Method of determining remedial control actions for a power system in an insecure state

Abstract

A method of determining remedial control actions for a power system in an insecure and unstable operating condition is provided. The power system has a plurality of generators injecting power into a network and each generator has a generator injection impedance and a stability boundary in the injection impedance plane. A system safety boundary is calculated based on a predetermined network operating safety margin for each generator, the generator injection impedance is compared with the safety boundary and it is determined whether each generator is safe or unsafe. A remedial control action is determined comprising a scheme for re-dispatching power generation for each unsafe generator to thereby establish a secure operating condition for the power system. A new safe operating point in the impedance plane for each unsafe generator may be determined, and a distance between the generator injection impedance and the new safe operating point is calculated under the assumption of constant voltage magnitude for each unsafe generator. The unsafe generator operation is remedied by reducing power generation of the unsafe generator.

Claims

1. A method of determining a remedial control action for a power system in an insecure operating condition, the power system having a plurality of generators injecting power into a network having a plurality of nodes and a plurality of branches, the plurality of generators being represented in the network by a plurality of nodes of power injection, each generator having a generator injection impedance and a stability boundary in an injection impedance plane, the method comprising calculating a system safety boundary in the injection impedance plane for each generator based on a predetermined network operating safety margin in relation to the system stability boundary, comparing for each generator the generator injection impedance with the safety boundary and determining whether each generator is safe or unsafe, reducing power generation for each generator determined to be unsafe; and determining a remedial control action, the remedial control action comprising a scheme for re-dispatching power generation for at least each unsafe generator to thereby establish a secure operating condition for the power system.

2. The method according to claim 1, wherein the remedial control action is performed by determining a new safe operating point in the impedance plane for each unsafe generator, calculating a distance between the generator injection impedance and the new safe operating point under the assumption of constant voltage magnitude at the node of power injection for each unsafe generator, wherein reducing power generation for each generator comprises reducing power generation of the unsafe generator to the new safe operating point.

3. The method according to claim 2, wherein remedial control action further comprises the steps of determining missing power in the power network due to the remedying action, determining available power reserves in the power network, and generating at least one re-dispatch solution.

4. The method according to claim 3, wherein a number of re-dispatch solutions are provided, and wherein the method further comprises the step of evaluating the number re-dispatch solutions and prioritize the number of re-dispatch solutions according pre-defined power system operation criteria.

5. The method according to claim 3, wherein the method further comprises the step of automatically performing a selected re-dispatch solution.

6. The method according to claim 1, wherein the method further comprises the step of determining a security boundary based on a predetermined network operating security margin in relation to the system stability boundary, and determining the new safe operating point at least on the security boundary.

7. The method according to claim 6, wherein the available power reserves for each safe generator in the system is determined as the distance between the determined injection impedance and a secure operating point at the system security boundary under the assumption of constant voltage magnitude at the node of power injection.

8. The method according to claim 1, wherein the power system is in an at least quasi steady state.

9. The method according to claim 1, wherein the stability boundary for each generator is determined in real-time.

10. The method according to claim 1, wherein the remedial control action is performed in real-time.

11. A method of determining a remedial control action in a power system in an insecure operating condition, the power system having a plurality of generators injecting power into a network having a plurality of nodes and a plurality of branches, the plurality of generators being represented in the network by a plurality of nodes of power injection, the method comprising: receiving stability information for the network, the stability information including information on a number of unsafe generators, restoring secure operation by determining a new safe operating point in an impedance plane for each unsafe generator, calculating a distance between a determined injection impedance and the new safe operating point under the assumption of constant voltage magnitude at the node of power injection for each unsafe generator, reducing power generation of the unsafe to the new safe operating point to thereby remedy operation of the unsafe generator.

12. A non-transitory computer readable medium having stored thereon instruction code for performing the method of claim 1 when said instruction code is run on a computer.

