 10 min. wind speed at Vansycle (V), Kennewick (K) and Goodnoe Hills (G).

A. Persistent Forecasting

PSS assumes the future wind speed is the same as the current one. For example, if vt is wind speed at time t at Vansycie, then k min. future wind speed is predicted as vt, or Vt+k = vt. PSS works very well for short-term forecasting, such as 10 min. due to the nature of wind.

PSS is usually taken as a reference and an advanced forecasting model is thought to be good if it outperforms PSS.

B. Trigonometric Direction Diurnal Model

The TDD model proposed by [9] is one of the most ad­vanced current space-time statistical forecasting models which generalizes the Regime-Switching Space-Time model [17] by taking wind direction into the model. We describe the TDD model with 10 min. ahead wind speed forecasting at Vansycie as an example.

Let vt, Kt, and Ct be 10 min. average wind speed at Vansy­cie, Kennewick and Goodnoe Hills at time t, and forecast vt+l, or 1 step ahead (10 min. ahead) wind speed. The TDD model assumes vt+l follows a truncated normal distribution on the nonnegative real domain, that is vt+l rv N+(f-Lt+l, at+l) (this can be detected by the density plots in Fig. 2), with center parameter f-Lt+l and scale parameter at+l. The key lies in modeling these two parameters appropriately.

Vansycle Kennewick Goodnoe Hills

� � .; .; � .; 0

.; �

0 0 0

Z � �

� .; , 10 15 20 " 30 0 , 10 15 20 " 30 0 , 10 15 20 " 30

Fig. 2. Density plot of 10 min. wind speed at Vansycle (V), Kennewick (K) and Goodnoe Hills (G).

The center parameter f-Lt+l is modeled as

f-Lt+l = Dt+1 + f-Lr+l' where Dt+l is made of trigonometric functions to fit the diurnal pattern of wind speed. Specifically,

Ds =do + d1 sin (2�S) + d2 cos (2�S) + d3 sin (�:S) + d4 cos (�:S),

where s = 1,2, ... ,24. The residual series after removing the diurnal pattern, f-Lr+l'

is modeled as a linear function of current and past (up to time lag h) wind speed and trigonometric functions of wind direction at Vansycie, as well as Kennewick and Goodnoe Hills as follows:

f-Lr+l =f (vt, ... , Vt;': __ h,K[, ... ,K[_h' K[, ... ,Cr-h, cos(eV,t), sin(eV,t),·· ., cos(eV,t_h), sin(eV,t_h) cos(eK,t), sin(eK,t),···, coS(eK,t_h), sin(eK,t_h) cos(eC,t), sin(eC,t),···, cos(eC,t_h), sin(eC,t_h)) '

(13)

where eV,t is wind direction at Vansycie at time t and Vt, K[, Cr, ev t' ex t' and ec t are residual series of wind speed and wi�d dir�ction at th� three locations without diurnal component.

The scale parameter at+l is modeled as

where bo, b1 > 0 and Vt is the volatility value: 1

v - (� '" ((v:r _ v:r )2 + (Kr _ Kr )2 t - 6 � t-i t-i-l t-i t-i-l i=O

) 1/2 + (Cr-i - Cr_i_l)2) .

(14)

The coefficients in (13) along with bo, b1 in (14) are estimated by the continuous ranked probability score (CRPS) method, see [18] for more details. Predictors in (13) are selected with the Bayesian Information Criteria (BIC), see [9] for details. This linear model is trained by data in 2002 with a 45 days sliding window, and for different k values, the models' structure are different, since different predictors would be selected into the linear equation. For example, for k = 5, table II displays correlation coefficients between 50 min. ahead wind speed at Vansycle and other variables at current time and up to past 40 min .. Numbers in bold indicate variables that are selected into the linear equation (13) for k = 5 at Vansycle.

Variable V cos(Ov) sin(Ov) K COS(OK) sin(OK) G cos(Oa) sin(Oa)

TABLE II CORRELATION COEFFICIENTS

t t -I t -2 t -3 0.99 0.98 0.97 0.96

-0.55 -0.24 -0.55 -0.24 -0.23 -0.55 -0.23 -0.55 0.78 0.78 0.78 0.78

-0.57 -0. 19 -0.57 -0. 19 -0.19 -0.57 -0. 18 -0.57 0.60 0.60 0.6 1 0.6 1

-0.29 -0.50 -0.29 -0.50 -0.50 -0.29 -0.50 -0.29

t -4 0.95

-0.55 -0.22 0.78

-0.57 -0. 18 0.6 1

-0.29 -0.50

So far, the predictive distribution N+(ILt+!, O't+l) is esti­mated, and here we take the median of the truncated normal distribution as wind speed forecast, which is defined as

Z02 = ILt+! + O't+1 . <I>-1 [1/2 + (1/2)<I>( -ILt+1)/O't+1],

where <I>( . ) is the cumulative distribution function of a standard normal distribution.

