Designing a smaller scale architecture of the wide area control system using modal sensitivity analysis. The contribution of the third work is to develop a suitable methodology for the practical realization of the two-layer Wide Area Control (WAC) architecture.
Intraplant mode oscillations
Local plant mode oscillations
Inter-area mode oscillations
Control mode oscillations
Torsional mode oscillations
Of all these oscillations, as mentioned earlier, the oscillations between areas are very difficult to control, and they cover a large part of the system.
Power system stabilizer (PSS)
Consequences of inter-area oscillations
Therefore, it can be concluded that inadequate damping of oscillations between zones is the main factor leading to system separation. The amount of damping and the frequency of oscillations varies with the operating conditions of the system.
Wide Area Monitoring Systems (WAMS)
Phasor measurement units
To estimate phase and frequency using PMUs, various algorithms have been reported in the literature. A comparative study of different phase and frequency estimation algorithms available in a power system is carried out in [19].
WAMS based damping control and communication network . 6
Motivation
This work contributes to the development of an improved scheme for the utility ranking of the source and sink points in the WAC loop in order to design an efficient reduced-scale WAC (RSWAC) system. This reveals the satisfactory performance of the proposed reduced scale WAC system even in the practical situation of limitations in data communication.
Introduction
Optimal Control theory
The above equations can be represented in the form of perturbed linearized equations as follows. The small-signal stability analysis can be performed based on the equations and transient analysis can be performed based on the equations.
Controllability and Observability
Stabilizability and Detectability
H 2 and H ∞ Norms
Computation of H 2 -Norm
Where Q is a Grammian of observability satisfying AQ+AQT +CCT = 0 and P is a Grammian of controllability satisfying ATP +AP +BTB = 0.
LQR Design through H 2 -norm
Computation of H ∞ -Norm
State Feedback Control and Output Feedback Control
The structural constraints on the above equivalent state response matrix can be derived explicitly as follows [29].
Structurally Constrained H 2 -Norm Optimization
The state and performance output equations can also be modified into the following forms. Using the latest forms of state equation, performance output equation and L2 rate, the structurally constrained H2 rate optimization problem can be formulated as follows [30].
Linear and Non-linear Kalman Filtering
Kalman Filter Algorithm
Extended Kalman Filter Algorithm
Unscented Kalman Filter
Summary
It includes the modeling of the entire power system, the problem of constrained measurements, and the implementation of a nonlinear Kalman filter with unknown inputs. A wide-area controller is designed using structure-constrained H2-norm optimization to solve the measurement-constrained problem with unknown load composition. The results show that the broadband controller provides good results even in the case of few measurements.
General Architecture of the WAC System
The state feedback controller generates WAC signals based on the observable dynamic states of the system. However, the performance of the controller can be superior in the case of the state feedback control. The state or output feedback controller is designed based on the linearized (i.e. small signal) model of the system.
However, the time delays that occur in the input signals to the WADC must be uniform due to the alignment of the timestamps.
Modeling of Power System
- Generator Modeling
- Exciter Model
- Turbine and Speed Governor Model
- Power System Stabilizer Model
- Network Modeling
The small-signal modeling of the above equations can be written in matrix form as follows. The small-signal modeling of each turbine and speed controller can be written as in (3.25). Therefore, the general small-signal modeling of exponential and polynomial loading models in terms of ∆VDli and ∆VQli can be written as.
The generalized small-signal modeling of dynamic states defined in multiplicative and additive dynamic loads in terms of ∆VDli and ∆VQli can be written as.
Limited Measurement Issue
Feedback Gain Matrix Structure
COI Calculation
Here, NG denotes the number of generators in the system and denotes the weight assigned to the rotor speed of the generator in the state feedback reference frame. The rotor angles with respect to the state feedback reference frame can be derived from the PMU measurements using (3.67). Otherwise, as is clear from (3.67), none of the rotor angle states will be observable with respect to the state feedback reference frame.
In that case, the state feedback reference frame can be chosen according to the COI of the generators of observable rotor angle states, whereas the weighting factors corresponding to the other generators can simply be set to zero.
Kalman Filter with unknown inputs in power system applications
For the COI reference frame, the weights are defined based on the inertial constants of the generators. However, it is not possible to include the rotor angle of the generator when defining the state feedback reference frame unless the rotor angle state of the specific generator is observable.
Case Study
Optimal wide area control with limited measurements
No penalty is applied to the entries in the columns corresponding to the state of the frequency and rotor angles of the generators (ie the penalty factor is set to zero). Compared to the ideal case, the eigenvalues of the closed-loop system in case 1 are slightly shifted towards the imaginary axis. Time variations of rotor speed (w.r.t COI) of generators 1 and 10 with and without state feedback controllers are plotted in Fig.
The performance of the state feedback controller designed for Case 1 is somewhat inferior to the performance of the ideal state feedback controller.
Design of wide area controller with unknown load composition 47
This chapter presents the design of a scaled-down architecture of a large-area surveillance system using modal sensitivity analysis. The utility rankings of source and sink points are usually performed based on the concepts of geometric observability and geometric controllability [24], [54]. This chapter contributes to the development of an improved scheme for ranking the utility of source and sink points in a WAC loop.
