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Coordinated operation of wind power and other resources considering power system requirements

Ying Wang, Kaifeng Zhang, Xianliang Teng, Qia Ding, and Xianchao Huang Citation: Journal of Renewable and Sustainable Energy 7, 023121 (2015); doi: 10.1063/1.4918287 View online: http://dx.doi.org/10.1063/1.4918287 View Table of Contents: http://scitation.aip.org/content/aip/journal/jrse/7/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Decentralized coordinated neural control of doubly fed induction generator based wind farm for power system stability support J. Renewable Sustainable Energy 6, 043126 (2014); 10.1063/1.4893436 A new comprehensive model to simulate the restructured power market for seasonal price signals by considering on the wind resources J. Renewable Sustainable Energy 6, 023104 (2014); 10.1063/1.4869141 Review: The use of geographic information systems in wind turbine and wind energy research J. Renewable Sustainable Energy 4, 012701 (2012); 10.1063/1.3673565 Solar and wind energy resources and prediction J. Renewable Sustainable Energy 1, 043105 (2009); 10.1063/1.3168403 Wind energy in India: Status and future prospects J. Renewable Sustainable Energy 1, 042701 (2009); 10.1063/1.3156003

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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 7, 023121 (2015)

Coordinated operation of wind power and other resources considering power system requirements

Ying Wang,1 Kaifeng Zhang,1,a) Xianliang Teng,2 Qia Ding,2 and Xianchao Huang3

Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, China 2 NARI Technology Development Co. Ltd., Nanjing 211106, China 3 School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China (Received 20 October 2014; accepted 3 April 2015; published online 15 April 2015)

1

Wind power is inherently variable, and thus it brings signi?cant challenges to the operation of electric power systems. Noting that there really exist many controllable and dispatchable resources in power systems, the coordination of wind power and these resources provides the possibility of overcoming the drawbacks of wind power. This paper discusses the determination of the coordination objectives of wind power and other resources. The key idea is that the coordination objectives should match with the operation requirements of real power systems. (1) For an integrated wind plant, the coordination objective is that the output of wind plant should meet the grid code requirement. In this regard, a coordinated control method of a wind-energy storage system to meet the ramp rate limit of grid code is proposed. (2) For an area with a high penetration of wind power, the coordination objective is that the output of regional hybrid system should contribute to the active power balance of the whole power system. In this regard, a coordinated dispatch method of wind-thermal-pumped hydro hybrid system (regional hybrid system) to make the combined output follow the trend of system load is established. Case C 2015 studies are conducted to verify the feasibility of the proposed methods. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4918287]

NOMENCLATURE Sets and indexes

K ; k set and index of time period

Variables

Cs k Ccurt k Cobj nhd k nhp k nhu k Pl;k Pg k Pp k

a)

cost of energy storage system in period k ($) cost of curtailing the wind power in period k ($) objective of wind-energy storage system ($) number of pumping units shut down in period k {0,1,…,N} number of pumping units in period k {0,1,…,N} number of pumping units started up in period k {0,1,…,N} system load in period k (MW) power output of wind-storage hybrid system in period k (MW) power penalized for violating the ramp rate limit of the grid code in period k (MW)

Email: kaifengzhang@seu.edu.cn 7, 023121-1

C 2015 AIP Publishing LLC V

1941-7012/2015/7(2)/023121/25/$30.00

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Ps k Pw k Pcurt k Phg k Php k 1min Pramp k ramp 10min Pk Pthm k Rl;k SOCk thp k tthm k hd Vk hu Vk

power charged and discharged of energy storage system in period k. Positive when discharged, negative otherwise (MW) wind power forecast in period k (MW) power curtailed of wind farm in period k (MW) generating power of pumped-hydro generation in period k (MW) pumping power of pumped-hydro generation in period k (MW) maximum ramp rate over 1 min (MW) maximum ramp rate over 10 min (MW) thermal unit output in period k (MW) step change of system load in period k (MW) state of charge of the energy storage in period k binary decision variable: “0” if pumped units are pumping in period k; “1” otherwise {0,1} binary decision variable: “1” if thermal unit is on in period k; “0” otherwise {0,1} volume of lower reservoir in period k (M m3) volume of upper reservoir in period k (M m3)

Parameters and constants

a b c Cthm;k h Hg Hp Js M N Ps max Pthm max Ps min Pthm min Phg max Php max Phg min Php min P 1min P 10min SOCmax SOCmin hd Vmax hu Vmax hd Vmin hu Vmin hu dmax dhu min DPthm max DPthm min gg gp

cost coef?cient of thermal unit ($) cost coef?cient of thermal unit ($/MW h) cost coef?cient of thermal unit ($/MW h2) cost of thermal generation in period k ($/MW h) safety margin coef?cient generating water ?ow of the pumped hydro plant pumping water ?ow of the pumped hydro plant rated capacity of energy storage (MW h) big M: a very large number number of pumped hydro units maximum power of energy storage (MW) maximum power output of the thermal unit (MW) minimum power of energy storage (MW) minimum power output of the thermal unit (MW) maximum generating power of the pumped hydro unit (MW) maximum pumping power of the pumped hydro unit (MW) minimum generating power of the pumped hydro unit (MW) minimum pumping power of the pumped hydro unit (MW) ramp rate limit over 1 min of grid code (MW) ramp rate limit over 10 min of grid code (MW) maximum state of charge of energy storage minimum state of charge of energy storage maximum limits of the lower reservoir (Mm3) maximum limits of the upper reservoir (Mm3) minimum limits of the lower reservoir (Mm3) minimum limits of the upper reservoir (Mm3) allowable maximum volume change (Mm3) allowable minimum volume change (Mm3) maximum power step change of the thermal unit (MW) minimum power step change of the thermal unit (MW) ef?ciency of the generating cycle of the pumped storage station ef?ciency of the pumping cycle of the pumped storage station

