IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 2, MAY 2010
685
Reliability Evaluation Considering Wind and Hydro Power Coordination
Rajesh Karki, Senior Member, IEEE, Po Hu, and Roy Billinton, Life Fellow, IEEE
Abstract—Wind energy application in electric power systems continues to increase globally. The contribution of wind farms to the overall system reliability is limited by the uncertainty in power output from these highly variable energy sources. The ability of a power system to absorb available wind energy and maintain the system reliability and stability is reduced as the wind penetration in the system is increased. It therefore becomes important to coordinate the operation of wind power with fast responding conventional generating units. Hydro facilities with energy storage capability can alleviate the impact of wind power fluctuations and also contribute to system adequacy. A methodology for an energy limited hydro plant and wind farm coordination is developed using a Monte Carlo simulation technique considering the chronological variation in the wind, water and the energy demand. The IEEE four-state model is incorporated in the developed technique to recognize the intermittent operation of hydro units. The proposed approach is applied to the IEEE-RTS, and quantitative assessment of reliability benefits from effective utilization of wind and water resources are conducted through a range of studies. The effects of major system parameters on the system adequacy are also investigated. Index Terms—Hydro power, Monte Carlo simulation, power system reliability, wind power.
, ,
Cut-in, rated, and cut-out wind speed of a wind turbine generator. Mean time to failure. Mean time to repair. Average reserve shut down time between periods of need. Average in service time per occasion of demand. Probability of starting failure. Water in-flow in a period, and a simulated year is divided into 13 periods. Volume of water in-flow at the th hour. Volume of water spilled at the th hour. Volume of water in the reservoir at the th hour. Volume of water utilized to generate electricity at the th hour. Volume of water in the reservoir at the th hour before the spillage of extra water.
NOMENCLATURE Time series value at time . and Auto regressive and moving average parameters of the model, respectively. A normal white noise process with zero mean and a variance of . Variance of the normal white noise process. Simulated wind speed at the th hour. and Historical hourly mean wind speed and standard deviation, respectively. Power output from a wind turbine generator when the wind speed is . Rated power output of a wind turbine generator.
Manuscript received June 09, 2009; revised August 12, 2009. First published November 10, 2009; current version published April 21, 2010. Paper no. TPWRS-00437-2009. The authors are with the Power System Research Group, Department of Electrical and Computer Engineering, University of Saskatchewan. Saskatoon, SK S7N 5A9, Canada (email: rajesh.karki@usask.ca; po.hu@usask.ca; roy.billinton@usask.ca). Digital Object Identifier 10.1109/TPWRS.2009.2032758
, Maximum and minimum reservoir volumes, respectively.
Net head of the water reservoir at the th hour.
Hydro reservoir model coefficients. Number of hydro units operated to supply the system load. Power output from a hydro unit. Gravitational constant. Overall efficiency of a hydro unit. Hydro turbine discharge rate. Specific weight of water. Opening area of the guide for each hydro turbine. Power output from a wind farm at the th hour. Power output from conventional generating units at the th hour. Coordination criterion. Rated capacity of a wind farm. Number of hydro units required to coordinate with wind power.
0885-8950/$26.00 ? 2009 IEEE
686
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 2, MAY 2010
Total number of hydro units. Number of hydro units assigned to coordinate with wind power that can be brought in the service state.
Power output from a hydro unit coordinated with wind power at the th hour.
