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Load frequency control plays a vital role in power system operation and control. LFC regulates the frequency of larger interconnected power systems and keeps the net interchange of power between the pool members at predetermined values for the corresponding changes in load demand. In this paper, the two-area, hydrothermal deregulated power system is considered with Redox Flow Batteries (RFB) in both the areas. RFB is an energy storage device, which converts electrical energy into chemical energy, that is used to meet the sudden requirement of real power load and hence very effective in reducing the peak shoots. With conventional proportional-integral (PI) controller, it is difficult to get the optimum solution. Hence, intelligent techniques are used to tune the PI controller of the LFC to improve the dynamic response. In the family of intelligent techniques, a recent nature inspired algorithm called the Flower Pollination Algorithm (FPA) gives the global minima solution. The optimal value of the controller is determined by minimizing the ISE. The results show that the proposed FPA tuned PI controller improves the dynamic response of the deregulated system faster than the PI controller for different cases. The simulation is implemented in MATLAB environment.

The complexity of power system is highly increasing due to the rapid increase in load. Operation and control of power system become an important task for secured and reliable operation. The objective of the LFC is to maintain the system frequency and tie line power flow constant for a transient change in load [

With the development in the power industry, the power system is in transition for restructuring and deregulation. Many researchers analyzed the problem of LFC in a deregulated environment for the past nine decades [

Many control strategies were employed in the past nine decades, to reduce the oscillations of change in frequency and tie-line power flow. Proportional Integral (PI) controller is mostly used as a controller in LFC because of ease of operation [

Several energy storage systems were available such Superconducting Energy storage system, batteries, etc. Tetsuo Sasaki et al. discussed that rechargeable batteries are not aged by frequent charging and discharging and have better response during overload when compared to other energy storage systems [

In this work, a two-area deregulated power system is considered in which area1 has two DISCOs, two non- reheat thermal units as GENCO1 and GENCO2. Similarly, area2 has two DISCOs, two hydro units as GENCO3 and GENCO4. Proportional Integral (PI) controller is used and the gain values were tuned by using Ziegler-Ni- chols and Flower Pollination algorithm. The performance of the controller was analyzed by using performance index. Further, an Energy storage device Redox Flow Batteries (RFB) was used to improve the LFC performance. The RFB stores energy and dissipates at a faster rate whenever required.

In this paper, Section 2 explains the block diagram model of two-area hydrothermal deregulated power system and Redox Flow battery principle of working. The overall transfer function model is explained in Section 3. Section 4 explains the tuning of the PI controller by Ziegler-Nichols and FPA. The simulation of the hydrothermal deregulated power system for different cases with PI controller and FPA tuned PI controller followed by a discussion is given in Section 5. From the simulation results and discussion, the conclusion is made in Section 6.

The power system model consists of two control areas connected by a tie line as shown in

Matrix (DPM), to visualize the contracts between GENCOs and DISCOs was introduced [

In the proposed deregulated system as shown in

where

Batteries are devices that store chemical energy and generate electricity by a reduction-oxidation (redox) reaction: i.e. a transformation of matter by electron transfer. The redox (reduction-oxidation) cell is a reversible fuel cell in which all electrochemical components are dissolved in the electrolyte. Redox flow batteries are rechargeable [

A vanadium RFB consists of an assembly of power cells in which the two electrolytes are separated by a proton exchange membrane. _{2}O_{5}) in sulfuric acid (H_{2}SO_{4}). The solution remains strongly acidic in use.

The following equations represent the working of the vanadium redox flow

(2)

where water (H_{2}O) and protons (H^{+}) are required in the cathodic reaction to maintain the charge balance. The advantages of RFB over the other energy storage systems are easy maintenance, load following, storage for long time period and fast response.

RFB, placed in both the areas to damp out oscillations i.e. improves the dynamic response of change in frequency and tie line power flow. RFB is placed in the area will be charged from the power from the units under balance condition. When the load demand increases the energy stored in the battery is released to the system. As the control mechanism brings the system to its new equilibrium condition, the battery charges it to its full value. Similarly, when the load decreases, the battery gets charged absorbing the excess power in the system. The absorbed excess power is released back after the system returns to its steady state.

Area 1 consists of two GENCOs, which have two identical non-reheat thermal units, and two DISCOs; Area2 has two GENCOs, which have two identical hydro units, and two DISCOs. _{1}, R_{2}, R_{3} and R_{4} are the governor regulation parameters of thermal units and hydro units for area1 and area2 in Hz /pu.MW respectively.

Area1 consists of two speed governing system, two non-reheat turbines and area2 has two mechanical hydro governor and hydro turbine. In order to simplify the frequency domain analysis, the transfer function is used to represent the components of the area.