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ps pg k pcurt phd phu

operation cost of energy storage system ($/MW h) electricity price in period k ($/MW h) wind curtail cost ($/MW h) shutdown cost of pumped hydro for pumping ($) startup cost of pumped hydro for pumping ($)

I. INTRODUCTION

As a clean and inexhaustible power source, the penetration level of wind power has been increasing worldwide. However, the variability of the wind output brings signi?cant challenges to the operation of electric power system. Meanwhile, there really exist many controllable and dispatchable resources in power systems, such as energy storage, hydro generation, and thermal generation. The coordination of wind power and these controllable and dispatchable resources provides the possibility of overcoming the drawbacks of wind power. Many studies have been focused on the coordination operation of wind power and other resources. Among these studies, the coordination objectives and corresponding methods vary a lot. In Ref. 1, the wind farm with battery energy storage is proposed to provide output as smooth as possible. Reference 2 uses hydropower to complement wind energy to produce constant power output. In Ref. 3, the coordination objective is to transform wind energy from an intermittent resource into a base-load electricity source. Based on ?lter-based methods, some studies mitigate the wind power ?uctuations in a certain frequency band.4–6 In Refs. 7–9, the coordination objective is to minimize the variance of the wind output. Also, there are some studies exploring the coordination of wind power and other resources to bene?t the daily operation of the whole power system. In a deregulated electricity market, wind power with other resources can be considered as merchant units to achieve energy arbitrage based on spot price ?uctuations.10 The hybrid system can also provide peak shaving, time shifting, and load following services.11–13 For a regulated power system, the electricity price is relatively ?xed. A special mode of wind farm with pumped-hydro system for regulated power system in China is designed in Ref. 14. Although much research has been devoted to the techniques and methods of coordination operation of wind power and other resources, very few discussions focus on whether their coordination objectives are really necessary and appropriate. For example, some studies try to smooth the ?uctuations of wind power as much as possible and produce constant power output. In fact, for a large power system, the load is always ?uctuating, and the system’s inertia is relatively large. Thus, small random ?uctuations of wind power have little impact on the operation of power systems. Meanwhile, a smoother output requires a larger energy storage, which leads to a higher cost. Therefore, it is not always necessary to smooth the ?uctuations too much. The authors of this study believe that the coordination objectives should match with the operation requirements of power system. Here, “match” means that the coordination objectives should neither dissatisfy nor far exceed the operation requirements. In terms of smoothing wind power, large ?uctuations, which harm the system safety, must be mitigated. For small ?uctuations, as discussed earlier, there is no need to do far beyond the operation requirements of power systems. Furthermore, different power systems have different requirements. It is necessary to design coordination objectives and corresponding methods according to different situations. Here are two examples illustrating the coordination objectives of wind power and other resources. (1) For an integrated wind plant, it is a must that the output of the wind plant should satisfy the technical requirements, usually as a part of the grid codes issued by the transmission system operators (TSOs). In the ?eld of active power control, the ramp rate of integrated wind power is required to be mitigated within the prescribed limit. Thus, the coordination objective should be set as mitigating the ramp rate of wind power to satisfy the technical requirements of grid code.

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(2) For an area with a high penetration of wind power, the generation should make contributions to the active power balance of the whole system. From an operational perspective, the operators would rather integrate wind power whose trend is more consistent with that of the system demand than the opposite, which is to release the stress of system dispatchers and operators. Thus, the coordination objective in this case should be set as making the combined output follow the trend of system load. In this paper, the problem of determining the coordination objectives in the ?eld of coordinating wind power and other resources is discussed, followed by the proposal of the coordination methods of each objective. The coordination methods focus on the two examples given above. The rest of this article is organized as follows:

? ? ? ?

Section II: The general coordination scheme of wind power with other resources, which present an overview of the coordination objectives and processes in Secs. III and IV. Section III: The coordinated control method of wind power with energy storage, for an integrated wind plant. Section IV: The coordinated dispatch method of wind-thermal-pumped hydro hybrid system, for an area with a high penetration of wind power. Section V: Conclusions.

II. GENERAL COORDINATION SCHEME

The general coordination scheme of wind power and other resources is composed of three steps:

? ? ?

Determination of coordination objectives Formulation of mathematical model for each coordination objective Deriving the solving algorithm for each mathematical model.

