Optimization of PID Controller for a Hybrid Power System using Particle Swarm Optimization Technique

With the advancement of technology, power demand is increasing day-by-day. Energy deficiency problem and increasing petroleum/diesel cost has resulted in severe impacts to many technical facts. Introduction of non- conventional energy sources such as wind and photovoltaic energy, which is clean and copiously present in nature, can be possible solutions to these problems.This paper presents optimization of a hybrid power system, with one of swarm intelligent algorithms named as particle swarm optimization (PSO).The hybrid system utilizes PID controllers for controlling its yield. It has been done by studying different combinations of diesel engine generator, wind turbine generator, aqua electrolyzer, fuel cell and battery.With the optimized system parameters, high quality power supply can be delivered to the load and the frequency fluctuations can also be minimized.


INTRODUCTION
The present era is expected to experience immense growth and challenges for power generation, supply and utilization. Now-adays the role of renewable energysources is increasing in an exponential rate. It is due to the reason that global awareness for the need of environment protection and requirement of reduction in dependency on fossil fuels in the field of power generation. Thus, exploration of many of the nonconventional sources and their integration to conventional sources are done to provide clean energy and supply the load demand in the most intelligent way [1,2].
"Hybrid Power Systems (HPS) are small set of co-operating units, generating electricity or electricity and heat, with diversified primary energy carriers (renewable and non-renewable), while the co-ordination of their operation takes place by utilization of advanced power electronics systems" [3]. Hybrid power systems by definition have been developed for the production and utilization of electrical power. HPS are independent of central and large electricity grid and integrate numerous different kinds of sources of power.Generally, HPScan work in connection with power grid or they can work alone as standalone system to provide power to different loads, from one to several homes or farms, small industrial plants up to large local customers. When connected to grid, HPS offer electrical power generated by various sources and fed the excess power back in the grid, in case of more power generation than load demand. Main purpose of hybrid power systems is to deliver power to isolated, remote loads where the price of the connection from long distance transmission or distribution grid is very high. Optimization plays an important role for improving systems performance and working.An optimization algorithm is a method of obtaining the optimum solution of a problem that can be achieved by following a technique and comparing numerous solutions iteratively. To find the best solution for large scale optimizationproblem, evolutionaryalgorithms are established. Evolutionaryalgorithms are populationbasedmetaheuristicalgorithmas they are inspired by natural biological evolution or social behavior of living beings. Particle swarm optimization is one of these algorithms. It has the upsides of simple usage, stable convergence characteristics, and good computational effectiveness [4].
Therefore, a hybrid power system is proposed in this paper with PID controllers optimized by particle swarm optimization technique. The proposed system can also be used in isolated small islands as a stand-alone system, to reduce fuel consumption of conventionally used in diesel/petrol generation systems and it is also good for global environment protection concerns.

PROPOSED HYBRID POWER SYSTEM
This segment depicts the basics of proposed hybrid power system. The generation subsystems comprise wind turbine generator, diesel engine generator, aqua electrolyzer and fuel cell.Aqua electrolyzer is utilized to change over the fluctuating intensity of wind turbine generator into hydrogen and give it as a fuel to fuel cell [5]. In this way power loss due to wind fluctuation can be minimized and system can be fully utilized.
For controlling the output of each subsystem, PID controller is used and for optimizing the controller performance particle swarm optimization (PSO) is used. The feedback gain parameters ( , , ) are also optimized using PSO to reduce the frequency and power deviations. A series of simulation has been carried out to prove its working for different combination of generation components.
Different cases are considered for simulation as shown in Table 1. For simulation all the subsystem is considered to be in first order.  [6].

Wind Turbine Generator(WTG)
The changes in speed of wind relies upon time and related to the past speed. A few models of wind speed have been established and utilized. In this paper Auto Regressive Moving Average (ARMA) model is utilized, in which the wind speed is represented by ARMA time-series which is given as [7]: Where, ∅ is autoregressive parameter in which i varies from 1 to n. is moving average parameter in which j varies from 1 to m.
is noise parameter with zero mean.The simulatedwindspeed can be calculated using the following equation [6]:

= +
(2) Where, is average wind speed and is standard deviation.

