Controlling the joint operation of a windfarm with a biomass plant using
a Kalman filter to minimize imbalance costs in the Belgian electricity
market
P.C.E. Geurts van Kessel
July 23, 2012
Abstract
A joint operation between a windfarm and a biomass plant is proposed where the biomass plant adjusts its production to compensate for weather randomness and to avoid the payment of imbalance costs. This is implemented by using a Kalman filter to model the process of electricity production forecasts versus actual production, which serves as input for the biomass control mechanism. We focus on reducing negative imbalance. The model is tested on real data from a 77MW windfarm and the results show that the proposed control mechanism is capable of reducing significantly the negative imbalance. However, the capacity of the biomass plant seems crucial for optimal compensation of the negative imbalances.
1
Introduction
In late 2011, Belgium had approximately 1,100 MW of installed wind-power capacity. The past few years we have seen a steady increase in the already significant level of such capacity, and this is expected to continue in the years to come [1]. The electricity generated by wind farms fluctuates considerably compared to conventional fossil-based electricity generation. The variable and un-predictable nature of wind energy obviously poses chal-lenges in terms of maintaining the balance and therefore security of the power grid [1]. In the electricity market, supply and demand has to be in exact equilibrium at all times due to the practically non-storable character of large scale electricity [2].
Within the Belgian electricity market, Balance Responsible Parties (BRPs) compete for supply and demand of electrical energy under supervision of a Transmission System Operator (TSO), who is respon-sible for maintaining the power balance in the power grid [3]. The Belgian TSO is Elia N.V. In order to control the power balance, all BRPs connected to the grid within the Belgian control area are required to provide the TSO with a day-ahead forecast of injections and withdrawals of electricity inside a single Program Time Unit (PTU) t with a duration of 15 minutes [2]. A deviation in actual production from the day-ahead forecast implies the payment of imbalance costs.
In the literature, several systems have been imposed to decrease power imbalances, including systems that try to take advantage of some kind of storage systems based in batteries [4], [5]. Another way to solve the problem is to combine different kinds of renewable resources, in order to reduce both the dependency of wind and the costs for imbalance. In their articles, [6]
and [7] provide a thorough overview of the literature in this field. Combined operation of hydro- and wind units has been proposed in [8], considering the uncertainties in both wind power generation and market prices. In [9], the utilization of a generic energy storage device for balancing the differences between forecasted and real productions in a windfarm is analyzed, when acting in a market environment. Cooperation between a wind farm and a conventional multi-resevoir hydropower system is considered in [10]. Two methods for minizing imbalances of windfarm power output are proposed by [11]; the first one considers the windfarm to bid alone in the day-ahead market, trying to minimize the risk of the bid and based on a statistical analysis of the expected production probability; the second one couples a hydro power plant with the windfarm, in order to minimize the imbalance costs incurred by the windfarm owner. Many researchers focus on a joint operation of hydro and wind. However, not all landscapes are suitable for this type of operation given the need for a height difference. Many researchers in this field, including the reseachers above, do investigate the potential of combining different types of renewable energy production techniques, but the ‘how’ question is left unanswered relatively often. They do model the system and calculate potential cost savings, but lack the development of a control policy.
to cover the possible imbalances between the predicted and real values of its power output [7].
In this thesis, combined operation of a windfarm with a biomass plant is examined. This will be done by using a Kalman filter to predict the state (energy production) at timestep k + 1 where k is 1 [min] and apply a control u for the biomass plant based on the predicted state for the next time-step.
The model proposed in this thesis can be implemented by windfarm owners that aim to minimize their imbal-ance costs by using a biomass installation. The struc-ture of this paper is organized as follows: Section 2 de-scribes the characteristics of the Belgian power system in more detail; Section 3 describes a windfarm and a biomass plant in mathematical terms, both in separate and joint operation; Section 4 introduces the Kalman filter as a computational method for generating short-term predictions and control Kalman filter application to our situation; in Section 5 the model is applied to the case of a Belgian windfarm operator; Section 5 shows the results of this application, using real data from a Belgian 77 [MW] windfarm ; and finally, in Section 6, the conclusions are exposed.
