Automation of Electric Power Systems  2020 : 85-97  DOI: 10.1007/978-981-13-9779-0_7
0

Citation 

Junjun Yang, Wei Xu, Shaofeng Liu, Xiancheng Ren and Xiaotong Xu. A Rapid Power Flow Analysis Method After UHVDC Fault Considering the Control Strategy of Automatic Equipment[J]. Automation of Electric Power Systems, 2020 : 85-97. DOI: 10.1007/978-981-13-9779-0_7.

Corresponding author

Junjun Yang, e-mail: yangjunjun@sgepri.sgcc.com.cn.
A Rapid Power Flow Analysis Method After UHVDC Fault Considering the Control Strategy of Automatic Equipment
Junjun Yang , Wei Xu , Shaofeng Liu , Xiancheng Ren and Xiaotong Xu     
NARI Group Corporation (State Grid Electric Power Research Institute), Nanjing 211106, China
Abstract: The unbalanced power caused by ultra-high voltage direct current (UHVDC) fault may lead to the overload of transmission section or violation of busbar voltage in local power grid. In serious cases, it may lead to cascading faults or large-scale blackout. In order to accurately simulate the power flow distribution after large-scale power shortage and determine the validity of disposal strategy dealing with serious fault, a rapid power flow analysis method after fault considering the control strategy of automatic equipment is proposed in this paper. Considering the influences of automatic equipment to power grid operation situation on different time scales, the control strategy of power system stability control devices, the primary frequency control, automatic generation control (AGC) and automatic voltage control (AVC) is simulated. The active power of the generator and load at each stage is determined. The active power of transmission section and voltage of busbars under large-scale unbalanced power can be determined rapidly for the disposal strategy optimization. Simulation results based on actual power grid show the effectiveness and viability of the method.
Key words: Ultra-high voltage    DC blocking fault    Stability section    Primary frequency modulation    Secondary frequency modulation    Secondary voltage regulation    
1 Introduction

UHVDC transmission system has the characteristics of wide transmission range, large transmission capacity and large reactive power consumption in converter stations. The unbalanced power caused by UHVDC blocking fault may lead to great changes in power grid operation situation. Under the new operation situation, it is very likely that the local power grid will operate beyond the stability limit, or the central busbar voltage will exceed the limit, which may induce cascading failures or large-scale power outages in serious cases. Dispatchers need to formulate accident disposal strategy according to the problems of the overload of transmission section and violation of busbar voltage to ensure the safe and stable operation of the power grid after the fault. It is urgent to quickly identify the weak links of power grid operation situation after UHVDC faults on line to provide basis for effective disposal strategies [1-3].

Automatic equipment such as power system stability control devices, the primary frequency control, automatic generation control (AGC) and automatic voltage control (AVC) affect operation situation after UHVDC fault on different time scales [4]. AVC generally adopts three-level voltage control based on soft partition, from low to high, and its control time constants are hour level, minute level and second level respectively. Therefore, power system stability control devices, the primary frequency control and the primary voltage control of AVC plays an important role in the process of power grid transition from transient state to steady state. The secondary voltage control of AGC and AVC plays a role in the frequency recovery process after the power grid transits to a steady state [5]. Therefore, it is necessary to simulate the acting time and operation strategies of various automatic equipment in order to obtain the accurate system power flow of the whole process after the fault.

Power flow analysis methods include power flow calculation and stability analysis based on time-domain simulation. Conventional power flow algorithm sets the active power of generators to a fixed value. The balancing machine shares the unbalanced power. It is difficult to accurately reflect the adjustment of generators with the change of system frequency [6]. The generator is set as PV node, and the power flow calculation can only simulate the third level voltage regulation of AVC. When the central busbar voltage exceeds the limit after fault, the power flow calculation cannot accurately simulate the preset reactive voltage control mode because the second level voltage regulation can specify the reactive power of the generators, capacitors and reactors. Stability analysis can accurately simulate the power flow changes after faults. For large power grid, the scale of severe AC/DC faults is very large. Detailed simulation analysis of all faults takes a long time, and it is difficult to meet the real-time requirements of on-line simulation and verification of disposal strategies [7].

