Stochastic Model Based Optimisation Path Study of Off-grid Optical Storage Microgrid Configuration and Economy

The day-ahead optimal scheduling model of off-grid photovoltaic storage microgrid aims at minimising the cost of its single-day operation [22], and day-ahead planning of the output of each device is carried out, and a stochastic model is used to describe its stochasticity, which comprehensively takes into account the technical characteristics of each distributed power source, constraints of the energy storage system, the peak-valley difference of the grid tariffs, and the characteristics of batch loads of off-grid photovoltaic storage microgrids to make the total operating cost of the off-grid photovoltaic storage microgrid minimum by arranging the charging/discharging of the storage system, the output of the controllable power supply output, etc. to minimise the total operating cost of the off-grid type photovoltaic storage microgrid.

The expression of the objective function is as follows: (5) minC=∑s=1Nf∑t=1TPrs*Fst\[\min C=\sum\limits_{s=1}^{{{N}_{f}}}{\sum\limits_{t=1}^{T}{P}}{{r}_{s}}*F_{s}^{t}\] (6) Fst=∑i=1NDG(Cf(PGis,t)+COM(PGis,t)+Ceav(PGis,t))+Cpp(PGrids,t)\[F_{s}^{t}=\sum\limits_{i=1}^{{{N}_{\text{DG}}}}{({{C}_{\text{f}}}(}P_{\text{G}i}^{s,t})+{{C}_{\text{OM}}}(P_{\text{G}i}^{s,t})+{{C}_{\text{eav}}}(P_{\text{G}i}^{s,t}))+{{C}_{\text{pp}}}(P_{\text{Grid}}^{s,t})\]

Where C is the total operating cost of the off-grid photovoltaic storage microgrid, and N_f is the total number of scenarios after the cut, i.e., the combination of the sample sets of wind, PV, and negative components. Pr_s denotes the probability of scenario s, which is equal to the product of the probability of each part of the sample. T is the total number of scheduling time periods, Fst−t$F_{s}^{t}-t$ denotes the operating cost under time period scenario s, and N_DG is the total number of distributed power sources, which include conventional generating units such as gas turbines and renewable generating units such as wind/photovoltaic. C_f(·) and C_OM(·) are the fuel consumption cost function and maintenance cost function when the unit is running, and C_eav(·) is the pollution emission cost function when the unit is running. PGist$P_{Gi}^{{{s}_{t}}}$ is the output of the distributed power source i in time period t.

In the intra-day optimal scheduling phase, let the controllable conventional units within the off-grid optical storage microgrid system include micro gas turbines and fuel cells, and the renewable energy units include wind power and photovoltaic [23]. At the sampling moment k, the vector consisting of the output power of the controllable conventional units, the charging/discharging power of the energy storage, the SOC (state of charge) of the energy storage, and the power purchased from the grid by the off-grid photovoltaic storage microgrid is selected as the state variable x(k): (7) x(k)=[ PMT(k),PFC(k),PESS(k),SESS(k),PGrid(k) ]T\[x(k)={{\left[ \begin{matrix} {{P}_{MT}}(k),{{P}_{FC}}(k),{{P}_{ESS}}(k),{{S}_{ESS}}(k),{{P}_{Grid}}(k) \\ \end{matrix} \right]}^{T}}\]

The vector consisting of the variations of the controlled conventional unit output and the storage output is selected as the control variable u(k): (8) u(k)=[ΔPMT(k),ΔPFC(k),ΔPESS(k)]T\[u(k)={{[\Delta {{P}_{MT}}(k),\Delta {{P}_{FC}}(k),\Delta {{P}_{ESS}}(k)]}^{T}}\]

The vector consisting of the output of wind power and PV renewable units and the load variation of off-grid photovoltaic storage microgrid is selected as the perturbation input r(k): (9) r(k)=[ΔPLoad(k),ΔPWT(k),ΔPPV(k)]T\[r(k)={{[\Delta {{P}_{Load}}(k),\Delta {{P}_{WT}}(k),\Delta {{P}_{PV}}(k)]}^{T}}\]

