POWER SYSTEM STABILIZATION

BACKGROUND OF THE INVENTION

[0001] Embodiments of the present invention relate generally to a power flow in a power system. More specifically, the embodiments relate to damping of power system oscillations.

[0002] The power system is a complex network comprising of numerous generators, transmission lines, a variety of loads and transformers. With increasing power demand in the power system, some transmission lines are more stressed than was planned when they were built. Since stressed conditions can lead a system to unstable conditions, power system stability has become an important issue. In simple terms, power system stability is defined as the ability of the power system to return to a normal state after a disturbance. The disturbance may be a fault, a loss of a generator or even a sudden increase in power loading which results in power oscillations in power system.

[0003] Small signal stability is a power system stability issue related to low frequency oscillations between generator rotors. It has been the main reason for many power blackouts across the world including the Western Electricity Co¬ordination Council (WECC) blackout of 1996. When the power system is heavily loaded, it often exhibits multi-mode oscillations because machine rotors, behaving as rigid bodies, oscillate with respect to one another using the electrical transmission lines between them to exchange energy. These oscillations generally lie in a frequency range between 0.1-3 Hz. The oscillations in this frequency range are generally analyzed in two main oscillation modes: 1) a local mode in the range of 1 to 3 Hz i.e., a generator or a group of generators in a plant swinging against the rest of the system and 2) an inter area mode in the range of 0.1 to 1 Hz i.e., machines in one group oscillate against machines in another group.

[0004] To stabilize the power system, damping measures to damp the power oscillations are utilized. Power system stabilizers (PSSs) are the most common damping control devices in power systems. Apart from PSSs, power oscillation damping (POD) can be effectively achieved through supplementary control of Flexible AC Transmission Systems (FACTS) devices installed in key transmission corridors. Traditionally, classical control theory has been adopted for design of such controllers which require an accurate model of the system at a particular (nominal) operating condition. However, lack of availability of accurate and updated information about each and every dynamic component of a large inter-connected system and its ever changing nature often puts a fundamental challenge on such model based approaches. Indirect adaptive controllers, which rely solely on system measurements, are useful for power system stabilizers (PSS) and also for the FACTS devices. These controllers are updated online based on the estimated model of the system and thus can adapt to the changes in operating conditions. However, present architectures of indirect adaptive controllers utilize complex multi-input multi-output (MIMO) structure. This leads to a multivariable controller, which is very complicated in nature.

[0005] For these and other reasons, there is a need for an improved indirect adaptive controller for power oscillation damping.

BRIEF DESCRIPTION OF THE INVENTION

[0006] In accordance with an embodiment of the present technique, a system for damping power system oscillations is provided. The system includes a damping device controller to generate a damping control signal to compensate for a plurality of oscillation modes in the power system oscillations. The damping device controller includes a plurality of outer closed loop paths each including an adaptive controller configured to determine an individual oscillation mode from at least one power system measurement signal. Each adaptive controller is fiirther configured to generate an adaptive control signal to shift at least one open loop pole of an inner loop path related to the individual oscillation mode to a closed loop location. The system further includes a damping device to generate a damping signal based on the damping control signal.

[0007] In accordance with another embodiment of the present technique, a method of damping power system oscillations in a power system network is provided. The method includes obtaining a plurality of power system measurement signals from a plurality of power system locations and generating a damping control signal to compensate for a plurality of oscillation modes in the power system oscillations. In the method, generating the damping control signal includes extracting an individual oscillation mode from each of the power system measurement signals generating a plurality of adaptive control signals to shift open loop poles related to the individual oscillation modes to a closed loop location. The method further includes injecting a damping signal in the power system network based on the control signal.

BRIEF DESCRIPTION OF DRAWINGS

[0008] These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

[0009] FIG. 1 is a graphical representation of exemplary power oscillations in a power system;

[0010] FIG. 2 is a schematic diagram of a power system illustrating a system for damping power system oscillations in accordance with an embodiment of the present technique;

[0011] FIG. 3 is a block diagram of an indirect adaptive controller for power oscillation damping (IACPOD);

[0012] FIG. 4 is a block diagram of a damping controller for damping power system oscillations in accordance with an embodiment of the present technique; and

[0013] FIG. 5 is a flow chart illustrating a method of damping power system oscillations in accordance with an embodiment of the present technique.