Therefore, the parameters such as primary frequency modulation, rotary backup and climbing rate of the generator, as well as the static frequency characteristics of the load, are integrated to determine the active power of the generator and load in each stage after fault. The control modes of reactive power sources such as generators, capacitors and reactors after fault are simulated according to the characteristics of node voltage and hierarchical partition control, thus realizing the rapid analysis of the active power of transmission section and voltage of busbars after UHVDC fault, and providing a feasible and effective method for the online development and verification of the disposal strategy.

2 Calculation Method of Three Stages Active Power 2.1 The Moment After Failure

At the moment of failure, only the voltage phase angle of the AC side node of the DC system changes abruptly, and the active sudden change of generators is calculated according to the power flow equation shrinking to the potential in the generator. At this stage, the generator output variation is approximately inversely proportional to the Electrical Distance between the generator and the power loss point. The calculation method of the power injection of the generator node i is shown in formula (1) [8].

$ {P_i} = \sum\limits_{j = 1}^{{N_S}} {{E_i}{E_j}\left( {{G_{ij}}\cos {\theta _{ij}} + {B_{ij}}\sin {\theta _{ij}}} \right)} + {E_i}{V_{{k_S}}}\left( {{G_{i{k_S}}}\cos {\theta _{i{k_S}}} + {B_{i{k_S}}}\sin {\theta _{i{k_S}}}} \right) = 0 $ (1)

where: NS is the number of generators in the AC power network S; Ei and Ej are internal potentials of generators i respectively; Gij and Bij are the real part and imaginary part of the mutual admittance between the generators i and j respectively; Vks is the voltage of the AC side bus ks of the DC system; Gij and Bij are the real part and imaginary part of the mutual admittance between the generator i and the AC side bus ks of the DC system respectively.

The power shortage ΔPDC caused by DC blocking fault is distributed to all generators according to synchronous power coefficient. Power flow calculation is carried out according to active power injection of all nodes at the moment of fault, and active and reactive power flows at transmission sections are counted. The synchronous power coefficient of each generator is calculated according to formula (2) [9, 10].

$ {P_{S,ik}} = {E_i}{V_{{k_S}}}{B_{i{k_S}}}\cos {\theta _{i{k_S}}} $ (2)
2.2 The Moment from Transient to Steady State

When the transient state transits to steady state, the active power is determined according to the primary frequency modulation parameters of the generator, the static frequency characteristics of the load and the unbalanced power.

Firstly, aiming at the AC power grid connected UHVDC, according to the control strategy and operation state of the power system stability control devices with the detection of UHVDC fault as the starting criterion, and the real-time information of power grid, the on-duty measures of the fault are determined, and the unbalanced power ΔPdis caused by the UHVDC fault and the on-duty measures implementation of each AC power grid is calculated [11].

Then, according to the static frequency characteristics of generator and load, the active power and system frequency deviation Δfdis after the safety control measures and primary frequency modulation are calculated, and the active power of transmission section during transient state to steady state is counted through power flow calculation.

The steps for calculating the steady-state active power of the generator and load node after the on-duty measures and primary frequency modulation are as follows.

Step 1: Calculate the frequency variation corresponding to primary frequency modulation and amplitude limitation of each generator:

$ \Delta {f_i} = \max \left( {\left| {{P_{G{N_i}}} - {P_{{G_i}}}} \right|,{\sigma _{{G_i}}}{P_{G{N_i}}}} \right)/{K_{{G_i}}}\;\;\;\;\;\;i = 1, \cdots ,{N_G} $ (3)

Step 2: Sort the generators from small to large according to |Δfi|, and then meet $\left|\Delta f_{i-1}\right| \leq\left|\Delta f_{i}\right|\left(i=1, \ldots, N_{G}\right)$, set k = 1, Δf0 = 0, ΔPS = 0.