In the coordination scheme, the determination of coordination objective is a critical issue, which has signi?cant consequences for the effectiveness and worthiness of coordination methods. The key idea is that the objectives of coordinating wind power with other resources should match with the operation requirements of power systems. As mentioned in Sec. I, “match” means that the coordination objectives should neither dissatisfy nor far exceed the operation requirements. On the one hand, it is a must to do what is indispensable. On the other hand, it is meaningless to do what is not essential. Furthermore, for different power systems with different wind power penetration levels, the operation requirements may be different. Even in the same power system, under different circumstances, the operation requirements may also be different. Two cases are studied: (1) Coordinated control to meet ramp rate limitations of grid code Large ramps, i.e., sudden increases or decreases in wind power output, have brought much focus. Many studies have observed great ramps during the operation of wind farms. Energinet.dk (the Danish Transmission System Operator) has observed that power ramps within a period of 10 min can be very intense.15 The ramp rate from the 160 MW offshore wind farm Horns Rev may reach the value of 10 MW/min, which introduces several challenges to the reliability of the power system in West Denmark. In the analysis of the wind power ramping behavior in ERCOT (Electric Reliability Council of Texas) conducted by NREL (National Renewable Energy Laboratory), short-term wind power ramping rates can be very high. Taking the maximum 10-min step change as an example, the wind power can ramp up at a rate of 936 MW per hour (or 77% of total wind capacity per hour) and ramp down at an even higher rate of 1056 MW per hour (or 87% of total wind capacity per hour).16 Moreover, ramping events can occur regularly. An investigation by Kamath ?nds that, in the Bonneville Power Administration territory, as wind generation increases, larger ramps become more common.17 There are short term effects derived from those ramps which could affect operation of the system. Conventional generations have to be ramped down or even shut down during the low

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load and high wind speed periods in order to fully utilize wind power, and to be ramped up or started up during the high load and low wind speed periods to supply system demand. To keep balance of the whole system, an increase in the power reserve must be allocated in advance. These effects are ampli?ed in power systems with weak interconnections and a high wind energy penetration, such as in the Iberian Peninsula of Spanish.18 As a result, many regions and countries have announced technical requirements for integrated wind farms, usually as a part of the grid codes issued by the TSOs. As for active power control, the ramp rate of integrated wind farm is required to be mitigated within the prescribed limit. Moreover, the ramp rates of different time-scales are required to be mitigated within different restrictions.19,20 Table I illustrates the ramp rate limits of integrated wind power in world-wide grid codes. For grid code compliance, various improved methods have been developed to mitigate the ramp rate of wind power, such as pitch angle control, wind curtailment control, and wind turbine shutdown control. Meanwhile, the coordination of wind power with other resources provides a signi?cant opportunity to solve this problem. For example, natural gas turbines are well-suited for their fast ramping rates. Hydroelectric and coal plants can also be used, though coal’s slower ramping rates generally limit its ability to smooth wind power. Complementary intermittent generation, such as solar PV (Photovoltaic) and demand-side management are also important possibilities. Energy storage presents an attractive option for ramp rate control. Compared with other resources, energy storage could charge and discharge electricity quickly, and afford wind farms more ?exible control service. Moreover, traditional generators may suffer from rotor fatigue when providing compensation for faster variations, which would impose additional high cost.24 In addition, the fuel cost and pollution could be avoided. Since a large-scale BESS (Battery Energy Storage System) is relatively expensive now, a method for optimizing the operation of such storage systems to ?t application constraints is a crucial task. Meanwhile, considering the cost decline of energy storage, it would be a promising way to mitigate the ramp rate to ful?ll the requirements of grid codes. In this ?eld, Refs. 25–27 have explored the ?lter-based approaches applied in energy storage to meet the ramp rate requirements. However, it is dif?cult to design an appropriate time constant for the ?lter device. The ?lter-based methods may lead to over compensation, which needs high capacity of energy storage. In this paper, an optimization method is introduced into the coordination of wind power with energy storage for grid code compliance. The proposed approach provides more precise control and requires less capacity of energy storage. The studied system consists of a wind farm and an energy storage system, as shown in Fig. 1. Both wind curtailment control and energy storage control are included. For wind power, forecast errors are reduced with shorter forecast period, the ?nite horizon optimization control method is chosen. The ?nite horizon optimization problem solves series of optimal control operations before each control horizon, but only part of control operations is implemented. The

TABLE I. Active power ramp rate limits of grid codes. Country Denmark USA Canada Ireland South Africa China Issuer Energinet.dk ERCOT AESO EIRGRID ESBNG NERSA SGCC inst. cap. <30 MW Over 1 min <3 MW Over 10 min <10 MW inst. cap. <100 MW Over 1 min <5% inst. cap. Ramp rate limit Over 1 min <5% inst. cap. Over 1 min <20% inst. cap. (Ref. 21) Over 1 min <6.5 MW (Ref. 22) Over 1 min and 10 min <30 MW inst. cap. <200 MW Over 1 min <4% inst. cap. <50 MW over 1 min (Ref. 23) inst. cap. <200 MW Over 1 min <inst. cap./10 Over 10 min <inst. cap./3 inst. cap. >200 MW Over 1 min <15 MW Over 10 min <50 MW inst. cap. >200 MW Over 1 min <2% inst. cap.

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FIG. 1. Wind-energy storage system.

diagram of ?nite horizon optimization is shown in Fig. 2. Besides, a ramp rate de?nition, which is especially suitable for ?nite horizon optimization control, is proposed. The details of this part are given in Sec. III. (2) Coordinated dispatch to follow load trend Drastic variability of wind farms makes it harder for system operators to make generation schedule. From an operational perspective, the correlation between generation and electrical load is extremely important when there is variable production from such as wind power in the power system.28 If wind power production has a tendency of following the load, e.g., wind power production increasing in the morning and decreasing in the evening, this has a bene?cial effect. Otherwise, if there is an opposite tendency between wind power and the load, it would be a troublesome matter. In the ?eld of power dispatch, previous studies appear to consider wind power as negative load, make generation schedule based on net load, and de?ned as the instantaneous system load minus wind power. In the present study, the authors note that the power system operators would rather integrate wind power whose trend is more consistent with that of the system demand, than the opposite. Based on day-ahead wind power forecast, a coordinated dispatch of windthermal-pumped hydro hybrid system to follow the trend of system load is proposed. Besides, a correlation index, which is especially suitable for dispatch optimization, is presented. The problem is formulated as a multi-objective optimization problem. This method is especially meaningful for a regulated power system, such as China.