C. Results

Wind speed forecasting results of the TDD model are transfered to wind power based on a particular manufacturer's power curve [12]. The results are compared with PSS based on the Mean Absolute Error (MAE) on 2003 data. For example, each hourly average wind speed during one day at Vansycle is predicted with 60 step ahead forecasting based on the TDD model and PSS, denoted by ft, t = 60,120, ... ,1440 and lit-I, while the true values are lit. Then the MAE for the TDD model is 214 (lit - ft)2 and 21 4 (lit - lIt_l)2 for PSS. Forecasting results for 1 and 2 hour ahead are compared in table III for July 7, 2003.

TABLE III MEAN ABSOLUTE ERROR OF WIND POWER FORECAS TS

Locations Vansycle Kennewick Goodnoe Hills

Models PSS TDD PSS TDD PSS TDD 1 hr ahead 203.3 175.3 237.0 207.0 247.2 220.4 2 hr ahead 370.4 258.9 377.4 326.4 32 1.6 239.3

IV. ILLUSTRATI VE EXA MPLE

In this section, details of simulation platform setup, illus­trative examples, simulation results and analysis are provided.

A. Simulation Platform Setup

The power grid of the Columbia River Basin where Vansy­cle (OR), Kennewick (WA) and Goodnoe Hills (WA) are located, are operated by Bonneville Power Administration (BPA). BPA is a self-funded non-profit agency which mar­kets wholesale electrical power in the northwest area [13]. Modified from the IEEE Reliability Test System (RTS-24), the simulation system of 4000 MW total installed capacity is configured according to the practical characteristics of BPA. The simulation system network is presented in Fig. 3.

Fig. 3. System Network Diagram

The generators are assigned as different kinds of power sources including hydropower, coal power, wind power, nat­ural gas power and nuclear power. The generator capacity portfolio (installed capacity percentage of different technolo­gies) is configured according to the generation portfolio of the practical BPA system [13].

The load profile is scaled from the historical load profile of the BPA system [14]. Simulation duration is 24 hours. Both energy balancing market and ancillary market including reserve market and regulation market are simulated. The market operating interval is set to be 10 minutes for both energy balancing market and ancillary market. Wind profile of 24 hours are collected and scaled from BPA System [17]. As is shown in Fig. 4, wind generation potentials at the three locations are respectively calculated according to the manufacturer's power curve. Wind energy which is over the maximum generation capability of wind turbines has been curtailed for security purpose. One hour ahead forecast data is used as the inputs of the established simulation system. The size of the MPC optimization window T is 6 (I hour).

The generator parameters are factored out and modified ac­cording to [16]. Ramping rates and marginal costs are applied as is shown in Table IV. Bus number, type, capacity (Cap), marginal cost (MC), and ramp rate (RP) of each generator are listed. The computation environment is in Matlab 2009 under a PC Windows 7 system.

B. Market Results Analysis

According to the results of the simulation system, the TDD model can increase the actual wind resources utilization, reduce system-wide generation cost, system ancillary services (including regulation and reserve services) cost, and the total system operating cost.

120

i �

100

:! c 80 J!! 0 Q. c 60 0 :;:: I!! ., c 40 ., Cl ." C � 20

Bus I 2 7 13 14 15 16 18 2 1 22 23

Time Sample (1 Omins)

Fig. 4. The Wind Generation Potential

TABLE IV GENERATORS CONFIGURATION

Type Cap (MW) MC ($/MWh) Hydro 400 6 Coal 200 37 Coal 350 35

Wind(GH) \00 3 Nuclear 1 10 2 1 Hydro 700 5 Hydro 650 3.7

Natural Gas 500 79 Hydro 800 3.5

Wind(VS) 1 10 2 Wind(KW) 80 I

RP (p.u.lmin) 0.08

0.008 1 0.0085

0. 1 0.004 0.074 0.059 0.05 1 0.08 1 0.05

0.094

The results of the electrical power system operating and power market are listed in Table V.