Number of peaking hydro units. Power output from a peaking hydro unit at the th hour. System load at the th hour. Total system power output at the th hour. Wind power dispatch restriction in percentage of the system load. I. INTRODUCTION
Portfolio Standard (RPS) in North America, Fixed Feed-inTariffs in Germany, Denmark, and Spain [1], and the Renewable Obligation in the U.K. [2] to promote renewable energy have established significantly high wind power penetra-tion targets. Wind intermittency may impede the integration of wind power as wind power penetration levels have increased in many countries [3]. System operators responsible for in-tegrating large wind farms have concerns about the system’s ability to absorb available wind energy and simultaneously maintain reliability. The amount of wind energy that can be absorbed by an electric power system can be greatly limited if the available conventional units are not able to respond quickly to the changes created by wind power fluctuations. Hydro power stations with a reservoir have an ability to change their power output quickly and act as an energy storage facility to store water during high wind periods, and increase output when
I
MPLEMENTATION of policies such as the Renew-able
and hydro generation pumping equipment is described in [15]. Wind power is interconnected to the grid and the hydro power is used as a backup option to compensate for the wind power fluctuations in a context of a global energy balance in [16]. Eco-nomic benefits for the integrated operation of large scale wind power plants with existing hydropower plants are investigated in [17]. The goals of coordinating wind and hydro power op-eration in these studies [13]–[17] are to maximize wind energy utilization, minimize wind curtailment due to transmission con-gestions, maximize economic operational profit, and to main-tain energy balance and system stability. The objective of these studies is mainly to evaluate the economic benefit from such co-ordination. The impacts of wind and hydro power coordination on the system adequacy have not been considered in previous studies. A Monte Carlo simulation (MCS) technique is developed in this paper to incorporate the coordination of wind power and an energy limited hydro system in a generating capacity ade-quacy assessment. The model developed in this paper is appli-cable to hydro systems of different storage capabilities, but not to pumped storage type systems. The four-state model [18] de-veloped by the IEEE Subcommittee on the Application of Prob-ability Methods is utilized to model hydro units that are intermit-tently operated in response to wind generation. The IEEE-RTS [19] is used as the test system. An energy-limited hydro system model presented in [20] is extended in this paper, and additional data on hydro plant characteristics, such as water in-flow, reser-voir volume, turbine discharge rates are used in the studies. A range of studies are conducted to investigate the reliability ben-efit of wind power coordinated with energy limited hydro units. II. PROPOSED TECHNIQUE The main focus in generating capacity adequacy evaluation is to assess the risk associated with the ability of the generating facilities to satisfy the system load demand. The generation system includes thermal, hydro, and wind turbine generator (WTG) units in this paper. A thermal unit is represented by a two-state Markov model [21]. A hydro unit is represented by the four-state model [18], in which the unit is brought into service only when required by the system. If hydro units start successfully when needed by the system, the power output depends on the hydro conditions during that instance. The power output from a WTG unit is determined by the wind regime at the wind farm location, and the WTG characteristics. Forced outage rates (FOR) of WTG units are not considered as they have in-significant impact on the overall system adequacy [7]. The load model is a chronological hourly load profile. The available system reserve margin in a given time interval is the difference between the available system capacity and the load. A negative margin indicates a load loss situation. System relia-bility indices, such as the loss of load expectation (LOLE), and the loss of energy expectation (LOEE) [21], can be calculated by simulating the available system reserve profile over a suf-ficiently long period of time. System simulations for long term adequacy studies are generally done using hourly time intervals. During each time interval, the state of the system is assumed to be constant, and all system changes occur at the beginning of the time intervals.
wind power goes down. There has been significant work on large scale integration of wind power into power systems [4], [5]. The system reliability concerns associated with the rapid growth of wind power in power systems, and the impact of variable nature of wind generation on power system adequacy has been reported in [6] and [7]. Reliability performance assessment of generating sys-tems including wind power and energy storage is presented in [8]–[11]. The coordination between wind farm and hydro power sta-tion has been explored in [12]–[17]. Most researchers agree that the value of wind and hydropower could be mutually enhanced by working together to produce a stable supply of electricity [12]. A planning algorithm is presented in [13] for a multi-reser-voir hydropower system coordinated with wind power to min-imize wind curtailment due to transmission congestions. The long term economic viability of the operation of a wind farm cooperating with two water reservoirs, involving a micro-hy-droelectric power plant and a water pump station is investigated in [14]. An hourly discretized optimization algorithm to iden-tify the optimum daily operational strategy for wind turbines
KARKI et al.: RELIABILITY EVALUATION CONSIDERING WIND AND HYDRO POWER COORDINATION
687
The simulation models for a wind farm and a hydro power plant are separately presented in Sections II-A and II-B, respectively. The detailed simulation process incorporating the coordination between wind and hydro plants is presented in Sections II-C. A. Wind Power Modeling The sequential simulation of a wind energy conversion system (WECS) involves the generation of hourly wind speeds over a sufficiently long period of time for a given site. It has been shown that any stationary stochastic system can be approximated as closely as required by a time series auto-regressive moving average (ARMA) model of order [22]. Reference [23] provides an approach for fitting time series wind speed models. Time series ARMA wind speed models developed using this approach can reproduce the high-order auto-correlation, the seasonal and diurnal distribution of the actual wind speed and therefore can be used in reliability studies of power systems including WECS. Wind speeds for a selected wind farm are simulated using the site-specific ARMA model mathematically expressed in (1):
Fig. 1. IEEE four-state model.
