In the marine electric power system, the marine generators will be disturbed by the large change of loads or the fault of the power system. The marine generators usually installed power system stabilizers to damp power system oscillations through the excitation control. This paper proposes a novel method to obtain optimal parameter values for Power System Stabilizer (PSS) to suppress low-frequency oscillations in the marine electric power system. In this paper, a newly developed immune clone selection algorithm was improved from the three aspects of the adaptive incentive degree, vaccination, and adaptive mutation strategies. Firstly, the typical PSS implementation type of leader-lag structure was adopted and the objective function was set in the optimization process. The performance of PSS tuned by improved immune clone selection algorithm was compared with PSS tuned by basic immune clone selection algorithm (ICSA) under various operating conditions and disturbances. Then, an improved immune clone selection algorithm (IICSA) optimization technique was implemented on two test systems for test purposes. Based on the simulations, it is found that an improved immune clone selection algorithm demonstrates superiority over the basic immune clone selection algorithm in getting a smaller number of iterations and fast convergence rates to achieve the optimal parameters of the power system stabilizers. Moreover, the proposed approach improves the stability and dynamic performance under various loads conditions and disturbances of the marine electric power system.

Due to the bad marine environment and the change of loads, the operation stability of the marine electric power system is affected. The marine generator is prone to produce low-frequency oscillations, which will affect the stability and performance of the marine electric power system.

Power system stabilizers are commonly used to improve the stability of marine electric power systems. By introducing a power system stabilizer to increase damping in the excitation control system of the marine generator, the dilemma of insufficient damping of the marine electric power system can be solved and the low-frequency oscillations can be suppressed [

In reference [

The main contribution of this paper is as follows:

Use of an improved immune clone selection algorithm to coordinate the power system stabilizers.

Development of an improved immune clone selection algorithm from three aspects: adaptive incentive degree, vaccination, and adaptive mutation strategies.

Comparison of the improved immune clone selection algorithm with other optimization techniques in tuning the parameters of power system stabilizers.

It analyzes the efficiency of the PSS controllers when the marine electric power system is under various operating conditions and disturbances.

The organization of the research is as follows: The modeling of the marine diesel generator and the structure of the PSS are introduced in

For diesel generator, the mathematical model is shown in

In

Herron-Philips's linearization model [

The marine diesel generator controller is shown in

The first-order transfer function of AVR [

The PSS controller adopts two lead-lag transfer functions [

In order to make the output deviation of the marine electric power system smaller and ensure good dynamic performance and good stability when the low-frequency oscillations occur. The error performance index

In

The flow of the basic immune clone selection algorithm is as follows:

Step 1: Generate the initial antibody population.

Step 2: The concentration of antibodies is obtained in

In

Antibody concentration index is shown in

Step 3: Judgment of the program termination. If the algorithm obtains the optimal value of power system stabilizers. Otherwise, the algorithm optimization is continued.

Step 4: Evaluation of antibody excitation degree. Antibody excitation degree is a comprehensive evaluation index based on antibody concentration and affinity.

Step 5: Promotion and inhibition of antibodies. Clone proliferation, clone mutation, clone suppression.

Step 6: Population refresh. Arrange the antibodies in order of their excitation. A part of the antibodies with low excitation degree in the population was removed. The new antibodies were randomly generated to supplement and update the original antibody population. To form a new population, proceed to Step 2.

If only the evaluation index based on antibody affinity is considered, it is difficult to ensure that the best solution can be selected. Comprehensive evaluation indexes based on antibody concentration and affinity were considered to avoid premature maturation and the local optimal solution. In

In

The lack of antibody gene crossover in the basic ICSA results in insufficient diversity of antibodies production. The introduction of a vaccination strategy based on the basic ICSA not only preserves the genes of the superior parent antibody, but also increases the probability of producing a superior antibody. To ensure that the best antibody in the population is selected. Antibody populations with high excitation were used as candidate vaccines. Vaccines were selected according to the roulette method [

Step 1: The sum of all antibody excitation degrees in the population can be calculated by

Step 2: The ratio of each antibody's incentive degree to the sum of the population's incentive degree can be calculated by

Step 3: The selection probability of antibody corresponds to the interval on the roulette wheel.

Step 4: Use roulette to select individuals randomly.

