Dynamic reactive power planning method for CSP-PV hybrid power generation system

ZHANG Hong，DONG Hai-ying,2，CHEN Zhao，HUANG Rong，DING Kun

(1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070，China；2. School of New Energy and Power Engineering, Lanzhou Jiaotong University, Lanzhou 730070，China；3. State Grid Gansu Electric Power Research Institute, Lanzhou 730050，China)

Abstract：Aiming at the faults of some weak nodes in the concentrated solar power-photovoltaic(CSP-PV)hybrid power generation system, it is impossible to restore the transient voltage only relying on the reactive power regulation capability of the system itself.We propose a dynamic reactive power planning method suitable for CSP-PV hybrid power generation system.The method determines the installation node of the dynamic reactive power compensation device and its compensation capacity based on the reactive power adjustment capability of the system itself.The critical fault node is determined by the transient voltage stability recovery index, and the weak node of the system is initially determined.Based on this, the sensitivity index is used to determine the installation node of the dynamic reactive power compensation device.Dynamic reactive power planning optimization model is established with the lowest investment cost of dynamic reactive power compensation device and the improvement of system transient voltage stability.Furthermore, the component of the reactive power compensation node is optimized by particle swarm optimization based on differential evolution(DE-PSO).The simulation results of the example system show that compared with the dynamic position compensation device installation location optimization method, the proposed method can improve the transient voltage stability of the system under the same reactive power compensation cost.

Key words：transient voltage recovery index; sensitivity index; dynamic reactive power planning optimization; particle swarm optimization based on differential evolution(DE-PSO)

0 Introduction

In recent years, renewable energy power generation industry has developed rapidly, especially its installaction capacity of grid-connected power has increased.Photovoltaic(PV)power generation has become a new growth point of renewable energy power generation after wind power[1].With the development of photothermal technology, concentrated solar power(CSP)has been paid more and more attention in the field of renewable energy power generation, and the concentrated solar power plant has good schedulability and controllability[2].The coordinated operation of CSP with large-scale photovoltaic power generation and AC/DC hybrid power grid can absorb/eliminate intermittent and stochastic renewable energy.Therefore, it is of great significance to construct a source-end energy power system based on photothermal-photovoltaic energy.

Normally, the reactive power of CSP-PV hybrid system can be dynamically adjusted by using synchronous generators and photovoltaic inverters to maintain the node voltage level in the system.However, it is unavailable to guarantee the safe and stable operation of the system completely by relying solely on photovoltaic inverters and synchronous generators.When disturbance and other faults occur in the system, some weak nodes in the system may experience unstable transient voltage, which may cause the system to collapse.The dynamic reactive power compensation device represented by static var compensator(SVC)can output reactive power rapidly after system failure, which can improve the transient voltage stability of the system and avoid transient voltage instability of weak nodes.Nevertheless, the precondition for solving this problem is to select the appropriate installation location and compensation capacity of dynamic reactive power compensation device[3-4].Therefore, it is of great theoretical value and practical significance to study the dynamic reactive power planning method for CSP-PV hybrid power generation system.

At present, research on CSP-PV hybrid power generation system and its reactive power planning is in its infancy, mostly taking conventional power systems or a single new energy power system as the research object of reactive power planning.Yan et al.proposed the reactive power compensation position of the power system and its determination methods of compensation capacity, but they mainly focused on improving the static voltage stability of the system rather than the transient voltage stability[5-8].For dynamic reactive power planning, static voltage stability analysis method in traditional theoretical research has occupied the mainstream.However, the static analysis method cannot accurately describe the dynamic process of the dynamic reactive power compensation device.Moreover, the dynamic reactive power compensation device mainly solves the transient voltage stability problem，not improving the static voltage stability margin.Therefore, dynamic reactive power planning based on transient voltage stability analysis method is more reasonable.In Ref.[9], based on the transient voltage instability principle, the limit resection time is taken as the optimization target to determine the optimal configuration scheme of the dynamic reactive power compensation device.In Ref.[10], the methods of control parameterization, trajectory sensitivity and singular value decomposition were used to discuss the location and capacity optimization of dynamic reactive power planning in detail.Zhou et al.proposed a dynamic reactive power optimization configuration method for reducing the risk of transient voltage instability with the lowest risk of transient voltage instability and the minimum cost of dynamic reactive power compensation[11].Yang et al.established a comprehensive reactive power planning model for AC/DC hybrid systems, improving the static and transient voltage stability of the grid through the minimum cost of reactive power investment[12].Yuan et al.provided a useful reference for the study of dynamic reactive power planning methods for CSP-PV hybrid power generation system[9-12].In summary, on the basis of considering the reactive power regulation capability of the system itself, determining the installation position and compensation capacity of the dynamic reactive power compensation device of the CSP-PV hybrid power generation system based on the transient voltage stability analysis method is the main solution to this problem in this paper.