2
The Belgian power system
2.1
The day-ahead market
As power production and consumption are largely pre-dictable, 95% of the energy is traded on a day-ahead market. Each BRP, responsible for balancing their own internal production and demand, can sell or buy extra energy on the energy market. For the TSO to verify the power balance, each BRP has to submit a forecast one day ahead of execution (D-1) before 14.00h. This fore-cast ˆPw,tdescribes the total amount of energy produced
by a windfarm in PTU t ∈ {1, 2, ..., 96} within day D. It is the responsiblity of the TSO that the forecasts for day D are in balance so that no energy suprplus or shortage will exist based on prior knowledge [3].
Figure 1 provides an overview of this process.
Figure 1: The Day ahead bidding principle [1]
When the BRP submits its day-ahead forecasts (nom-inations), the total of injections must be equal to the total of off-takes on a quarter-hourly basis at every con-nection point. The TSO evaluates the forecasts in the context of its duties of operating and maintaining the Belgian grid, including considerations of safety, reliabil-ity and efficiency. In particular, if the balance obligation is not respected, the TSO has the right to reject all or part of the forecasts [1]. The TSO informs the BRP on
Day D-1 before 18h00 whether BRPs day-ahead fore-casts are confirmed or not and what are the reasons for possible rejections. This aspect has no implications for this study, where it is assumed the forecasts for day D are confirmed.
Figure 2: Load on the Belgium grid for one week
Figure 2 shows actual measurements from the Belgian TSO Elia of a typical load profile (energy comsumption) for the Belgian control area over the course of a week. This profile shows a clear distinction between day and night, with a load of 12 GW during a workday and 9-10 GW in the weekend, while the load at night is consistent, 7-8 GW, during the whole week. Within a day, the average load consistently shows a minimum at 04h00 and a maximum between 07h00 - 09h00 and between 18h00 - 20h00.
Figure 3 gives an overview of the Belgian power sys-tem. It describes the relation between participants with offtake contracts (buyers) and participants with deliv-ery contracts (power producers). The role of the TSO, Elia, is already discussed. BELPEX is the Belgium power exchange market, which determines the energy price pBP X. Figure 4 shows per 24h, the yearly average pBP X in EUR/MWh.
Figure 3: Graphical overview of the Belgium power system
2.2
Green certificates
production portfolio. In fact, green certificates are sub-sidies. In this system, the producers of renewable energy receive certificates at their disposal according to the vol-ume of renewable energy produced. These certificates are then transferred to the buyers of that electricity so that they do not have to pay the penalties for the per-centage of renewable energy they would use. The im-plementation of such a system has a stimulating effect on the production of renewable energy in Belgium. The federal, Flemish and Walloon governments have devel-oped a scheme requiring system operators to purchase green energy certificates at a set minimum price pgreen
[12]. Table 1 provides an overview of pgreenfor different
types of renewable energy techniques.
Table 1: Belgian green certificate price pgreen for different
types of renewable energy production techniques
Description pgreenin EUR/MWh
Onshore windfarms 50 Offshore windfarms 107
Solar energy 150
Hydro 50
Other including biomass 20
2.3
Imbalance prices and costs
The imbalance prices pP OSand pN EG[EUR/MWh]
rep-resent the prices related to imbalance in the system due to a deviation of actual production Pw,t from the
day-ahead forecast ˆPw,t defined as
Dt∗= DtN EG if ˆPw,t− Pw,t> 0; DP OS t if ˆPw,t− Pw,t< 0; DtZERO if ˆPw,t− Pw,t= 0; (1)
where Dt∗ is the deviation in [kWh] or [MWh], depending on the magnitudes of ˆPw,t and Pw,t. When
the power producer has an energy surplus (DP OS t ),
the TSO buys this surplus energy at pP OS. Vice
versa, when the power producer has an energy shortage (DN EG
t ), the power producer buys the lacking energy
from the TSO at pN EG [3]. DtP OS is called positive imbalance, DtN EG is called negative imbalance.
Figure 4 shows the yearly average values for pBP X, pN EG and pP OS over the course of a day. Note that
pP OS< pBP X< pN EG ∀t
In addition, it is important to note that pN EG are ac-tual costs that have to be paid to the TSO, where pP OS is the price the power producer gets for the generated electricity surplus DP OS
t . The difference between pBP X
and pP OS can be considered as opportunity costs.
