The guidance and support of all friends and family who contributed to this project was essential to the success of the project. With the main ideology of considering load disturbances, And these disturbances are treated by dynamic ZIP load modeling (which is not in the literature). Designing a broadband controller requires the design of a small-signal model of a power system with a generator unit, a transmission line, and a load.
Study of damping of inter-zone oscillations induced in tie-line connected subsystems for load disturbances using LQR control as well as H∞ control techniques. The state feedback gain matrix is determined using LQR control optimization, it considers the entire set of state variables as input. Whereas in the case of H∞ optimization the states given as inputs to the controller can be chosen such that a structural constraint on the state feedback gain from the H∞ control can be imposed by choosing the required states as inputs to the controller.
The MATLAB/Simulink environment is used for statespace model design, controller design and time domain analysis of the modeled controllers. The traditional approach to damping control is to add a power system stabilizer to the power system. Unless PSS is tuned, there are many wide area control techniques used to stabilize power system disturbances.
And the obtained state feedback matrix is used as the wide input signal for the exciter model to dampen the generator rotor angle oscillations.
Desired small signal model of the power system
Stability studies for power system
Detailed discussion on rotor angle stability
Low frequency oscillation in power systems
Introduction of the dynamical system
The ability of a system to maintain synchronism even after a disturbance has been introduced into it. A fundamental factor in this problem is the way in which the power output of synchronous machines changes as the rotors oscillate. Where x(t) is called a single-valued and time-varying state variable, u(t) is a single-valued and time-varying input, y(t) is a single-valued and time-varying output.
State variables X(t) represent the dynamic behavior of the entire system and are minimal in number.
Stability analysis of a homogeneous system
Wide area monitoring system (WAMS)
Organization of thesis
In paper [6], it is stated that a thyristor-controlled series capacitor (TCSC) is amplified with a 15-machine, 5-zone power supply system for the control of induced disturbances, which is given global signal measurements. Then, loop transfer recovery (LTR) is used to strengthen the robustness of the controller in case of errors and unknown disturbances. In the following document [7], for large power systems, there will be connecting lines that connect different subsystems. If these tie lines are poorly connected, oscillation between zones is difficult to control using decentralized controllers.
In this paper [8], Design sparse gain and block sparse feedback that minimize variance amplification using H2 norm for distributed systems. There are several H2-norm methods used in the system to incorporate the structural constraint. In this paper [9], a centralized damping controller is designed for power grid oscillations between zones.
In this paper, the line currents and the current injections were considered as the inputs that have been observed to improve the effectiveness of the design. In this paper [12] necessary and sufficient conditions for pole/zero cancellations in the close-loop transfer function from input disturbances to error signals in the general H∞ problem are given. This paper [13] discusses some open issues in the design of dynamic output feedback control.
An extensive analysis is made of the implementation of PSS and the installation of synchrocondensers at the locations. This paper [16] states that the main problem in the massive power system is that the induced oscillations are of low frequency and are not well controlled. In addition, a restriction on the placement of the pole is also imposed during the design of the controller.
Low order controllers are more performance efficient than the latter. If the input does not affect the state change, the matrix B will be zero. The D matrix is a forward matrix and allows the output of the system to directly affect the input of the system. The base forward matrix for most components is zero.
Generating Unit
- Generator modeling
- Generator unit modeling
- Turbine modeling
- Speed governing system modeling
- Excitation system modeling
- Modeling of power system stabilizer(PSS)
WhereA is the system matrix, and relates the current state to the state change ∆x. This section presents the basic dynamic equations of the three-phase balanced symmetrical synchronous machine. The coil orientation, assumed polarities and the rotor position reference are mentioned in the above figure.
In the above figure (3.1) the q-axis directs the d-axis and the angle θ is made by the q-axis with respect to the toa-axis in a counterclockwise direction. Using the above convention, the abc system is converted to dq format using the following transformation matrix. The assumptions made while modeling the generator are that the stator has three coils each in one phase of a, b and c.