FIG. 2. Finite horizon optimization control.

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The studied system consists of a wind farm, a thermal generation, and a pumped-hydro storage system, as shown in Fig. 3. To apply the proposed dispatch strategy, the coordination for day-ahead scheduling is mainly composed of four steps:

? ? ? ?

The wind farm forecasts day-ahead wind power output. The system operator informs the wind-thermal-pumped hydro hybrid system of the day-ahead load forecast. The wind-thermal-pumped hydro hybrid system optimizes the output plan and submits it to the system operator. The system operator makes schedule for the other generation units according to the received output plan of the wind-thermal-pumped hydro hybrid system.

III. COORDINATED CONTROL TO MEET RAMP RATE LIMITS OF GRID CODE A. Ramp rate definition

In many grid codes, the maximum ramp rate over a time period is limited. However, there is no standard way in which the ramp rate is de?ned mathematically. Therefore, there are different ways in which we can interpret the “increase or decrease in energy output” or “the rate-of-change of output power.” The typical de?nitions of ramp rate over period T are as follows: (1) Step change: Output change from the start to the end of the period, de?ned as jP?t ? T ? ? P?t?j.29 Some studies apply the step change in mean value from one period to the next, de?ned as jPmean ?t ? T ? ? Pmean ?t?j.30,31 (2) Max-Min: The difference between the minimum and maximum value of wind generation over the time period T:32 max fP?t?; P?t ? 1?; :::P?t ? T ?g ? min fP?t?; P?t ? 1?; :::P?t ? T ?g: (1)

In this paper, we develop a robust metric to de?ne the ramp rate, which is especially suitable for ?nite horizon optimization control to meet ramp rate limit of grid codes. It is expressed as max fjP?t? ? P?t ? i?jg; i ? 1; 2; :::; T : The de?nition proposed overcomes the drawbacks of the above: (1) The de?nition of the step change may miss the maximal ramp if it occurs between the two endpoints. It focuses only on the two endpoints of the interval being considered. If the maximum ramps occur between the two endpoints, the endpoints themselves may not exhibit a (2)

FIG. 3. Wind-thermal-pumped hydro hybrid system.

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large change in magnitude. For the proposed de?nition, the process of ?nite horizon optimization control guarantees that all the ramps will be controlled within the limit and the maximum ramp will not be missed. (2) The de?nition of the “Max-Min” may lead to control mistakes at some situations. When solving optimization problem of the current control horizon, the data of the previous control horizon are utilized. If there are control mistakes in the previous control horizon, it may lead to control mistakes in the current control horizon. For example, Fig. 4 shows the control of the previous control horizon is not successful, i.e., the maximum ramp is larger than the ramp rate limit of grid code. For the time point t at current control horizon, if only P?t2 ? P?t? P?t1 ?, the “Max-Min” over [t-T, t] would equal to P?t1 ? ? P?t2 ?. In this situation, the P?t? makes no difference on the calculation result of the maximum ramp rate at point t. It means the optimized result is somewhat random. In Fig. 4, the dotted line illustrates the P?t? increases largely and violates the ramp rate limit again, which leads to a new control mistake. For the proposed de?nition, the P?t? makes a difference on the calculation result of the maximum ramp rate at point t. For each time point t, the jP?t? ? P?t ? i?j will be limited. If there were mistakes in the previous control horizon, the control validity of the current control horizon would not be affected. For the above reasons, the proposed de?nition of ramp rate is suitable for ?nite horizon optimization control for meeting ramp rate limits of grid code.

B. Mathematical formulation

An energy storage station is assumed to be installed in the wind generation plant. The coordination control of the hybrid system to meet the ramp rate limitation of grid code is addressed as a ?nite horizon optimization problem. The optimization period is 20 min. The time interval is 10 s.

1. Objective function

The optimization objective function represents the whole objective of the studied system. The optimization objective of a wind-energy storage system is maximizing the pro?t of the system (income minus cost), as well as meeting the ramp rate requirements of grid code. The objective function consists of four parts: (a) income from power output to the grid, (b) curt operation cost of energy storage system (Cs k ), (c) cost of curtailing wind power (Ck ), (d) penalty for violating the ramp rate limit of the grid code

FIG. 4. Example of control mistakes.

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K X g s curt ?pg ? M ? jP p k Pk ? Ck ? Ck k j?: k?1

Max Cobj ?

(3)

In this objective function, the parts (a), (b), and (c) constitute the pro?t, and the penalty function M ? jPp k j is introduced into the objective function to guarantee the wind-energy storage system could try its best to meet the ramp rate limits. Operation cost of energy storage system varies among different kinds of energy storage, which is divided further into ?xed ($/kW/yr) and variable ($/kW h) cost. It depends on the cost of the charging current as well as optionally fossil fuel costs (in case of conventional compressed air energy storage, CAES). In this paper, the operation cost of energy storage system is considered to be linearly proportional to the absolute value of Ps k for simpli?cation

s Cs k ? ps ? jPk j:

(4)