All prices p are determined by a traditional market mechanism based on supply and demand. Although figure 2 is based on a weekly load profile, it’s clear
Figure 4: Yearly average pBP X, pP OSand pN EGper quar-ter
Figure 5: Unbalance per month over 2011 [EUR]
that daily energy prices in figure 4 follow roughly the same pattern as the demand curve in figure 2. Note that when demand for energy increases rapidly (early morning around 06h30 and early evening around 18h00), the difference between pBP X and pN EGreaches
its maximum, while the difference between pBP X and
pP OS reaches its minimum. This means that during
these hours, a shortage of energy is the least desirable, and a surplus of energy is the least problematic. In case DZERO
t , there is no deviation at all. A detailled
overview of the imbalance price build-up can be found in [1]. Figure 5 shows the actual monthly imbalance costs over 2011, where the red and green bars show the costs for negative and positive imbalances respectively. The red and green lines in figure 5 show the average pN EG and pP OS respectively on a monthly basis. The
data is obtained from the same windfarm as where the control mechanism will be tested on in Section 5.
The objective of this paper is to develop a control mechanism for a biomass plant that decreases the num-ber of negative imbalance situations, i.e. DN EG
t
First, figure 5 clearly shows that the costs of negative imbalance form the majority of all imbalance costs. This trend is consistent through the years, based on inter-views with employees from the case company (see sec-tion 5).
Secondly, in this thesis the day-ahead forecast is treated as a given. More specifically, where electricity shortage can be compensated by the biomass plant, energy sur-plus is more difficult to incorporate in a biomass control mechanism. The best way to prevent DP OS
t situations
is better day-ahead forecasting. The day-ahead forecast needs to be updated with some ‘biomass buffer’ that can absorb the potential energy surplus by decreasing the actual biomass output. Figure 6 shows this illus-trative use of the biomass plant in a situation of excess wind power generation. All numbers are fictive and in kWh.
Figure 6: Illustrative use of the biomass plant
Lastly, DN EG
t implies actual payments, while DtP OS
are “just opportunity costs”. In addition, the re-newable energy producer obtains green certificates for all kWh that have been produced, also for excess generated kWh. Therefore, there is no incentive in using biomass to decrease the actual electric-ity production to reach the day-ahead forecast since it would result in a (significant)loss of green certificates.
3
Modeling
3.1
Introduction
In order to analyze the optimal operation of the com-bined wind-biomass plant, the stand alone operation of a windfarm and a biomass plant are described first. The day-ahead forecast ˆPw,tis variable in the planning
pro-cess but is constant in the operation propro-cess.
3.2
Independent scheduling
3.2.1 Windfarm stand-alone operation
The revenue of a windfarm is the difference between the revenues from the energy sold and the costs for the in-curred imbalance [13] and [11]. For the sake of simplic-ity, the operational costs of the windfarm are supposed to be negligible, although this is not realistic. The stand alone-operation of the windfarm can be described as fol-lows:
pBP Xt Pw,t+ pgreenPw,t− ht, ∀t (2)
with the constraint
0 ≤ Pw,t≤ Pw,max, ∀t (3)
where pBP X
t is the market price, pgreen are the green
certificates (both in EUR/MWh) and
ht= pN EGt (max{0, ˆPw,t− Pw,t}) (4)
is the penalty to be paid over PTU t in EUR. 3.2.2 Biomass stand-alone operation
As for the the biomass plant, the stand alone-operation can be described as:
pBP Xt Pb,t+ pgreenPb,t, ∀t (5)
with the constraint
0 ≤ Pb,t≤ Pb,max, ∀t (6)
where Pb,max the is maximum capacity of the biomass
plant, directly imposing the upper bound of Pb,t.
The objective of the biomass plant is to cover the neg-ative imbalances of the windfarm. Hence the biomass plant aims to coordinate with the windfarm, trying to partially compensate the wind power imbalances. Ac-cording to this objective, the plant should adjust the operation at small discrete time-steps, either reducing or increasing the bio gas generation, trying to cover the negative imbalances of the windfarm [6].
3.3
Combined operation
During operation, Pˆw,t and Pw,k from the auction
process and the actual wind production respectively are known. The aim is to choose the optimal value of the actual biomass electricity production, Pb,t in order
W rt= pBP Xt Pw,t+ pgreenPw,t− ht (8)
is the wind revenue in PTU t in EUR/MWh,
Brt= pBP Xt Pb,t+ pgreenPb,t (9)
is the biomass revenue in PTU t in EUR and
ht= pN EGt (max{0, ˆPw,t− Pw,t}) (10)
is the penalty to be paid over PTU t in EUR. Note that Eq. (10) is the same as Eq. (4) but is stated here for completion.