Ψ2q=Xmqiq+Xmqi1q+X2qi2q (3.17) The reactances used in the above equations are called model parameters and are calculated using the following formulas. Several steps must be followed to initialize the system states mentioned in equation (3.20). To obtain the initialized values of the states, we need the voltage of the generator connection bus (LV), the output of the active and reactive power of the generator.
Obtain d- and q-axis voltage or current quantities relative to the Kron reference frame based on the relationship between the dq phasor and the steady-state phasor. Now the steam flow is, the supply of steam starts from the boiler and the steam thus obtained is sent to the steam chest. Now the task of the steam chest is to increase the steam pressure and it is sent to the turbine assembly.
The steam can be reheated after being sent to the HP turbine, or can be reheated at the junction between IP and LP. And in this arrangement, all the stages of the turbine are placed on the same axis. Exciter: Exciter is the device that supplies direct current to the synchronous field winding of the machine, creating the power stage of the excitation system.
Power System Stabilizer: Power system stabilizer provides an additional input signal to the regulator as mentioned in the previous point, which helps to minimize power system oscillations. There are other input signals from the input to the exciter that can be used to reduce the oscillations.
Combined state space model of the generator compo- nentsnents
Network and Load modeling
The above matrix equation can be rearranged and the load current for a particular load bus can be realized as follows:
Integration of the power system components
WAC design using Linear-quadratic regulator (LQR) strat- egy
They are the state weighting matrix and the input weighting matrix of LQR optimization problem, respectively. According to the LQR control problem, the system (equation 1.1) is controlled by state feedback. Considering the eigenvalues, the observable states are determined and the weights are given high for the observable states and less for the unobservable states.
WAC controller design using H ∞ optimization technique
Depending on how the problem is formulated, the effect of the H∞ technique can be assessed in terms of stabilization of the system or the performance of the system. Both of the above properties in the controller can be achieved using a concept called asH∞loop shaping. This method of classical looping will design the controller with concepts of multi-variable frequency response.
Thus, we get a good robust performance and also optimize the system frequency response which is close to the system bandwidth, thereby additionally achieving a robust stable control scheme. PlantP has two inputs, the exogenous input w, which includes disturbances, and the system input variables u. There are two outputs, the performance z and the measured variables v, which we use to control the system.[24]
In the above chapter (3.0) we discussed how to get the equation of state of the entire power system. Now for the H∞controller design we need the equations for performance output and measured output of power system.
Computation of performance channel and measured out- puts
A case study was carried out for a system with 68 buses and 16 machines, where the load on bus 18 was reduced by 40%. The following figure (5.1) shows the dynamic response of the generator speed (COI) with LQR controller compared to the case without controller. The following figure (5.2) shows the dynamic response of the COI of the generator speed with H∞ controller compared to the case with LQR controller.
The oscillations considered in this work are due to the load disturbances caused due to the sudden variation in the nominal power at a specific load bus. In this thesis, the small signal modeling of the power system with generator unit, transmission line and load is explained. The generator unit modeling includes generator, turbine, speed controller, generator and power system stabilizer modeling.
The small signal model is done taking into account the disturbance in nominal power of the load. The load disturbance taken into account is the percentage change in the nominal power (active or reactive) at a load bus. Thus, controller performance is tested by observing the dynamic response of the rotor angle of the generator.
The LQR controller gives the stabilized results for the load disturbances caused in the generator conditions. Now H∞ optimization controller results are compared with the LQR controller results and the former gives better performance with the structural constraints implemented on the feedback gain matrix. Wang, “Design of Power System Damping Controller Using Multiple Input Signals,” IEEE Control Systems Magazine, pp.
Sarkar, “A comparative study on LQR and H∞ control for fading oscillations in power system network considering different operating points”, 2014 International Conference on Smart Electric Grid (ISEG), Guntur, pp. controller in the presence of multiple load types,” 2016 National Power Systems Conference (NPSC), Bhubaneswar, p. 12] J. Sefton, K. Glover, "Pole/zero cancellations in the general H∞ problem with respect to a two-block design," Systems and Control Letters, vol.