The binary loci method [

In order to ensure the randomness and diversity of antibodies, adaptive variation in

The specific flow of the IICSA algorithm is as follows:

Step 1: Generation of the initial antibody population. The initial population was composed of the antibody memory bank and the general population. The size of the antibody population was 30 and the number of antibody memory banks accounted for 40% of the population.

Step 2: Calculate the adaptive excitation degree of the antibody. Put the first M antibodies with the highest excitation into the antibody memory bank. The antibody memory bank is updated.

Step 3: Antibody cloning. The antibody was cloned from the antibody memory bank. The clonal scale of each antibody was determined according to the excitation degree of the antibody in the antibody memory bank.

Step 4: Vaccination. Vaccines come from an antibody memory bank. The probability of each antibody being selected is determined according to the excitation degree of the antibody. Roulette algorithm was used to select vaccines. Vaccination was conducted by multi-point cross vaccination.

Step 5: Clone variation. For inoculated antibodies, adaptive variation and gaussian variation based on antibody affinity were used.

Step 6: Clone suppression. The excitation degree of each antibody was calculated after the mutation. The first M antibodies with the highest excitation degree were re-selected and put into the antibody memory bank to realize the update of the antibody memory bank. After the update of antibody memory, all the remaining antibodies were eliminated.

Step 7: Population regeneration. At the end of each iteration of the algorithm, the population needs to be updated. The updated population still consists of the antibody memory bank and the general population. The maximum number of iterations of the algorithm is 100.

Step 8: Judgment of termination conditions. When the termination conditions are satisfied, output the optimal parameters of the marine electric power system stabilizer. Otherwise, go to Step 2.

In

The objective function evolution with ICSA based PSS and IICSA based PSS as a function of generation is shown in

In order to illustrate the efficiency of the improved immune clonal selection algorithm, the salp swarm algorithm (SSA) [

The parameters of these controllers are optimized by improved immune clonal selection algorithm. The objective function is in

Controllers | |||||
---|---|---|---|---|---|

PI | 0.5832 | 0.7268 | - | - | - |

PID | 1.9683 | 0.8724 | 2.1560 | - | - |

FOPID | 2.6147 | 0.6172 | 2.2685 | 1.2663 | 1.4056 |

The proposed marine electric power system can be found in [

The parameters of the marine generator in the simulation are set as follows [

In the same case, PSS parameters optimization results of basic ICSA and IICSA algorithms are shown in

Parameters | Fitness function value | |||
---|---|---|---|---|

ICSA-PSS | 12.1230 | 0.2892 | 2.8863 | 0.1528 |

IICSA-PSS | 23.8134 | 0.3311 | 3.9016 | 0.1496 |

In order to verify the excellent effect of the IICSA algorithm to optimize the stabilizer parameters of the marine electric power system. The marine electric power system is disturbed by 15% load changes, a 10% increase of excitation voltage reference value, and a sudden short circuit fault of the marine generator. The rotor speed deviation and generator terminal voltage deviation were observed under three conditions: no PSS (the marine electric power system is without PSS), PSS parameters optimized by ICSA, PSS parameters optimized by IICSA.

The +15% load changes on the marine electric power system start at 2.5 s and end at 4.5 s. It is a small type of disturbance for a marine electric power system. The generator rotor speed deviation and generator terminal voltage deviation are shown in

After being disturbed, the time of the transition process is 2 s and the number of oscillations is 3 when the PSS is optimized by ICSA. However, the time of the transition process is 1 s and the number of oscillations is 1 when the PSS is optimized by IICSA. In terms of generator terminal voltage deviation, the voltage deviation is 6.18% when the power system stabilizer is optimized by IICSA, which is higher than the power system stabilizer is optimized by ICSA. The voltage deviation is 5.65% when the power system stabilizer is optimized by ICSA. But, the IICSA optimized power system stabilizer exhibits better damping than ICSA optimized power system stabilizer.