4
Computational methods
4.1
Introduction
For today’s power systems and windfarm owners it is ex-tremely important to know how wind behaves at specific windfarms in terms of operations and scheduling. Wind power production forecasting and simulation could be achieved either through physical or statistical models, or their combinations [14]. Among statistical approaches in this field, Markov decision processes (MDPs) pro-vide a mathematical framework for modeling decision making in situations where outcomes are partly ran-dom and partly under the control of a decision maker. MDPs are useful for studying a wide range of optimiza-tion problems solved via dynamic programming. MDPs were known at least as early as the 1950s. Today MDPs are used in a broad variety of areas, including automated control, economics, manufacturing and robotics.
More precisely, a Markov Decision Process is a dis-crete time stochastic control process. At each time step, the process is in some state S, and the decision maker may choose any control action u from a set of actions U . Alternatively, Usis the finite set of actions that is
avail-able in state S. Pu(Si, Sj) is the probability that action
u in state Siat time t will lead to state Sjat time t + 1.
Markov decision processes are an extension of Markov chains; the difference is the addition of control actions u.
Markov chains are a popular tool to model, forecast and simulate the wind speed (and electricity produc-tion) in a discrete and statistical way. In their article, [15] used a continuous Markov chain to model turbulent wind speeds based on past measurements at a single site. Moreover, [16] used first-order Markov transition ma-trices to model the three-hour average wind speed and direction data in Algeria. No application of MDPs for controlling joint operation of a windfarm with a biomass plant were found in literature. For a Markov decision process application in wind power series data, the one-step transition matrix P contains the probability that the generated electricity by the windfarm, when in some
state Si, will move into another state Sjat the next
sam-pling time. A one-step, i.e. first order, transition matrix P could be represented as p11 . . . p1n .. . . .. ... pn1 . . . pnn (11)
Each entry of this matrix is a probability and these sat-isfy the following conditions: 0 ≤ pij; P
n
j=1pij = 1;
i, j = 1, . . . , r [17, 14].
However, our objective is to minimize negative im-balances DN EG
t as optimally as possible. Therefore, in
order to find an optimal control policy, we need some actual measurements from the current time step to be included in the prediction of state x for the next time step. Besides, the biomass plant has a very short ad-justment time of around 1 [min], enabling us develop a control mechanism to balance potential imbalances within a PTU t. A Kalman filter was found suitable for this application.
4.2
The Kalman filter
Within the significant toolbox of mathematical tools that can be used for stochastic estimation of noisy mea-surements, one of the most well-known and often-used tools is the Kalman filter. The Kalman filter is named after Rudolph E. Kalman, who in 1960 published his famous paper describing a recursive solution to the descrete-data linear filtering problem [18, 19]. The Kalman filter is essentially a set of mathematical equations that implement a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance when some presumed conditions are met. Since the time of its introduction, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. This is likely due in large part to advances in digital computing that made the use of the filter practical, but also to the relative simplicity and robust nature of the filter itself. The Kalman filter can be seen in action on most GPS systems. As a car enters a tunnel the GPS signal is lost, but the navigation device will continue to try to maintain the position based on the Kalman filter model. A complete tutorial about Kalman filtering is provided in [18, 20].
The Kalman filter addresses the general problem of trying to estimate the state x ∈Kn of a discrete-time
controlled process that is governed by the linear stochas-tic difference equation
xk= Axk−1+ Buk−1+ wk−1 (12)
with a measurement z ∈Kmthat is
The n×n matrix A relates the state at the previous time step to the state at the current step, in the absence of either a driving function or process noise. The m × n matrix H in the measurement equation relates the state to the measurement zk.
The random variables wk and vk respresent the
pro-cess and measurement noise respectively. They are as-sumed to be independent of each other and with normal probability distributions:
p(w) ≈ N (0, Q) (14) p(v) ≈ N (0, R) (15) In general, the process noise covariance Q and measurement noise covariance R matrices might change with each time step or measurement, however in the case of windfarms we consider them constant since the process is the same each time step and the measurements are measured exactly the same way each timestep with high accuracy.