(1) where is the time series value at time , and are the auto regressive and moving average parameters of the model, respectively. is a normal white noise process with zero mean and a variance of (i.e., ), where NID denotes normally independently distributed. The ARMA model for swift current (SC) wind regime is given in (2). Historical wind speed data for the site were obtained from Environment Canada. Swift current lies in the southern part of Saskatchewan province in Canada, and has an average wind speed of 5.6 m/s. The wind regime at this location is used in the wind farm studies presented in this paper:
where and are historical hourly mean wind speed and stan-dard deviation, respectively, for the wind site. The hourly wind speed obtained from the time series model is used with (4), shown at the bottom of the page, to determine the available power output from a WTG [24]. The symbols , and stand for the cut-in, rated and cut-out wind speed, respectively. is the rated power of a WTG. The constants A, B, C are determined by , and [24]. Each WTG is exposed to the same wind regime character-ized by the geographic location, and provides the same power output within a time interval. The power outputs of the indi-vidual WTG are aggregated to obtain the total wind farm output at each time interval. B. Hydro Plant Modeling Hydro units assigned as peaking units operate for relatively short periods and are frequently started and interrupted. The IEEE Subcommittee on the Application of Probability Methods proposed the four-state model for peaking units. This model includes the reserve shutdown and forced out but not needed states, and is shown in Fig. 1. The proposed method represents hydro units by the IEEE fourstate model in order to recognize the ability of hydro units to quickly start and stop in response to the system requirements considering the system conditions and operating constraints. The status of hydro units during each hour is simulated consid-ering the system load level, the power output from other conven-tional units and the wind farm, and the energy limitation due to water availability and reservoir capacity. After determining the status of hydro units, the power output from hydro units in State 1 in Fig. 1 is determined by water conditions in the reser-voir. T and D parameters shown in Fig. 1 are required when the four-state model is used in an analytical method. In a MCS approach, the transitions between the State 0 and State 1, and
(2)
The wind speed using (3):
at hour “ ” can then be simulated
(3)
(4)
688
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 2, MAY 2010
TABLE I MEAN VALUE OF WATER IN-FLOW
water volume in the reservoir at th hour before the spillage of extra water; maximum reservoir volume; volume of the water utilized to generate electricity during th hour; volume of the water spilled during th hour. The net head of the hydro plant at hour is then calculated by the following approximate (9) when is greater than the minimum reservoir volume : (9) where and are model coefficients. Peaking hydro units are not in service when the power output from other generating units in the system, such as WTG and thermal units, is sufficient to meet the system load. In this condition, water can be stored in the reservoir. If the power output from other generating units is inadequate, an appropriate number of hydro units is operated to supply the load. The power output from a hydro unit can be obtained using (10) and (11): (10) (11) where gravitational constant in ;
between the State 2 and State 3 are simulated chronologically based on the demand placed on the hydro units to meet the load or to balance the wind power fluctuations as described in the five steps in the next subsection. The potential energy in water stored in a reservoir is transformed into electrical energy by means of hydro turbines and generators. The input energy is associated with water in-flow to the reservoir, and the output energy with the electricity generation. The water in-flow mainly comes from rainfall, which depends on the weather conditions. Three types of weather con-ditions are considered in a year: wet, dry, and normal. Each type of weather condition has the same probability of occur-rence, and is randomly chosen during a simulation. The hydro plant model and water in-flow model in [20] are extended in this paper to incorporate wind power model, fourstate gener-ation unit model and to include various operating constraints for wind and hydro coordination. It is assumed that the water in-flow has a normal distribution, and the value of is obtained using the Box and Muller method [25]. A year is divided into 13 periods in this paper. Each pe-riod consists of 672 h with the same weather condition. The mean values of water in-flow data in each period are shown in the next section in Table I, and the standard deviation about the corresponding mean value is 5%. The hourly water in-flow into the reservoir can be obtained using (5):