Therefore, we propose a dynamic reactive power planning method suitable for CSP-PV hybrid power generation system.Based on the reactive power regulation capability of the system itself, this method combines the transient voltage stability recovery index and the sensitivity index to determine the reactive power compensation node with the lowest investment cost of dynamic reactive power compensation device and the improvement of system transient voltage stability, and uses the partical swarm optimization based on differential evolution(DE-PSO)algorithm to optimize the installation capacity of the compensation node.The simulation results of the example system verify the accuracy and effectiveness of the proposed method.

1 Node selection of dynamic reactive power planning

1.1 Transient voltage stability recovery index

Different faults lead to the risks of transient voltage instability being different.Some faults will not lead to transient voltage instability even if they occur.On the contrary, some faults may lead to serious transient voltage instability.The voltage response curve after grid faults is shown in Fig.1, wheret0is the fault time,t1is the fault clearing time,tris the cutoff time, andU0is the normal operating voltage.

Fig.1 Voltage response curve with faults

Transient voltage instability will lead to the collapse of the power system.The transient voltage recovery index(TVRI)is used to measure the voltage recovery ability after the system fault[12].The transient voltage recovery index of nodeiis defined as

(1)

In order to program and calculateMi, Eq.(1)can be differentiated into

(2)

wherehis the calculated step length in time domain simulation.

The transient voltage stability indicator of the entire system is determined by the maximum value of all nodes and defined as

(3)

whereMirepresents the transient voltage transient state of nodei.The smaller theM, the stronger the transient voltage recovery ability of the system.Installing the dynamic reactive power compensation device can improve the transient voltage stability of the system.

1.2 Node selection index of dynamic reactive power planning

The node selection of dynamic reactive power planning is mainly targeted at the weak nodes with transient voltage stability, which can be determined by the sensitivity between the compensation capacity of dynamic reactive power compensation device andMi.The sensitivity can measure the effect of improving the transient voltage stability of the system by installing equal-capacity dynamic reactive power compensation device at different compensation nodes.The sensitivity is defined as

(4)

whereMiis transient voltage stability recovery index of nodeiwithout dynamic reactive power compensation device,Mi,ΔQiis the transient voltage stability recovery index after installing the reactive compensation capacity ΔQat nodei, and ΔQis taken as a fixed value of 100 Mvar.

The larger value ofNiindicates that reactive power compensation with equal capacity at this node can maximize the transient voltage stability of the node.Therefore, the node with larger value ofNiis selected as the compensation node.

2 Dynamic reactive power planning optimization model of CSP-PV hybrid system

2.1 Optimization objective

Our work aims to study how to improve the transient voltage stability of CSP-PV hybrid generation system with the minimum investment cost of dynamic reactive power compensation device[12].The SVC is taken as an example to carry out reactive power planning for the dynamic reactive power compensation device.The minimum investment cost of the reactive power compensation device is taken as the optimization objective, and the transient voltage stability of the system is taken as the penalty function to establish the objective functionfand its mathematical model is

minf=C+M×η,

(5)

(6)

whereCis the investment cost of SVC;ηis the penalty function factor;δi(1 or 0), indicates whether nodeiis equipped with SVC;Cpuris the unit price of SVC;Qsvc,iis the planning capacity of SVC;Cinsis the installed cost of SVC, anddis the number of compensating nodes.

