IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 2, APRIL 2014
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A Robust Wind Power Optimization Method for Look-Ahead Power Dispatch Wenchuan Wu, Member, IEEE, Jianhua Chen, Boming Zhang, Fellow, IEEE, and Hongbin Sun, Senior Member, IEEE
Abstract—The main purpose of the look-ahead dispatch is to manage operational uncertainties over the next several hours, with benefits for the exploitation of renewable energy resources. This paper describes a robust optimization (RO) model for wind power look-ahead dispatch. The model calculates allowable interval solutions for wind power generation and provides optimal economic solutions for conventional power generation to mitigate the uncertainty inherent to wind power. By introducing the interval values as control targets for wind farms, the method can reduce the curtailment of wind power and the frequency of regulation. Interval wind power look-ahead dispatch is a two-layer RO problem, which can be transformed into a quadratic programming problem using strong duality theory, allowing for a more straightforward solution. The results of numerical simulations using the IEEE RTS system, as well as field tests using a 1.8-GW transmission system, are reported. Index Terms—Dynamic economic dispatch, robust optimization (RO), wind power dispatch.
NOMENCLATURE
Decision variables of the robust optimization model. Dual variables of the robust optimization model. Element at row and column of the coefficient matrix . Lower/upper interval bounds of variation for the uncertainty parameter. Uncertainty parameter for the decision variables. Lower/upper variation bound of . Minimum value of the upward/downward spinning reserve capacity for the system during the time period . Output power unit generated during the time period . The most economic wind generation schedule for wind farm during the time period .
Manuscript received August 28, 2013; revised October 24, 2013 and November 27, 2013; accepted December 03, 2013. Date of publication January 24, 2014; date of current version March 18, 2014. This work was supported in part by the National Key Basic Research Program of China (2013CB228205) and in part by the National Science Foundation of China (51177080 and 51190105). The authors are with the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSTE.2013.2294467
RO
Actual available wind generation for wind farm during the time period . Upward/downward spinning reserve contribution of unit during the time period . Output power of wind farm generated under different scenarios during the time period . System load demand during the time period . Set of conventional units/wind units. Lower/upper limits of the allowable wind power generation interval for wind farm during the time period . Lower/upper limits of predicted wind power generation interval for wind farm during the time period . Total number of transmission interfaces. Quasi-steady-state generation distribution shift factor of unit to transmission interface . Upward/downward power generation adjusting amount for unit during the time period . Minimum/maximum generation output of unit . Upward/downward ramping rate of unit during the time period . Initial period in the schedule time horizon. Total number of periods in the schedule time horizon. Lower/upper flow limit of transmission interface with bus loads excluded. Maximum positive/negative load on the transmission interface during the time period . Robust optimization.
I. INTRODUCTION ARGE-SCALE integration of renewable power generation facilities involves significant technical challenges, largely because of the unpredictable nature of natural energy resources and the difficulties in controlling the energy conversion. Therefore, the look-ahead dispatch method, which reschedules the units based on up-to-date forecasts of renewable power
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generation, is proposed to improve the utilization of renewable energy resources. This mode of generation rescheduling, which is essentially a receding horizontal-based dynamic dispatch method, has proved to be an effective method to reduce the power imbalances caused by the unpredictable capacity of renewable energy resources, and could lead to a much higher wind power utilization than conventional day-ahead dynamic dispatch and intra-day static economic dispatch [1]–[3]. However, the look-ahead dispatch method is still a “deterministic” model-based solution strategy, which is unable to directly take the uncertainty of wind power output into account. Hence, the operational security cannot be guaranteed, and the model can provide unfeasible solution scenarios, even with small perturbations of the power levels [4]. This is reflected in aspects including deficiencies of the unit reserve capacity or lack of transmission capacity, which is a threat to the operation of the power grid when the penetration of wind power into the system is high. Therefore, a “safe” look-ahead dispatch method is required to effectively handle the uncertainty of wind power generation. Stochastic optimization [5], [6] and chance-constrained stochastic optimization [7], [8] have been the most popular methods to account for uncertainties in power generation. However, the computational solutions to the stochastic optimization problem are intractable and only an approximate model can be used. Moreover, the probabilistic distribution of the uncertainty parameters must be given, which is problematic in real-world applications. Robust optimization (RO) is first reported by Soyster [9] in the early 1970s and more recently has been re-activated by Ben-Tal and Nemirovski [10]–[12]. In general, the RO model is tractable and can be applied to similar problems as stochastic optimization. RO can be viewed as a complementary approach to stochastic optimization to handle the optimization problems with uncertain data. For a given bounded uncertain dataset of various parameters, the optimal solution of RO should satisfy all the constraints of the problem for all data from this set. Compared with stochastic optimization, RO is more attractive because it requires less knowledge of the uncertainty parameters and can be solved more easily. A detailed discussion of the RO method can be found in [4]. Although the RO method has gained substantial popularity in many fields, a few authors have considered power systems. Ref. [13] reported a two-stage adaptive RO model with a min–max objective for the security constrained unit commitment problem in the presence of nodal net injection uncertainty, and Benders’ decomposition was combined with an outer approximation technique algorithm to solve it. Ref. [14] focused on the self-scheduling problem in electricity markets under uncertain pricing constraints and developed a new selfscheduling model with a max–min optimization structure under box and ellipsoidal price uncertainty based on RO. By using the dual theory, this model can be reformulated into a quadratic programming (QP) problem. Ref. [15] described a RO approach incorporating pumped-storage hydro units, with a max–min structure to hedge wind power output uncertainty. Again, Benders’ decomposition algorithm was applied to solve the problem.
