Rolling Generation Dispatch Based on Ultra-short-term Wind Power Forecast

The power systems economic and safety operation considering large-scale wind power penetration are now facing great challenges, which are based on reliable power supply and predictable load demands in the past. A rolling generation dispatch model based on ultra-short-term wind power forecast was proposed. In generation dispatch process, the model rolling corrects not only the conventional units power output but also the power from wind farm, simultaneously. Second order Markov chain model was utilized to modify wind power prediction error state (WPPES) and update forecast results of wind power over the remaining dispatch periods. The prime-dual affine scaling interior point method was used to solve the proposed model that taken into account the constraints of multi-periods power balance, unit output adjustment, up spinning reserve and down spinning reserve.


Introduction
With the shortage of energy worldwide and the environmental concerns of the public, researchers are working on integrating effectively renewable resources in existing power grids [1].As the most promising renewable power in technology and economy currently, wind power generation has gradually become a major alternative form.However, wind energy is non stationary and uncontrollable, that result in the uncertainty and intermittence of wind power output and more difficulties to forecast.Therefore, electric power systems economic and safety operation considering large-scale wind power penetration are now facing great challenges, which are based on reliable power supply and predictable load demands in the past.
Advanced power system dispatch technology [2][3][4] is one of keys for reducing the impacts of the intermittent and uncertainty of wind power output.Economic dispatch (ED) is a method to schedule the generator outputs with the predicted load demands over a certain period of time so as to operate an electric power system most economically [5].The classical ED problem involved only conventional thermal energy power generators.From the recent investigations, security economic dispatch in wind power integrated systems using a conditional risk method was introduced in article [6], a dynamic economic dispatch model based on stochastic programming was introduced in paper [7], optimizing economic/environmental dispatch with wind and thermal units was introduced in paper [8].These researches basically concentrated in dealing with the scheduling and unit commitment problem day-ahead.However, the characteristic of the predicting accuracy of wind power that decreases with the lapse of time will seriously impair the reasonableness of day-ahead scheduling, and bring about heavy burden for regulation services which are provided by automatic generation control (AGC).It is necessary to consider linking up day-ahead scheduling and AGC on the time scale by more meticulous generation diapatch modes.To achieve this we must incorporate the latest predictive information of wind power into the generation dispatch process.
The objective of this paper is to incorporate ultrashort-term wind power predictive information into the classical economic dispatch problem and propose a rolling generation dispatch mode.In Section II, a method, which is based on the use of discrete time Markov chain models of second order, will be utilized to modify the wind power prediction error state (WPPES) and update forecast results of wind power over the remaining periods.Section III will discuss the system power balance rolling constraints in each dispatch period.Afterward, a rolling generation dispatch model based on ultra-shortterm wind power forecast is proposed, which rolling correct not only the conventional units power output but also the power from the wind farm, simultaneously.In Sec-tion IV, the prime-dual affine scaling interior point method was used to solve the proposed model.In Section V, the simulation of the ten-unit test system demonstrates the economy and effectiveness of the proposed method.Finally, in Section VI, conclusions are drawn.

Markov Chain Transition Matrices Estimation of WPPES
Non parametric discrete time Markov Chain models have been largely used for generating synthetic wind speed and wind power time series [9][10], providing simulation results that usually offer excellent fit for both the probability density function and the autocorrelation function of the generated wind power time series.In this paper, in order to avoid the cumulative error form wind forecast to wind power, transition matrices of WPPES are directly estimated using second order Markov model as follows: for each , where is the prediction error state over the time interval In a discrete finite Markov process,the probability of a state at any step only depends on the previous state [11].
For N states, the transition matrix, , is an matrix.The generic element, , represents the probability that the state of process at P( ) S .An estimate for can be obtained as: ( ) where indicates the number of transitions from state to state S observed in the sequence of WPPES data .

Forcecasing Procedure in Generation Dispatch
The WPPES time series,  W , of a wind farm must be s established on the basis of historical wind power data beforehand by where W average power generated by the wind farm over ( ) . Indicating with ( ) h t  the state probabilities vector at time :

( ), , ( )
whose generic i-th element, ( ) , represents the probability that W ( ) It is possible to obtain the state probabilities vector at time , as follows:

( ) P( )
The ultra-short-term wind power forecast procedure can be defined by ( 5) and   , the observed state probability vectors at time -1 h and -2 h , which are computed utilizing only the most recent data collected in the time window.Bye modifying the WPPES over the remaining dispatch periods utilizing the maximum probability state, future wind power can be rolling updated.

Rolling Generation Dispatch Model
In general situation, day-ahead dispatch is divided into contiguous and equispaced intervals of length = t  , totally 96 periods a day.Wind power fast fluctuations, especially minute-to-minute variations, are mostly smoothed by units' inertia and control dead zones [12], so it can be concluded that not all of wind power fluctuations will impair the reasonableness of day-ahead scheduling.In order to link up rolling dispatch and day-ahead scheduling., the time axis is also divided into intervals of length 15min =15 min t  , updating wind power predictive values and rolling correct units power output and the power from the wind farm every 15 min.

Power Balance Rolling Constraints
At the initial time in dispatch period h, system power balance rolling constraints are established as: where the latest forecast system load in period t.