Cost of curtailing wind power refers to extra economic loss besides the selling pro?t reduction. On the one hand, curtailing wind power needs adjusting pitch angles or cutting out wind turbines, which are likely to increase wear in variable-pitch systems and lead to higher equipment cost. On the other hand, curtailing wind power would bring negative in?uences to wind farms, such as decline in annual utilization hours, which is one of the key performance indicators for wind plants. Take Chinese wind farms for instance, they might have less feed-in tariff if they could not reach certain requirements from local government. Here, we introduce the cost of curtailing wind power to re?ect the extra economic loss as well as discourage wind power curtailment. Considering the complexity of this cost, it is considered to be linearly proportional to Pcurt for convenience k ? pcurt ? Pcurt Ccurt k k : (5)

In the penalty function M ? jPp k j, the penalty coef?cient M is a constant. Generally, the penalty coef?cient should be set as a big enough number to ensure the penalizing effectiveness. However, if M is too large, the penalty function might impact the objective function considerably, the penalty function might impact the objective function considerably, while the economic pro?t would be overwhelmed by the penalty function during the optimization procedure. In practice, we have tried several values and 100 is ?nally chosen in Secs. III D and III E, Sec. III F meanwhile, the optimization results with different M are compared in Sec. III F.

2. Constraints

This optimization problem is subject to the following:

s w curt Pg k ? Pk ? Pk ? Pk ;

(6) (7) (8) (9) (10) (11)

Ps min SOCmin

Ps k SOCk

Ps max ; SOCmax ;

SOCk?1 ? SOCk ? Pramp k Pramp k

1min

Ps k DT ? 100% ; Js

g ? maxfjPg k ? Pk?i jg; i ? 1; 2; :::; 6; g ? maxfjPg k ? Pk?i jg; i ? 1; 2; :::; 60;

10min

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Pp k ?

h i 1 1min 1min sgn Pramp ? P 1min ? h ? 1 ? Pramp ? P 1min ? h k k 2 h i 1 10min 10min ? P 10min ? h ? 1 ? Pramp ? P 10min ? h : ? sgn Pramp k k 2

(12)

The power balance equation of wind-storage system is shown in (6). The constraints (7)–(9) represent the operational limits of the energy storage. The ramp rate over 1 min and 10 min is shown in (10) and (11), respectively. Equation (12) represents the power penalized for violating the ramp rate limits over 1 min and 10 min. The sign function is de?ned as follows: 8 x>0 <1 (13) sgn?x? ? 0 x?0 : ?1 x < 0:

3. Optimization with genetic algorithm (GA)

In the optimization problem above, the ramp rate limit constraints are nonsmooth and nonlinear. Optimization algorithms based on continuous method are not appropriate. GA has an ability to transform a dynamic nested optimization problem into an overall static one. For this reason, genetic algorithm is selected to solve this problem. All GA runs has the following standard characteristics:

? ? ? ? ? ? ?

Probability of crossover: 1.0 Probability of mutation: 0.002 Population size: 100 Number of generations in each run: 300 Linear rank-based ?tness function. The selective pressure is 1.8. Roulette wheel selection Uniform crossover. The mixing ratio is 0.5, meaning the offspring has approximately half of the genes from ?rst parent and the other half from second parent, although cross over points can be randomly chosen.

C. Case study

The testing data is based on an actual wind-solar-storage demonstration project in China. The installed capacity of wind farm is 100 MW. According to the Grid Code in China, the ramp rate of this wind farm must be limited within 10 MW every 1 min and 33.3 MW every 10 min. Other parameters are given in Table II. Electricity price pg k highly varies in different regions. Based on the parameters in Ref. 14, the price within the period of 9:00–23:00 is 0.13 $/kW h, and the price within the period of 23:00–9:00 the next day is 0.067 $/kW h. For the study period is 20 min, the electricity price is ?xed on 0.1 $/kW h for simplicity. Energy storage operation cost varies greatly among different kinds of storage. According to Ref. 33, a report StoRE project in EU, the operation cost of pumped hydro energy storage (PHES) is nearly 0.43 $/kW h, whereas the cost of CAES is 0.01–0.3 $/kW h. In Ref. 34, the operation cost of CAES is 0.003 $/kW h. In this section, ps is set as 0.1 $/kW h in Secs. III D and III E, and the price impacts are analyzed in Sec. III F.

TABLE II. Parameters of wind-storage system. Ps min (MW) ?10 Ps max (MW) 10 SOCmin 0.2 SOCmax 0.8 Js (MW h) 10

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Wind curtailing cost pcurt is set as 0.01 $/kW h in Secs. III D and III E, and the price impacts are analyzed in Sec. III F. The initial SOC (State of Charge) is set as 50%.

D. Optimization results

In this part, two scenarios of wind power are studied. The wind power forecast is shown in Fig. 5 by curve. The wind power in scenario 2 is more variable than that in scenario 1. The curve in gray shaded area is the control result of the previous control horizon. The bar graph indicates whether the ramp rate limits are violated. “1” means the ramp rate limit over 1 min is violated, “2” means the ramp rate limit over 10 min are violated, “3” means the ramp rate limits over 1 min and 10 min are violated. As shown in Fig. 5, the ramp rate limits are violated many times before optimization. The optimization outputs of wind-energy system are shown in Fig. 6. The bar graph is zero, meaning that all the outputs comply with the ramp rate limits. Fig. 7 indicates the wind power curtailment, energy storage output, and SOC. The energy storage is discharged at valley wind time. It should be noted that the energy storage is not being fully charged at peak wind time. The reason is that in this case the cost of energy storage is much higher than that of the wind curtailment. In other words, compared with decreasing output by charging energy storage, it is more cost saving by curtailing wind power.

FIG. 5. Wind power forecast and violation of the ramp rate limit.

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FIG. 6. Optimization results.