The vector consisting of the purchased power from the grid and the storage charge state is selected as the output variable y(k): (10) y(k)=[PGrid(k),SESS(k)]T\[y(k)={{[{{P}_{Grid}}(k),{{S}_{ESS}}(k)]}^{T}}\]

The resulting multi-input multi-output state space model is built as shown in Eqs. (11) and (12): (11) x(k+Δt)=[ PMT(k+Δt)PFC(k+Δt)PESS(k+Δt)SESS(k+Δt)PGrid(k+Δt) ]=[ 10000010000010000−ηΔtEESS1000001 ][ PMT(k)PFC(k)PESS(k)SESS(k)PGrid(k) ]+[ 10001000100−ηΔtEESS−1−1−1 ][ ΔPMT(k)ΔPEC(k)ΔPESS(k) ]+[ 0000000000001−1−1 ][ ΔPLoad(k)ΔPWT(k)ΔPPV(k) ]\[\begin{align} & x(k+\Delta t)=\left[ \begin{matrix} {{P}_{MT}}(k+\Delta t) \\ {{P}_{FC}}(k+\Delta t) \\ {{P}_{ESS}}(k+\Delta t) \\ {{S}_{ESS}}(k+\Delta t) \\ {{P}_{Grid}}(k+\Delta t) \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & -\eta \frac{\Delta t}{{{E}_{ESS}}} & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ \end{matrix} \right]\left[ \begin{matrix} {{P}_{MT}}(k) \\ {{P}_{FC}}(k) \\ {{P}_{ESS}}(k) \\ {{S}_{ESS}}(k) \\ {{P}_{Grid}}(k) \\ \end{matrix} \right] \\ & +\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & -\eta \frac{\Delta t}{{{E}_{ESS}}} \\ -1 & -1 & -1 \\ \end{matrix} \right]\left[ \begin{matrix} \Delta {{P}_{MT}}(k) \\ \Delta {{P}_{EC}}(k) \\ \Delta {{P}_{ESS}}(k) \\ \end{matrix} \right]+\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & -1 & -1 \\ \end{matrix} \right]\left[ \begin{matrix} \Delta {{P}_{Load}}(k) \\ \Delta {{P}_{WT}}(k) \\ \Delta {{P}_{PV}}(k) \\ \end{matrix} \right] \\ \end{align}\] (12) y(k)=[ PGrid(k)SESS(k) ]=[ 0000100010 ]⋅[ PMT(k)PFC(k)PESS(k)SESS(k)PGrid(k) ]T\[\begin{align} & y(k)=\left[ \begin{matrix} {{P}_{\text{Grid}}}(k) \\ {{S}_{\text{ESS}}}(k) \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \\ \end{matrix} \right] \\ & \cdot {{\left[ \begin{matrix} {{P}_{\text{MT}}}(k) & {{P}_{\text{FC}}}(k) & {{P}_{\text{ESS}}}(k) & {{S}_{\text{ESS}}}(k) & {{P}_{\text{Grid}}}(k) \\ \end{matrix} \right]}^{\text{T}}} \\ \end{align}\]

The above state-space model is solved iteratively and iteratively, predicting p step forward to obtain a vector Y_f consisting of the predicted values of the output variables in the prediction time domain pΔt: (13) Yf=[PGridf(k+Δt),SESSf(k+Δt),⋯,PGridf(k+pΔt),SESSf(k+pΔt)]T\[{{Y}_{f}}={{[P_{Grid}^{f}(k+\Delta t),S_{ESS}^{f}(k+\Delta t),\cdots ,P_{Grid}^{f}(k+p\Delta t),S_{ESS}^{f}(k+p\Delta t)]}^{T}}\]