Step 3: Calculate the frequency modulation coefficient of the system when the generator k, ..., N0 participates in primary frequency modulation:

$ {K_{{S_k}}} = \sum\limits_{p = k}^{{N_G}} {{K_{{G_p}}}} + \sum\limits_{j = 1}^{{N_S}} {{K_{{D_j}}}} $ (4)

where: KDj is the active static frequency characteristic coefficient of load j.

Step 4: Calculate the corresponding active adjustment ΔPSi when the frequency deviation changes from Δfk-1 to Δfk.

$ \Delta {P_{{S_k}}} = {K_{{S_k}}}\left( {\Delta {f_k} - \Delta {f_{k - 1}}} \right) $ (5)

Update ΔPS = ΔPS + ΔPSk.

Step 5: If ΔPS < ΔPdis, set k = k + 1, return to Step 3; Otherwise, the frequency deviation Δfdis corresponding to the system power deficiency ΔPdis is calculated.

$ \Delta {f_{dis}} = \Delta {f_k} - \left( {\Delta {P_S} - \Delta {P_{dis}}} \right)/{K_{{S_k}}} $ (6)

Step 6: Calculate the shared power of each generator and load when the system frequency deviation is Δfdis. If Δfdis < Δfi, the shared power of generator i is

$ \Delta {P_{{G_i}}} = {K_{{G_i}}}\Delta {f_{dis}} $ (7)

Otherwise, the power allocated by the generator i is

$ \Delta {P_{{G_i}}} = \max \left( {\left( {{P_{G{N_i}}} - {P_{{G_i}}}} \right),{\sigma _{{G_i}}}{P_{G{N_i}}}} \right) $ (8)

the power allocated by the load j is

$ \Delta {P_{{D_j}}} = {K_{{G_j}}}\Delta {f_{dis}} $ (9)

For PQ node, the reactive power of generator and load is determined respectively according to the initial reactive power factor to ensure the accuracy of power flow results [12].

2.3 The Moment After Secondary Frequency Regulation

During the operation of the secondary frequency regulation, the generator and load active power are determined according to the rotation reserve and climbing rate of the generator, the static frequency characteristics of the load and the frequency deviation during transient to steady state [13].

Firstly, considering the active static frequency characteristic coefficient of the load and the generator rotation standby, the total time for the system frequency to return to the rated value after the UHVDC lockout fault is calculated:

(1) Calculate the total active power regulation ΔPAGC of the generator when the system frequency returns to the rated value according to formula (10)

$ \Delta {P_{AGC}} = \Delta {f_{dis}}\sum\limits_{j = 1}^{{N_S}} {{K_{{D_j}}}} $ (10)

where: NS is the number of load nodes and KDj is the active static frequency characteristic coefficient of node load.

(2) According to formula (11), calculating the corresponding time Δti after each generator rotates for standby adjustment.

$ \Delta {t_i} = \Delta {P_{GS{R_i}}}/{\xi _{{G_i}}} $ (11)

where: ΔPGSRi and ξGi are the rotation reserve and climbing rate of the generator respectively.

(3) Sort the generators from small to large according to Δti, and then meet $\left|\Delta t_{i-1}\right| \leq\left|\Delta t_{i}\right|\left(i=1, \cdots, N_{G}\right)$, set k = 1, Δf0 = 0, ΔPA = 0.

(4) Calculate the active power adjustment ΔPAi from Δti-1 to Δti.

$ \Delta {P_{{A_i}}} = \sum\limits_{p = k}^{{N_G}} {{\xi _{{G_p}}}\left( {\Delta {t_i} - \Delta {t_{i - 1}}} \right)} $ (12)

Update ΔPA = ΔPA + ΔPAi.

