CHAPTER 3 DECENTRALIZED COORDINATED SECONDARY VOLTAGE
3.3 Simulation results for 5000 bus network
3.3.4 Validation of the proposed algorithm
The effectiveness of the DCSVC controller on 5000 bus power grid is validated through the following simulation scenarios:
3.3.4.1 Scenario 1- Sudden load variation
To validate the robustness of the proposed DCSVC, all active and reactive loads in the grid are
suddenly increased by 10% at t= 10sec.. Figure 3.6 shows the simulation results for cases with
and without DCSVC. As can be observed from Figure 3.6.a, the proposed DCSVC is able to maintain the voltage deviation of pilot buses within 0.5% after transients. However, the results with no DCSVC show that without any secondary voltage controller the steady state voltage error could not be compensated. Figure 3.6.b also illustrates the injected reactive power by compensator located at pilot buses.
a) Voltage error on pilot buses b) Injected reactive power by Compensators
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3.3.4.2 Scenario 2- Change the reference value of the pilot bus
In another scenario, the reference of all the 34 pilot nodes are suddenly increased by 3% at 1 sec. to evaluate the tracking feature of the DCSVC. As can be seen from Figure 3.7.a, the proposed method is able to reduce the voltage deviation, i.e., the difference between the reference voltage and measured voltage on pilot nodes, to less than 0.5% on all pilot nodes while without having any DCSVC the primary controllers on pilot buses are not able to track the new voltage set-point. The steady state error of 3% can be seen in this case without any DCSVC. Figure 3.6.b also shows the injected reactive power by the compensators to change the voltage on pilot nodes.
a) Voltage error on pilot buses b) Injected reactive power by Compensators
Figure 3.7 Scenario2-DCSVC (solid line) vs. No DCSVC (dashed line) cases
3.3.4.3 Scenario 3- Impact of communication delays
The communication delay in power systems is dependent on the communication channel spec- ifications as well as protocols that are used to send & receive the data. This delay may vary from few milliseconds to hundreds of milliseconds. Since the time constant of the CSVC al- gorithm is much larger than such a natural delay, its effect on the closed loop stability can be neglected. However, with the rising concerns regarding to cybersecurity of power grids,
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the existence of malicious attacks may lead to larger time delays in the order of few seconds Chen & Sun (2014).
To investigate the effect of such a threat on the performance of the proposed DCSVC algorithm, a delay of 10sec. is considered on the communication channel between the controller and the power system for Scenario 1. Although the discrete model of Equation 3.1 is delay free, the
effect of communication delays can be considered by adding new poles located at z= 0. In this
way, the state space model of Equation 3.1 is modified as follows:
xd1(k + 1) = u(k) · · · xdn−1(k + 1) = xdn−2(k) xdn(k + 1) = xdn−1(k) x(k + 1) = Ax(k) + Buxnd(k) + Bvv(k) + d(k) ym(k) = Cmx(k) + Dvmv(k) yu(k) = Cux(k) + Dvuv(k) (3.7)
In this formulation, new states, xd1, · · · , xdnare added to model n-steps of input delay.
Figure 3.8 compares the simulation results for the two cases of MPC controllers, one with modeled delay as Equation 3.7 and the other without any delay model based on Equation 3.1. As can be seen in this figure, for the case without any modeled delay, the DMPC controller can not compensate the oscillations caused by the delay. However, considering delay model by DMPC has led to a better performance in which the oscillations are damped out to less than 2% p.u. in less than 60 seconds.
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a) Voltage error on pilot buses b) Injected reactive power by Compensators
Figure 3.8 Scenario3-DCSVC (solid line) vs. No DCSVC (dashed line) cases
3.3.4.4 Real-time performance
The real-time performance of the DCSVCs is measured for Scenario 1. The maximum compu- tation time of DCSVCs, per one control interval, i.e. 10 seconds, is 5 milliseconds. This means that for 5000 bus test-case, the proposed DCSVC can be easily implemented in real-time.
3.3.4.5 Convergence of the MPC algorithm
The convergence of the QP solver used in this paper and described in Schmid & Biegler (1994) depends mainly on whether all of the constraints are satisfied or whether some of them are vi- olated. As described in Schmid & Biegler (1994), the algorithm starts from an initial guess of optimal solution which is the closed form solution of the unconstrained problem. If all the con- straints are satisfied using this solution, then it will be considered as optimal value. Otherwise, an iterative process starts to determine the active constraint set satisfying the standard optimal- ity conditions. If the algorithm detects any unfeasibility, the iterative process terminates and the MPC uses the last successful optimal value as the solution. Such an unfeasible situation usually occurs when the number of control variables is smaller than number of outputs or when all the control variables reach their limits.
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In particular, for the secondary voltage control problem, the topology of the power system may affect the convergence of the algorithm. Indeed, an unfeasible situation, in which the optimization problem does not converge, may occur when the number of the compensator devices is smaller than the number of pilot buses. The same issue may rise for the case in which the reactive power required to compensate the voltage at a pilot node cannot be provided by the corresponding compensator devices in the grid due to their saturation.