In order to deal with the fluctuations caused by the prediction errors of the renewable energy output and the off-grid optical storage microgrid load on the system operation, and to achieve the tracking of the output variables to the day-ahead scheduled values, the vector R_da consisting of the day-ahead scheduled values of the output variables in the prediction time domain pΔt is selected as the target of the tracking control: (14) Rda=[PGridda(k+Δt),SESSda(k+Δt),⋯,PGridda(k+pΔt),SESSda(k+pΔt)]T\[{{R}_{da}}={{[P_{Grid}^{da}(k+\Delta t),S_{ESS}^{da}(k+\Delta t),\cdots ,P_{Grid}^{da}(k+p\Delta t),S_{ESS}^{da}(k+p\Delta t)]}^{T}}\]

The goal of intraday optimal scheduling is to minimise the error between the predicted output values of the output variables and the planned values for the previous day, and to ensure that the amount of adjustment variation of each controllable device in the system is as small as possible, so the intraday rolling optimal scheduling problem can be transformed into the following form: (15) minJ=(Rda−Yf)TWerr(Rda−Yf)+UTQuU\[\min J={{({{R}_{da}}-{{Y}_{f}})}^{T}}{{W}_{err}}({{R}_{da}}-{{Y}_{f}})+{{U}^{T}}{{Q}_{u}}U\] (16) s.t.{ ΔPMTmin≤ΔPMTt≤ΔPMTmaxPMTmin≤PMTt≤PMTmaxΔPFCmin≤ΔPFCt≤ΔPFCmaxΔPFCmin≤PFCt≤PFCmaxΔPESSmin≤ΔPESSt≤ΔPESSmaxPESSmin≤PESSt≤PESSmaxSESSmin≤SESSt≤SESSmax\[s.t.\left\{ \begin{matrix} \Delta P_{MT}^{\min }\le \Delta P_{MT}^{t}\le \Delta P_{MT}^{\max } \\ P_{MT}^{\min }\le P_{MT}^{t}\le P_{MT}^{\max } \\ \Delta P_{FC}^{\min }\le \Delta P_{FC}^{t}\le \Delta P_{FC}^{\max } \\ \Delta P_{FC}^{\min }\le P_{FC}^{t}\le P_{FC}^{\max } \\ \Delta P_{ESS}^{\min }\le \Delta P_{ESS}^{t}\le \Delta P_{ESS}^{\max } \\ P_{ESS}^{\min }\le P_{ESS}^{t}\le P_{ESS}^{\max } \\ S_{ESS}^{\min }\le S_{ESS}^{t}\le S_{ESS}^{\max } \\ \end{matrix} \right.\]

Where W_eπ is the matrix of weight coefficients for the prediction output error and Q_u is the matrix of weight coefficients for the control variables.

The SOC value of the energy storage system at time t can be obtained from the charge state at the previous moment by charging/discharging, while considering the amount of self-discharge loss of the energy storage system. The calculation formula is shown in Eq: (21) SESSs,t=SESSs,t−1(1−σ)+ηPESSs,tΔtEESS\[S_{ESS}^{s,t}=S_{ESS}^{s,t-1}(1-\sigma )+\eta \frac{P_{ESS}^{s,t}\Delta t}{{{E}_{ESS}}}\]

Where SESSt\[S_{ESS}^{t}\] is the state of charge of the energy storage system at the t time period, SESSc.t-1$S_{ESS}^{c.t-1}$ is the state of charge of the energy storage system at the t–1 time, σ is the self-discharge rate of the energy storage system, η is the charging/discharging efficiency of the energy storage system, which has a certain amount of power loss during charging/discharging, E_ESS represents the total capacity of the energy storage system, and Δt is the time interval.

The SOC of the energy storage system should be within its specified upper and lower limits, viz: (22) SESSmin≤SESSs,t≤SESSmax\[S_{ESS}^{\min }\le S_{ESS}^{s,t}\le S_{ESS}^{\max }\]

Where SESSmax\[S_{ESS}^{\max }\] is the maximum value of the SOC of the energy storage system and SESSmin\[S_{ESS}^{\min }\] is the minimum value of the SOC of the energy storage system.

