Evaluation of intermittent-distributed-generation hosting capability of a distribution system with integrated energy-storage systems

0 Introduction

The consensus on green and sustainable development and the steady progress of renewable energy generation technology have resulted in a continuous increase in the penetration of distributed generations (DGs) from renewable energy sources (RESs) such as distributed wind turbines and photovoltaic (PV) systems, in the distribution system concerned.The rapid expansion of the renewable energy industry has reduced the cost of distributed renewable energy generation.The share of PV and wind power generation in the total generation quantity demonstrates an increasing trend in many countries around the globe including China.Specific to China, economic advantages would replace policy subsidies as the chief impeller of growth in the installed capacity of renewable DGs.Renewable energy generation represented by wind power and PV units would transform from fossil energy supplements to alternative energy sources.This indicates that its rapid capacity increase can be maintained.However, the intermittent outputs from renewable DGs are detrimental to the security and economics of the distribution system concerned.To solve or mitigate the security and economic problems in the operation of distribution systems with intermittent renewable DGs, it is necessary to examine the potential impacts of their integration at the planning stage, so as to ensure that the distribution system concerned be capable of accommodating these DGs.To this end, it is necessary to evaluate the hosting capability of the distribution system for intermittent renewable DGs.The distributed generation hosting capability evaluation (DGHCE) of a distribution system involves the determination of the maximum capacity for accommodating intermittent distributed generation considering system operation constraints.The hosting capability evaluation problem has been investigated in certain existing publications [1-14].

Several optimization models have been developed considering different focuses, characteristics, and constraints.Accordingly, certain optimization methods are employed to solve these optimization models depending on their characteristics.These include conventional optimization methods such as nonlinear programming,modern heuristic optimization methods such as genetic algorithms, and stochastic optimization methods such as robust optimization.When stochastic factors are considered,the optimization model attained would be a stochastic one.With regard to the problem of hosting-capability evaluation at the planning stage, many stochastic factors are included,and the problem could be formulated as a stochastic optimization problem.The distributed generation (DG)integration planning problem is formulated as a stochastic optimization problem in [1], with voltage constraints described as soft constraints represented by the violation probability.In addition, the voltage constraints are expressed as a function of the expected DG installed capacity to forecast the voltage profile.Different voltage characteristics associated with each PV integration scheme are analyzed and utilized to identify vulnerable segments in each feeder in [2].At the planning stage, it is difficult to accurately determine the probability distribution of the power outputs of DGs.As an alternative tool for addressing uncertainty,robust optimization (RO) methods that do not require accurate probability distributions of stochastic variables can be used to address the stochastic characteristics of DG power outputs and loads.An RO method that considers the regulation of static Var compensators (SVCs) and on-load tap changers (OLTCs) is presented in [3].On this basis, a two-stage RO model based on the three-phase power flow model is developed for a distribution system in [4].Here,active network management techniques are applied to enhance the hosting capability for intermittent renewable DG power outputs.

The existing methods to enhance the DG hosting capability mainly include network reconfiguration, OLTC regulation, reactive power compensation, application of energy storage systems (ESSs), and implementation of demand response [5-12].However, the simultaneous employment of the reactive power regulation capability of DGs and reactive power compensators has been considered infrequently in existing publications.Similarly, the joint operation optimization of ESSs and SVCs has seldom been considered although it is commonly employed in practical applications [13-14].Although certain publications have addressed the optimal siting and sizing problem of ESSs or SVCs, most of these considered only a single property while maintaining the others constant [3, 6].Simultaneously optimal siting and sizing of multiple ESSs and SVCs to enhance the hosting capability for intermittent DG has not been investigated systematically.Given this background,an RO-based method is developed in this study to evaluate the hosting capability for intermittent DG considering the applications of ESSs and SVCs.The main work reported in this paper can be summarized as follows:

1) The reactive power output regulation of DGs is considered.The effect of reactive power regulation of DGs on DGHCE is investigated.

2) An RO-based method is presented for simultaneously optimal siting and sizing of ESSs and SVCs.

The remainder of the paper is organized as follows.The distribution system model is described in Section 1.The RO-based DGHCE model and the solving algorithm are presented in Section 2.Case studies are used to demonstrate the proposed method in Section 3.Finally, the paper is concluded in Section 4.