13. A system for determining a remedial control action for a power system in an insecure operating condition, the power system having a plurality of generators injecting power into a network having a plurality of nodes and a plurality of branches, the plurality of generators being represented in the network by a plurality of nodes of power injection, each generator having a generator injection impedance and a stability boundary in an injection impedance plane, the system comprising a processor; and a non-transitory computer readable medium coupled to the processor that stores instruction code that when executed by the processor causes the processor to: calculate a system safety boundary in the injection impedance plane for each generator based on a predetermined network operating safety margin in relation to the system stability boundary, compare for each generator the generator injection impedance with the safety boundary and determining whether each generator is safe or unsafe, control each generator determined to be unsafe to reduce power generation, and determine a remedial control action, the remedial control action comprising a scheme for re-dispatching power generation for at least each unsafe generator to thereby establish a stable operating condition for the power system.

14. The system according to claim 13, the system further comprising a power system regulator configured to implement the remedial control action in the power system.

15. The method according to claim 4, wherein the method further comprises the step of automatically performing a selected re-dispatch solution.

16. The method according to claim 2, wherein the method further comprises the step of determining a security boundary based on a predetermined network operating security margin in relation to the system stability boundary, and determining the new safe operating point at least on the security boundary.

17. The method according to any claim 2, wherein the power system is in an at least quasi steady state.

18. The method according to claim 2, wherein the stability boundary for each generator is determined in real-time.

19. The method according to claim 2, wherein the remedial control action is performed in real-time.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1a shows an electric power system, FIG. 1b shows synchronized measurements from two nodes of the electric power system, and FIG. 1c shows the resulting phasors in an impedance plane,

(2) FIG. 2 shows a generalized electric power system, where system loads are represented as impedances and the generators are assumed to maintain constant terminal voltage,

(3) FIG. 3 shows the boundary of aperiodic small signal stability in the injection impedance plane,

(4) FIG. 4 shows a flow chart of a method according to the present invention,

(5) FIG. 5 shows an exemplary power system having five synchronous generators,

(6) FIG. 6 shows the exemplary power system in FIG. 5 wherein some transmission lines are out of service,

(7) FIG. 7a shows the operating points for four of the generators of FIGS. 4 and 5 in the impedance plane for a power system in a stable operating condition,

(8) FIG. 7b shows the operating points for the four generators of FIG. 7a in the impedance plane for a power system in an unstable operating condition,

(9) FIG. 7c shows the operating points for the four generators in the impedance plane for a power system after a remedial control action have been performed,

(10) FIG. 8 show the safety boundary, the stability boundary and the security boundary in an injection impedance plane,

(11) FIG. 9 shows a flow chart of a sequence for a remedial control action using a fast and an optimized approach, respectively,

(12) FIG. 10 shows a flow chart illustrating a determination of a remedial control action,

(13) FIG. 11 shows a flow chart illustrating the determination and carrying out of a remedial control action.

DETAILED DESCRIPTION OF THE DRAWINGS

(14) In the present description the following terms may be interpreted as follows:

(15) Power stability is the ability of an electric power system, for a given initial operating condition, to regain a state of equilibrium after being subjected to a physical disturbance, with most system variables bound so that practically the entire system remains intact.

(16) Rotor angle stability: The term refers to the ability of synchronous machines, such as generators, to remain in synchronism after being subjected to a disturbance. Small signal rotor angle stability concerns the stability of the system steady state point, and may appear as an aperiodic (non-oscillatory) increase of the rotor angle due to lack of synchronizing torque, or as rotor oscillations of increasing amplitude due to lack of sufficient damping torque.

(17) Aperiodic small signal stability is used to refer to the ability of the system generators to establish sufficient synchronizing torque for a given equilibrium condition. An aperiodic small signal instability appears as aperiodic (non-oscillatory) increase of the rotor angle and subsequent loss of synchronism following a very small disturbance, such as a small increase in applied mechanical power to a generator, or small changes in the system loading.

(18) Frequency stability: relates to the ability of a power system to maintain steady frequency following a severe system disturbance resulting in a significant imbalance between generation and load.

(19) Voltage stability: Refers to the ability of a power system to maintain steady voltages at all nodes in the system after being subjected to a disturbance from a given initial operating condition. Voltage stability is dependent on the system ability to restore equilibrium between load demand and supply.

(20) The terms “bus” and “node” may in the following both be used interchangeably to indicate interconnections in a power system.