In addition, the scheduling of the microgrid has a certain periodicity, in order to ensure that the energy storage system can meet the operational requirements of the next day, and at the same time to avoid excessive consumption of the battery’s service life, the SOC values of the energy storage system at the initial and ending moments of the scheduling cycle should be consistent, i.e: (23) SESSs,t=0=SESSs,t=T\[S_{ESS}^{s,t=0}=S_{ESS}^{s,t=T}\]

In order to further optimise the configuration of off-grid optical storage microgrids and their economics, this study builds an optimisation system for battery storage of optical storage microgrids at the same time on the basis of the proposed stochastic model-based configuration optimisation method, which is used to improve the economics of optical storage microgrids. Energy storage has become an indispensable and important step in smart grids and microgrids, and it also plays a decisive and auxiliary role in the field of distributed generation, which is very crucial for the power balance stability and energy conversion of off-grid photovoltaic storage microgrids. There are many types of energy storage, such as battery storage and pumped storage. Lead-acid batteries are widely used because of their low price, pure technology, and ability to be produced in large quantities. Therefore, this paper selects lead-acid batteries as the energy storage system. With the development of power electronics and computer technology, energy storage system has become a vital part of the power system. At present, lead-acid batteries are widely used because of their advantages, such as low price, pure technology and mass production.

The electrolyte temperature θ is: (24) dθdt=1Cθ(Ps−θ−θaRθ)\[\frac{d\theta }{dt}=\frac{1}{{{C}_{\theta }}}\left( {{P}_{s}}-\frac{\theta -{{\theta }_{a}}}{{{R}_{\theta }}} \right)\] (25) Ps=I2R0+Im2R2+I12R1+IpUpN\[{{P}_{s}}={{I}^{2}}{{R}_{0}}+I_{m}^{2}{{R}_{2}}+I_{1}^{2}{{R}_{1}}+{{I}_{p}}{{U}_{pN}}\]

Where R_θ is the thermal resistance between the battery and the surrounding environment, R₂ is the overcharge resistance, R₁ is the capacitive internal resistance, R₀ is the equivalent internal resistance, C_e is the thermal capacity of the battery, P_s is the power consumed by the internal resistance of the battery, θ_a is the ambient temperature, I is the discharge current, E_m is the equivalent electric potential.

The expression for the capacity C function of the battery is: (26) C(I,θ)=KcC0*(1−θ/θf)ε1+(Kc−1)(I/I*)δ\[C(I,\theta )=\frac{{{K}_{c}}{{C}_{{{0}^{*}}}}{{(1-\theta /{{\theta }_{f}})}^{\varepsilon }}}{1+({{K}_{c}}-1){{(I/{{I}^{*}})}^{\delta }}}\]

θ_f represents the electrolyte temperature, typically -40 °C, Kε,C0*,ε,I*,δ $${K_\varepsilon },C_0^*,\varepsilon ,{I^*},\delta $$ is an empirical factor.

The battery output Q_e(t) is: (27) Qe(t)=Qe0+∫0t−Im(τ)dτ\[{{Q}_{e}}(t)={{Q}_{e0}}+\int_{0}^{t}{-}{{I}_{m}}(\tau )d\tau \]

where Q_e0 represents the initial charge.

The state of charge SOC, depth of charge DOC is: (28) { SOC=1−Qe/C(0,θ)DOC=1−Qe/C(Iavg,θ)\[\left\{ \begin{array}{*{35}{l}} SOC=1-{{Q}_{e}}/C(0,\theta ) \\ DOC=1-{{Q}_{e}}/C({{I}_{avg}},\theta ) \\ \end{array} \right.\] (29) { Em=Em0−KE(273+θ)(1−SOC)R0=R00[ 1+A0(1−SOC) ]R1=−R10ln(DOC)C1=τ1/R1R2=R20exp[A21(1−SOC)]/{1+exp(A22Im/I*)}\[\left\{ \begin{matrix} {{E}_{m}}={{E}_{m0}}-{{K}_{E}}(273+\theta )(1-SOC) \\ {{R}_{0}}={{R}_{00}}\left[ 1+{{A}_{0}}(1-SOC) \right] \\ {{R}_{1}}=-{{R}_{10}}\ln (DOC) \\ {{C}_{1}}={{\tau }_{1}}/{{R}_{1}} \\ {{R}_{2}}={{R}_{20}}\exp [{{A}_{21}}(1-SOC)]/\{1+\exp ({{A}_{22}}{{I}_{m}}/{{I}^{*}})\} \\ \end{matrix} \right.\]

Where, E_mo is the open circuit voltage of the battery at full charge in V, I_avg is the average discharge current in A, R₀₀ is the internal resistance at full charge in mΩ. R₁₀,K_E,A₀,A₂₁,A₂₂,R₂₀,τ₁ is the empirical coefficient.