1 Distribution system modeling

1.1 DistFlow model

At present, the distribution system in China is generally constructed in a closed-loop manner and operated in an open-loop mode.From a system operation perspective, the distribution system is a radial network.The well-established DistFlow model is used to describe the complex power flow at any node i∈N:

where N is the set of all nodes in the distribution system except the root node (i.e., the node connected with the transmission system; generally, the secondary side of the substation transformer); Vsub is the rated secondary voltage of the supply transformer; tp is the tap position of the OLTC; a is the step size; Vi is the magnitude of the voltage of Node i; Pi,i+1 and Qi,i+1 are the active and reactive power flows, respectively, from Node i to Node i + 1; + is the load demand at Node i; is the complex power output of the DG at Node i: and are the charging and discharging power, respectively, of the ESS at Node i; is the reactive power output of the SVC at Node i;ri ,i+ 1 + jxi,i +1 is the impedance of the line between Nodes i and i + 1.

The aforementioned DistFlow equations can be simplified as follows by applying the linearization technique presented in [15]:

Based on the linearized model, the complex power flow in each branch and the voltage at each node can be expressed by the voltage magnitude of the root node and the power injections of the other nodes.In a radial network, exactly one route exists from the root node to any other node, say Node i. It is denoted as Route i and can be represented by the set of branches along the route.Then, the topology of the radial distribution system can be described thoroughly by the route-branch incidence matrix[Tij].If Branch j is on Route i, Tij=1.Otherwise, Tij=0.By introducing [Bij] (which is the transpose of [Tij]), the power flow between any two nodes can be represented using the power injections at the nodes:

A set of voltage recursion equations can be derived by assigning different values to i in (9).After the recursion process, the voltage magnitude of any Node i can be represented as

where Xij is the sum of resistances for all the overlapping branches with respect to Routes i and j (i.e., the sum of resistances for overlapping branches between root node and Node i and branches between the root node and Node j).Xij is the sum of reactances for all the overlapping branches with respect to Routes i and j (i.e., the sum of reactances for overlapping branches between the root node and Node i and branches between the root node and Node j).

1.2 Operation constraints of a distribution system

The following operation constraints need to be considered for determining the hosting capability for intermittent power outputs of a distribution system:

1) Bus voltage deviation constraints

The Chinese national standard GB/T 12325-2008 entitled “Power quality: Deviation of supply voltage,”explicitly specifies the voltage deviation requirements.These can be formulated as

where Vmin and Vmax are the lower and upper limits,respectively, for the voltage level at Bus i.Their values are 93% and 107%, respectively, of the nominal voltage for a distribution system with a voltage level below 20 kV,according to the Chinese national standard [16].

2) Thermal capacity constraint of a transformer

where psub and qsub are the active power and reactive power,respectively, flowing through a given transformer.Ssub,max is the maximum permitted apparent power of this transformer.

3) Line thermal capacity constraints

where Si,max is the maximum permitted apparent power of line i.

The nonlinear thermal capacity constraints complicate the problem and hinder its resolution.Therefore, a polygonal inner-approximation method is employed for linearization to facilitate the solving of the problem.The linearized equations are formulated as

where αc, βc, and δc are the sets of linearization coefficients of the constraints (see Table A1).

4) Upstream system power exchange constraints

The distribution system is connected to the upstream system (i.e., a transmission system or a distribution system at a higher voltage level) through a transformer.The exchanged power is limited by the following constraints:

where psub,max and psub,min are the upper and lower limits,respectively, of the exchanged active power.qsub,max and qsub,min are the upper and lower limits, respectively, of the exchanged reactive power.

2 DGHCE model and solution method

2.1 Strategy for enhancing the hosting capability for intermittent power outputs from DGs

The existing strategies for enhancing the DG hosting capability of a distribution system mainly include voltage control, network reconfiguration, reactive power compensation, applications of ESSs, demand response,and regulation of the power outputs of DGs.In practice, a combination of multiple strategies is generally considered to enhance the hosting capability to the required or expected level.In this study, the coordination among OLTCs, SVCs,and DGs is considered for coordinated voltage control.