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 2, APRIL 2014
In the previous published works, the models with min–max or max–min objectives are typically used in RO, such as the RO unit commitment problem, in which an important premise is that wind power can be fully absorbed by the grid no matter how large and volatile its value is. However, this is not always the case in some power grids. As is known, the precision of day-ahead wind prediction is very low [22], which means a large uncertainty of wind power output at dayahead especially when wind power integration is high. To cope with such a large uncertainty, a very conservative result from the economical aspect will be obtained with the RO model, which is not the expectation of operators. Hence, a more suitable scenario for RO application is the look-ahead dispatch, in which the wind prediction error is much lower as the prediction is with a shorter time horizon and in a rolling up-to-date manner. Meantime, wind curtailment is sometimes a must for a feasible and practically meaningful generation schedule as there may not be enough reserve for it, especially during the load demand valley time periods at night. But wind curtailment is rarely considered in the published RO works. In addition, the RO solution is generally in the form of set-point values, which makes it a hard work for wind farms to follow because of their poor controllability. What’s more, as the set-point values are often changing violently, frequent regulating may make the wind turbine fatigue. This paper describes a new robust wind power dispatch framework with minimum wind power curtailment and interval wind power schedule for wind farms with a set-point value-based schedule for the thermal units. On the one hand, with minimum wind power curtailment considered, wind power becomes partially controlled, which is beneficial for mitigating the uncertainty of wind power, especially when the reserve from the thermal units is not enough. On the other hand, by introducing the interval values as control targets for wind farms, it becomes much easier for wind farms to follow the generation schedules, and wind power curtailment can be reduced, as well as the frequency of regulation for wind turbines. In this framework, the predicted power output interval of each wind farm is sent to the control center, wherein a robust interval wind power optimization method is used to calculate the allowable power output of the wind farm. The allowable power output intervals for minimum possible wind curtailment are sent back to each farm as their control targets for the forthcoming time periods and economical optimal solutions for conventional units are applied; the combination of these two approaches mitigates the uncertainty in wind power generation. The paper is organized as follows. Section II introduces the concept of the robust power dispatch model considering wind power integration, which is a worst-case securityconstrained economic dispatch model. Section III presents a detailed expression of the worst-case optimization model and the proposed robust interval optimization model for the look-ahead wind power dispatch. Section IV details the solution method, which is based on strong duality theory. Numerical simulations using IEEE RTS, as well as field tests using a provincial grid system, are described in Section V. Section VI concludes the paper.
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II. THE CONCEPT OF THE ROBUST POWER DISPATCH MODEL CONSIDERING WIND POWER INTEGRATION In wind power look-ahead dispatch, the control framework can be summarized, as shown in Fig. 1. It is a two-layer hierarchical control system, which includes a central control system, as well as the wind farm and power plant control systems. is periodically sent The predicted wind output interval from the wind farms to the control center, where the robust interval optimization algorithm is executed, and the optimized look-ahead power generation schedules are sent back to the wind farms and power stations. At the wind farms, the lookahead power generation schedule is the optimal allowable . Although for the conventional power generation interval plants, the schedules are set-point values rather than the interval values. A robust wind power dispatch problem can be formulated as follows, in brief, where the decision variables are , , , and :
Fig. 1. Two-level hierarchical wind power dispatch framework.