(21) FIG. 1a shows a power system 1, where a Phasor Measurement Unit (PMU), or another measurement device that provide synchronized measurements in real time, of voltage and current phasors along with frequency measurements, is installed at node 1 and node 2. The synchronized measurements are shown in FIG. 1b, for node 1 and node 2, respectively.

(22) FIG. 1c shows the resulting phasors {right arrow over (V)}.sub.1 and {right arrow over (V)}.sub.2 plotted in the same complex plane. The phase difference θ between the signals from node 1 and node 2, respectively, is indicated.

(23) Power network real-time measurements of system parameter may provide a so called full observability of the system grid. The full network observability may then be used to establish a deterministic representation of the system conditions, where the system representation has the following characteristics or preconditions: All power injections into the system enter the network in a node of constant steady state voltage magnitude.

(24) This may result in the introduction of additional network nodes and branches compared to the physical system depending on the type machine excitation control and status of machine protection The load is represented as impedances in the network

(25) Hereby, some longer term load dynamics may not be included in the model and the method preferably evaluates the instantaneous operating conditions, so therefore the instantaneous impedance as seen from the generators is preferably represented.

(26) By representing the power injections at nodes of constant steady state voltage magnitude may result in a reduction of the degrees of freedom associated with the determination of the boundaries for aperiodic small signal stability.

(27) An exemplary power system 10 is shown in FIG. 2. FIG. 2 shows the power system 10 where all loads are represented as constant impedances 13 and where all generators 11 are assumed to maintain a constant terminal voltage. With all system impedances 13 known, the system operating conditions can be determined from the generators 11 terminal voltages (V.sub.1, V.sub.2, V.sub.3 and V.sub.4).

(28) The power system 10 comprises the generators 11 and the network 14. In the network 14, the generators are represented by nodes of power injection 16. The nodes 15 and the impedances 13 are interconnected via branches 12. The generators are in FIG. 2 assumed to maintain a constant terminal voltage. Thus, the generalized notation used below corresponds to a generalized system as shown in FIG. 2.

(29) FIG. 3 shows how the stability boundary 16 for aperiodic small signal stability appears in an injection impedance plane 18 for a given generator, such as generators 11 as shown in FIG. 2. The boundary may be derived from the below expression

(30) $Z_{\mathrm{inj}}=-\frac{Z_{\mathrm{TH}}\sin \theta }{\sin {\varphi }_{\mathrm{TH}}}$
wherein Z.sub.TH is the system Thevenin Impedance as seen from the generator, Z.sub.inj is the injection impedance; φ.sub.TH is the angle of the system, and Z.sub.th the Thevenin Impedance.

(31) The stability boundary 16 thus appears as a circle in the Impendance plane and when Z.sub.inj equals the above expression, the circle has a radius of r=Z.sub.TH(2 sin φ.sub.TH). Operating the power system outside the circle, that is with an injection impedance larger than Z.sub.TH(2 sin φ.sub.TH) indicates a stable operating condition where a relative increase in the phase angle at the node of injection results in increased injection. An operation inside the circle that is with an injection impedance smaller than Z.sub.TH(2 sin φ.sub.TH) represents an unstable condition characterized in that in this condition, a decrease in the injected power will result in an increase of the phase angle at the node of injection. By utilizing the above equation, the aperiodic small signal stability of a given generator may therefore be described by the following set of inequalities, so that C is the criteria for stability for a given generator is

(32) $C=.Math.\frac{{\stackrel{\_}{Z}}_{\mathrm{inj}}.Math.\left(2\sin {\varphi }_{\mathrm{TH}}\right)+j.Math.Z_{\mathrm{TH}}}{Z_{\mathrm{TH}}}.Math.\{\begin{array}{cc}>1& \mathrm{Stable}\mathrm{operation}\\ =1& \mathrm{At}\mathrm{the}\mathrm{boundary}\\ <1& \mathrm{Unstable}\mathrm{operation}\end{array}$

(33) Thus, from the above, it is seen that an insecure or unstable operation condition may be detected by modelling the power system as suggested in FIGS. 2 and 3.