The current I_p is: (30) IP=UPNGP0exp[UPN/UP0+AP(1−θ/θf)]\[{{I}_{P}}={{U}_{PN}}{{G}_{P0}}\exp [{{U}_{PN}}/{{U}_{P0}}+{{A}_{P}}(1-\theta /{{\theta }_{f}})]\]

Where, U_pN is the node voltage and G_p0,U_p0,A_p is the empirical coefficient.

The battery terminal voltage is: (31) U=Em+IR0+ImR2+I1R1\[U={{E}_{m}}+I{{R}_{0}}+{{I}_{m}}{{R}_{2}}+{{I}_{1}}{{R}_{1}}\]

Bidirectional DC chopper converter with boost, buck two kinds of operation, bidirectional DC chopper converter circuit of the basic composition of the two fully-controlled devices VT, inductance L, two capacitors C and two uncontrollable devices VD, the low-voltage side of the power supply is expressed in U₁, the high-voltage side of the power supply is expressed in U₂.

The high voltage side power supply U₂ charges said inductor, the inductor L terminal voltage is shown by U₂–U₁, and the charging time is shown by t_on, which is the time when the fully controlled device VT₁ is switched on, so that (U₂–U₁)I_Lt_on can be used to represent the energy absorbed by the inductor, and in the course of the normal operation of the fully controlled device VT₁, the current of the inductor varies very little, so that it does not reflect its consumed power. In the case of full-control device off, the inductor discharge energy to the capacitor charging, inductor terminal voltage with U₁, energy release time to t_off shows that the full-control device VT₁ is in the off state of time, so can be used to U₁I_Lt_off on behalf of the energy released by the inductor. Normally the bidirectional DC chopper converter operates in buck mode, which requires that the energy stored in the inductor in the cycle is equal to the energy released from the inductor, i.e.: (32) (U2−U1)ILton=U1ILtoff\[({{U}_{2}}-{{U}_{1}}){{I}_{L}}{{t}_{on}}={{U}_{1}}{{I}_{L}}{{t}_{off}}\]

Setting D1=tonT${{D}_{1}}=\frac{{{t}_{on}}}{T}$ and simplifying the equation gives: (33) U1=D1U2\[{{U}_{1}}={{D}_{1}}{{U}_{2}}\]

Since 0 < D₁ < 1, the Buck circuit is a buck circuit.

The bidirectional DC chopper converter operates in the boost mode (VT₁ disconnected), and the specific analysis process is the same as the Boost converter in the PV subsystem, which is used to denote the duty cycle of the fully-controlled device, is obtained: (34) U2=11−D2U1\[{{U}_{2}}=\frac{1}{1-{{D}_{2}}}{{U}_{1}}\]

As can be seen from Eq. the bidirectional DC chopper converter has boost and buck functions.

In this paper, the monthly average wind speed, light intensity, and ambient temperature (latitude and longitude are 41.2° and 95.7°, respectively; altitude is 1542 m, wind speed measurement height is 12 m, and ambient temperature is land temperature) of a region in northwest China are obtained based on the RETScreen Expert software, and the specific data are shown in Table 1. Modeling and building the simulation structure in HOMER Pro software set the relevant parameters, in which the AC load power and DC load power are 1245.26kWh/d and 998.65kWh/d, respectively, and the peak power of the two are 89.64kW and 69.72kW, respectively, and the transferrable load power and peak power are 51.42kWh/d and 35.00 kW, the thermal load power and its peak power are 124.68kWh/d and 7.94kW, the load daily disturbance factor is 5% and hourly disturbance factor is 10%. The initial state of the hydrogen storage tank is 80%, the initial state of the battery is 90%, and the minimum charge state is 20%. The proportion of off-grid renewable energy is not less than 60%, and the system’s operating reserve capacity is 20%. According to the data in the table, it can be seen that the region has good wind and light resources, which is suitable for establishing an off-grid microgrid system with renewable energy generation, including wind turbines and photovoltaic. The renewable energy generation in the distributed power supply of the microgrid system only considers two kinds of renewable energy generation systems: wind power generation system and photovoltaic power generation system; therefore, the microgrid system needs to be configured with diesel generators or fuel cells as a backup power source, which is used to ensure the power supply reliability requirements of important loads.