2.2 Constraints

1)Power flow equations constraint is

(7)

wherePiandQiare the active power and reactive power injected into nodei, respectively;Qsvc,iis the reactive power output of the SVC at nodei, and if there is no reactive power compensation device at the node,Qsvc,i=0;PL,iandQL,iare active load and reactive load of nodei, respectively;UiandUjare the voltages of nodeiand nodej, respectively;GijandBijare the conductance and susceptance of the circuit, respectively;θijis the phase angle difference between the voltages of nodeiand nodej.

2)Active power output constraint of solar-thermal power generation unit is

(8)

3)Active power output constraint of photovoltaic power generation unit is

(9)

4)Reactive power output constraint of solar-thermal power generation unit is

(10)

5)Reactive power output constraint of photovoltaic power generation unit is

(11)

6)Node voltage constraint of system is

(12)

7)Reactive power planning capacity constraint of SVC is

(13)

8)Dynamic differential equation constraint

The dynamic differential equation describes the response characteristics of dynamic components(generator excitation system, dynamic reactive power compensation device, etc.)[13-14], and it is expressed as

(14)

wherex,yanduare the state vector, algebraic vector, and control vactor, respectively.Dynamic differential equations need to meet the initial conditions as

g(x0,y0,u0)=0,

(15)

wherex0,y0andu0are the initial values of state vector, algebraic vector and control vector, respectively.

The dynamic differential equation can be transformed into a difference equation form by integral discretization method.Here the implicit integral method is adopted, which can be expressed as

(16)

wherexkandxk+1are state vectors of thekth and(k+1)th step state, respectively;f(xk,tk)andf(xk+1,tk+1)are the corresponding functions of thekth step and(k+1)th step, respectively.

9)When improving the transient voltage stability of the system, the rotor stability constraint of the generator must be satisfied.The stability constraint of the rotor of the generator is

max(Δδt)≤ε,

(17)

where Δδis the power angle difference between generators; andεis the maximum value of angle difference.

10)Power angle stability constraint is

δmax≤δi(t)-δCOI(t)≤δmax,

(18)

(19)

whereδi(t)is the angular displacement of the rotor of the generator rotor;Diis time constant of the inertia of the generator; and here letδminandδmaxbe-120° and 120°, respectively.

The regulating tap of transformer can only change the reactive power distribution in a small range, therefore it cannot provide reactive power source.In general, the tap adjustment is used as the final adjustment method in voltage control.In this paper, the position of the tap of the on-load regulating transformer is set to remain unchanged[15].

3 Model calculation

3.1 Algorithm principle

Basic particle swarm optimization(PSO)is prone to fall into the local optimal solution due to its poor global search ability and lacking of algorithm diversity.Therefore, we adopt DE-PSO algorithm to solve the model.Differential evolution algorithm is of a great advantage to maintaining population diversity and searching ability, therefore introducing it into PSO algorithm can enhance algorithm diversity and searching ability.The fact that the particle flies too fast will lead to local convergence of the algorithm in the process of particle evolution, thus introducing speed control strategy into PSO algorithm can improve the algorithm global search performance.The specific steps of the algorithm can be found in Ref.[16].

3.2 Process of dynamic reactive power planning

The process of dynamic reactive power planning is shown in Fig.2.

Fig.2 Flow chart of dynamic reactive power planning

The specific steps are as follows.

1)Transient voltage stability recovery index and sensitivity index are combined to determine the weak node, namely reactive power compensation node.

2)A dynamic reactive power planning optimization model is established to improve the transient voltage stability of the CSP-PV power generation system with the lowest investment cost of dynamic reactive power compensation device.

3)DE-PSO algorithm is used to optimize the reactive power compensation capacity of the node.