The Kalman filter process has two steps: the predic-tion step, where the next state of the system is predicted given the previous measurements, and the update step, where the current state of the system is estimated given the measurement at that time step. The steps translate to equations as follows [20]: ˆ x−k = Aˆxk−1+ Buk−1 (16) Pk−= APk−1AT + Q (17) Kk= Pk−HT (HPk−HT + R) (18) ˆ xk= ˆx−k + Kk(zk− H ˆx−k) (19) Pk= (I − KkH)Pk− (20) where ˆ
x−k is the predicted mean of the state, on time step k before seeing the measurement
Pk− is the predicted covariance of the state, on time step k before seeing the measurement
Kk is the Kalman filter gain, which tells how much
the predictions should be corrected on time step k based on the measurements
ˆ
xk is the estimated mean of the state, on time step k
after seeing the measurement (i.e. the ’update’) Pk is the estimated covariance of the state, on time step
k after seeing the measurement (i.e. the ’update’) Figure 7 provides a graphical overview of the Kalman filter. Note the initial estimates ˆx−k−1 and Pk−1− which serve as initial input for the Kalman filter.
Figure 7: A complete picture of the operation of the Kalman filter
In essence, the Kalman filter has two ways to estimate a state, the first relies on perfect knowledge of the mea-surements of the output, so that R has a (very) small value. Under these circumstances the measurement update equation becomes basically ˆxk = Kkzk. This is
applicable to our situation. The second way is relying on perfect knowledge of matrixes A and B and any inputs to the system u. In this case the Kalman filter gain Kk is zero and the filter applies the normal state
space equations. This condition would require R to be large compared with HPk−HT approaching infinitely
noisy measurements. For more deep investigation of the Kalman Filter see reference [20].
4.3
Filter tuning parameters
The Kalman filter has two tuning parameters: the mea-surement noise covariance R and the process covariance Q. In the actual implementation of the filter, R is usu-ally measured prior to operation of the filter. Measuring the measurement error covariance R is generally prac-tical because the measurements are needed anyway for running the filter.
The determination of the process noise covariance Q is generally more difficult as we typically do not have the ability to directly observe the process we are es-timating [20]. Under conditions where Q and R are constant, both the Kalman gain Kk and the
estima-tion error covaricance Pk will stabilize quickly and then
4.4
Prediction horizon
A power producer is only penalized for a deviation from its forecast at the end of a PTU. Hence, the power pro-ducer is free to have any power profile during a PTU. The biomass plant has an adjustment time of 1 [min]. Therefore, we split up PTU t into discrete time-steps k ∈ {1, 2, . . . , 15} of 1 [min].
Now let xk be the state of the plant at timestep k,
ˆ
xk+1 the Kalman-predicted state at the next timestep
and yk+1 be the ”desired” state at k + 1. It follows
easily that yk+1 is reachable from xk+1 when we
have a control mechanism for the biomass installation so that state ˆxk+1 reaches state yk+1. This control
mechanism is activated at timestep k, respecting the 1 [min] adjustment time of the biomass plant. The ques-tion is how to obtain the desired state y within the PTU. For determining the desired state in the next time-step we need to know the behaviour of the electricity production within a PTU.
Figure 8: Production data from a 77 [MW] Belgium wind-farm
Figure 8 shows the electricity production data from a 77 [MW] windfarm in the southern part of Belgium for sevens 15 [min] time intervals. The plots are from different days and different times of the day. Figure 8 shows that it’s fair to assume that the electricity pro-duction during a single PTU can be treated as linear, i.e the electricity production is almost equally distributed among the 15 minutes. This is shown in Figure 9.
4.5
Control
4.5.1 Introduction
From the linearity in Figure 9 follows that within PTU t:
yk =
ˆ Pw,t
15 k (21)
Figure 9: Energy production within a single PTU
where yk is the desired state at timestep k and ˆPw,t is
the day-ahead forecast for PTU t.
From eq. (21) follows that y15= ˆPw,t. Now
Sk= k
X
i=1
xk (22)
where xk is the actual (measured) state for timestep k
and Sk is the total (cumulative) amount of electricity
produced until timestep k within PTU t. From k ≤ 15 follows that for any k
Sk+ 15 X i=k+1 xi= Pw,t (23) 4.5.2 Control uk
The control vector uk is used so that yk− ˆxk has to be
minimized. That means yk− ˆx−k
has to be minimized, which means, according to the Kalman formula
yk− (Aˆxk−1+ Buk−1)
has to be minimized.