TABLE V SYS TEM OPERATING RES ULTS

TOO PSS PSSITOO

Total system cost $ 1,094,235 $ 1,233,353 12.7%

Generation cost $526,309 $535,2 19 1.7%

Reserve cost $278,4 12 $336,434 20.8%

Regulation cost $289,5 12 $36 1,699 25.0%

Ancillary Services $567,925 $698,133 23.0%

Total wind generation 3,098 MWh 2,764 MWh 89.2%

It can be observed in Table V that the system-wide wind generation using the TDD model is 12.1 % higher than using the PSS model. Given the same wind pressure pattern and system load pattern, the TDD model enables a higher wind resources utilization and a higher wind generation ratio than other technologies. This is because the increased accuracy of the TDD model decreases the wind resources which are going to be wasted by underestimation of wind generation potential in forecast. And therefore, a lower generation cost (1.7%) can be achieved with more wind resources utilized than conventional resources such as coal and natural gas.

In Fig. 5, the actual wind generation output at Goodnoe

100

c 80 � I!! ., c ., 60 Cl ." C � iii 40

� c(

20

I--TD� PS&- .:... AvailabilitYI

20 40 60 80 100 120 140 Time Samle (10 mins)

Fig. 5. Actual Wind Generation at Goodnoe Hills

Hills is presented. The MAE value of actual wind generation output by using the TDD model is 220.4 while the MAE value of actual wind generation output by using the PSS model is 247.2. A lower MAE value indicate a lower forecast error (or average wind forecast deviation). And hence, wind forecast produced by the TDD model is more accurate than the PSS model.

It can also be observed that due to the better wind forecast quality of the TDD model, less underestimation of wind potential is introduced. The energy generated by a wind farm in Goodnoe Hills by using the TDD model is much higher (44%) than the wind energy generated by using the PSS model.

Besides, the improvement of wind forecast quality in the TDD model will also reduce the uncertainty of wind gen­eration scheduling. A lower mean absolute error (MAE), or average wind deviation between forecast value and actual value, applies on the simulation day for the TDD model (201.0), which is compared with the PSS model (229.2). It can be verified in Table V that the lower uncertainty of wind generation scheduling costs less in power system ancillary services (decreased by 23.0%) including reserve (decreased by 20.8%) and regulation services (decreased by 25.0%).

The system overall reserve requirement takes account of uncertainty in both wind generation uncertainty (or wind forecast errors) and load level uncertainty (or load forecast errors). The selected reserve capacity is used to compensate the energy imbalance within time frame of half an hour to 2 hours. In Fig. 6, the total system reserve requirement is compared between using the TDD model for wind forecast and the PSS model for wind forecast. It can be observed that by using the TDD model, due to the improved forecast accuracy, the overall reserve requirement can be reduced.

Regulation services also help to compensate the energy imbalance of the system in order to keep the system frequency within a secure range. Different from reserve services, regula­tion capacity is used to smooth out the short-time (l min. to 10 mins) frequency fluctuation and energy imbalance. It can

450 ·FPsSI � � 400 .................. .

� C 350 .. � 300 .:; <T 250 � � 200 .. � 150 ii 100 -0 ... 50

O+-�-+�--��-r�--r-���-;--��

i" !. C " E i!? -:; g-" 0: c 0 1; -:; CI " 0:

� ...

o 20 40 60 80 100 120 140 Time Sample (10 mins)

Fig. 6. Total System Reserve Service Requirement

280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140

Time Sample (10 mins)

Fig. 7. Total System Regulation Service Requirement

be seen from Fig. 7, the TDD model can decrease the system requirement for regulation services and therefore reduce the corresponding regulation cost.

Because of the reduction in both energy balancing market (total generation cost) and ancillary services market by using the TDD model, the total system operating cost has been reduced by 12.7% compared with using the PSS modeL

V. CONCLUSIONS

In this paper, we incorporated a spatio-temporal wind forecast model (TDD model) in power system economic dispatch. Compared with conventional temporal-only wind forecast models such as the PSS model, the TDD model considers both the local and geographically correlated wind farms for wind forecast. By leveraging both temporal and spatial wind historical data, more accurate wind forecasts can be obtained. We illustrated the potential economic benefits of more accurate wind forecast in a modified IEEE RTS 24 bus system. It was observed that the TDD model can increase the wind resources utilization, and reduce the system costs in both

energy balancing and ancillary services. In our future work, we plan to investigate the potential

applicability of the proposed dispatch model to large-scale wind farms such as offshore wind farms. Given the more consistent wind pattern over larger geographical area, the potential benefits of the proposed method could be higher. An­other important direction for future research is to analyze the tradeoff between communication/computation burden and the improved economic benefits by incorporating more spatially correlated wind data into power system dispatch models.

ACKNOWLEDGEMENTS

The work of the first two authors was supported in part by Texas Engineering Experiment Station and National Science Foundation ECCS Grant #1029873. The work of the last two authors was supported in part by NSF Grant DMS-1007504.

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