(34) FIG. 4 shows a flow chart 40 showing a method of remedying an instable power system. In 41, an instability is detected, and it may further be determined that the system is in at least a quasi steady state and the insecure node is identified in 42. In 43, a new safe or stable operating point is determined, and missing power to arrive at the new safe operating point is determined in 44. It is envisaged that the method may be terminated here by providing the information of the missing power. However, the method may further comprise the step of determining the power reserves of the reamining generators in 45, and generate one or more re-dispatch solutions in 46. Preferably, the solutions are automatically evaluated and ranked with respect to predefined criteria, and the best re-dispatch solution may be executed in the power system.

(35) FIG. 5 shows a model of a power system having five generators 51, 52, 53, 54 and 55, a plurality of 2-winding transformers 56, and loads indicated by arrows 57, interconnected by transmission lines 58 interconnecting nodes 59.

(36) In the following a scenario is described, wherein a chain of events leads to a loss of aperiodic small signal stability of a manually excited generator. In the pre-fault conditions, the system may be characterized by the following parameters, where P is the power of the generators 51, 52, 53, 54, 55, and P/P.sub.max is the utilization factor, i.e. the percentage of power with respect to maximum injectable power and size is the maximum injectable power for the generator.

(37) TABLE-US-00001 Generator G1 G2 G3 G4 G5 P [MW]: 100.00 68.00 55.00 20.00 130.61 Size 200.00 75.00 75.00 25.00 inf [MV A]: P/P.sub.max in 50.00 90.67 73.33 80.00 — [%]

(38) It is seen that the generator G2, 52, is operated close to its limits having a utilization factor of 90.67%, thus the power system is in a highly loaded state. In order to provoke an instability, the power system was further stressed by applying two disturbances, one after another, as seen in FIG. 6, wherein the transmission lines 60 and 61 are out of service. The disturbances were the tripping of two transmission lines 60 and 61, which for example may be caused by a short circuit of a transmission line due to a tree contact.

(39) At a time t=0 sec, the simulation begins and the power system is in a stable and steady condition. At time t=2 s, the line 60 is tripped. The tripping of this line leads to oscillations in the system which damps out after approximately 15 s. At time t=40 s another line, line 61 is tripped. This causes a fluctuation which damp out within 5-10 s, but the voltage magnitudes at other nodes begin to slowly decrease. At time t=100 seconds, the voltage collapses.

(40) Thus, it is seen that even small disturbances may in e.g. cases where the load is high, lead to collapse of the power system.

(41) By monitoring the power system, with a method, e.g. as disclosed by Hjörtur Jóhannsson and described under the prior art section, aperiodic small signal instability may be detected immediately after they occur. Initially at t=0.08 seconds, when no disturbances has occurred, all the generators, G1 to G5, 51, 52, 53, 54, and 55 are operating in a stable mode as seen in FIG. 7a, where all generator operating points are outside of the stability boundary. However, from FIG. 7b, it is seen that shortly after the second disturbance at time t=41.16 seconds, the operating point of the generator G1, 51, is seen to have moved to the unstable side of the stability boundary 70 as shown in the normalized injection impedance plane.

(42) To apply a remedial control action a security and a safety boundary were chosen to be a power injection margin of 0.5% and 0.1% of the maximum power injection into the node of constant voltage magnitude, respectively, and the stability boundary 70, the security boundary 71 and the safety boundary 72 are shown in FIG. 7c. In FIG. 7c, at t=52.35 seconds the remedial control action has been applied, and it is seen that after the remedial control action, the generator operating point for generator G1, 51, has been moved to the security boundary 71 in the normalized injection impedance plane.

(43) Thus, by performing remedial control actions, the collapse of the power system was avoided.

(44) The stability boundary 80, the security boundary 81 and the safety boundary 82 are shown in more detail in the normalized injection impedance plane in FIG. 8.

(45) It is seen that the remedial control action is triggered when the safety boundary 82 is crossed, and thus, as the generator, e.g. generator 51, reaches the safety boundary 82, the necessary power reduction for generator G1, 51, to bring the generator G1, 51, from an operating point 83 on the safety boundary to a new safe operating point 84 on the security boundary 81 is determined.