The cost parameters of the off-grid optical storage microgrid equipment obtained by combining the design of the battery storage system proposed in this paper are shown in Table 2. The installation cost of the diesel generator and fuel cell is 850 Yuan/kW and 16,800 Yuan/kW, respectively, and the replacement cost is 590 Yuan/kW and 14,200 Yuan/kW. The cost of the diesel generator and gas boiler is 5.08 Yuan/L and 3.52 Yuan/m³, respectively. The installation cost of the off-grid type optical storage microgrid controller is 18,000 Yuan.

There are many optimisation schemes under different operation strategies for different types of combinations, and in this paper, the optimal allocation of the capacity of off-grid microgrid energy storage system under typical different types of combinations is selected. The results obtained from the analysis using the stochastic model proposed above are shown in Table 3. The results of the economic indicators for the capacity optimisation of the off-grid microgrid energy storage system are shown in Table 4, where NPC and LCOE represent the total NPV cost and the averaged cost of energy, respectively, and LLR and REU represent the load default rate and the renewable energy utilisation rate, respectively. In scenarios A1 and B1, i.e., wind storage microgrid system, the only distributed power source in the system is the wind power system, and the energy storage device is a single lead-acid battery. Scenarios A2 and B2, i.e., the photovoltaic storage microgrid system, in which the distributed power source is only the photovoltaic power generation system, and the energy storage device is a single lead-acid battery. Scheme A3 and Scheme B3, i.e., wind energy storage microgrid system, the distributed power sources in the system include wind power generation system and photovoltaic power generation system, and the energy storage device is a single lead-acid battery. Scheme A4 and Scheme B4, i.e., wind-diesel storage microgrid system, the distributed power sources in the system include wind power generation system, photovoltaic power generation system and diesel generator, and the energy storage device is a single lead-acid battery. Scheme A5 and Scheme B5, i.e., wind-scenic fuel cell hybrid energy storage microgrid system, where the distributed power sources in the system include wind power generation system, photovoltaic power generation system, and fuel cell, and the energy storage system is a hybrid energy storage system composed of hydrogen energy storage system and lead-acid battery. Under the current natural resource conditions, the off-grid microgrid system has the lowest total net present value cost of the system (A5=121,692,284.2yuan and B5=130,535,773.8yuan) under the combination of scenario 5 type (i.e., hybrid energy storage microgrid system with wind and fuel cells). Combining the results obtained from the stochastic model analysis, the wind-scenic fuel cell hybrid energy storage system (Scenario A5) is the optimal configuration combination with a renewable energy utilisation rate (99.86%) close to 100%, a low averaged chemical energy cost (1.51yuan), an improved load default rate (5.49%), and meets the system power supply reliability requirements. It indicates that the energy storage system with this optimal combination of resource allocation has the smallest total NPV cost and the optimal evaluation indexes for the off-grid photovoltaic storage microgrid system under the cyclic charging operation strategy.