(5) If ΔPA < ΔPAGC, set k = k + 1, return to Step 3); Otherwise, the total time DTAGC for the system frequency to return to the rated value is

$ \Delta {T_{AGC}} = \Delta {t_{i - 1}} + \left( {\Delta {T_{AGC}} - \Delta {P_A}} \right)/\sum\limits_{p = k}^{{N_G}} {{\xi _{{G_p}}}} $ (13)

Then, according to the set time interval ΔT, the active power of the generator and load node at the moment kΔT after secondary frequency regulation is calculated, and the active power of transmission section at the moment kΔT is counted through power flow calculation. The calculation method of node active power is as follows:

If ΔTikΔT, the shared power of generator i is

$ \Delta {P_{{G_i}}} = {\xi _{{G_i}}}k\Delta T $ (14)

Otherwise, the shared power of generator i is

$ \Delta {P_{{G_i}}} = \Delta {P_{GS{R_i}}} $ (15)

The system frequency is

$ \Delta {f_k} = \sum\limits_{p = 1}^{{N_G}} {\Delta {P_{{G_p}}}} /\sum\limits_{j = 1}^{{N_S}} {{K_{{D_j}}}} $ (16)

Shared power of load j is

$ \Delta {P_{{D_j}}} = {K_{{D_j}}}\Delta {f_k} $ (17)

Finally, according to the node type (e.g. PQ node), the reactive power of generator and load is determined respectively according to the initial power factor.

3 Calculation Method of Reactive Voltage

Reactive power and voltage control in large power grid generally adopts third level control mode. The first level voltage control compensates for rapid and random voltage changes by keeping the output variables as close to the set value as possible. The first level voltage control is mainly controlled by an exciter and is second level control, which can be simulated by power flow calculation. The secondary voltage control is controlled by the speed regulating action and is minute level. When the central busbar voltage deviates, the set value of the primary voltage controller is changed according to a predetermined control rule. The third level voltage control takes economic operation as the optimization objective and gives the set voltage of central busbar [13].

When a fault occurs, if the central busbar voltage exceeds the limit during transition to steady state, secondary voltage control is required to ensure the voltage level of the power grid at this time. The reactive voltage control measures include reactive power output of units, switching of capacitors and reactors. How to comprehensively consider the coordination between multiple types of continuous discrete hybrid regulation measures and accurately generate secondary voltage control strategies is the key to reactive voltage calculation after fault [14, 15]. The thesis proposes a method of secondary voltage control strategy based on the calculation results of active power after fault. The specific steps are as follows:

(1) The central busbar voltage is calculated based on the active and reactive power after fault, and the voltage margin is calculated according to the upper limit and the lower limit of busbar voltage. the calculation formula is as follows:

$ {\eta _v} = \left\{ \begin{array}{l} \max \left( {\frac{{{V_H} - V}}{{{V_H} - {V_M}}}, - 1} \right) \times 100\;\;\;\;\;V \ge {V_M}\\ \max \left( {\frac{{V - {V_L}}}{{{V_M} - {V_L}}}, - 1} \right) \times 100\;\;\;\;\;\;V < {V_M} \end{array} \right. $ (18)

where: ηv is the voltage margin, V is the actual bus voltage, VH is the upper bus voltage limit, VL is the lower bus voltage limit, $V_{M}=\frac{\left(V_{H}+V_{L}\right)}{2}$.

(2) When the voltage margin ηv is less than 0, i.e. the central busbar voltage exceeds the limit, the control strategy, operation state, adjustable space and other information in the partition where the central bus is located are obtained.