The transfer function of speed governor of area1 is given by Equation (3)

where K_{Gj} is the gain of the j^{th} governor and T_{Gj} is the time constant of the j^{th} governor.

The non-reheat turbine model is given by Equation (4)

where, K_{Tj} is the gain of the j^{th} non-reheat turbine and T_{Tj} is the time constant of the j^{th} non-reheat turbine.

In hydro units, water is the main source for producing mechanical energy, which is the input to the turbine. Function of speed governor of hydro unit is similar to that of steam governor. In this work, the low head hydro unit is considered [

where, K_{Hj} is the gain of the j^{th} hydro governor and T_{Hj} is the time constant of the j^{th} hydro governor.

where, T_{Rj} is the reset time of the j^{th} hydraulic amplifier and T_{2j} is the time constant of the j^{th} hydraulic amplifier.

Water is used as an input for the turbine and is connected to hydro governor. Transfer function of hydro turbine is given by Equation (7)

where T_{wj} is the time constant of the j^{th} hydro turbine.

The model of the power system is given by Equation (8)

where, K_{P} is the gain of the i^{th} area power system and T_{P} is the time constant of the i^{th} area power system.

The values of K_{P} and T_{P} are given by

system frequency and D_{i} is expressed as percent change in load by percent change in frequency.

The scheduled steady state tie line power flow from area1 to area2 is the difference between the demand of DISCOs in the area2 from GENCOs in the area1 and the demand of DISCOs in area1 from the GENCOs in area2, which is given in Equation (9),

The tie line power flow from area1 to area2 is the product of the tie line coefficient and the difference between the change in frequency in area 1 and the change in frequency in area2, as given by Equation (10),

Equation (11) gives the error in the tie line power flow from area1 to area2, which is the difference between the actual and scheduled value of the tie line power.

Equation (12) gives the error in tie line power flow from area2 to area1 is given.

As both the areas are assumed to be identical, a_{12} = −1.

Equation (13) gives the Area Control Error (ACE) of area1, which is the summation of the bias factor with the deviation of the frequency and the change in tie-line power flows. Similarly, Equation (14) gives the ACE of area2.

As there are more than one GENCOs in each area, the Area Control Error (ACE) signal has to be given in proportion to their participation in LFC. The coefficient that distributes the ACE to all GENCOs is called as “ACE participation factor” (Apf). The summation of Apf should be always unity for each area. Hence, the ACE Participation factors for area 1 are Apf_{11}, Apf_{12}. Similarly, for the area2 are Apf_{21}, Apf_{22}.

Redox Flow Battery (RFB) is connected to the power system of both areas, in which the input given is the change in frequency (real power) of that area and output will be as per the load requirement and either charges or discharges the power. As RFB has fast response, hunting due to delay in response does not occur [_{rfb}) is given Equation (15)

where K_{rfb} is the gain of a RFB and T_{rfb} is the time constant of RFB in seconds.

The performance of the system poor and even possibly unstable, if the controllers are not tuned properly. The conventional PI controller is tuned by Ziegler-Nichols and FPA methods.

Proportional control mode will be good when the rate of change of error is high and this mode improves the transient performance. The Integral control mode is efficient when the error is low and this mode improves the steady state. The derivative control mode increases the noise and makes the system less stable because of its high sensitivity even though it has the advantage of reducing the overshoot [

In this work, the Proportional Integral controller because of its simplicity and flexibility. The mathematical model of PI controller is given in Equation (16).

where K_{P} is the P controller gain and K_{I} is I controller gain and U_{PI} is the controlled output of the PI controller and ACE is the Area Control Error of the concerned area.

In designing the optimization based PI controller, the objective function may be defined based on the desired specifications and proper parameter settings to ensure that the system stable. Performance Indices that are usually used in design are Integral Time Absolute Error (ITAE), Integral Squared Error (ISE), Integral Time Squared Error (ITSE) and Integral Absolute Error (IAE). In this paper, the ISE is used as the objective function to optimize the parameters of the PI controller because this index will reduce larger errors quickly resulting in the fast response to the system.

Equation (17) gives the performance index used to optimize (minimization of the error).

where Δf_{1} and Δf_{2} are the change in frequency of area1 and area2 and ΔP_{tie1,2} is the change in tieline power flow.

One of nature inspired population based algorithm is Flower Pollination Algorithm (FPA) proposed by Xin-she Yang (2012). The primary aim of this FPA is to produce the optimal reproduction of plant species by surviving the fittest of the flowering plants.