SVCs have the following advantages over shunt capacity banks.First, unlike shunt capacity banks, which can only provide capacitive reactive power, SVCs can provide both capacitive and inductive reactive power and be adjusted continuously and smoothly.Second, SVCs could respond rapidly when the system is subjected to a disturbance,with better automatic monitoring and tracking capability to perform accurate and rapid voltage support.Thereby,significant reactive power fluctuation can be prevented.

As a result of rapid technical development, RESs have gained the capability to provide grid support by adjusting active and reactive power outputs.Considering the increasing penetration of RESs in distribution systems,RESs are required to perform power control and voltage regulation in a similar manner as conventional fossil fuelfired generators.The Chinese industry standard NB/T 32015-2013 entitled “Technical rule for distributed resources connected to distribution network” specifies that converter-based DGs connected to a distribution network with a voltage level of 10 (or 6) kV and 35 kV should be capable of continuously adjusting their power factor from 0.98 (leading) to 0.98 (lagging).The DGs should be capable of regulating their reactive power outputs according to the voltage level at the point of connection [17].Although the capability of regulating the active power output by a DG is also required by the standard, the reduction of active power output contravenes the policy of fully accommodating renewable energy generation.Therefore, the reactive power regulation capability of DGs is considered in the evaluation of the hosting capability for renewable energy generation by a distribution system, whereas the active power regulation is not.

2.2 DGHCE modeling

1) Renewable energy sources

A polyhedral uncertainty set is established for DG outputs.The power outputs of each DG can be defined as the sum of a deterministic power output and an uncertain power output.The upper and lower bounds of the uncertain deviation are determined based on historical data.Based on the polyhedral uncertainty set, the active power output of a DG can be expressed as

where is the deterministic power output of the DG at Node i. and denote the downward and upward deviation ranges, respectively, of the DG.G is the set of candidate nodes that can accommodate DGs.

The DG output coefficient is introduced to determine the installed capacity of the DG at Node i (denoted as :

where is the DG output coefficient considering the uncertainty; is the deterministic output coefficient of the DG;anddenote the downward and upward deviation ranges, respectively, of the DG; and denote the downward and upward normalized deviation variables,respectively, of the DG.

The installed capacity at each node is non-negative:

According to the Chinese industry standard NB/T 32015-2013 entitled “Technical rule for distributed resources connected to the distribution network,” the reactive power outputs of a converter-based RES comply with the following constraint:

2) OLTC

The tap position of an OLTC can be flexibly adjusted:

where tpmin and tpmax are the lower and upper limits,respectively, of the tap position of the OLTC.J is a set of integers denoting all the feasible tap positions.

3) SVC

The sizes and quantities of SVCs are limited by the following constraints:

where is the binary investment decision variable of SVC at Node i; and are the lower and upper power output limit coefficients, respectively, for SVCs at Node i; is the installed capacity of SVC at Node i; and QSVC is a set denoting all the feasible sizing of SVCs.NSVC is the total number of nodes that are scheduled to be installed with SVCs.

4) ESS

The ESS model can be described by a set of simplified linearized equations.It is assumed that the charging and discharging power levels during a certain time period Δt are constant.The energy stored in an ESS can be formulated as

where is the stored energy of the ESS at Node i at time t; and are the charging and discharging power, respectively, of the ESS in the time period from t to t + 1; ηc and ηd are the charging and discharging efficiencies, respectively, of the ESS.Equation (29)ensures that the initial state of stored energy in the ESS is equal to the final state.

The charging and discharging power limits are considered in (30) and (31).and are the maximum values of charging power and discharging power,respectively.The stored energy is limited in (32).andare the minimum and maximum states of charge of the ESS, respectively. is the sizing of the ESS at Node i.and are the binary decision variables denoting that the ESS is charging and discharging, respectively.WSTO is a set that denotes all the feasible sizing of ESSs.Considering that the storage equipment cannot be charged and discharged simultaneously in a scheduling period, the following constraint should be introduced:

Considering that the available quantity of ESSs in a distribution system is generally limited, the following constraints are introduced:

whereis the binary investment decision variable of the ESS at Node i.NSTO is the total number of nodes in the distribution system that are scheduled to be installed with an ESS.

As a consequence, the DGHCE problem can be summarized as follows:

The decision variables are andThese denote the installed capacity of the DG at each candidate node and the siting and sizing of SVC and ESS at each node, respectively.