The utility metrics for source and sink points in the WAC loop are defined based on modal sensitivities instead of the geometric controllability/observability.
Principle of wide area controller design and implementation
In [47], the time delays in WAM and WAC networks are shown separately on the input and output sides of the wide area attenuation controller, respectively. Therefore, the net time delay effect can be lumped on the output side of the wide area attenuation controller (which can be easily proven using the original transfer function representation of the transport delay). By considering the disturbance input, the equation of state for the extended plant can be rewritten as,
The state vector of the augmented plant (which includes both the plant and delay states) is denoted by x.
Proposed scheme for the scale reduction of the WAC system
The gain of the Feedback Path i−j (i.e. from the ith input signal to the jth output signal) is denoted by Gwac,j,i. The usefulness (for damping inter-area oscillations) of different input and output signals of the wide area damping controller should be evaluated from the. The utility indices calculated for the input and output signals of the wide-area attenuation controller must be converted to source and sink utility indices, respectively.
According to [24] and [54], the elements of the mode-path susceptibility matrix must be defined as follows.
Simulation results
The outputs from the wide area damping controller are fed to the generators excitation control systems. 4.3, it can be seen that several eigenvalues lie to the right of the 10% attenuation line prior to the insertion of any wide area attenuation controller. Here, the rotor angles are referenced to the COI of the system (ie the COI of all the generators in the system).
Oscillations at the rotor corners can be quickly damped through the incorporation of the proposed wide area damping controller.
Experimental Validation
It should be noted that the communication delay in the WAC loop is in fact random in nature. For the sake of simplicity and not to lose focus on the real context, the wider area damping controller design in this work is performed by adopting fixed time delay in the WAC loop. The communication delay considered in the wide area damping controller design can be interpreted as the average time delay to return the WAC signal.
The SWAC loop architecture remains the same as in the case of zero communication delay (please see previous section).
Summary
This chapter presents a design of the supplementary wide area attenuation controller that can practically fit into the architecture of the two-layer WAC system. On the other hand, such a communication network should not be used in the supplementary WAC loop. Although the basic concept (i.e., one layer with the communication network and another layer without the communication network) of the two-layer WAC system has already been reported in the literature, no work could be found to date regarding the practical realization of the supplementary controller.
The proposed design of the supplementary WADC is achieved by the H2-norm optimization after imposing the necessary constraints.
Overview of the conventional WAC system
The detailed mathematical procedure is derived for solving the above-mentioned structurally constrained H2 norm optimization problem. The H∞ norm optimization can provide a robust design, while better transient response can be achieved through the H2 norm optimization [59].
Bi-layer WAC architecture and the proposed design
Proposed configuration of the supplementary WADC
The input and signal flow to the additional WAC circuit must be limited to make it free of any extensive communication requirements. The vector ys,k indicates the measurements collected from the kth neighborhood of the controlled device to be fed into the additional WAC circuit. The contribution of other devices in generating the additional WAC signal for the kth device is indicated by Gsw,k,l.
In this case, the additional WADC can be effectively implemented as a collection of local controllers.
Design methodology for the proposed supplementary WADC . 79
However, the methodology proposed in [30], [1] can be directly applied only if Csy (i.e. the output matrix of measurements) is an identity matrix. The WAC main loop WADC is designed with due consideration of the appropriate time delay. The performance of conventional WADC is significantly degraded due to data communication delay.
Even after the insertion of the special damping controller for large area, persistent oscillations in the rotor angle are observed.
Overall summary
WAC Design with limited Measurements and with unknown load com-
In addition, regardless of the load in the system, it is enough to design a controller by assuming that all the loads are static and of CP type.
Reduced-scale architecture of the wide area control system
Practical supplementary controller design
Degradation of the main WAC loop performance due to communication delay has been observed through RT experiments. The complementary controller was found to retain the ability to significantly counterbalance the time delay effect in the main WAC circuit.
Future scopes of work
Fault tolerant wide area control
Structurally constrained H ∞ -norm optimized WAC design
WAC design for a large power system
Definition and Classification of Power System Stability IEEE/CIGRE Joint Working Group on Stability Terms and Definitions. Robust control of cross-domain oscillation damping in a power system with superconducting magnetic energy storage devices. Evaluation of two methods for selecting broadband signals for power system damping control.
Dynamic State Estimation in Power System Applying the Extended Kalman Filter with Unknown Inputs to Phasor Measurements.
The block diagram of PSS
General WAMS structure
Control center block diagram
General architecture of the traditional WAC system
The structures of feedback gain matrices corresponding to conven-
The New England 39-bus system
Eigenvalues of the open loop system
Structure of the feedback gain matrix with limited states in Case 1
Comparison of closed loop eigenvalues in Case 1 with the closed loop
Dynamic responses of generator speeds (COI referred) in Case 1 for
Structure of the feedback gain matrix with limited states in Case 2
Comparison of closed loop eigenvalues in Case 2 with the closed loop
![Figure 3.3: The structures of feedback gain matrices corresponding to conventional, sparsity promoting [1] and proposed LQR optimizations respectively.](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10474022.0/59.892.198.711.101.483/structures-feedback-matrices-corresponding-conventional-promoting-optimizations-respectively.webp)