In this world, there are a million types of flowering plants in nature, 80% of them were flowering species. The main purpose of a flower is ultimately reproduction via pollination. Transfer of pollens from one flower to another flower on the same plant (self-Pollination-Abiotic) or another plant (Cross Pollination-Biotic). This transformation may occur by pollinators such as wind, birds, insects, bats and other animals. FPA has better performance when compare to others in terms of accuracy, and convergence speed [

The following four rules were employed to explain concept of flower pollination

1) Cross Pollination and Biotic were considered as Global Pollination and pollinators movement is considered which follows the Levy flight movement.

2) Local Pollination takes place in Abiotic and self-Pollination.

3) Pollinators like birds, insects may develop flower constancy, which is equivalent to the reproduction probability and will be proportional to the similarity of two flowers involved.

4) Switching from local to global pollination or vice versa can be controlled by the probability p ∈ [0, 1].

In global pollination, pollinators like birds, wind, insects carry out flower pollen and they travel over a long distance. This global pollination (i.e. rule 1 and 3) can be written as in Equation (18)

where x_{ik} is the pollen i at iteration k, g_{*} is the current best solution among the solutions for the current iteration. Here γ is the scaling factor used to control the step size. L(λ) is the step size parameter, in specific the Levy-flights-movement which shows the strength of the pollination.

As the pollinators travel over a long distance with different distance movements, levy flight is used to show the travelling characteristic which is shown in Equation (19). Assume L > 0 forms the Levy distribution.

where Г(λ) is the standard gamma function and Levy distribution will be valid for longer steps S > 0. Rule 2 and 3 were for local pollination can be shown in Equation (20) as follows

where ε is a local random lie from 0 to 1.

The objective function is to minimize the objective shown in Equation (17). Number of flowers is 20 and the maximum number of iterations is 100.

Step 1: Initialize the population of flowers (control variables P and I of each area)

Step 2: Calculate the fitness function of each flower (i.e. Min ISE) and select the global flower from the population

Step3: For each flower generate a random number, if the random number less than switch probability go to step 5

Step 4: Implement global pollination and go to step 6

Step 5: select a flower randomly for local pollination, then go to step

Step 6: pollinate a flower with global flower by using _{i} is the values of K_{P} and K_{I}.

Step 7: up to N number of flowers do step 2 to 6

Step 8: go to step 3 to 6 till the maximum iterations is reached, get the global flower as the best fitness value index (optimal values of K_{P} and K_{I} of the controller).

For the transfer function diagram shown in

Pool-co transaction i.e GENCO in each are participate equally in LFC. Area Control Error (ACE) participator factor (Apf’s) is as follows:

DISCOs have contracted with each GENCO. Assume load change occurs in area1 alone, i.e. 0.1 (pu MW) load change in DISCO1 and DISCO2. DISCO3 and DISCO4 does not demand power from any other GENCOs, then corresponding “cpfs” is zero. The DPM for the above case is as follows

In addition, the demand of DISCOs in (pu MW) is as follows: ΔP_{L}_{1} = 0.1, ΔP_{L}_{2} = 0.1, ΔP_{L}_{3} = 0, ΔP_{L}_{4} = 0. Since the uncontracted load is taken to be zero ΔP_{UC}_{1} = 0, ΔP_{UC}_{2} = 0. The scheduled tie-line power flow over the tie-line is zero, i.e. under steady state condition the generation of GENCOs must match the demand of the DISCOs in contract with it. The generated power (or) contracted power supplied by the GENCO is given as

By using equation 21, ΔP_{g}_{1} = 0.1 (pu∙Mw), ΔP_{g}_{2} = 0.1(pu∙Mw), ΔP_{g}_{3} = 0 (pu∙Mw) and ΔP_{g}_{4} = 0 (pu∙Mw).

Figures 5(a)-(c) show the comparison of PI and FPA tuned PI controller for dynamic response of change in frequency (Hz) for each area and the tie line power flow (pu∙MW) between them which settles at 0.00 (pu∙MW). From Figures 5(a)-(c) it can be inferred that FPA tuned gain values of PI controller gives better results in terms of settling time, overshoot and undershoot.

Bilateral transaction, i.e. all DISCOs contracts with the GENCOs for power as per the following DPM,

GENCO participate in LFC as given by the following Apf’s i.e.

The demand of DISCOs in (pu×MW) is ΔP_{L}_{1} = 0.1, ΔP_{L}_{2} = 0.1, ΔP_{L}_{3} = 0, and ΔP_{L}_{4} = 0. As the uncontracted load is considered to be zero, ΔP_{UC}_{1} = 0, ΔP_{UC}_{2} = 0. Each DISCO demands 0.1 (pu∙MW) power from GENCO as shown by “cpfs” in DPM.

Hence

Figures 6(a)-(c) show the dynamic response of change in frequency (Hz) for each area and the tieline power flow (pu∙Mw) between them which settles at −0.05 (pu∙Mw).