4)If the number of iterations exceeds the maximum number of iterations, the process ends and output the final dynamic reactive power compensation capacity.Otherwise, update the particle speed and position and continue to search for the optimal value.

4 Simulation analysis

4.1 Basic data and parameters

The example system is modified by the normal IEEE39 node system, as shown in Fig.3.The CSP plant and PV power plant are connected to the node 35 and node 38, respectively, and there are no power supply at other nodes.The basic parameters of the system are shown in Ref.[17].The loads are all configured in the proportion of 50% induction motor and 50% constant impedance[18], and the model parameters are shown in Ref.[18].Set the maximum reactive power output of the concentrating solar power plant and the photovoltaic power plant at 400 Mvar.The example system is simulated by Matlab and PSD-BPA software[19].The SVC is installed on four nodes.The cost parameters of SVC are as follows: installation costCinsis 20 ten thousand Yuan, the unit price of reactive power compensationCpuris 32 ten thousand Yuan/Mvar.The fault duration is 100 ms, the integration time inMis 3 s, and the compensation capacity range of SVC is 0-300 Mvar.The population number of DE-PSO algorithm is 100, the maximum capacity of external document is 100, the number of feedback particles is 20, the maximum number of iteration is 250, andc1andc2are random numbers in[1.5,2.5].

Fig.3 Test system

4.2 Critical fault nodes

Dertermining the location and capacity of dynamic reactive power compensation device is an integer nonlinear programming problem.In order to quickly and accurately determine the installation nodes of the dynamic reactive power compensation device, the critical fault nodes of the system are firstly determined, and then the installation nodes are determined.The critical fault nodes are determined byM.The larger theM, the higher the failure probability of the node.PerformingN-1 three-phase short-circuit scanning for the system, and calculating the transient voltage stability recovery index of each node through time domain simulation and Eq.(1), the results are shown in Fig.4.

Fig.4 TVRI of each node

It can be seen from Fig.4 that the transient voltage stability of nodes 16, 17, 19, 20 and 24 are poor, and thus transient voltage instability may occur.Among them, the transient voltage stability recovery ability of nodes 20 and 24 is stronger than that of nodes 16, 17 and 19.Among the other nodes, the transient voltage stability recovery ability of nodes 21 and 22 is weak.

Based on the above analysis, we select nodes 20 and 24, nodes 21 and 22 for fault simulation, respectively.At this time, SVC is not installed on the system, only relying on the reactive power provided by the PV inverter and synchronous generator to support the transient voltage recovery.The simulation results are shown in Figs.5 and 6.

It can be seen from the simulation results that the transient voltage instability risks of all nodes are different.For the fault of nodes 21 and 22, the transient voltage can be restored and stabilized by the system photovoltaic inverter and synchronous generator; However, for nodes 20 and 24, only relying on PV inverber and synchronous generator of the system are not sufficient for transient voltage stability recovery, and it also needs reactive power compensation device.Meanwhile, except for nodes 16, 17, 19, 20 and 24, other nodes can realize the transient voltage stability based on the reactive power regulation ability of the system itself.

Fig.6 Fault voltage curves of nodes 21 and 22

Based on the above simulation analysis, we select nodes 16, 17, 19, 20 and 24 as critical fault nodes.

4.3 Installation node of dynamic reactive power compensation device

In section 4.2, we only preliminarily determine the installation nodes of the dynamic reactive power compensation device.In order to avoid over-compensation or under-compensation, it is necessary to further determine installation position based on the sensitivity index of each node.The photovoltaic inverter in PV plant and the synchronous generator in CSP plant can adjust reactive power.Dynamic reactive power compensation device is not generally installed on the bus at which they are located, and the corresponding nodes do not need to calculate its sensitivity.The sensitivity indexes of other nodes are calculated by Eq.(4), the results are shown in Fig.7.