DETAILED DESCRIPTION OF THE INVENTION

[0014] As used herein, the term "controller" refers to software, hardware, or firmware, or any combination of these, or any system, process, or functionality that performs or facilitates the processes described herein.

[0015] When introducing elements of various embodiments of the present invention, the articles "a," "an," "the," and "said" are intended to mean that there are one or more of the elements. The terms "comprising," "including," and "having" are intended to be inclusive and mean that there may be additional elements other than the listed elements.

[0016] FIG. 1 shows a graphical plot 10 of exemplary power oscillations in a power system. A horizontal axis 14 represents time in seconds whereas a vertical axis 12 represents power flow in a transmission line in per unit (pu). A curve 18 shows power oscillations in the transmission line power flow without a damping controller. Even though only power oscillations are shown here, it should be noted that the oscillations may be present in any other signal such as a voltage or a current or even a generator rotor speed. A power demand on the transmission line gets changed from 2 pu to around 3 pu at 10 seconds. At this transition, power oscillations in curve 18 starts and they increase slowly in amplitude. If these oscillations are not damped, the respective power network may become unstable and may result in a power blackout.

[0017] A curve 16 shows power oscillations in the transmission line power flow with a damping device such as an AVR or a FACTS device. As can be seen, when a damping controller is used along with the damping device, the power oscillations attenuate quickly, and the power flow settles down to meet the new demand in around 16 seconds. A spike around 10 seconds is the result of damping controller parameters and depends on a damping controller gain value.

Also based on Fourier series principles, it can be seen that curve 18 may be split into multiple oscillation modes or sinusoidal components of different frequencies. Sinusoidal signals have a property that if two signals 180 degrees out of phase are added, the resultant signal amplitude becomes zero. In control theory the sinusoidal signal may be represented in terms of a eigenvalue X which may be given as:

A,=a±JG> = f(t-i)x(t) m
K J x(t-i)+xr(t)P(t-i)xct) v ;

In equation (7) above, A is a forgetting factor and P is a covariance matrix and at sample time equal to t are given as:

X(t) = 1_M^M (8) p(t) _ [i-*(t)xr(t)]p(t-i) (9)

In an embodiment, £0 ls a constant with a value equal to 0.8. Thus, at every sample, the system model generates the predicted output y(t) based on updated values in the regressor X(t) and the parameter vector 9(t) and based on the predicted output y(t) inter-area oscillation modes of interest are detected. In an embodiment, inter-area oscillation modes may range from 0.1 Hz to 1.0 Hz and local-mode oscillation mode may range from 1.0 Hz to 3.0 Hz.

[0023] It should be noted that the appropriate identification of the oscillation mode of interest from the predicted output y(t) depends on the choice of sampling frequency. The sampling time of sampling frequency may vary from 20 ms to 100 ms. In one embodiment of the present technique, a sampling time of 80 ms provided good results.

[0024] Referring back to FIG. 3, once the online estimator 72 determines the inter-area oscillation modes of interest, controller 76 provides an appropriate control signal u(t) to damp these inter-area oscillation modes. In an embodiment, controller 76 may include an adaptive controller and controller design module 74 utilizes a pole shifting control algorithm to compute the controller coefficients for controller 76. In one embodiment, a feedback control loop has the form:

U(z)F(z)=-Y(z)G(z) (10)

where, G{z) = I"^2"' md F& = 1 + I^i*1 + fiz~^ ■ In one embodiment, control polynomials ng and nf are given as ng=nb-l and nr=na-l, where na and nb are system polynomials as described earlier and gj and fi are control parameters that need to be determined. In general, the underlying design problem for the controller is to shift open-loop poles of the system (i.e., equation 2) radially by a pole shifting factor a towards a unit circle in a pole zero plot so that the closed loop characteristics equation assume the form:

A(z'')F(z')+ B(z')G(z')= A(az-1) (11)

[0025] The controller parameters are derived by controller design module 74 based on the equality equation 10. For example, let D be a matrix of control parameter & and fi? i.e., D=[fi, f2,....,fnf, go, gi,--,gngff, then D can be determined by solving above equality based on the value of the pole shifting factor a. The control signal u(t) which will compensate for the inter-area oscillation mode of the interest can then be expressed as:

u(t)=f(t).D (12)

where bnfb> ai< 02,....,anJT. Thus, the optimization problem becomes min a J(t+1, a)= min aJ£#(f+l>Vr(t+l)]2 (14) subject to constraints — — (1 — a)