4 Fulfilling the Design Criteria
The mean error is larger in the noisy scenario compared to the noise-free. Though not consistently lower, the average shown in Table 2.1 shows that the new controller is an order of magnitude closer to zero mean error compared to the current controller.
σ µ
Measurements 17.74 -3.27
Current 23.11 -2.78
New 25.72 0.29
Table 2.1: Standard deviation and mean throughout the whole month of simulation. Mea-surements are the measured values with the controller running at that time. Current is a simulation with the current controller and new is the simulation with the new controller.
Figure 2.12 shows the price difference between the two controllers. Analysing the price shows that on most days the new controller performs better. On day 20, the primary reserves limit the controller, so that a large deviation occurs over a long period of time which is detrimental for the earnings of the controller. On average the difference is 240 eper day, which means an earning of almost 90,000eper year.
5 10 15 20 25 30
−6000
−4000
−2000 0 2000 4000 6000
Day
Difference in euros
Figure 2.12: Price difference between the current controller and the new controller. Pos-itive difference means that the new controller is cheaper (earns more money for DONG Energy).
of the controller grows almost linearly with the the number of effectuators while still converging to the same optimum as the centralised solution. This is a signifi-cant improvement in lowering the computationally complexity over the centralised solution. It is also shown that already at 2-3 effectuators, the Dantzig-Wolfe de-composition is faster than the centralised solution. Furthermore, it is possible to distribute the optimisation problem among multiple processors, giving an advan-tage which exploits the trends toward computers with multiple processors.
Flexibility The design method fulfils the objective of flexibility through an object-oriented design with data encapsulation and clear interfaces. It ensures that the controller is easily maintainable in case of updates of the controller such as adding and removing effectuators.
Performance The design method itself does not ensure that the performance cri-terion is met, so that a controller design with the developed method performs as well as the current controller. However, the developed method ensures that if anℓ1 -norm based MPC can be constructed to fulfil the performance criterion, the design hierarchical design will also fulfil the criterion. In Section 2.3 as well as [Edlund et al., 2008, nd], simulations show that anℓ1-norm based MPC can be constructed, which improves the performance in terms of standard deviation and mean value, as well as improve the economic performance by a better distribution of the control actions.
The scalability and flexibility criteria have both been treated and fulfilled by the design method, while the performance criterion is dependent on the specific implementation.
The design method has been utilised for controller synthesis for the current power plant portfolio and the resulting controller fulfills the performance criterion. Thus, all criteria established in the hypothesis can be fulfilled by the design method.
3 Summary of Contributions
The main contributions of this thesis consist of six papers regarding different aspects of the portfolio control. This chapter summarises the contributions made in the project. The papers are not included in a chronological order, but in an order that takes the reader from the motivation to the solution in a logical way.
3.1 Stability of the Current Controller
In [Edlund et al., 2009a] the current load balancing controller structure was analysed.
[Wood and Wollenberg, 1996] give the structure of an automatic generation controller which is used for balance control by the TSOs and is very similar in structure to the load balancing controller treated in this thesis. The stucture in [Wood and Wollenberg, 1996]
is expanded to include rate of change constraints which are required for the controller to meet the requirements for operating in the western Denmark.
A linear approximation of the implemented structure is shown in Figure 3.1.
-+ +
G1
G2
GN
s x
x 1
Ti kp1
kp1
s-1
s x
x
s-1
1 Ti
s x
x 1
Ti
s-1 kp2
kp2
kpN
kpN
+
+ +
y
...
...
...
...
r
Figure 3.1: Linear approximation of the load balancing controller structure.
Using the definition of internal stability [Zhou et al., 1996; Skogestad and Postleth-waite, 2005], it is proven that the current controller structure is internally unstable. The in-stability cannot be seen in the portfolio output, but result in the effectuators drifting away from the production plan in opposite directions. The instability can be shown through numeric simulations as well as in real data as shown in Figure 3.2. In the figure two
effectuators are shown which at 3 hours drift away from the optimal production plan and stay there for many hours.
0 5 10 15 20
−40
−20 0 20 40 60 80
Time [hours]
Correction Signal [MW]
Generator 1 Generator 2
Figure 3.2: Correction signals from the controller. The correction signals drift apart and stay on opposite sides of the optimal production plan for several hours.
[Edlund et al., 2009a] give two proposals for salvaging the controller. One of them is a stronger parallel run which forces all effectuators towards the same correction. Parallel run is commonly used within the power plant industry when two or more similar subsys-tems have to work in parallel to complete a task. When using PI-controllers in parallel, the subsystems will in general not contribute equally when equilibrium is reached. In order to obtain this behaviour, parallel run is introduced. The parallel run drives the integrators towards the same value, thereby ensuring that the behaviour seen in the example above, where two generators drift in opposite directions, is avoided. However, increasing the strength of the parallel run will decrease the ability to make fast changes. The other pro-posed solution is to make a smarter distribution of the amount of correction signal each effectuator receives. The latter has been implemented in the current system as a result of this paper.