It can be seen from Fig.7 that the equal-capacity reactive power compensation of different nodes has different effects on the transient voltage stability recovery ability.For some nodes, it can significantly improve their transient voltage stability recovery ability.On the basis of the critical fault nodes, we select nodes 16, 19, 20 and 24 with the maximum sensitivity index as the installation nodes of dynamic reactive power compensation device, and the sensitivity index values of nodes 16 and 19 are smaller than that of nodes 20 and 24.The fault simulation is performed for nodes 16 and 19.Fig.8 shows the fault voltage curve without SVC installed, Fig.9 shows the fault voltage curve with SVC installed, and Fig.10 shows the curve of reactive power output of the SVC.

Fig.7 SI of each node

Fig.8 Fault voltage curves of nodes 16 and 19 without SVC installed

Fig.9 Fault voltage curves of nodes 16 and 19 with SVC installed

Fig.10 Reactive power output curve of SVC

It can be seen from the simulation results that if the faults of nodes 16 and 19 occur, the fast response characteristic of the SVC can provide reactive support for the system fault nodes, so that its transient voltage can be quickly restored and stabilized.

Based on the calculation indexes in Sections 4.2 and 4.3 as well as simulation results, it can be seen that based on dynamic reactive power planning optimization, the transient voltage can be restored and stabilized once the faults of the system nodes occur.

4.4 Capacity configuration of dynamic reactive power compensation device

In Section 4.3, the compensation node of the reactive power compensation device is determined, and the effect of the dynamic reactive power compensation device on the transient voltage stability recovery is qualitatively analyzed, but the installation capacity of the reactive power compensation node and the investment cost of the reactive power compensation device are not determined.Our work focuses on determining configuration capacity of the SVC and reactive power compensation costs by using reactive power planning method in Fig.2.The optimization results are shown in Table 1 and Fig.11.Scheme 1 is proposed in this paper, and scheme 2 has the same reactive power compensation capacity at the installation nodes and its compensation cost is the same as that of scheme 1.Fig.11 shows the optimal results of four-time independent operations.

Table 1 Installation capacity of each node under two schemes

Comparing scheme 1 and scheme 2, it can be seen that under the same cost of reactive compensation, the transient voltage recovery ability of the system based on scheme 1 is stronger.In Fig.11, the results of four-time independent operations are basically the same time, which indicates that the proposed method has better stability.

Fig.11 Results of four independent optimization trials

4.5 Comparison of optimization algorithms

The optimization results by basic PSO algorithm, GA-PSO algorithm[20]and DE-PSO algorithm are compared and the results are shown in Table 2 and Fig.12.

Table 2 Installation capacity of each node under two schemes

Fig.12 Optimization results of PSO algorithm,GA-PSO algorithm and DE-PSO algorithm

It can be seen from Fig.12that the DE-PSO algorithm requires less reactive power compensation costs and time domain simulation times for improving the transient voltage stability of the system, and has stronger transient voltage stability recovery ability, which indicates that the DE-PSO algorithm has better convergence rate and optimization ability.

5 Conclusions

This paper presents a dynamic reactive power planning scheme for the CSP-PV hybrid system.From theoretical analysis and simulation results, it can be applied to engineering practice.However, there is a certain difference between theory and engineering, it is expected to play a certain reference role in relevant research work and practical engineering in this field.The main conclusions are as follows:

1)Compared with the methods only considering the optimal installation location of dynamic reactive power compensation device, the proposed method has better effect on improving the transient voltage performance of the system under the same reactive power compensation cost.

2)The dynamic reactive power planning optimization model can improve the transient voltage stability of the system and reduce the investment cost of SVC.

3)Through the transient voltage stability recovery index and sensitivity index, the installation node of SVC is determined from the region to the node, which not only improves the speed and accuracy in searching for compensating nodes, but also reduces the number of system optimization variables and computational complexity.

4)Compared with basic PSO algorithm and GA-PSO algorithm, DE-PSO algorithm has better convergence rate and optimization ability in solving the dynamic reactive power planning optimization model.

5)Establishing a reasonable calculation system based on actual engineering is the basis for ensuring the correctness of the above research.Therefore, the accuracy of the proposed method should be studied by the actual engineering example system in the future.