2.3 Solution methodology

Robust optimization is a semi-infinite optimization problem and therefore, difficult to solve directly.In this study, a robust counterpart is constructed and then linearized by the dual theory to transform the semiinfinite optimization problem into a mixed-integer linear programming problem.

For convenient comprehension, all the variables are divided into four categories: the DG installation decision vector y, power flow vector pf, uncertainty factor vector u,and investment decision variable vector for ESSs and SVCs z.The detailed matchup is shown in (39):

The proposed model can be expressed as

where G1 to G5 are the corresponding coefficient matrices for variables in the constraints.

Considering an optimization problem that has k constraints with uncertain variables, Ji is the set of uncertainty factors in the ith constraint of the optimization problem.According to the method proposed in [18],the conservative parameter Γ is introduced to adjust the conservativeness of the model, and Γ is assumed to be an integer in this study.G1i-G5i are the corresponding coefficient matrices for variables in the ith constraint.The ith constraint, which contains uncertain variables, can be transformed into

When all the conservative parameters are equal to zero (i.e., Γi = 0，∀i≤k), the uncertainties of uncertain variables are not considered.Then, the problem becomes a deterministic one.When all Γi adopt extreme values,the model is equivalent to the Soyster model presented in [19].Furthermore, the optimization results would be exceptionally conservative.The maximization forms are introduced in the constraints of the robust counterpart.Therefore, the problem is still nonlinear.An embedded GUROBI solver with the YALMIP interface is used to linearize the problem according to the duality theory.The detailed theoretical basis is presented in [20].

3 Case studies

In this section, the performance of the proposed robust optimization approach is investigated through a modified version of the IEEE 33-bus distribution system.First, the configuration of the system is demonstrated.Secondly,the effectiveness of the presented method is examined in the worst scenario.Finally, the impacts of different device configuration schemes and reactive power regulation of DGs are investigated.

3.1 Test system and considerations

A modified version of the IEEE 33-bus distribution system is used for a case study, as shown in Fig.1.The reference voltage of the system is 10.5 kV, and the bus voltage of the root node is 10.5 kV.It is assumed that the substation transformer at the root node is equipped with an OLTC that has 17 tap positions, which enables voltage regulation in the range of ±10%.The rated capacity of the transformer is 3,150 kVA.Seven nodes (G1-G7) are set to be the candidates for DG installation (see Fig.1).The DGs can be installed at one or more of these seven nodes.In this work,DGs are considered to be a combination of wind turbines and PV systems that account for 40% and 60%, respectively,of the DG installed capacity at each node.Three ESSs are planned to connect to any independent nodes.The maximum capacity of each ESS is specified to be 3 MWh considering the constraints of land availability and construction costs.The charging and discharging rates are assumed to be 0.25,and both charging and discharging efficiency are 90%.More specifically, the maximum charging and discharging power are 0.75 MW for an ESS whose rated capacity is 3 MWh.Two of the 32 independent nodes are expected to be installed with an SVC whose adjustable range of reactive power can be ±0.5 MVar, ±0.7 MVar, or ±0.9 MVar.The permitted active power exchange with the upstream power system ranges from -10 MW to 10 MW, and the permitted reactive power exchange ranges from -7 MW to 7 MW through the substation transformer.The linearization coefficients for the polygonal inner-approximation of thermal constraints are presented in Appendix A.

Fig.1 Modified version of IEEE 33-bus test system

3.2 Effectiveness of proposed method

In this section, Γ adopts the maximum value in each constraint to illustrate the robustness of the presented approach for evaluating hosting capability.The allocation of the installed capacity at each candidate node when Γ adopts the maximum value is presented in Table 1.The configurations of ESSs and SVCs are shown in Table 2.The worst scenario corresponding to the maximum DG outputs and minimum load level in the time scale of one day is used to examine the robustness of the proposed method.The active power balance of the test system in the worst scenario is shown in Fig.2.The operation states of three ESSs in the worst scenario are shown in Fig.3.The operation states of SVCs in the worst scenario are shown in Fig.4.It can be demonstrated that in the worst-case scenario, the active power exchange between the test system and upstream power system approaches the upper limit of 10 MW many times without exceeding it.According to the power flow calculation, all the constraints are satisfied considering the DG output uncertainty with the optimized integration scheme.In conclusion, the optimized solution immunizes against the worst cases.The constraints would not be violated even in the most conservative hypothesis when the conservative parameters are maximized.