(3) The objectives are the minimum deviation between the central busbar voltage and the target value and the minimum reactive power regulation amount of each node. The constraints are linearization constraints, namely, generator reactive power upper and lower limits, capacitors and reactors reactive power upper and lower limits, central busbar voltage upper and lower limits, control busbar voltage upper and lower limits, control busbar voltage step size constraints, key busbar voltage upper and lower limits, etc. the mathematical model is constructed as follows:

$ \left\{ \begin{array}{l} \mathop {\min }\limits_{\Delta {Q_g},\Delta {Q_c}} {\left\| {{V_p} - V_p^{ref}} \right\|^2} + a\Delta {Q_g} + b\Delta {Q_c}\\ s.t.\;\;\;\;\;V_p^L \le {V_p} \le V_p^H\\ \;\;\;\;\;\;\;\;V_h^L \le {V_h} \le V_h^H\\ \;\;\;\;\;\;\;\;V_c^L \le {V_c} \le V_c^H\\ \;\;\;\;\;\;\;\;{C_{vg}}\Delta {Q_g} \le \Delta V_H^{\max }\\ \;\;\;\;\;\;\;\;{\underline Q _g} \le {Q_g} + \Delta {Q_g} \le {{\bar Q}_g}\\ \;\;\;\;\;\;\;\;{\underline Q _c} \le {Q_c} + \Delta {Q_c} \le {{\bar Q}_c} \end{array} \right. $ (19)

where: Vp is central busbar voltage, Vpref is the target value of central busbar voltage, a and b are the weight coefficients, VpL and VpH are the lower limit and the upper limit of central busbar voltage, Vh is control busbar voltage, VhL and VhH are the lower limit and the upper limit of control busbar voltage, Vc is key busbar voltage, VcL and VcH are the lower limit and the upper limit of key busbar voltage, ΔVHmax is the control busbar voltage step size, Qg is the generator reactive power, Qg and Qg are the lower limit and upper limit of generator reactive power, ΔQg is the generator reactive power adjustment, Qc is the capacitor/reactor reactive power, Qc and Qc are the lower limit and upper limit of the capacitor/reactor reactive power, ΔQc is the capacitor/reactor reactive power adjustment.

(4) Dividing into two stages to make partition optimization decision, combining unified optimization with step-by-step decision to solve the problem of coordinated control of continuous discrete variables.

(1) Continuously processing discrete strategies such as capacitors and reactors switching, solving the extended coordinated secondary voltage control model, and giving reactive power of generators, capacitors and reactors;

(2) Carrying out safety constraint condition check and normalization treatment on reactive power output of the capacitors and reactors, and switching on and off the capacitors and reactors if the action condition is met;

(3) Recalculating busbar voltage and reactive power after switching capacitors and reactors;

(4) Establishing a secondary voltage control model considering only the reactive power output of the unit under the new state, and giving the reactive power control strategy of the unit.

Among them, step (1) gives the overall voltage and reactive power distribution in the region, and step (2), (3) and (4) distribute control instructions between capacitor/reactor and units according to the coordination principle.

4 Power Flow Calculation Process After Fault

Considering comprehensively the acting time and operation strategies of various automatic devices, the power flow after fault is rapidly calculated to obtain the overload transmission section and key busbar information. The specific steps are as follows:

Step 1: Obtain power grid operation mode data, active static frequency characteristic coefficient of load and frequency modulation parameter of generator from EMS system, and obtain current operation state, fixed value, pressing plate state of power system stability control devices and collected power grid real-time information from safety automatic device management system.

Step 2: For the AC power grid connected by UHVDC, the internal potential of the generator is calculated respectively according to the subsynchronous reactance of the generator to form a reduced-order admittance matrix that shrinks to the internal potential node of the generator and blocks the AC side bus kS of the DC system.

Step 3: The unbalanced power caused by UHVDC fault is distributed to all generators according to synchronous power coefficient, and the power flow calculation is carried out according to the active power injection of all nodes at the moment of fault, and the active power of transmission sections is counted. Calculate the synchronous power coefficient of each generator according to formula (20):

$ {P_{S,ik}} = {E_i}{V_{{k_S}}}{B_{i{k_S}}}\cos {\theta _{i{k_S}}} $ (20)

Step 4: According to the control strategy and operation state of the safety control system with the detected UHVDC blocking fault as the starting criterion, and the real-time information of the power grid operation situation, the on-duty measures for the fault under the current operation situation are determined, and the unbalanced power ΔPdis caused by the UHVDC fault and the on-duty measures implementation of each AC power grid are calculated.