Figures 6 (a)-(c) show the comparison of PI and FPA tuned PI controller for dynamic response of change in frequency (Hz) for each area and the tie line power flow (pu∙Mw) between them which settles at −0.05 (pu∙Mw). From Figures 6(a)-(c) it reveals that FPA tuned gain values of the PI controller gives better response in terms of settling time, overshoot and undershoot.

Case | Controller | Layout | Settling time (s) | Overshoot | Undershoot |
---|---|---|---|---|---|

Case 1 | PI | Area 1 | 12 | 0.042 (Hz) | −0.14 (Hz) |

Area 2 | 42 | 0.002 (Hz) | −0.006 (Hz) | ||

Tie line | 38 | 0.0019 (pu∙Mw) | −0.008 (pu∙Mw) | ||

FPA_PI | Area 1 | 2 | 0.03 (Hz) | −0.08 (Hz) | |

Area 2 | 10 | 0.0015 (Hz) | −0.0018 (Hz) | ||

Tie line | 9 | 0.00018 (pu∙Mw) | −0.0002 (pu∙Mw) | ||

Case 2 | PI | Area 1 | 18 | 0.048 (Hz) | −0.21 (Hz) |

Area 2 | 38 | 0.15 (Hz) | −0.73 (Hz) | ||

Tie line | 22 | 0.18 (pu∙Mw) | −0.055 (pu∙Mw) | ||

FPA_PI | Area 1 | 9 | 0.01 (Hz) | −0.17 (Hz) | |

Area 2 | 32 | 0.12 (Hz) | −0.7 (Hz) | ||

Tie line | 8 | 0 (pu∙Mw) | −0.05 (pu∙Mw) |

and Bilateral transactions. From the table for case 1, performance of the controllers shows that, FPA_PI controller gives 84% of improvement in settling time over PI. There is lesser undershoot for FPA_PI in change in area2 whereas PI has −0.002 (Hz). Similarly FPA_PI controller gives 98% settling time of tie line when compared with PI controller.

For case2, the settling time of FPA_PI controllers is found to be 50% of improvement in settling time over PI, 20% improvement in settling time of area2 over PI and 64% improvement in settling time of tie line over PI. FPA_PI has no overshoot in the tie line power whereas PI has 0.00018 (pu∙Mw). FPA_PI settles exactly at −0.05 (pu∙Mw) and PI settles at −0.052 (pu∙Mw)

Thus, a two-area hydrothermal deregulated power system is considered, which consists of two identical reheater thermal units in one area and two identical hydro units in another area. Both the areas are connected with RFB, which acts faster than governor mechanism thereby reducing the oscillations due to load disturbances. Two different types of transactions were considered such as pool-co and bilateral transactions. Simulations were done to the system considered with a PI controller whose gain values were tuned by Ziegler- Nichols and FPA methods. Integral Square Error of the system was considered as an objective function to be minimized for tuning the gains of PI using FPA. The obtained results were compared with which FPA tuned parameters of PI which, gives better results, measured by means settling time, overshoot and undershoot when compared to PI. For the same system, the non-linearity such as Governor Dead Band, Generation Rate Constraints and Time Delay may be considered for the future work.

D. Lakshmi,A. Peer Fathima,Ranganath Muthu, (2016) A Novel Flower Pollination Algorithm to Solve Load Frequency Control for a Hydro-Thermal Deregulated Power System. Circuits and Systems,07,166-178. doi: 10.4236/cs.2016.74016

Rating P_{ri} = 2000 MW, Inertia Constant H_{i} = 5 s, Damping Coefficient D_{i} = 1/120 pu MW/Hz, Power System Gain Constant K_{Pi} = 120 Hz/pu MW, Power system Time constants T_{Pi} = 20s, Speed Regulation R_{j} = 2.4 Hz/pu MW, Governor Time Constants T_{Gj} = 0.08 s, Turbine Time Constants T_{Tj} = 0.3 s, Hydro governor K_{Hj} = 1.0, Hydro governor time constant T_{Hj} = 48.7 s, Reset time of hydraulic amplifier T_{Rj} = 5s, Time constant of hydraulic amplifier T_{2j} = 0.513 s, Time constant of hydro turbine T_{wj} = 1 s Bias factor B_{i} = 0.425 pu∙MW/Hz, Tie line Power constant T_{12} = 0.0707, System frequency f = 60 Hz, a_{12} = 1, Redox Flow Battery Gain constant K_{rfbi} = 1.8, Redox Flow Battery Time constant T_{rfbi} = 0 s. Number of flowers = 20, Maximum iterations = 100, λ = 1.5, γ = 0.1, p = 0.8.