(46) In the present example, the necessary active power reduction is determined to be 22.43 MW which corresponds to the distance between the operating point 83 and the new safe operating point 84 in the injection impedance plane along the line 85 of constant voltage. Subsequently, the method determined the available active power reserves of the remaining stable generators. The available power reserves for generators 52, 53 and 54 are seen below:

(47) TABLE-US-00002 Generator 2 3 4 ΔP.sub.reserve [MW]: 9.71 9.69 4.90 P [MW]: 64.92 64.93 19.98 Size [MV A]: 75.00 75.00 25.00 P.sub.inj, max in [MW]: 76.31 80.91 33.30

(48) It should be noted, that the generators' power reserves are limited due to the particular size of the machine and that the maximum injection power was in this case not the limiting factor. The next step was to identify the possible solutions to substitute the missing power. It was found, that none of the remaining generators provide a sufficient power reserve to handle the missing power by itself. In the current case only a group solution provides the necessary power reserves. Eventually a solution was found, where the generators 52 to 54 participate and take over the missing power. The table below shows the changes applied to each generator as well as the new active power injection and utilization factor.

(49) TABLE-US-00003 Generator: 1 2 3 4 5 ΔP [MW]: −22.43 MW 8.96 8.96 4.52 — P [MW]: 157.35 73.88 73.88 24.50 51.62 Size [MV A]: 200.0 75.00 75.00 25.00 inf P/P.sub.max in [%]: 78.68 98.5 98.5 98.00 —

(50) The remedial control action may be performed in a number of ways, assuming that an early warning method, such as the early warning method described by Johansson above, provides continous information of any instability in the system. In FIG. 9, a flow chart 90 shows an overview of the method. The Early Warning Method may be running continuously in the background, and reading PMU data sets in real time or periodically, step 91, and update the power system model with every PMU data set, step 92, and determine the aperiodic small signal stability margin for each generator in the system, step 93. If one of the generators stability margin falls below the defined safety margin or even instability of a generator operating point is detected, the remedial control action is initiated. First, the steadiness of the power system is evaluated in step 94 or possibly in step 94a or 94b. If the system is insecure and in steady state, possible remedial control actions are determined, step 95. Step 95 is shown to include the evaluation and the ranking of the found solutions. In step 96, re-dispatch of power generation is effectuated.

(51) In FIG. 10, a more detailed flow chart 100 illustrating the method of determining a remedial control action is provided. In step 101, an instability is detected and the system is found to be in at least a quasi steady state. In the next step, 102, the node that triggered the instability is identified. In steps 103, 104 and 105, it is analyzed, if the node is an active or passive node. Depending on the status of the node, the calculation of the necessary power reduction is determined in step 106. After the power reduction is calculated, the available power reserves are determined, step 107, and different possible reschedule solutions for the available generators are analyzed. In step 108, a re-dispatch solution is generated and the solutions are evaluated and ranked according to pre-defined criteria in step 109.

(52) In FIG. 11, a remedial control action routine 110 to determine and carry out the remedial control action is shown. The remedial control action routine is executed in case of a shortfall of the stability margin of at least one of the generators in the system, the routine determines the relative electrical distance between the generators in step 111, and determine the active nodes of constant voltage magnitude in step 112, in step 113 an insecure node is identified, and the necessary power reduction to restore security margin is determined in step 114. In step 115, the available power reserves of the other generators are determined, and the possible remedial control actions to restore a secure state are found in step 116. The solutions are verified, evaluated and listed in step 117, and the generator output parameters are updated according to the chosen remedial control action. Thus, the routine analyses the conditions of the remaining generators, determines their power reserves and derives possible remedial control actions, in order to restore a stable and secure system condition.

(53) Expressions such as “comprise”, “include”, “incorporate”, “contain”, “is” and “have” are to be construed in a non-exclusive manner when interpreting the description and its associated claims, namely construed to allow for other items or components which are not explicitly defined also to be present. Reference to the singular is also to be construed as being a reference to the plural and vice versa.

(54) A person skilled in the art will readily appreciate that various parameters disclosed in the description may be modified and that various embodiments disclosed and/or claimed may be combined without departing from the scope of the invention.