Step 5: According to the static frequency characteristics of each generator and load, the active power and the system frequency deviation Δfdis after the safety control measures and primary frequency modulation action of the generator are calculated, and the active power of the transmission section during transition to steady state after fault is calculated and counted through power flow calculation.

Step 6: If the central busbar voltage exceeds the limit due to the power flow change, the secondary voltage regulation of AVC is simulated, and the reactive power of the generator and the capacitor/reactor are calculated according to the node type and the reactive voltage control model, so as to obtain the node voltages of the central busbar and the key busbar during transition to steady state.

Step 7: According to the total active power adjustment ΔPAGC of the generator, the total time ΔTAGC is calculated when the system frequency returns to the rated value.

Step 8: According to a given time interval ΔT, the active power of the generator and the load after secondary frequency regulation is calculated, and the active power of transmission section at the moment jΔT is counted through power flow calculation.

Step 9: The active power of transmission section is compared with the stability limit to determine the time scale when the active power is greater than the stability limit; The busbar voltage is compared with the voltage limit to determine the time scale when the busbar voltage exceeds the limit.

Step 10: Identify unsafe faults according to the overload transmission section and voltage violation busbar, accurately simulate the off-line disposal strategy for unsafe faults, and give a prompt as to whether the disposal strategy is reasonable.

The rapid analysis process of active power and busbar voltage after UHVDC fault is shown in Fig. 1.

Fig.1 Rapid analysis process of the active power and voltage after UHVDC fault

5 Verification of Examples

Taking the on-line operation data of East China Power Grid as an example, the validity of the estimation method of active power and central busbar voltage after UHVDC fault is verified. The power flow is balanced under the current state of the power grid, and the active power loss is 3563.0 MW after a DC blocking fault. Table 1 shows the active power of some generator and load nodes at the moment of the fault, the transient transition to steady state and the secondary frequency regulation operation.

Table 1 Results of device active power after fault (Unit: MW)

From Table 1, it can be seen that the active power of the unit suddenly changes at the moment of UHVDC fault, and the power change of the generator is approximately inversely proportional to the Electrical Distance between the generator and the power loss point. After fault, due to primary frequency modulation and load frequency characteristics of the generator, the active power of the generator decreases relative to the moment of the fault. After secondary frequency regulation unit operates, the load returns to the active power before the fault, and the active power of the generator transits to a new equilibrium state.

According to the changes of node active power and reactive power, power flow files of three stages are respectively formed, and the active power of each stage section is obtained based on power flow calculation. the active power change of some transmission sections after UHVDC fault is shown in Table 2.

Table 2 Results of the active power of transmission section after UHVDC fault (Unit: MW)

After transient to steady state, the AVC secondary voltage control strategy is accurately simulated, and the calculation results of some bus voltages after UHVDC fault are compared as shown in Table 3. After AVC secondary voltage control, the voltage quality is improved.

Table 3 Comparison of busbar voltage before and after secondary voltage regulation (Unit: kV)

6 Conclusion

In view of the unbalanced power caused by UHVDC fault, this thesis comprehensively considers the influence of automatic equipment such as power system stability control devices, the primary frequency control, automatic generation control (AGC) and automatic voltage control (AVC) on the operation situation of the power grid after the fault in different time scales, accurately simulates the acting time and operation strategies of various automatic equipment, and realizes the rapid analysis of active power and busbar voltage under large-scale unbalanced power. The simulation results verify the correctness and practicability of the proposed method, which is conducive to quickly and accurately determining the overload of transmission section or violation of busbar voltage, and provides the basis for formulating reasonable and effective fault disposal strategies.

Acknowledgments  The work described in this paper was supported by "Research and Application of Global Analysis and Prevention key Technologies Adapt to Active Dispatching of Power Grid" program.

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