Marine diesel generator excitation voltage reference value is increased by 10%. It starts at 2 s and ends at 2.2 s. By observing

After being disturbed, the time of the transition process is 2 s and the number of oscillations is 4 when the PSS is optimized by ICSA. However, the time of the transition process is 1 s and the number of oscillations is 1 when the PSS is optimized by IICSA. In terms of generator terminal voltage deviation, the terminal voltage deviation is 3.43% when the marine generator adopts a power system stabilizer optimized by ICSA. However, the generator terminal voltage deviation is 2.84% that optimized by IICSA. It is showing that the system having IICSA optimized PSS shows better performance than the system having ICSA optimized PSS.

A short circuit fault of marine diesel generator. The short circuit starts at 2 s and ends at 2.2 s. The rotor speed deviation of the marine generator for short circuit is shown in

After the short circuit of the marine generator, it can reach a stable state in 3.5 s. In terms of the generator terminal voltage deviation, the generator terminal voltage deviation is 0.26 when the marine generator adopts ICSA to optimize the power system stabilizer, while it is 0.23 when the power system stabilizer is optimized by IICSA. After being disturbed, the time of the transition process is 1.9 s and the number of oscillations is 4 when the PSS is optimized by ICSA. But, the time of the transition process is 1.3 s and the number of oscillations is 1 when the PSS is optimized by IICSA. So, the marine electric power system having IICSA optimized PSS shows better performance than the marine electric power system having ICSA optimized PSS.

The study will be extended to multimachine power systems in the following sections.

The 10 machines 39 bus system [

This work presented an improved immune clone selection algorithm to tune the parameters of the power system stabilizers for marine generator excitation control and then compared with a basic immune clone selection algorithm. The objective function is to minimize output deviation of the marine electric power system smaller and to ensure good dynamic performance and good stability when the low-frequency oscillations occur.

The proposed improved immune clone selection algorithm adopts adaptive excitation, vaccination, and adaptive mutation strategies. Then, the improved immune clone selection algorithm gets a smaller number of iterations and fast convergence rates to achieve the optimal parameters of the power system stabilizers than the basic immune clone selection algorithm, the salp swarm algorithm, and the grasshopper optimization algorithm. The final value is 0.1496 from the 21 iterations for the improved immune clone selection algorithm to optimize the parameters of the power system stabilizer.

The low-frequency oscillations caused by various load conditions disturbances and three-phase fault can be significantly suppressed better by installing power system stabilizers in the marine generators. The rotor speed deviation is 1.4% and the settling time is 1.3 after the short circuit of the marine generator for improved immune clone selection algorithm while the rotor speed deviation is 1.8% and the settling time is 1.9 for the basic immune clone selection algorithm. The simulation results show that the power system stabilizers optimized by an improved immune clone selection algorithm can greatly improve the stability and dynamic performance under various operating conditions and disturbances of the marine electric power system. Moreover, the proposed approach presents better performance than the basic immune clone selection algorithm to tune the parameters of power system stabilizers.

Future studies will be focused on the following two aspects:

The proposed controller will be compared with a new control structure that hasn't been used for PSSs.

To compare the performance of hybrid algorithms (immune clone selection algorithm and genetic algorithm) with a single algorithm to tune the parameters of power system stabilizers.

Rotor angle deviation

Rotor speed deviation

Quadratic axis transient potential deviation

Excitation voltage deviation

Rotor angle

Rotor speed

Quadratic axis transient potential

Excitation voltage

Inertia coefficient

Damping coefficient

Synchronous speed

Direct axis open-circuit time constant

Mechanical torque

Gain of AVR

Time constant of AVR

Output signal of the PSS

Constants of the linearized model of synchronous machine

Gain of PSS

Time constant of washout filter

PSS's lead–lag time constants

Speed of the generator

Reference speed

Terminal voltage

Reference voltage

Stabilizers’ output

PSS's output limits

Integral of time-absolute error

Population size

Encoding dimension of the antibody

Similarity threshold

Affinity weight coefficient

Current iteration number

Maximum iteration number

Total amount of antibody after cloning

Number of antibodies to be cloned

Antibody gene before mutation

Antibody gene after mutation

Direct axis reactance of the generator

Direct axis transient reactance of the generator

Direct axis sub transient reactance of the generator

Quadratic axis reactance of the generator

Quadratic sub axis reactance of the generator

Direct axis leakage reactance of stator winding

Direct axis open-circuit time constant

Excitation winding time constant of generator suddenly short circuit

Damping winding time constant of generator suddenly short circuit