Although Kalman filters are designed to host a con-trol system, the concon-trol in this thesis is left outside the Kalman algorithm. The Kalman filter is used in its most basic form - single variable with a constant model ma-trix. There are two reasons for developing a separate control mechanism:
2. During the joint operation of the windfarm and the biomass plant, activating a biomass generator causes a power ’spike’. The Kalman-hosted con-trol system would have been subjected to the same smoothing as the windfarm outputs and that is not realistic.
If the generated electricity by the windfarm is greater than expected, i.e. yk < ˆx−k, no biomass is needed. In
case yk> ˆx−k, a function f is created
f (ui) = yk− (x−k + ui) (24)
where ui is the number of generators generating energy
in the biomass plant with i = {1, 2, . . . , n}. The control mechanism automatically calculates the optimal u∗i for every time-step. When the biomass plant occasionally generates more energy than necessary for time-step k (due to discrete steps of 700 kW of control capacity), the contoller adjusts the biomass energy production for the next time-step.
If all answers for f (ui) result in an energy shortage,
the control activates all generators (un) to at least try
to compensate as much as possible.
5
Implementation
5.1
Data
The proposed control strategy is tested using real minute-to-minute production data and the day-ahead forecasts from a windfarm in Southern Belgium. The data is obtained from the owner of this windfarm, a Belgian renewable energy producer. Minute-to-minute data used for this thesis are from three days: January 18th 2011, January 28th 2011 and February 10th 2011. Unfortunately, there was no data available from other seasons.
5.2
Kalman filter settings
The settings for the Kalman filter include the state ma-trix A, the control mama-trix B, the observation mama-trix H and the values for the process and measurement noise covariances Q and R.
Table 2: Kalman filter input parameters
Parameter Description Value A State transition matrix 1
B Control matrix 0
H Measurement transition matrix 1 Q Process noise covariance 0.1 R Measurement noise covariance 1e−6
Changes in wind speed vwind
k occur relatively smooth,
especially on a small time scale. In other words, vwindk ≈ vwind
k+1 (25)
where k = 1 [min]. Therefore, the state transition matrix A, which relates the state at the previous time-step to the state at the current time-step, is set to 1 assuming the state at the next time-step will be the same as the current state
A = 1 0 . . . 0 0 1 . . . 0 .. . ... . .. ... 0 0 . . . 1 (26)
The control matrix B has been set to zero, since the control is left outside the Kalman filter. See subsection 4.5 for explanation. B = 0 0 .. . 0 (27)
Observation matrix H translates the true (measured) state into the Kalman algorithm. Since the measure-ments are obtained directly from the TSO, we don’t as-sume error on these measurements; the measurements from the TSO must be translated to system states one to one. In addition, the measurements are in the same space as the state space (e.g. both kWh or MWh).
H =1 0 (28)
According to Eq. 15 and Eq. 14, the process covari-ance Q and the measurement covaricovari-ance R are normally distributed with zero mean. Section 4.3 elaborates on the difficulty of finding the optimal values for Q and R. However, in this case there is little process noise since (a) we know the process and (b) the process does not change over time. After tuning manually, the value for Q is set at 0.1. The measurement noise has even a smaller value since the measurements are directly ob-tained from the turbines at the windfarm. These mea-surements have a very high accuracy and are always measured the same way. The value for R is set at 1e−6.
5.3
Characteristics of the windfarm and
the biomass plant
The biomass plant uses of a gasification technique. Gasification is a process that converts organic or fos-sil based materials into carbon monoxide, hydrogen and carbon dioxide. This is achieved by reacting the mate-rial at high temperatures (>700◦ Celsius), with a con-trolled amount of oxygen and/or steam. The gas feeds a generator which produces electricity. For the biomass plant, the following assumtions have been made:
2. Feedstock has been assumed widely available. 3. The setup time of 1 [min] (see Table 3) is only true
when the biomass plant has already generated gas. It’s assumed that the biomass plant always pro-duces gas.
Table 3: Windfarm and biomass characteristics
Parameter Description Value Windfarm
Pw,max Total windfarm power 77000 kW
Number of turbines 11 Power per turbine 7000 kW Biomass plant
Pb,max Total biomass power 6300 kW
Capacity per generator 700 MW Number of generators 9 Setup time 1 [min]
The control ui respresents 9 biomass engines of 700
kW that can be turned on and off with a 1 [min] setup time so i = {1, 2, . . . , 9}. All power capacity data is expressed in kW. All energy data is expressed in kWh where kWh is the amount of electricity one generator generates in one hour when running at full capacity. In this case, one generator would produce 700 kWh when running one hour at full capacity. However, since the model works on a minute-to-minute basis where k = 1, kWh is devided by 60:
700
60 = 11.67 (29) where 11.67 is kWh/min. Accordingly, the maximum amount of energy one generator can generate in one PTU is 175 kWh/quarter. The results of the states of the biomass plant are shown in Table 4.
