System Transient Stability Assessment Considering Renewables LVRT

The transient stability assessment of the power system is a conventional yet significant topic in the research field of power system[21]. The transient stability of a power system is categorized as rotor angle stability and basically reveals the capability of the generation within the system to regain synchronization after suffering from disturbances. The time frame studied is generally short term, 3-5 seconds after the disturbance and won’t extend to be beyond 10-20 seconds for very large scale systems. For system transient stability assessment, most researchers focus on finding the stability region[22] of the system facing a particular disturbance which provides the critical clearing time[23] indicating the allowed time for the manual or automatic fault clearing actions to be taken to prevent the system collapse. There are some other critical concepts that are explained as follows for convenience in the subsequent narrative.

Synchronous Generator Rotor Angles and Angular Velocity: For each synchronous generator serving as a power source in the power system, its rotor angle



refers to the phase angle difference between its terminal electromotive force

E

and voltage

U

at the connection point to

the bulk system as is shown in Figure. 1 and Figure. 2. ₀ refers to the synchronous angular velocity of the system. For 60 Hz system, ₀ 60 2  . Both the rotor angles and their angular velocities serve as system transient states.

Power system disturbances: The disturbances in a power system is generally defined as the sudden changes in system parameters or operation quantities happening in the system. For small

~

U

U UL

UG

E

xG x_T x_L

I

Figure. 1. Simple system diagram.

U I E

q-Axis

d-Axis

 UL

jIxL

jIx

0

Figure. 2. Simple system phases.

disturbances, system dynamics can be linearized to be analyzed for simplicity, while large disturbances can not[24], [25]. The faults appearing in the system can be taken as a typical kind of disturbances.

Pre-fault, Fault-on, Post-fault system states: These three terms refer to the three stages of the fault happening and clearing. The pre-fault stage indicates the system states prior to the fault happening. The fault-on stage refers to the scenario where the concerned fault is acting and not cleared yet. The post-fault states indicate the system states after the fault is cleared. Normal system transient stability assessment mainly considers the post-fault initial state which is the system state right after the fault is cleared.

System State Space Model: The state space model of the system is in the form of differential-algebraic equation (DAE) set in terms of the aforementioned states, which is derived with the synchronous generators’ dynamic swing equations (differential part) and static power flow equations (algebraic part) [26]. It reveals the time behavior of the system, or to be more specific, the mechanical and electrical power balance of the synchronous generators and power flow balance within the system.

Stable Equilibrium Point (SEP): The stable equilibrium point of the system refers to the system operating condition where the generators and the loads reach a balanced and stable operating condition, the equilibria. The system is to stay in this equilibria until other disturbance(s) happen.

In the state space, this equilibrium is illustrated with a point indicating the corresponding vector of states.

Stability Region (SR): The stability region of a system under certain disturbance is a region if the state space, where all the state point within this region are certified to be stable. Any operating

trajectory of the system starting with these points are guaranteed to converge to the SEP inside it.

Normally there is only one SEP in each stability region. It is a typical invariant set where trajectories can never exit once enter it.

The most intuitive method to conduct the assessment is the time domain simulation[27] based on the system state space model. However, there are several deficiencies in the time simulation method. It is significantly time-consuming to conduct the simulation, especially for large scale systems. For different fault clearing time, there have to be different simulations conducted respectively which means that the simulation results are in the form of the system being stable or unstable for each fault and clearing time scenario. Many researchers have proposed to use direct methods to find estimated stability region in the state space which provides a clear idea of the stable boundary of the post-fault system states after suffering disturbances[28]–[30]. This approach is much more efficient and effective. The main objective is to find a proper energy function which best reveals the dynamic and energy damping characteristics of the original system that is modeled with differential and algebraic equations.

Besides the equality constraints in the form of these algebraic equations, the system can also be restricted by other operation limits in the form of inequality constraints. With RES’s integration into the system, the LVRT curve can serve as a typical type of inequality constraints to maintain the RES’s online. It can be projected toward the real world scenarios where the faults are cleared quickly and operators would like to have as little renewable energy capacity tripped offline as possible. Therefore, there is a need to find an approach transform the LVRT operation constraints into the state space and to estimate the LVRT constrained stability region targeting at providing the system operator with reference about clearing the faults while keeping RES’s in the system functioning.

In document Renewable Energy Integrated Power System Stability Assessment with Validated System Model Based on PMU Measurements. Chen Wang (Page 13-17)