Optimal Controller for Wind Energy Conversion Systems

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Now the need for a controller which satisfies the following conditions arises. Reduce steady state error of the output signal Reject disturbance. The open loop system response depicted in Figure 2, shows the vital need of advanced controller for reducing error and convergence increment. One of the simplest controllers that seem to be capable of satisfying all the above conditions is a Lead-Lag controller.

Figure 2. open loop response of WECS

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3. HBMO Algorithm

The honey bee is a social insect that can survive only as a member of a community, or colony. The colony inhabits an enclosed cavity. A colony of honey bees consist of a queen, several hundred drones, 30,000 to 80,000 workers and broods during the active season. A colony of bees is a large family of bees living in one bee-hive. The queen is the most important member of the hive because she is the one that keeps the hive going by producing new queen and worker bees ^[13]. Drones' role is to mate with the queen. Tasks of worker bees are several such as: rearing brood, tending the queen and drones, cleaning, regulating temperature, gather nectar, pollen, water, etc. Broods arise either from fertilized (represents queen or worker) or unfertilized (represents drones) eggs. The HBMO Algorithm is the combination of several different methods corresponded to a different phase of the mating process of the queen. In the marriage process, the queen(s) mate during their mating flights far from the nest. A mating flight starts with a dance performed by the queen who then starts a mating flight during which the drones follow the queen and mate with her in the air. In each mating, sperm reaches the spermatheca and accumulates there to form the genetic pool of the colony. The queen’s size of spermatheca number equals to the maximum number of mating of the queen in a single mating flight is determined. When the queen mates successfully, the genotype of the drone is stored. At the start of the flight, the queen is initialized with some energy content and returns to her nest when her energy is within some threshold from zero or when her spermatheca is full. In developing the algorithm, the functionality of workers is restricted to brood care, and therefore, each worker may be represented as a heuristic which acts to improve and/or take care of a set of broods. A drone mates with a queen probabilistically using an annealing function as ^[14]:

(4)

Where Prob (Q, D) is the probability of adding the sperm of drone D to the spermatheca of queen Q (that is, the probability of a successful mating); ∆ (f) is the absolute difference between the fitness of D (i.e., f (D)) and the fitness of Q (i.e., f (Q)); and S (t) is the speed of the queen at time t. It is apparent that this function acts as an annealing function, where the probability of mating is high when both the queen is still in the start of her mating–flight and therefore her speed is high, or when the fitness of the drone is as good as the queen’s. After each transition in space, the queen’s speed, S(t), and energy, E(t), decay using the following equations:

(5)

(6)

Figure 3. Algorithm and computational flowchart of HBMO

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Figure 4. Schematic of proposed controller desining

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where α is a factor and γ is the amount of energy reduction after each transition. Also, Algorithm and computational flowchart of HBMO method to optimize the WECS controller parameters is presented in Figure 4.

Thus, HBMO algorithm may be constructed with the following five main stages:

A. The algorithm starts with the mating–flight, where a queen (best solution) selects drones probabilistically to form the spermatheca (list of drones). A drone is then selected from the list at random for the creation of broods.

B. Creation of new broods by crossoverring the drones’ genotypes with the queen’s.

C. Use of workers (heuristics) to conduct local search on broods (trial solutions).

D. Adaptation of workers’ fitness based on the amount of improvement achieved on broods.

E. Replacement of weaker queens by fitter broods.

4. Controller Designing Based on HBMO

Due to develop of system controllers, the conventioal contreollers are used widely in power system applications. making applicable of conventional controllers is simple againist the new controllers of power systems ^[14]. The Lead-Lag controllers are widely used in most cases of power systems controllers which compensat very well. One of the most benefits of these controllers is the easily implemention in analog and digital systems. If these controllers are designed optimaly, indubitable they become one of the most implimanted controllers in modern systems. This paper introduce a new optimal Lead-Lag controller, which is used of HBMO algorithm to designing the controller of wind energy conversion system in order to control of output power. The overall controller schematic is shown in Figure 4.

Lead-Lag general controller is expressed in equation (7) which the controller parameters should be optimized using the proposed algorithm. In the load variations, it is obvious that the transient mode of the WECS system depends on the controller parameters. The conventional controller designing method are not viable to be implemented because this system is an absolute nonlinear system. So these methods would have not efficient performance in the system.

(7)

In order to design controller optimal controller using HBMO for the WECS from the speed vaiation curve, we consider the worst condition for load design controllers for these conditions. Figure 5, depicts the worst condition for wind variation in the system.

Figure 5. Worst case of wind speed variation

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At first, problem should be written as an optimization problem and then by appliyning the proposed optimization method, the best Lead-Lag controller is achieved. Selecting objective function is the most important part of this optimization problem. Because, choosing different objective functions may completely change the particles variation state. In optimization problem we considered the power error signal in order to achieved the best controller.

(8)

Where, tsim is the simulation time in which objective function is calculated, the is the real speed of turbine and is the reference speed signal. We are reminded that whatever the objective function is a small amount in this case the answer will be more optimized. Each optimizing problem is optimized under a number of constraints. At this problem constraints should be expressed as .

(9)

Where, are in the interval [0.01 10] and in the interval [1 500].

In this problem, the number of particles, dimension of the particles, and the number of repeatations are selected 40, 3, 80, respectively. After optimization, results are determined as below:

(10)

5. Simulation Results

The conventional PID controller has initial and random values in proportional, integral and derivative coefficients as below:

(11)

Closed loop system response to the input shown in Figure 1, in the absence of disturbance is plotted in Figure 6. According to Figure 6, Proposed PID controller gives a satisfactory closed loop response when there is no disturbance. In order to check the capability of the designed Proposed PID controller in the presence of disturbance, a major disturbance on the firing angle of the thyristor at 35 seconds is applied (See Figure 7).

Figure 6. System response using conventional PID controller

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Figure 7. System response using conventional PID controller for thyristor disturbance

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Figure 8. System response using proposed controller based on HBMO

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Figure 9. System response using proposed controller which disturbance has been applied to firing angle

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In order to qualify the proposed controller, closed loop system responses to the input shown in Fig 3, in the absence of disturbance and uncertainty, with disturbance applied to firing angle of the thyristor, with disturbance applied to output speed of the given turbine and with parametric uncertainty are depicted in Figs 8 through 12 respectively. It is also desired to check whether the proposed controller is capable of rejecting disturbances and being robust to uncertainties simultaneously. Fig.13 depict corresponding control signal in the presence of both the disturbance and the uncertainty. According to Figs 8 through 13 one can say that the proposed controller is much more effective than conventional PID controller. The proposed controller offers a fast response with almost zero overshoot and is very operational in rejecting disturbances. It could be easily seen that our controller behaves effectively and pretty fast when a disturbance is applied. It also operates pretty well when there are parametric uncertainties.

Figure 10. System response with proposed controller which disturbance applied to firing angle at 10

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Figure 11. Uncertain system response with proposed controller

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Figure 12. Control signal with both the disturbance and the uncertainty

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