Aqua Electrolyzer (AE)
Electrolysis is used for the production of hydrogen by absorbing any fluctuations in the output power from WTG by aqua electrolyzers. The produced hydrogen is kept within the hydrogen tank and utilized by fuel cells. The requirement of the load is fulfilled by total output from WTG, DEG and FC. The transfer function of the aqua electrolyzer system is given as follows [5]: Where, K is the gain and T is time constants of system.

Fuel Cell (FC)
The fuel cell generates electric power by reverse electrolysis; that is the reaction of oxygen and hydrogen which forms water. It is similar to the oxidation/reduction process of a battery.In fuel cell, reaction takes place in fuel (not in electrodes) [8].In the past few years, fuel cell generation have gained more attention due to the advantages, such as onsite installation, diversity of fuels, low pollution, reusability of exhaust heat and high efficiency. The transfer function of the fuel cell generation system is given as follows [5]: Journal of Power Electronics and Devices Volume 4 Issue 3 Where, K is the gain and T is time constants of system.

Diesel Engine Generator (DEG)
A DEG consists of diesel engine and electric generator to provide electrical energy and various ancillary devices, such as control systems, circuit breakers etc. Diesel engine generator can produce steady and reliable electrical energy at required voltages and power levels [9]. During power outages, emergency backup electrical generators powered by diesel engine provide reliable, immediate and full-strength electric power. The transfer function is given as follows: Where, K is the gain and T is time constants of system.

Control Strategy
The control strategy is obtained by controlling the power error which is the difference between the load demand ( )and net power generated ( ) [6].
Where, is the power generated by wind turbine generator.
is the power generated by diesel engine generator.
is the power generated by fuel cell.
is the power generated by aqua electrolyzer. Hence, the net controlling power error, ∆ = − Change in power generation affect the frequency response in power systems. For an ideal system the relation between frequency and power deviation is given as following [5]: Where, ∆ is the variation of generating power. k is the system frequency characteristic constant. In a practical system, slow response is observed in the frequency.Hence equation (8) can be modified as [6]: Equation (9) can also be represented as: Where, M is inertia constant & D is damping constant.

PID Controller and Performance Index
APID controller consist the arrangement for Proportional, Integral and Derivative actions, which attempts to minimize the error between a measured process variable and a desired set point. Ttransfer function of PID controller is given as: Optimization of performance of the system can be carried out by adjusting performance index. Lower value of index is preferred for running a robust system. The performance index is defined as a  [11,12].Since integral square error always results in positive error and it allows to discriminate over damped system from under damped system, hence it is used as fitness function to analyze performance of PID controllers. Using ISE, power error is calculated to design optimum system,which is defined as: .dt (12) Where, e is power error obtained in the simulation time t and k isthe variable in terms of the value of , and . Limits taken for electrolyzer, fuel cell and DEG are from zero to 1.0, 0.3 and 0.8 per unit respectively.

Particle Swarm Optimization (PSO)
Swarm intelligence is a branch of nature inspired approaches which is used for function optimization. PSO is based on the combined nature of self-structured systems. It mimics the behaviors of bird flocking [13,14].PSO learn from the situation and practice it for solving the optimization problems. Particle used in PSO represents single solution in search space and is analogous to the bird. Every particle has a fitness value which is estimated by optimizing the fitness function. The particles also have velocities to direct its flyingand all the particles go through the search area to obtain the best result by chasing the current optimum particle [4]. A basic flowchart of PSO is shown in Fig.2 to explain its working.  Step 3.Every time after iteration, respective position of all particles is reorganized. This is done by using the following equation (14) ( +1) = ( ) + ( +1) (14) Step 4.Update particle best position and globalbest position using equation (15) and (16).
Step 5.The process continues to repeat from Step 2 to Step 4 until a sufficient good fitness is obtained.Otherwise, the process will automatically stop after reachingmaximum set number of iterations. Once we get global best fitness, algorithm is then terminated. Case IV.In this case wind power, battery and diesel engine generators contribute to supply the load. Working procedure of system is same as explained in case I. The transfer function for battery is given below [4]: Where, K is the gain and T is time constants of system. Also, limits for controller of battery is considered as ±0.5 per unit.