Table 4: Biomass plant states
State Hourly kWh Quarterly kWh Minute kWh
u0 - - -u1 700 175 11,67 u2 1400 350 23,33 u3 2100 525 35,00 u4 2800 700 46,67 u5 3500 875 58,33 u6 4200 1050 70,00 u7 4900 1225 81,67 u8 5600 1400 93,33 u9 6300 1575 105,00
In addition, note that the model is programmed in such a way that the number of generators is variable. Pb,max= 6.3 MW in this base case scenario, but can be
increased to see how the control behaves.
6
Results
The proposed control mechanism to cover negative im-balances is tested using real production data and fore-casts for a day, verifying whether the production pro-gram of the biomass plant covers the negative imbal-ances of the windfarm. The graphs in this section are all from January 28th 2011. The other days, January 18th and February 10th 2011, showed comparable re-sults. All modelling and simulations in this thesis have been performed with Python c .
6.1
Kalman filter
Figure 10 shows the actual production versus the Kalman predictions for one day.
Figure 10: Kalman prediction for January 28th
Figure 11 shows the first 15 minutes of the same day. Both graphs show that the Kalman filter produces ac-curate predictions of the state at the next time-step. Figure 12 shows for 16 randomly chosen minutes the day-ahead forecast, the Kalman filter prediction, and the actual measured value. The graph clearly shows that in the majority of minutes, the Kalman filter comes (very) close to the actual value.
6.2
Controller performance
Figure 13 shows the control for January 28th 2011. The light blue line shows the actual measurements from the windfarm per minute, the green line shows the desired state per minute and the blue dots show the Kalman prediction for time-step k plus the added biomass elec-tricity to cover imbalance.
Until k ≈ 450, the biomass plant covers nearly all occured imbalances. However, between k ≈ 450 and k ≈ 750 the negative imbalance DN EG
k >Pb,max, leaving
Figure 13: Control mechanism Jan. 28th with 6300 kW biomass
Figure 14: Control mechanism Jan. 28th with 24500 kW biomass
capable of balancing the wholde negative imbalance due to the constraint Pb,max. In order to get better insight
in controller performance, figure 14 shows the same plot with 24500 kW biomass capacity instead of 6300 kW. The graph shows that almost all imbalances are covered with some exceptions between k ≈ 500 and k ≈ 600.
Furthermore, figure 13-14 show some situations (around k ≈ 800) where windfarm output is greater than desired. In those situations, the controller
de-creases the biomass output to zero to avoid even more positive deviation.
Figure 11: 15 [min] Kalman prediction
Figure 12: Kalman performance for 16 randomly chosen minutes from January 28th 2011
first PTU (k = 690 to k = 705), the green line shows the desired cumulative state in kWh/min. Note that the desired state y at k = 705 corresponds to the day ahead forecast of the 47th PTU (705/15), i.e. y705 = ˆPw,47.
The light blue line is the electricity production of the windfarm. The red line shows the electricity production of the biomass plant and lastly, the dark blue line plots the sum of wind and biomass electricity production.
For the first two PTUs, the biomass plant is run-ning at full capacity. However, the plant does not have enough capacity to cover all imbalances given the gap between the dark blue and the green line. For the last two PTUs, windfarm electricity output increases due to stronger wind and the controller adjusts the biomass plant accordingly. This results in a dark blue line that covers the green line almost perfectly.
Figure 15: 6300 kW biomass control [per min]
Figure 16: Cumulative power [per 15 min]
6.3
Optimal plant size
Figure 13 and 14 show that the size of the biomass plant need to be in proportion with the size of the windfarm to cover at least a significant share of negative imbalances. The question rises how much biomass capacity, in [MW], is needed to cover X% of all negative imbalances. To get insight into this question, the model automatically identifies the ’worst case’ time-step kworstcase, i.e. k
with the largest negative imbalance within the dataset, and applies a what-if analysis on kworstcase. The model
feeds kworstcasewith ui, i = {0, 1, 2, . . . , 51}. Since u1=
0.7 [MW], u51corresponds with a biomass plant
capac-ity of 35 [MW]. Figure 17 shows the capaccapac-ity of biomass needed to cover X% of negative imbalances. In this fig-ure, reaching 100% means that all negative imbalance during kworstcase is compensated by the biomass plant.