overall efficiency of the hydro unit equal to 0.8; turbine discharge rate, with minimum and maximum limitations of 10.6 and , respectively; specific weight of water equal to ;
opening area of the guide for each hydro turbine, and has a maximum limit of . The volume of the water calculated using (12): utilized in the th hour can be
(5)
The water spilled and water volume in the reservoir the th hour are calculated at the beginning of this hour using at
(12)
(6)–(8):
where
C. Simulation of Wind and Hydro Power Coordination The main purpose of coordinating hydro plant operation with wind fluctuations is to maximize the utilization of renewable re(6) sources while maintaining the system stability and security. The coordination can however have significant impact on the system (7) adequacy. Utilizing wind energy to allow accumulation of water for peak hour usage can increase system adequacy, whereas, (8) using up water to balance wind power fluctuations can decrease system adequacy. The overall impact of wind and hydro coordination on system adequacy, therefore, requires a comprehensive
KARKI et al.: RELIABILITY EVALUATION CONSIDERING WIND AND HYDRO POWER COORDINATION
689
model that can incorporate the constraints associated with the coordinated operation of the wind and hydro systems. The presented method considers energy limitations in the hydro reservoir while implementing the four-state model described in Fig. 1. A number of hydro units are assigned to operate in coordination with wind power to offset the power imbalance caused by wind fluctuation, and the rest are assigned as peaking units in this study. If the power output from the wind farm is less than a specified value termed as the coordination criterion, the hydro units assigned to coordinate with wind power are responsible for providing the required support. The simulation process and the calculation of the system adequacy indices are described in the following steps. Step 1) Determine the power output time series from the wind farm using the ARMA wind speed model for the selected wind regime and power curve technique. Step 2) Calculate the power output time series for the conventional generating units represented by two-state models. Step 3) A coordination criterion (F), which is a percentage of the rated wind farm capacity , is applied to decide the need for hydro units to support wind generation. F is taken close to the capacity factor of the wind farm in this study, since this is the longterm average power output from the wind farm. The number of hydro units required to coordinate with wind power is k, where . M is the total number of hydro units. As hydro units can be on forced outage, the number of hydro units that can be brought in the “In service” state in a time interval is less than or equal to k. If , all the hydro units that are assigned to coordinate with wind power are required to provide their support. If , no support from hydro units is required. The relationship between k and is shown in (13):
available to reduce the loss of load when :
(15) The power output from a peaking hydro unit is calculated using (16), and the upper bound for is shown in (17) as there is limitation in water usage as earlier described:
(16) (17) After calculating the power output from the wind farm, the base units and the hydro units during each time interval, the total system power output is calculated using (18):
(18) Step 5)is compared with the system load for each time interval to determine if a loss of load situation exists. The loss of load and the loss of energy is computed using (19) and (20), respectively:
(19) (20) The reliability indices LOLE, LOEE, Average Water used to produce Electricity (AWE), Average Water Spilled (AWS), and Average Volume of reservoir (AVolume) for a number of sample years (N) are obtained using (21) to (25), respectively:
(13) The power output from a hydro unit coordinated with wind power is calculated using (14):
(21) (14) Step 4) After determining the number of hydro units required to coordinate with wind power and the total power output from them, the number of peaking hydro units and their power output is calculated. The relationship between and is shown in (15). It should be noted that the hydro units that are assigned to coordinate with wind power are still (22) (23) (24) (25)