SIMULATION RESULTS
In this section, simulation results of the several studied cases and their analysis is given. Simulation time of 120 sec and sampling time is taken as 20 msec for each case. Also, power demand is constant at 1.0 per unit.For DEG a delay of 20 sec is taken as it does not respondinstantaneously. Fig.3 it can be noticed that DEG and WTG contribute 0.4 pu and 0.6 pu power respectively so that total power generation will reach to power demand i. e. 1 pu.Also, when output from the WTG changes unexpectedly, this system is unable to provide high-quality power to the load. The reason is that diesel generators have very large time constant. Thus, DEG does not provide immediate response to load demand. Fig.4 it can be noticed that DEG, WTG and FC contribute 0.38 pu, 0.6 pu and 0.02 pu power respectively, so that total power generation will reach to power demand i. e. 1 pu. Power generated by aqua electrolyzer is not considered, as it provides input power to fuel cell and does not contribute directly to power generation. Also, the error in the power required is huge when the power generated by WTGvaries quickly over a broad range. Though, the error in required supply turns out to be around zero and the system is able to provide sufficient power tomeetrequired load.Time constant of aqua electrolyzersfor power utilization is small so,these are used to absorb the variations in WTG output power.Thus, this system can deliver high-quality power to load when the output of wind turbines varies rapidly. In similar way, this system controls the frequency appropriately.

Case II.From
Journal of Power Electronics and Devices Volume 4 Issue 3

Fig: 3. Case I. (a) Total power generated, (b) Frequency Deviation, (c) Power generated by wind turbine generator, (d) Power generated by Diesel engine generator
Case III. It can be clearly seen from Fig. 5 that DEG and FC contribute 0.8 pu and 0.2 pu power respectively, so that total power generation will reach to power demand i. e. 1 pu. Power generated by aqua electrolyzer is not considered, as it provides input power to fuel cell and does not contribute directly to power generation. Also, there is no fluctuation in total power generation due to absence of wind effect. From above results, it can be noticed that rapid variation ingenerated power byWTG affects the error in supply demand and turn out to be zero, as entire output power ofWTG is utilized in electrolysis. Thus, for this system it is possible to provide very high-quality power to the load requirement with sudden changes in wind turbine output power. Fig.6 it is observed that WTG and battery contribute 0.6 pu and 0.4 pu power respectively so that total power generation will reach to power demand i. e. 1 pu. Also, DEG generation reaches to zero as soon as battery supply to its maximum power. From the results, it can be noticed that this system is also able to provide good quality power to fulfill the required load, with sudden change in wind turbine generator output. But use of battery is limited by its charging/discharging capacity and inverter capacity. Here, it is considered that, if the battery power goes below 50% then it injunct discharge operation and when battery power reaches above 100% it injuncts charge operation.

DISCUSSIONS
From the simulation results, it is clear that in Case I simulation, the system is the least expensive system in comparison to other systems but in case of sudden change in wind speed or wind turbine output power, it is unable to deliver good quality power to the load. For system of case III, it is possible to deliver very high-quality power to the load demand with sudden changes in wind turbine output power. But overall performance is not effective, as the entire output of wind generator is utilized in electrolysis. The system of case IV can provide high quality power to the load but the system is expensive as it contains battery with large capacity. The lifespan of battery is very small due to frequent charging and discharging operation. The hybrid system of case II provides high quality power in comparison to case I and it is most effective and less expensive system in comparison to case III and case IV systems. The frequency response characteristics presented in Table 4 with peak value and settling time shows that system of case II provides good frequency response with the tuning of PID controllers. Also, global best settles on minimum value in case II as compared to other cases. Hence it provides better convergence.