Cost Function for Conventional Generator
For the conventional generators, a quadratic cost function will be assumed, which is practical for most of the cases.The total operating cost over the remaining dispatch periods h to 96, , are expressed as: where i indicates operating cost of i-th conventional generator, which can be represented by where i , i and i c are cost coefficients for the i-th conventional generator, which are found from the input-output curves of the generators and are dependent on the particular type of fuel used [13].a b

Abandoned Wind Power Calculate
Based on the ultra-short-term wind power forecast values, abandoned wind power over the remaining dispatch periods can be calculated as follows: where 2 ( h W t f P  abandoned wind power over the periods h to96; * h W t P  ultra-short-term forecast power output from the wind farm in period t.
3) Generator power operating limits: where are the minimum and the maximum power outputs of i-th generator, respectively.

4) Regulation deviation limits:
In order to ensure the relevance of day-ahead scheduleing and rolling scheduleing,the maximum regulation deviation for conventional generators are set as: where i  is the maximum regulation deviation allowable for i-th generators.5) Up and down spinning reserve constraints: Integrated large-scale wind power, the system needs additional spinning reserve capacity to reduce the probability of load shedding and release regulation capability of AGC generators.

Rolling Generation Dispatch Model
The penalty factor,  , is incorporate into rolling gen- eration dispatch model for coordinating the contradictory relations between minimizing operating cost of conventional generators and not abandoning wind power .In this paper,  is set at a value more than equivalent cost for converting per unit of wind power into conventional generator output, taking value in the numerical example.Based on ( 6)-( 17) the rolling generation dispatch model can be written as follows: where F total cost over the remaining dispatch periods h to 96; H quadratic coefficient matrix of the objective function; c coefficient vector of one degree term; x power output variables from conventional generators and wind farm; ( ) h x ( ) g x equality constraint function; inequality constraint function, whose upper and lower limit is g and g , respectively.

Solving Method
The primary problem in this paper, a convex quadratic programming problem due to H is a positive semidefinite matrix, was divided into a series of logarithmic barrier sub-problems, and then prime-dual affine scaling interior point method [14] was utilized to get the optimal solution along the direction of original-Lagrange dual center path through iterations.First, the linear constraints from ( 19) to (20) were converted to the following standard forms: . .( ) the Lagrange dual problem can be obtained as (22).
where , y z are Lagrange multiplier vectors of the equality and inequality constraints, respectively.is an , Introducing the barrier parameter, (  > , and making meets perturbed Karush-Kuhn-Tucker (KKT) conditions as follows: where


x and ( )  w will converge to the optimal solution of the primary problem and the Lagrange dual problem.

Algorithm Steps
Step1 Input the original parameters and power output interpolations scheduled in the previous period.Update the latest forecast load demand and ultra-short-term forecast wind power over the remaining periods.
Step2 Give the initial point x y z , satisfing interior conditions.Set admissible error value  .
obtain solution of the search direction Calculate the step length parameter,  , in this direction.
Go to Step3.

Test System
The ten-unit test system is used in this paper to demonstrate the performance of the proposed method.The demand of the system was divided into 24 intervalsor.Conventional generator data and the latest forecast load x ,x H c 0 0 0 0 , data can be found in Tables 1 and 2. The test system was integrated with a wind farm, described by operation data of an actual wind farm, including 56 wind turbines of 2.5 MW, totally 140 MW.Curves of wind power drawn based on day-ahead forecast date, ultra-short-term forecast date obtained through second order Markov model and actual output date one day can be seen in Fig. 1.In general, the trends in curve 1 are much more similar to those in curve 3 then in curve 2. Figure 1 also shows that scheduleing only according to day-ahead forecast will result in a certain difference, which will impair the reasonableness of conventional generators power output scheduling ,and may cause a waste of wind energy resources.curve1(day-ahead forecast) curve2(ultra-short-term forecast) curve3(actual output)  .In this case, the computation time is 1.94s and iteration times are 14, that can meet the needs of online rolling generation dispatch computing.The objective function values before and after correction are shown in Table 3, which shows that after rolling correction average abandoned wind power per one period has reduced 15.2371MW and operating cost for conventional generators has been saved 71192 $.Thus, rolling generation dispatch can not only reduce abandoned wind power, but also make the power system economizing in energy consumption with more wind power accommodated.

Conclusions
In this paper, a rolling generation dispatch model based on ultra-short-term wind power forecast, utilizing Markov chain model method, was proposed.In generation dispatch process, the model rolling correct not only the conventional units power output but also the power from wind farm, simultaneously.The simulation results illustrates that the model can effectively promote power system accommodating wind power and optimizing the operation cost.Rolling generation dispatch is necessary in the background of the rapid development of wind power, energy conservation and emission reduction. t 2 represent coefficient matrix of the constraints function in (21), 1 , 2 indicate constant term vectors, is an unit column vector.By introducing , go to Step5.Step5 Determine the search direction and step length.By solving the following equation:

Figure 1 .
Figure 1.Curves of wind power forecast and actual output of 24-hours.
 power from the wind farm in period t after h times corrected.When h equals to 0, it represents day-ahead forecast power output from the wind farm; of conventional power generators;  ( ) h P t  i G t P h  -power from the i-th conventional generator in period t after h times corrected.When h equals to 0, it represents day-ahead schedule power output;