From duality theory, the following formula holds: Therefore, (1) is equivalent to the following expression [17]:
Equation (1.1) denotes the inequality constraints, such as the reserve requirement constraints, transmission line (interface) flow constraints, and ramping rate constraints for conventional units, which must be hold for any variation of wind power output; (1.2) denotes the output limit constraints for the conventional units; and (1.3) denotes that the scheduled wind power output interval should be located in the predicted wind output interval . In (1), denotes the power output of conventional units. We can see that not only the uncertainty parameters in (1), which denote the uncertain wind power output, are the decision variables in the model need to be solved, but also is the allowable . wind power output interval Constraint (1.1) can be transformed into the following model, which makes (1) a two-layer optimization model as follows:
In real-world applications, the constraint may be too strict because the available wind power generation cannot be completely absorbed due to the limitations of spinning reserves or transmission interface capacities in some time periods. Therefore, the lower bound of the allowable wind power generation interval should be less than or equal to the lower limit of the predicted wind power generation interval
This is a typical QP problem and these problems can be efficiently solved using existing techniques, such as the interior point method. Note that the expression in (2), which can be interpreted as the security requirements of the system under the worst-case scenarios of uncertain parameters, is the key aspect of the robust interval optimization model. Therefore, the next section will describe (2) in detail. III. DETAILED ROBUST WIND POWER OPTIMIZATION MODEL
where and denote the th row of matrices and respectively. Equation (2) can be further transformed into
!
!
!
and its corresponding dual problem can be expressed as
,
A. Worst-Case Scenario for Wind Power Output In RO, the worst-case scenario is a set of parameter values such that security for any other scenarios can be guaranteed if and only if there is a feasible solution under this scenario [14]. Therefore, an analysis of the possible worst-case scenarios for wind power output is a prerequisite for this approach. The constraints include power balance, transmission interface flow, spinning reserve, ramping rate, and output power generation limits. Violation of the transmission interface flow constraints or spinning reserve constraints may lead to the curtailment of wind power. Therefore, the following four worst-case scenarios should be satisfied to guarantee the system security.
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1) The worst-case scenario for the positive spinning reserve constraint is
actual power system realistically and it is independent on the choice of slack bus. Equation (10) indicates that the transmission interface power flow must always be within its upper limit for the operational security of the power grid. 4) The worst-case scenario for the negative transmission interface flow constraint is
where and will be modeled as decision variables in the robust interval optimization problem and the following constraints should be met for wind farms:
2) The worst-case scenario for the negative spinning reserve constraint is
Equation (11) indicates that the transmission interface power flow must also be within its lower limit for the operational security of the power grid. B. Robust Interval Wind Power Optimization Model
For these worst-case scenarios, the total upward adjusted power and downward adjusted power for conventional units during the time period can be calculated from
As the look-ahead dispatch is a type of dynamic economic and should be distributed among the dispatch, conventional units and the following constraints should be satisfied between any two adjacent time periods:
Section III-A described the necessary conditions to determine the allowable wind power generation interval from a system security point of view. However, it is not sufficient to consider only security; economics should also be considered. With this, the robust interval optimization can be developed as follows: 1) Objective Function: The objective function involves two parts: the generation cost for conventional units and the penalty cost of possible wind curtailment for wind farms, where the generation cost is usually expressed as a quadratic function, in practice. Also when wind curtailment is considered, the upper limits of the maximum allowable wind power generation interval must be lower than the upper limits of the predicted wind power generation interval for every wind farm. Meantime, the lower limits of maximum allowable wind power generation interval must be lower than or equal to the lower limits of the predicted wind power generation interval for every wind farm for a feasible and practically meaningful generation schedule, as is expressed later in constraints (19) and (20). Hence, the penalty cost of possible wind curtailment can be expressed to be proportional to the magnitude of the difference between the predicted wind power output interval and the allowable wind power output interval to reach the objective of maximum wind power utilization. To be more concentrated, the costs associated with spinning reserve are neglected in the proposed model
3) The worst-case scenario for the positive transmission interface flow constraint is
where and represent the quasi-steady-state sensitivity [21], which can simulate physical response of an
where is the penalty coefficient and the selection of is based on the equal incremental principle. The incremental of the
WU et al.: ROBUST WIND POWER OPTIMIZATION METHOD FOR LOOK-AHEAD POWER DISPATCH
generation cost for conventional units and wind generators can be, respectively, expressed as
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6) The ramping rate constraint is
7) The power balance constraints are
8) The generation output limit constraint is where and usually take positive values. Obviously, the following conditions can be hold as long as > is satisfied:
