Stochastic Assessment of Opportunities for Wind
Power Curtailment
George Koustas, George Papaefthymiou, Member IEEE, Bart C.Ummels, Member IEEE
and Lou van der Sluis, Senior Member IEEE
Electrical Power System Laboratory (EPS), Faculty of Electrical Engineering, Mathematics & Computer Science,
Delft University of Technology (TU Delft), P.O. Box 5031, 2600 GA Delft, the Netherlands
e-mail:
g.papaefthymiou@tudelft.nl.
Abstract— An important characteristic of wind power is its
sto-chastic and non-dispatchable nature. Because of the development of wind power in recent years, stochasticity is becoming a driving parameter in the power system. Unpredicted and excessive power flows in the power system may be a result of this, especially since the pace of wind power developments is faster than transmission system re-inforcements. These developments, in combination with the limited operational flexibility of the conventional generation units within short time-spans, makes the future integration of large-scale wind power in the power system a challenging task. Temporary curtailment of wind power might provide a favourable solution for this, especially if this lifts barriers for further growth of wind power capacity. This paper presents a stochastic methodology for the assessment of the advantages and disadvantages of wind power curtailment as a solution for system congestion in relation to increasing wind power penetration. The method is applied in a number of case studies and is shown to reduce line overloading risks and power flow distribution variability, thereby increasing the feasibility for further wind power development.
Index Terms— Monte Carlo simulation, wind curtailment, power
flow, wind power.
I. INTRODUCTION
I
N the past decade, wind power has become the fastest-growing generation technology for renewable energy. At the beginning of 2006, the worldwide installed capacity of wind power was about 60GW , corresponding to an energy production of about 120T W h per year [1]. In Europe, wind power is becoming a generation technology of significance. In particular, as presented in the 2006 annual report of the European Wind Energy Association (EWEA), the total wind power capacity installed in 2006 reached 7.6GW , correspond-ing to an increase of 23% compared to the previous year [2]. Such a large-scale integration of wind generation causes several challenges in the management of a power system due to the non-dispatchable nature of the wind. One of the main challenges for the future is to see how systems with significant wind power penetration can be operated and designed for efficient integration without violating system security.In power systems there must be a continuous power balance between generation and load. Owing to the variability and unpredictability of wind power production, significant amounts of wind power complicate power system balancing [3]. In particular, when the share of wind energy in the system increases, there will be cases when wind power will cover or threaten to exceed system load. In such cases, the surplus of
wind energy may be curtailed, i.e. some wind power plants have to be shut down, or several wind power plants have to decrease their production. In order to prevent wind power curtailment, large-scale energy storage solutions may be used to store excess wind energy, but these are often not available. Another solution is to use international interconnections to other regions to export this excess of power. In this case, the limiting factor is the transmission capacity between the neighboring regions and the ability of this region to absorb this excess of wind power [1].
Certainly, wind power curtailment has economic conse-quences due to opportunity losses. The wind power producer loses part of its revenue, which will have an impact on the investment payback time. Often, such possibilities are not taken into account in investment plannings for wind farm projects. As discussed in [4], as the total wind capacity in the system increases, the output of the conventional generation running at the same time will be reduced. Eventually, a limit is reached below which the conventional generation cannot be further reduced due to technical reasons (minimum output lim-itations) and wind curtailment is required [5]. The installation of additional wind parks in the system, even though leading to an increasing participation of wind energy in the total energy mix, will lead to more frequent occurences for curtailment in case flexibility measures in conventional generation plant are not applied. As presented in [4], for the case of Ireland at approximately 4000M W of wind generation, ”the curtailment of the last wind turbine will be such that it can only operate for a few hours per year, near the times of system maximum demand”.
non time-dependent stochastic phenomenon, necessitating the use of large datasets for the deduction of statistically coherent results [7]. In order to tackle this problem, instead of the
chronological approach of directly using recorded datasets for
the analysis, the stochastic approach should be followed, i.e. simulation techniques should be used for the modeling of the system inputs stochasticity.
In this paper, the Monte-Carlo Simulation (MCS) method-ology developed in [8] is applied for the system stochastic modeling. In section II, the sampling of the system stochastic inputs (loads and wind power) is performed based on the respective marginal distributions and the underlying stochastic dependencies. In section III the implementation of wind power curtailment to the system operation is presented, while in section IV the impact of wind power penetration and wind curtailment on a specific power system is elaborated.
II. MONTE-CARLOSIMULATIONMETHODOLOGY
According to the probabilistic formulation of the problem, the stochastic system inputs (loads-wind generation) are mod-eled as random variables (r.v.’s) that follow specific probability distributions obtained by statistical analysis of related data [9]. These r.v.’s contain all necessary information for the stochastic assessment of wind curtailment to the power system. The proposed methodology for modelling the uncertainty of the stochastic inputs involves two basic steps [8]:
1) Marginal distributions: The system inputs are sampled based on the underlying distributions obtained by wind speed data. As is the general practice in MCS, for the sampling of a r.v. X with continuous invertible cumulative distribution function FX, first a uniform
random number U in [0, 1] is generated and then the transformation x = FX−1(u) is applied, where u is a realization of U [10]. In this case the samples x follow the distribution FX.
2) Stochastic dependence structure: The configuration of the dependence structure between the r.v.’s is derived. The point is to capture the prevailing dependence struc-ture that holds between the stochastic inputs. For ex-ample, in case of the wind, the wind speed patterns in different sites are correlated. In order to capture the mutual dependencies, the rank correlation ρris used and
[11].
The sampling of the r.v.’s is performed based on the theory of Joint Normal Transform methodology (JNT), in which the two main steps of MCS are combined. For the generation of n r.v.’s X = [X1, ..., Xn] correlated according to the n × n
correlation matrix R, the following steps are followed [12]: 1) Generate a set of n normals N = [N1, ..., Nn],
corre-lated based on correlation matrix R.
2) Transform the normals to uniforms. This is performed by the transformation U = FN(N ) where FN is the
cumulative distribution function (cdf) of the correspond-ing normal and U is the resulted n-dimensional uniform distribution.
3) Transform the correlated uniforms U into the desired marginals X, by applying the inverse transformation Xi= FX−1i(U ).
Specifically for the 2 stochastic inputs of this paper, the JNT has the following configuration:
• Concerning the wind power sampling, the wind speed
marginal distributions at the generation sites are consid-ered Weibull distributions and the wind speed patterns are highly correlated following a product moment correlation of 0.8. Hence, this will be the configuration of MCS for the sampled wind speed patterns concerning the marginals and the dependence structure. The wind speed distributions are transformed to wind power output using the static wind speed/power output characteristic of the wind turbine generators used [8].
• The MCS for the sampling of the stochastic load pattern shall take into account the fact that the load is highly time-dependent, following a periodical pattern with a period of one day. Hence, the stochastic behaviour of the loads is studied with the method of Time Frames
Analysis (TFA) [6], according to which the period of the
pattern is sliced in Time Frames (TF) where the load has similar statistical characteristics. The load in each TF is modelled by superimposing a random variable to the time-conditional mean. The practice in this study will be to slice the time period in 4 TFs; the load in each TF will follow a normal distribution with specific mean value and standard deviation, while within the TF the loads are almost independent following a product moment correlation of 0.3.
These distributions are propagated through the system model, which is in this case the steady-state system model [13], and the respective system state (node voltage) and output (line power flows) distributions are obtained.
III. WIND CURTAILMENT IMPLEMENTATION
As discussed in the introduction, the first and most impor-tant task of the transmission system operator is to maintain the power balance in the system. As the output of wind generation is increased or the load demand is decreased, the output of CG units running at the time is reduced in order to keep the system in balance. Eventually, each CG unit will reach a limit below which its output cannot be reduced further. De-commitment of these units is often difficult from an operational point of view, and involves lengthy minimum down-times. In order to prevent excess power flows to neighboring systems, it may therefore be more preferable to temporarilty curtail wind generation.
The total amount of CG regulating power required at any time depends on the sum of the system load and the wind power. In order to determine the total amount of regulating power on the system scale, the wind power is regarded as negative load and the netload at each system bus can be defined as the load demand minus the wind power at this bus:
PN L(i) = PL(i) − PW(i), ∀i ∈ [1, nbus= 39] (1)
where PL is the load and PW is the injected wind power.
In this context, PN L(i) actually corresponds to the power
injection at the respective system bus i.
the introduction of wind curtailment, the power balance for the whole system is performed according to the following equation: nbus X i=1 PCG(i) + Pslack= nbus X i=1 PN L(i) + Plosses+ DPw (2)
where DPwis the curtailed wind power for the whole system.
The minimum operational setpoint of the CG units is set to 30% of their nominal power output. Due to this restriction, wind curtailment is necessary when the netload is so low that it pushes the CG setpoint to 30%. In these cases, there is excess of generated power (from the co-generation of CG and wind). With the application of wind curtailment, there power balance is restored in the system, so for each sample it holds:
nbus X i=1 Pin(i) = nbus X i=1 Pout(i) ⇒ nbus X i=1 PCG(i) = nbus X i=1 PN L(i) + DPw⇒ DPw= 0.3 · nbus X i=1 PCG,N(i) − nbus X i=1 PN L(i) (3)
Algorithm 1 gives the regulation of setpoint x for the CG units and the wind power curtailed for each sample.
Algorithm 1 Regulation of the setpoint x of the CG units for i = 1 : allsamples do if 30% ≤ nbus X j=1 PN L(i) nbus X j=1 PCG,N(i) = x(i) ≤ 100% then
regulate CG, so that PCG(i, j) = x(i) · PCG,N(i, j),
∀j ∈ [1, nCG= 10]
else
if x(i) < 30% then
regulate CG, so that PCG(i, j) = 30% · PCG,N(i, j)
and curtail wind: DPw= 0.3· nbus X i=1 PCG,N− nbus X i=1 PN L else
regulate CG, so that x(i) = 1
end if end if end for
IV. APPLICATION TO APOWERSYSTEM WITH AHIGH
WINDPOWERPENETRATION A. System Data
As a case study for the estimation of the impact of wind curtailment, the 39 bus - 46 branch IEEE New England test network of Fig. 1 is used [8]. The system is considered to be equipped with thermal CG units. Hydro-power, which is commonly regarded as an ideal solution for balancing wind power variations, is totally absent. Bus 31 is the slack bus and corresponds to the interconnections with the neighbouring
W1 W2 W3 W4 W6 W7 W9 W10 W11 W12 W13 W14 W15 W5 W8
Fig. 1: IEEE New England Test System
systems. In this study, a distributed wind penetration scenario is investigated with the connection of 15 wind parks dispersed all over the power system. Each park is considered to be a uniform generation unit and all parks are of equal nominal power1. The wind penetration level is defined as the ratio of the total installed nominal wind power to the total installed CG: x = nbus X i=1 Pw,N(i) nbus X j=1 PCG,N(j) (4)
B. Stochastic wind generation
The total installed CG power is PCG,tot= 6000M W , hence
a x% wind penetration level means that the installed power of each wind park will be:
Pw,N = x% ·
PCG,tot
15 = x% · 400M W (5)
The sampling of the system inputs is performed based on the MCS methodology described in section II.
C. Results
The Load Flow analysis was programmed in PSS/E. The output set is the 46 transmission lines power flow distributions, the slack bus power flow and the system losses. Nine study cases are considered, comprising of the no-wind-penetration case and 4 wind penetration scenarios with and without wind curtailment, in which the penetration level is ranging from 0% to 100% with a step of 25%.
1’Uniform generation unit’ means that the wind speed pattern is considered
−25000 −2000 −1500 −1000 −500 0 500 1000 1500 20 40 60 80 100 power (MW) number of samples 0% 25% 50%
Fig. 2: Slack bus power flow distributions without curtailment.
1) Slack bus: The slack bus is responsible for restoring the
power balance in the system; hence, its power flow distribution gives important information concerning the system behaviour. In Fig. 2, the slack bus power flow distributions for the study cases without wind curtailment are given. The study stops at 50% wind penetration level, because PSS/E faces a convergence error for higher penetration levels. This error comes from the excessive transmission lines power flows. The increase in wind penetration leads to an increase in the variability of the power flows at the slack bus due to the induced stochasticity of wind generation. The increase in wind penetration pushes the occurrences towards lower and negative power flow values. This means that the probability of import of power through the slack bus decreases. The thermal units are pushed towards their minimum setpoint and the excessive power is driven to the slack bus (negative power flows as seen from the slack bus) and the neighbouring systems.
Besides, there are about 2500 out of the 10.000 samples concentrated at the zero power flow at the slack bus for all the penetration levels, but it cannot be observed to Fig. 2 due to the limited y-axis range. This means that there is 25% probability that there is a power balance to the system, corresponding to 25% of the operational time.
The study cases of wind curtailment implementation, is depicted in Fig. 3. PSS/E converges even for 100% wind pen-etration due the relieved transmission lines power flows. Also, the slack bus power flows don’t take negative values even for high levels of wind penetrations because the excess generated wind power is curtailed. A concentration of probability mass is observed in small values (0 − 100M W ), corresponding to the cases of the slack bus providing for the system losses. This occurs due to the increased system generation (CG+wind) which is sufficient to cover the load.
2) System power flows: The increasing wind penetration
leads to an increase in the variability of the power flows for all the system lines. Fig. 4 gives the distributions of the power flows in line 15 for all wind penetration levels. The presence of stochastic generation in the system results to highly bi-directional power flows. The vertical system structure is changed to a horizontal one, where the distri-bution systems become active, exchanging power with the
0 500 1000 1500 0 20 40 60 80 100 power (MW) number of samples 0% 25% 50% 75% 100%
Fig. 3: Slack bus power flow distributions with curtailment.