E. With/without energy storage system

The optimization results with and without energy storage system are compared. The results without energy storage system are shown in Fig. 8. It could be seen that in scenario 1 (less variable scenario), the outputs could meet the ramp rate limits. While in scenario 2 (more variable scenario), the outputs violate the ramp rate limits from time point 33 to 39. It is because in scenario 2, the wind power falls sharply at the beginning of the current control horizon. At this time, the outputs in the previous control horizon are ?xed. Therefore, it is dif?cult to meet the ramp rate limits merely by curtailing wind power. In Table III, the costs and pro?ts of the wind-energy storage system with and without the energy storage are compared. It can be seen that the energy storage system would contribute to lessening the wind power curtailment. And the pro?t of the system with energy storage could be either higher or lower than that without energy storage system in different wind power scenarios.

F. Sensitivity analysis

In this part, the in?uences of different wind curtailing cost pcurt , energy storage system cost Cs k , and penalty coef?cient M are studied.

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FIG. 7. Wind power curtailed, energy storage output, and SOC.

The pro?ts with different wind curtailing cost and energy storage system cost are shown in Fig. 9. It is obvious that the pro?ts are sensitive to the wind curtailing cost and energy storage operation cost. While the costs are increasing, the pro?t is decreasing. The optimization objectives during GA optimization procedures with different penalty coef?cients M from 20 to 150 are shown in Fig. 10. It is obvious that the objectives with different M vary dramatically at the beginning. After about 50 generations, the penalized wind power turns to be nearly zero, and the objectives with different M could reach approximately the same optimal solution. In conclusion, the results indicate solution performance with all above penalty coef?cients is satisfactory.

G. Computational performance

This problem is simulated on a personal computer (Inter Core i5-4440, CPU (Central Processing Unit) 3.1 GHz, 8.00 GB, 64 bit). The variation of the optimization objective during one of the GA optimization procedures is shown in Fig. 11. It can be noted that a near optimal solution was derived during the early stages of the GA generations evolution. The computation time of once optimization is within 2 min.

IV. COORDINATED DISPATCH TO FOLLOW LOAD TREND A. Correlation index

In the ?eld of analyzing the relationship of wind power and load, the Pearson correlation coef?cient has been widely used.35 It is a measure of the linear correlation between two

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FIG. 8. Optimization results (without energy storage system).

variables X and Y, giving a value between ?1 and ?1 inclusive, where 1 is total positive correlation, 0 is no correlation, and ?1 is negative correlation. That formula for sample correlation coef?cient r is

N X ??Yn ? Y ? ?X n ? X n?1 ?s???????????????????????????? : r ?x; y? ? s???????????????????????????? N N X X 2 ?2 ?X n ? X ? ?Yn ? Y n?1 n?1

(14)

TABLE III. Costs and pro?ts with/without energy storage system. Scenario 1 Scenario Energy storage system Pro?t ($) Selling ($) Cost of storage ($) Power curtailed (kW h) Without 1801.42 1813.48 0 1204.17 With 1796.40 1871.04 64.30 1032.50 Without 1440.40 1467.32 0 2686.67 Scenario 2 With 1629.67 1739.28 100.76 883.6

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FIG. 9. Pro?ts with different prices (Scenario 1).

FIG. 10. GA optimization process with different M (Scenario 1).

FIG. 11. Variations of optimization objective during GA optimization process.

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However, the sample correlation coef?cient only represents the linear correlation. It does not show the quantity relationship of the variables. For example, the sample correlation coef?cient between Xn and Yn is as the same as that between Xn and kYn 6b?k > 0?,

N X ? ??kYn ? b ? kY ?b ?Xn ? X n?1 N X n? 1

??Yn ? Y ? ?Xn ? X

r ?x; ky ? b? ? s?????????????????????????????s????????????????????????????????????????????????? ? s?????????????????????????????s???????????????????????????? : N N N N X X X X ?2 ?2 ?b ?2 ?2 ?kYn ? b ? kY ?X n ? X ?Xn ? X ?Y n ? Y

n?1 n?1 n?1 n?1

(15) Assume that Xn is the system load and Yn is the hybrid generation of wind-thermal-pumped hydro hybrid system, the value of sample correlation coef?cient cannot re?ect how much the generation of hybrid system makes contributions to following the trend of load. As shown in Fig. 12, the correlation coef?cients between load and G1, G2, G3 are all the same (equal to 1.0). However, it is not reasonable to treat G1, G2, and G3 as the same. For example, while the load is rapidly rising at around 8 a.m., the rise in G2/G3 is much larger than that in G1. Thus, compared with G1, G2, and G3 contribute more to following the trend of load. In this paper, a different correlation coef?cient is proposed to overcome the disadvantages of sample correlation coef?cient. The proposed correlation coef?cient is the Euclidean distance between points RX ?n? and RY ?n?. The formula is v??????????????????????????????????????????????????????? u N ?1 u 1 X r ? x; y ? ? t ?RX ?n? ? RY ?n??2 ; N ? 1 n?1 where RX ?n? ? X?n ? 1? ? X?n?: (17)

(16)

The proposed correlation coef?cient could re?ect how much the generation of hybrid system makes contributions to following the trend of load. The proposed correlation coef?cient equaling to 0 means the data points are exactly in the same trend. The effect of following the trend of load is better while the proposed correlation coef?cient is smaller. For example, the proposed correlation coef?cients between load and G2/G3 are 31.7, which are smaller than that

FIG. 12. Load and generation.

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of G1 (38.6). The results indicate that the G2 and G3 make more contributions to following the trend of load as expected.