Table 1 Installed capacity allocation of DGs (MW)

G1 G2 G3 G4 G5 G6 G7 Total 12.7266 0 0 6.8890 2.0487 0 0.7731 22.4374

Table 2 Optimal siting and sizing of ESSs and SVCs

Equipment type ESS1 ESS2 ESS3 SVC1 SVC2 Location(Node) 4 21 27 1 19 Size 3 MWh 3 MWh 3 MWh 0.9 MVar 0.7 MVar

Fig.2 Active power balance in the worst scenario

Fig.3 Operation states of ESSs in the worst scenario

Fig.4 Operation states of SVCs in the worst scenario

3.3 Impact of the hosting capability enhancement schemes

As shown in Fig.2 and Fig.3, when the DG has a relatively high output from 11:00 to 15:00, the exchange power between the test system and upstream system approaches the upper limit, and the ESSs work mainly in a charging mode to absorb the excess active power.When the overall output of DGs attains the lowest level from 4:00 to 7:00, the ESSs work mainly in a discharging mode to maintain the steady power exchange with the upstream system.In conclusion, the ESSs play a vital role in peakshaving and compliance with power exchange constraints.

The DG hosting capabilities under different device configuration schemes are evaluated and are shown in Table 3.Four configuration schemes are considered.The configuration scheme that applies both ESSs and SVCs is denoted as Scheme A.Only SVCs are applied in Scheme B,and only ESSs are applied in Scheme C.Neither ESS nor SVC is applied in Scheme D.The reactive power regulation capability of DG is considered in all the schemes.The proposed robust optimization approach is used to determine the DG hosting capability under each configuration scheme separately.The optimization results are shown in Table 3.The application of ESSs in Schemes A and C results in a significant enhancement in the DG hosting capability compared with the configuration schemes without ESSs.The operation states of SVCs and ESSs in each scheme are shown in Fig.5.In Schemes A and B, SVCs mainly provide reactive power output from 17:00 to 7:00 when the illumination intensity is low, whereby the reactive power output of PV systems is low.From 9:00 to 16:00, SVCs are mainly implemented to mitigate the voltage fluctuation caused by the volatility of DG output and loads.Compared with Scheme A, reactive power regulations of SVCs are more frequent in Scheme B owing to the absence of ESSs.The operation states of ESSs shown in Fig.5 imply that the enhancement of hosting capability is owing to the peak-shaving capability of ESSs, which contributes to the accommodation of the DG output during peak hours.

Table 3 Optimization results under diverse device configuration schemes

Configuration scheme Scheme A Scheme B Scheme C Scheme D Hosting capability 22.4374 MW 19.0020 MW 22.4374 MW 18.7249 MW ESS1 location 4 4 /ESS1 size 3 MWh / 3 MWh /ESS2 location 21 / 21 /ESS2 size 3 MWh / 3 MWh /ESS3 location 27 / 27 /ESS3 size 3 MWh / 3 MWh /SVC1 location 1 2 / /SVC1 size 0.9 MVar 0.7 MVar / /SVC2 location 19 19 / /SVC2 size 0.7 MVar 0.5 MVar / /

Table 4 Hosting capabilities under different power factors (MW)

Location Power factor adjustable 0.98 lagging 0.98 leading unity 5 3.6800 0 8.7728 7.4893 10 0 0 0 0 15 1.8930 2.7843 0.3257 0.3781 21 3.7176 7.3277 5.2288 4.7375 24 6.1813 1.3344 3.6975 5.8284 27 0 0 0 0 30 3.2530 4.7326 0 0 Total 18.7249 16.1792 18.0249 18.4480

Fig.5 Operation states of SVCs and ESSs under different device configuration schemes