Figure 17: Negative imbalance coverage ratio January 28th
Figure 18: Biomass capacity versus cumulative desired states
Reaching 100% means that all imbalances of the day are covered. However, note that the horizontal line ends slightly above 100%. This is because of the small pos-itive imbalance which can be seen in figure 13 between k ≈ 780 and k ≈ 880.
The results show that the initial Pb,max of 6.3 [MW]
covers the negative imbalances for January 28th 2011 for ≈ 20%. For January 18th and February 10th 2011, the 6.3 [MW] biomass plant covers the negative imbalances for 25% and 40% respectively. To cover all imbalances, a 30 [MW] biomass plant is needed on January 28th, while a 17 [MW] and a 13 [MW] biomass plant are needed to cover all imbalances on January 18th and February 10th 2011, respectively.
7
Conclusion
and
further
re-search
In the near future wind energy will have an important share in our total energy production portfolio. This forces us to solve the reliability problem of this energy
source. The objective of this thesis was to develop a con-trol mechanism for a biomass plant in order to decrease the number of negative imbalance situations. Negative imbalance situations occur when the windfarm produces less energy than expected due to the inherent variable nature of wind. A deviation between the forecasted production and actual production of the windfarm im-plies the payment of imbalance costs and this deviation should therefore be compensated by a biomass plant. In this way, renewable energy producers reduce their risk due to the uncertainty in the wind power prediction and in prices of the penalties for imbalance.
First, a Kalman filter was build and adjusted to operate within a single Program Time Unit (PTU) with a duration of 15 [min]. The Kalman filter was capable of providing good estimates of the next minute state ˆx−k+1. Based on these good simulation results, a control policy uk was formulated in a way that it
minimizes the difference between the predicted state ˆ
x−k+1 and the desired state yk+1, which could be easily
obtained from the day-ahead forecast.
The results show that the control is capable of mini-mizing the negative imbalance (energy shortage) fairly well. However, the degree to which the imbalances are covered depend heavily on the capacity of the biomass plant.
In the literature, little is known about the joint oper-ation of a winfarm with a biomass plant for balancing purposes. To our knowledge, this thesis is the first to report on the joint operation of wind and biomass by using a Kalman filter. In essence, the method using biomass is not only limited to wind energy, but equally applicable to any other renewable energy source facing the same reliability challenges, like solar energy.
Although the Kalman filter in this thesis provides good estimates of the next state, extra research might improve results after applying the Autocovariance Least-Squares (ALS) technique for calculating optimal values for Q and R, the “tuning” parameters of the filter. In addition, all conclusions are based on 3 one-day datasets. Further research with more datasets (preferable one year data) is necessary to examine the effects of the mechanism proposed in this thesis.
Therefore, a statistical analysis needs to be performed on a significant amount of minute-to-minute production data (preferably several years) to find the average and standard deviation for all daily 1440 minutes. While analyzing, seasonality should be taken into account.
The question rises whether the control policy intro-duced in this thesis is the optimal control policy in the context of our goal of minimizing negative imbal-ances and therefore maximizing revenues of the wind-farm. The control policy in this paper does not fully exploit all opportunities, especially from an economical point of view. Therefore, recommendations for further research include the following: first, the model should be extended with the current market (BELPEX) price and the prices for positive and negative imbalance. For example, the control policy should automatically adjust to the situation where the selling price of your excess produced electricity approximately equals the market price, i.e. pBP Xt ≈ pP OSt . In that situation there are
hardly any opportunity costs allowing full production of the biomass plant.
Second, the (variable) operational costs for both the windfarm and the biomass plant are considered negligi-ble in this thesis, which is not realistic. Adding these costs into the model and control policy will provide more realistic results.
Acknowledgments
From the operations faculty of the University of Gronin-gen, the author would like to thank first supervisory Nicky van Foreest for his valuable insights and discus-sions and Stuart Zhu for being the second supervisor for this thesis project. Furthermore, the author would like to thank all the people from WindVision, especially Paula Souto Perez and Andr´e-Stephane van der Goor for their contributions to understanding the problem and finding the right data.
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