−1000 −50 0 50 100 150 200 500 1000 1500 2000 2500 3000 power (MW) number of samples 0% 25% 50% 75% 100%
Fig. 4: Power flows in line 15 for all wind penetration levels.
transmission system bidirectionally. This is justified by the bi-directional power flow distributions for line 15.
The impact of wind curtailment can be seen in Fig. 5 which gives the power flow distributions at line 13 for 50% wind penetration with and without curtailment. It can be seen that curtailment has the following result:
1) Decreases the power flow range (variability).
2) Shifts the power flow distributions towards lower ab-solute values.
Especially for the case of line 13 it seems that the whole distribution is shifted towards lower power flow values and the heavy tail of the distribution is cleared. The loadings of the lines are decreasing to values which are closer to the values obtained without wind. This is an important advantage since the overall generated power has been increased whereas the power flows have been kept to such low values that the lines are not overloaded.
The effects mentioned can be also depicted at Fig. 6, which gives the boxplot of power flows for specific lines for 50% wind penetration, without and with curtailment. For each transmission line 2 boxplots are given, the first one (from the left) is without wind curtailment and the second with curtailment.
4 4 7 7 13 13 16 16 19 19 20 20 21 21 29 29 34 34 42 42 44 44 −1000 −800 −600 −400 −200 0 200 400 600 800 power (MW) transmission lines
Fig. 6: Boxplot of transmission lines power flows, without and with curtailment.
0 100 200 300 400 500 600 700 0 20 40 60 80 100 120 140 160 180 200 power (MW) number of samples no curtailment curtailment
Fig. 5: Power flows in line 13 for 50% wind penetration.
plot of the overloading probability for all lines for a wind penetration of 50% for 2 cases: without and with curtailment2. We can see that the heavily loaded lines are relieved due to curtailment, whereas for lines with low probability of overloading, the curtailment is less effective, leaving the over-loading probability almost unchanged; hence, if we consider the response of the heavily loaded lines more critical for the evaluation of curtailment, we can accept wind curtailment as an adequate solution for limiting the excessive power flows in transmission lines.
3) Economic assessment of wind curtailment: When
im-plementing a solution such as wind power curtailment, it is important to know the amount of energy loss and how much economically viable is this solution. When we deal with 2For the derivation of the transmission lines overloading limits, the
follow-ing acknowledgement is taken into account: When the system is operatfollow-ing without wind penetration, the transmission lines are overloaded only for 5% of the samples. 25%0 50% 75% 100% 500 1000 1500 2000 2500
wind penetration level
Power (MW)
curtailed wind
wind production/curtailment wind production/no curtailment
Fig. 8: Energy for several wind penetration levels
discrete time instances (samples of MCS), then the energy yield from the sum of the instances is given by:
E = 1 n n X i=1 (6) where n is the number of instances.
Eq. (6) corresponds actually the mean value of power P for a period of time. Hence, the mean value of a power distribution gives the energy yield for a specific period of time. Applying this procedure, we take the wind energy potential, the wind energy yield with curtailment and the energy loss due to curtailment for all wind penetration levels(Fig.8).
0 4 8 12 16 20 24 28 32 36 40 44 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 transmission lines overloading probability no curtailment curtailment
Fig. 7: Overloading probabilities of the transmission lines
power output even though wind power is curtailed in lower wind speeds compared with the lower wind power penetration. Also, the slopes are different for the 3 plots, for each interval between the wind penetration levels, which means that the share of energy loss due to curtailment changes with increasing wind penetration.
V. CONCLUSION
In this paper, a stochastic methodology assessment of wind curtailment in a power system is presented. The probabilistic system analysis shows that the injection of stochastic gener-ation in a distributed scheme (fifteen wind parks connected all over the system) results to highly bi-directional power flows. The vertical system structure is changed to a horizontal one, where the distribution systems become active, exchanging power with the transmission system bi-directionally.
The method of wind curtailment is applied in the sense of maintaining the power balance in the system and prevent the excessive power generation which is driven towards the neighbouring systems through the slack bus. The solution of the wind curtailment can be applied to achieve:
1) Limitation of excessive power flows in the transmission system, reducing the risk of overloading
2) Reduction of the variability of the power flow distribu-tions caused by wind power
3) Increase of the potential for further wind energy devel-opment
Hence, wind curtailment could be a solution for the im-provement of power system operation with large-scale wind power.
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