Traditionally, renewable energy sources such as wind turbines and PV systems operate with a constant and lagging power factor.In this case, DGs consume reactive power.Given this background, there is a significant demand for synchronous generators in the system to produce reactive power.In a distribution system with fewer synchronous generators, more reactive compensation devices are required.However, most of the present advanced DG integration standards stipulate that all DGs should be equipped with reactive power regulation capability that can provide reactive power as well as consume reactive power according to the voltage magnitude at the point of connection or the instructions of the system operators.As shown in Table 3, the application of SVCs does not significantly impact the hosting capability.It is reasonable to infer that the large-scale integration of DGs with reactive power regulation capability undercut the requirements for the reactive power compensation provided by SVCs.This is because the reactive power regulation capability of DGs is comparable with that of SVCs when the installed capacity is adequately high.In the configuration schemes without the application of the ESSs, the hosting capability would decrease from 19.0020 MW to 18.7249 MW (by 1.48%)if SVCs are not installed (see Table 3).When ESSs are installed so that the installed DG capacity is higher than those of schemes without ESSs, the absence of SVCs does not impact the DG hosting capability.The application of SVC can provide efficient reactive power regulation when the installed DG capacity is marginal, considering that the power output of intermittent RESs may be negligible in certain periods.However, when the installed DG capacity is adequately high and the complementary effect of power output between PV systems and wind turbines is taken advantage of, the massive application of SVCs may incur excess investment while only marginally impacting DG hosting capability.

The impact of the reactive power regulation capability is investigated further through a comparison of the DG hosting capability under different power factors of DGs.The application of ESSs and SVCs is not considered to prevent interference.The hosting capability and DG allocation under different power factors are listed in Table 4.Compared with traditional RESs whose power factor is fixed at 0.98(lagging), the test system is capable of accommodating 15.74% higher capacity by using RESs whose power factor can vary continuously in the range from 0.98 (lagging) to 0.98 (leading).DGs are capable of adjusting reactive power outputs automatically during extreme events and thereby,provide dynamic support to the system.The maximum hosting capability of DG is enhanced marginally with an adjustable power factor compared with those obtained with a leading power factor or unity power factor.To conclude, equipping DG with reactive power regulation capability would substantially enhance the reactive power regulation capability of the distribution system, particularly in distribution systems with high DG penetration.The converter-based renewable energy sources have reactive power regulation capability comparable with those of traditional synchronous generators.Therefore, the reactive power regulation capability of DG should be taken into account while considering the reactive power compensation schemes of a distribution system, so as to prevent excessive investment and fully utilize RESs.

4 Conclusion

A method for evaluating the hosting capability for intermittent renewable energy generation by a distribution system is presented considering the application of ESSs,SVCs, OLTCs, and the reactive power regulation capability of DGs.An RO-based DGHCE model and an efficient solving algorithm are presented.Simulation results of case studies demonstrate that the proposed method immunizes against the uncertainty of the DG output even in the most extreme scenario.The joint application of ESSs, SVCs, and OLTCs can substantially enhance the DG hosting capability of the distribution system.Among these, ESSs exert the most significant impact.Based on a comparison of the hosting capability under different configuration schemes and DG power factors, it is concluded that the reactive power regulation of DGs exerts a positive impact on the enhancement of hosting capability by providing reserved reactive power.According to the test case, compared with traditional RESs whose power factor is fixed at 0.98(lagging), the test system is capable of accommodating 15.74% higher capacity by using RESs whose power factor can vary continuously in the range from 0.98 (lagging) to 0.98 (leading).Considering the extensive requirements of reactive power regulation capability in industry standards for all types of DGs, the participation of DGs in the system reactive power regulation needs to be considered comprehensively so as to reduce investment costs.

Appendix A

Table A1 Coefficients of the linearized thermal capacity constraints

α β δ 1 0.2679 -1

continue

α β δ 1 1-1.366 0.2679 1 -1-0.2679 1 -1-1 1 -1.366-1 0.2679 -1-1 -0.2679 -1-1 -1 -1.366-0.2679 -1 -1-1 -1 -1.366-0.2679 -1 -1 0.2679 -1 -1 1-1 -1.366 1-0.2679 -1

Acknowledgements

This work is supported by the Scientific and Technological Project of SGCC Headquarters entitled“Smart Distribution Network and Ubiquitous Power Internet of Things Integrated Development Collaborative Planning Technology Research” (5400-201956447A-0-0-00).

Declaration of Competing Interest

We declare that we have no conflict of interest.