B. Mathematical formulation

A hydro pumping storage station and a thermal generation plant are assumed to be installed in the regional hybrid system. The coordination dispatch of the hybrid system to follow the system load is addressed as an optimization problem. The optimization period is 1 day. The time interval is 1 h.

1. Objective function

This problem is formulated as a multi-objective optimization problem. (1) The regional hybrid system is required to follow the trend of load as much as possible. The proposed correlation coef?cient of system load and the wind-thermal-pumped hydro hybrid generation is minimized v?????????????????????????????????????????? u K ?1 ? u 1 X ?2 min r ?x; y? ? t Rl ? Rg : k K ? 1 k?1 k

l The Rg k and Pk are de?ned by

(18)

Rlk ? Plk?1 ? Plk ;

hg hg hp hp w w thm thm Rg k ? Pk?1 ? Pk ? Pk?1 ? Pk ? Pk?1 ? Pk ? Pk?1 ? Pk :

(19) (20)

(2) The economic bene?t of the regional hybrid system is maximized, which consists three parts: (a) Income from power output to the grid. (b) Fuel cost, startup and shutdown cost of the thermal unit. Fuel cost is a second order polynomial function, which is de?ned as thm 2 a ? bPthm k ? c?Pk ? . (c) Startup and shutdown cost of the pumped hydro for pumping. As pumping and generating of pumped hydro units are complementary working states, the additional costs of the startup and shutdown for generating are relatively low and could be neglected as in Ref. 14,

K X k ?1

max

hg hp w thm thm hu hd ?pg k ?Pk ? Pk ? Pk ? Pk ? ? Ck ? phu nk ? phd nk ?:

(21)

2. Constraints

This optimization problem is subject to the following: (1) Thermal generation constraints:

thm Pthm min ? tk

Pthm k

Pthm max ; DPthm max ;

(22) (23) (24)

?DPthm min

thm Pthm k?1 ? Pk

tthm ! k

Pthm k : Pthm max

(2) Pumped-hydro storage operation constraints10,14

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hu Vmin hd Vmin hu Vk hd Vk

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hu Vmax ; hd Vmax ;

(25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36)

hg hp hu hu Vk ? Vk ?1 ? up?Pk ; Hp ? ? down?Pk ; Hp ?; hg hp hu hu ? Vk Vk ?1 ? up?Pk ; Hg ? ? down?Pk ; Hg ?;

dhu min

K X k?1

hu hu V24 ? V1

dhu max ; 4N ;

hd nhu k ? nk

hp hu hd nhp k?1 ? nk ? nk ? nk ; hp nhp k Pmin hp Phg min ? tk

Php k Phg k

hp Php max nk ; hp Phg max ? tk ? N ;

thp k ?1?

1 hp n ; N k

hu hd nhp k ; nk ; nk 2 f0; 1; :::; N g;

thp k 2 f0; 1g :

The thermal generation constraints include generation limitations and ramp up/down rate constraints through constraints (22)–(24). Constraints (25) and (26) represent the volume limit of the upper and lower reservoir. The water balance equations (expressed in terms of energy) are shown in (27) and (28). Constraint (29) represents the volume change between the beginning and end of a single day. Every set of pumped hydro unit is limited to startup and shutdown at most twice every day. So the total times cannot exceed 4N, as shown in (30).The change in the number of pumping units is de?ned in (31). Constraints (32) and (33) represent the pumping and generating power limit of the pumped unit, and also guarantee that the pumped hydro unit does not work simultaneously as a pump and a turbine by means of the binary variable thp k . This variable is set to a null value by (34) when any of the units is working as a pump. This is a multi-objective optimization problem. Here, the method named as lexicographic goal programming36,37 is chosen to solve this problem. In lexicographic goal programming, different goals are categorized into several levels of preemptive priorities. A goal with a lowerlevel priority is more important than a goal with a higher-level priority. This method formulates and solves a number of sequential goal programming problems. By this way, the multiobjective optimization problem is transformed into several sequential single-objective optimization problems. In this problem, the ?rst objective, i.e., following the trend of load as much as possible, is the main goal. Thus, the ?rst objective is of the ?rst-level priority. And the second objective, i.e., maximizing the economic bene?t, is of the second-level priority. In the ?rst-level priority problem, only the ?rst objective and corresponding constraints are considered First : min ?18? s:t: ?22? ??36? :

The objective (18) may lead to multiple solutions to the ?rst-level priority problem, which has been discussed in Sec. IV A. Thus, the second-level priority problem is formulated. In the second-level priority problem, the objective of the ?rst-level priority problem is used as hard

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TABLE IV. Parameters of pumped-hydro plant in the designed case.

hu Vmin (km3) hu Vmax (km3) hd Vmin (km3) hd Vmax (km3)

481.5 Php min 10 Hg (m) 329.2

3 dhu min (Mm )

1314 Php max (MW) 13 Hp (m) 335.3

3 dhu max (Mm )

296.7 Phg min (MW) 6 gp 0.907 phu ($) 166.67

1129.2 Phg max (MW) 15 gg 0.927 phd ($) 166.67

(MW)

?42

42

TABLE V. Parameters of the thermal unit. Pmin thm (MW) 12.5 a ($) 62.3 Pmax thm (MW) 50 b ($/MW h) 7.47 DPmin thm (MW) 15 c ($/MW h) 5 ? 10?4

2

DPmax thm (MW) ?15 Start up/shut down fuel 224

FIG. 13. Wind power and load forecast.