In this paper, the distributed wind-solar complementary off-grid type optical storage grid system constructed on an island in the Zhoushan area is taken as the object of empirical analysis, and the optimal configuration scheme obtained by applying the stochastic model analysis to the optical storage grid is used with the battery storage optimisation system. Each of the selected colloidal batteries has a rated capacity of 100Ah, a permissible maximum depth of discharge of 85%, a lifetime of 12.5 years, and an investment cost and a replacement cost of 2,600 yuan and 1,750 yuan, respectively. The service life of a single turbine is 26 years, with an acquisition cost and replacement cost of 85,264 yuan and 39,452 yuan, respectively.The lifespan of a PV array is 26 years, and it costs 950 yuan to acquire.The service life of the entire off-grid photovoltaic storage microgrid system is 26 years, and the average annual interest rate is assumed to be constant at 8.5 per cent.

Based on the wind speed and solar radiation measurements in the region between 2019-2021, which were obtained from the sensor samples every 20 minutes, these data were statistically analysed, and the Weibull probability distribution function and the distribution function were used to fit the wind speed and solar radiation intensity, respectively, to obtain the stochastic characteristics for each time point of 24 hours. The statistical characteristics of the stochastic characteristic parameters of wind speed and solar radiation intensity for the region at 11 a.m. for the annual average and spring, summer, autumn and winter seasons are shown in Table 5. The annual mean wind speed Weibull distribution parameters k and c are 2.43 and 6.51, respectively, and the solar radiation Beta distribution parameters α and β are 2.39 and 0.55, respectively.

The battery is put into operation initially at 50% so that the optimal configuration obtained by the stochastic model of the photovoltaic storage microgrid system operates continuously to supply power for four typical days, during which the battery changes are shown in Fig. 1. It can be seen that on the first day of operation, there is an excess of energy, and some of the power cannot be stored because the battery is already fully charged. In the next three days of operation, the batteries were cyclical. The wind turbine, photovoltaic array, and battery bank in the photovoltaic storage microgrid system achieved the optimal ratio by replenishing the power discharged from the battery on the same day.

Figure 1.

Don’t consider seasonal battery SOC changes

The fluctuation patterns of wind and light resources in the offline optical storage microgrid system show a certain seasonality, with different typical daily average wind power curves and photovoltaic power curves representing the spring, summer, autumn and winter seasons. Due to the use of air conditioning in summer and winter, then the average daily load curves in summer and winter seasons need to be added with the corresponding power consumed by air conditioning operations.Considering these seasonal factors, the off-grid photovoltaic storage microgrid system configured based on the methodology of this paper was operated continuously for 7 days, during which the battery changes are shown in Fig. 2. It can be seen that in springtime, due to the abundant wind and light resources, the battery has less chance to participate in the power supply, and most of the time it is in the full charge state. In winter, due to the large load demand, the battery needs to assist the system power supply, and the total amount of discharged power is slightly larger than the total amount of charged power. The overall balanced use of energy is achieved, which shows that the configuration scheme of the optical storage microgrid system obtained from the stochastic model in this paper is also robust in the face of resource changes caused by seasons.

Figure 2.

Consider seasonal battery soc changes

The high cost of energy storage systems has become one of the bottlenecks in their development. In this paper, in order to study the impact of applying a stochastic model and battery optimisation system on the cost optimisation of off-grid optical storage microgrids, the cost of the optimised system is now compared and analysed with the cost of the original scenario. The original scenario is to retain the original investment cost of the optimized energy storage capacity configuration scheme, while only recalculating the system indicators.The new scenario is to re-optimise the optimal allocation of energy storage capacity in the system, and to calculate various indicators of the system. The results of the analysis of the metrics of the optimised energy storage scenarios under the original and new scenarios are shown in Table 6. Compared to the original configuration scheme, the new optical storage microgrid and energy storage capacity configuration scheme causes an increase in the scheme’s economy, and all operational indicators of the system are improved. The optical storage yield of the optical storage microgrid increases from 13.24% to 16.47%, and the total cost spent by the system decreases from 25481635.52 yuan to 22635487.92 yuan. In the original scheme, when the initial investment cost of energy storage is high, it seems very uneconomical to configure a larger capacity of energy storage to improve system operation and PV utilization. The optimal configuration and battery optimisation system obtained by using the stochastic model in this paper can obtain better system operation levels and higher photovoltaic storage utilisation rate under the condition of guaranteeing a lower level of the initial investment cost of energy storage.