Naoto Kakimoto

Monitoring of interarea oscillation mode by synchronized phasor measurement

There is a low-frequency interarea oscillation mode in middle and western 60-Hz areas of Japan. Its stability determines available transfer capacity of a tie-line. We propose a method of monitoring its stability by phasor measurements synchronized using the global positioning system. The phase angle between two places deviates randomly. However, its Fourier spectrum shows a clear peak corresponding to the interarea mode. We estimate its frequency and damping from the spectrum. The estimation results agree well with those obtained by curve fitting for large disturbances. It is also possible to estimate the eigenvector. We examine how the eigenvalue varies with the total generation and power flow in the areas.

Performance of gas turbine-based plants during frequency drops

A combined cycle power plant, which combines a gas turbine and a steam turbine, can achieve high energy efficiency. Many combined cycle plants have been installed in the world. However, a large-scale blackout occurred in Malaysia in 1996. Combined cycle and gas turbine plants sequentially tripped out. The cause of this chain trip was thought to be a system frequency drop. Considering these backgrounds, it is important to study dynamic behavior of combined cycle plants. Several dynamic models of the combined cycle plant have been proposed. In our analysis, we use some of them and build a model for a single-shaft combined cycle plant. We execute numerical simulations to see how the combined cycle behaves when the system frequency drops.

Subsynchronous resonance damping control of thyristor-controlled series capacitor

A thyristor-controlled series capacitor (TCSC) substantially improves transmission capacity. It also mitigates subsynchronous resonance (SSR) accompanying conventional series capacitors. With an appropriate angle of thyristor firing, electrical damping becomes almost zero, which is called SSR neutral. This quality comes from TCSC itself. However, negative damping still remains and is large for firing angle 170~800° where little current flows through thyristors. This paper deals with control of firing angle. First, we oscillate the firing angle at a given frequency, and present an analytical method of calculating electrical damping. Next, we show that the damping improves at all frequencies if the firing angle oscillation is in phase with that of rotor angle. Synchronizing torque decreases, however, so a limit must be put on the control gain. Lastly, we execute numerical simulations to verify our analytical results.

Instability of interarea oscillation mode by autoparametric resonance

There is a low-frequency interarea oscillation mode in middle and western 60-Hz areas of Japan. The mode is damped, i.e., stable for small disturbances, but diverges in an oscillatory manner for large disturbances. It restricts power transmission in the areas. This paper shows that the instability is caused by nonlinear interactions between a few modes. The areas are represented with West30-machine system model prepared by the IEE of Japan. Numerical simulations are executed to obtain a critical case in which generator swings last without diverging or damping. Natural oscillation modes contained in the swings, are then calculated. Two modes have strong interactions with the interarea mode, and act so as to deteriorate its damping. Last, we examine how their influence changes with load level of the system.

Stable region for autoparametric resonance in longitudinal power systems

In longitudinal power systems, there is the possibility that a low-frequency oscillation mode may become unstable because of autoparametric resonance. The resonance occurs through interaction between two oscillation modes. In this paper, we calculate the stable region for the resonance by considering the interaction of the modes. First, we calculate steady-state solutions by the harmonic balance method. The steady-state solutions are stable or unstable. If we decrease the amplitude of one mode in an unstable solution, the modes decay. Conversely, if we increase the amplitude, the modes diverge. Namely, the unstable solution is located on the boundary of the stable solution. The amplitudes of the modes are rarely the same as those of the steady-state solution. However, the amplitudes approach a steady state after some transients. If the steady state is in the stable region, the system is stable. If it is in the unstable region, it diverges. Lastly, we estimate the amount of damping torques necessary to stabilize the system with the newly calculated stable region. We have obtained results similar to those derived from the Mathieu diagram, for example, a certain amount of damping torques can stabilize the system irrespective of its size. AVRs can substantially reduce the amount of damping torques and other quantities.

Theoretical equation for frequency response of thyristor-controlled reactor

Static VAr compensators (SVC) and thyristor-controlled series capacitors (TCSC) are composed of thyristor-controlled reactors (TCR) and capacitor banks. We derive theoretical equations for TCR admittance, which are important in studying harmonic instability and subsynchronous resonance.

Clarification of the SSR mitigation mechanism of a TCSC

A thyristor controlled series capacitor (TCSC) is considered to be effective not only for flow control and stabilization of power systems, but also for mitigation of subsynchronous resonance (SSR). This paper clarifies the SSR mitigation mechanism of a TCSC. First, using time simulations, we show that SSR appears and disappears depending on the firing angle of the TCSC. Next, we show that the frequency characteristics vary considerably with the firing angle. Further, we show that SSR occurs in TCSC-compensated systems as well as in conventional series-capacitor-compensated systems when 60 Hz minus the electrical resonance frequency of a transmission system coincides with the torsional oscillation frequency of a generator-turbine shaft. TCSC can avert SSR by changing the firing angle and by shifting the electrical resonance frequency. Next, we propose an equivalent circuit to TCSC which consists of a series capacitor in parallel with a resistor and a reactor. We adjust the parameters so that it shows the same frequency characteristics as TCSC. We apply it to time simulations to see if it is equivalent to TCSC. Finally, we perform an eigenvalue analysis on the equivalent circuit. We obtain results that correspond to the time simulations.

On the possibility of SSR in longitudinal power systems

This paper presents a theoretical consideration on the possibility of subsynchronous resonance (SSR) in longitudinal power systems. Shunt capacitors are used for reactive power compensation in our country, but series capacitors are not used in general. The possibility of SSR is therefore small. However, if power transmission increases, and accordingly, if shunt compensation increases in amount, there is no guarantee that SSR will never occur. First, we investigate network impedance viewed from a generator. Its resonance frequencies become lower with increasing transmission power. One of them gets subsynchronous if the power exceeds a certain value. In this area, there is some possibility of SSR, which is confirmed with the damping property of the generator. The admittance matrix of the load buses is singular at the resonance frequencies. Their number is equal to the dimension of the matrix. The frequencies are common to all generators but not limited to one particular generator. One of them becomes equal to 60 Hz as we increase transmission power. We regard this power as a limit for SSR. However, steady-state stability limit is lower than this limit, and steady operation is not possible at the limit. Therefore, it is impossible to enter the area of SSR. Thus, we conclude that SSR does not occur in shunt compensated systems. However, this property is easily lost if some series compensation is introduced.