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constraint so that the obtained solution does not violate the objective of the ?rst-level priority problem, Second : max ?19? s:t: ?18?; ?22? ??36?:

Each problem contains quadratic constraints and semi-continuous variables, which can be solved by optimization software ILOG CPLEX.38 For comparing the effects of the conventional correlation index with the proposed one, the mathematical model which applies the conventional correlation index is formulated as well. Compared to the model above, the (18) is replaced by (37), which is derived from (16),

K X g Pg k ? Pk

Plk ? Plk (37)

k?1 s???????????????????????????????? ; min r ? s???????????????????????????????? 2 2 X K K X g Pg Plk ? Plk k ? Pk k?1 k?1

where

FIG. 14. Wind-thermal-pumped hydro hybrid output.

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hg hp w thm Pg k ? Pk ? Pk ? Pk ? Pk :

(38)

Since the conventional correlation index is nonlinear, the problem is solved by optimization software GAMS/DICOPT.39

C. Case studies 1. Test system

A test system was created based upon the parameters of the wind-pumped hydro system in Ref. 14, in which the pumped hydro plant is designed as 5% of the scale of the Bath County Pumped Hydro Storage Plant in the USA. In this paper, the pumped hydro plant was designed as 3% of the scale of the Bath County Pumped Hydro Storage Plant. The parameters are shown in Table IV. Table V indicates the parameters of the thermal unit, which is based on the parameters in Ref. 40. Electricity price within the period of 9:00–23:00 is 0.133 $/kW h, and the price within the period of 23:00–9:00 the next day is 0.067 $/kW h.

FIG. 15. Output of thermal and pumped-hydro units.

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Data of typical daily provincial load and data of the wind farm forecast are shown in Fig. 13 by curve. It can be seen that the variations of wind power and system load in scenario 2 are larger than those in scenario 1.

2. Results analysis

Figs. 14–17 illustrate the optimization results for wind-thermal-pumped hydro hybrid system. The hybrid output of wind-thermal-pumped hydro hybrid system is given in Fig. 14. It shows that the output in scenario 2 is more variable due to the larger variation in system demand. The generating power of thermal unit and pumped hydro system is shown in Fig. 15. The thermal unit decreases its output during 12–18 h in scenario 1 (less variable scenario), whereas shut down during 14–16 h in scenario 2 (more variable scenario).The numbers of pumping unit starting up and shutting down for each period are given in Fig. 16. The water volumes of upper and lower reservoir are shown in Fig. 17. The results indicate that the output of wind-thermal-pumped hydro hybrid system follows the load curve as we expected. The results of the model which applies the conventional correlation index (hereinafter “conventional method”) with the proposed one (hereinafter “proposed method”) are compared. The values of the conventional and proposed correlation index are given in Table VI. It could be seen that with optimization method, the values of the indexes turn better. In the conventional

FIG. 16. Start up and shut down of pumping units.

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FIG. 17. Volumes of upper and lower reservoir.

method, the conventional index is the best. And in the proposed method, the proposed index is the best. The results illustrate the validation of the simulation study. The outputs of the wind-thermal-pumped hydro system in scenario 1 are shown in Fig. 18. The output trends of both the conventional and proposed methods could follow the trend of the load. However, the degrees of following load are different. The proposed method makes more contribution to follow the trend of load, while the curve of the conventional method follows the load curve at a relatively ?xed proportion. For example, in morning peak time (point 8–9), the load increases by 2300 MW, which is the fastest increase throughout the day. The output of the conventional method increases by 14.5 MW and that of the proposed one increases 110 MW. From points 12 to 13, the load decreases by 500 MW. The output of the conventional method decreases by MW and that of the proposed one decreases by 109 MW. Therefore, from

TABLE VI. Comparison of the index value (Scenario 1). Conventional index Without optimization Conventional method Proposed method ?0.687 0.982 0.489 Proposed index 901.3 883.0 864.5

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FIG. 18. Comparison of the output power (Scenario 1).

the perspective of the system operation, the hybrid system in the proposed method makes more contribution to follow the trend of the system load. Meanwhile, the hybrid system makes its best to follow the trend of load, which relieves the operation pressures of the other units in the whole power system. For the security constraints have been included, the results of the proposed method meet the safety requirements of system operation.

V. CONCLUSIONS

This paper mainly discusses the objectives and corresponding methods of coordinating wind power with other controllable and dispatchable resources. In this ?eld, the determination of coordination objective is a critical issue. The key idea is that the coordination objectives should match with the operation requirements of the real power systems. For an integrated wind plant, it is necessary to comply with the grid code for integrated wind farms. For an area with a high penetration of wind power, it is bene?cial to contribute to the active power balance of the whole power system. Considering above objectives, the mathematical model for each objective is formulated. For an integrated wind plant, a coordinated control model of a wind-energy storage system to meet the ramp rate limit of grid code is established. For an area with a high penetration of wind power, a coordinated dispatch model of wind-thermal-pumped hydro hybrid system to follow the trend of load is established. Case studies are conducted to verify the model effectiveness. For different power systems, the operation requirements may vary a lot. The proposed methods provide an interesting way to explore how to coordinate wind power with other controllable and dispatchable resources, which can be promoted and generalized to other applications in world-wide power systems.

ACKNOWLEDGMENTS

This work was supported by National Natural Science Foundation of China (Grant Nos. 51177019, 51107037, and 51477157), and State Grid Corporation of China (Research on Probabilistic Economic Dispatch and Security Correction with Large-scale Renewable Energy Integration).

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